# Metabolic Control Analysis: A Tool for Designing Strategies to Manipulate Metabolic Pathways

Authors: Rafael Moreno-Sánchez; Emma Saavedra; Sara Rodríguez-Enríquez; Viridiana Olín-Sandoval
Journal: Journal of Biomedicine and Biotechnology
 (2008)

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## Abstract

The traditional experimental approaches used for changing the flux or the concentration of a particular metabolite of a metabolic pathway have been mostly based on the inhibition or over-expression of the presumed rate-limiting step.  However, the attempts to manipulate a metabolic pathway by following such approach have proved to be unsuccessful.  Metabolic Control Analysis (MCA) establishes how to determine, quantitatively, the degree of control that a given enzyme exerts on flux and on the concentration of metabolites, thus substituting the intuitive, qualitative concept of rate limiting step.  Moreover, MCA helps to understand (i) the underlying mechanisms by which a given enzyme exerts high or low control and (ii) why the control of the pathway is shared by several pathway enzymes and transporters.  By applying MCA it is possible to identify the steps that should be modified to achieve a successful alteration of flux or metabolite concentration in pathways of biotechnological (e.g., large scale metabolite production) or clinical relevance (e.g., drug therapy).  The different MCA experimental approaches developed for the determination of the flux-control distribution in several pathways are described.  Full understanding of the pathway properties when working under a variety of conditions can help to attain a successful manipulation of flux and metabolite concentration.


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## Body

## 1. Introduction

Is an effort to manipulate the metabolism of an organism worthy and reasonable, knowing
that this cellular process has been continuously modified and refined through
evolution and natural selection for adapting, in the most convenient manner, to
the ongoing environmental conditions? The
answer to this question seems obvious when three broad areas of research and
development are identified in which manipulation of metabolic pathways is
relevant: (a) drug design to treat diseases, (b) genetic engineering of
organisms of biotechnological interest, and (c) genetic syndromes therapy.Historically, drug design was
the first area in which modification of metabolism was tried: the primary goal
of drug administration is the inhibition of essential metabolic pathways, for
example, in a parasite or a tumor cell. Thus, any metabolic pathway can be a potential
therapeutic target. In the absence of a solid
theoretical background that may build a strategy for the rational design of
drugs, the pharmaceutical industry has applied the knowledge of inorganic and
organic chemistry for the arbitrary and rather randomized modification of
metabolic intermediaries by replacing hydrogen atoms in a model molecule with
any other element or compound. This
approach has been successful in the battle against many diseases. However, in
many other instances such an approach has been unsuccessful.The era of rational drug
design probably started in the 50s when Hans Krebs proposed that, after having
an exact description of a metabolic pathway, the “pacemaker” enzyme or
“rate-limiting step” had to be identified. This approach certainly decreased the amount
of intermediaries to be chemically modified, focusing only on the substrates,
products, and allosteric effectors of the “rate-limiting step,” instead of dispersing
efforts on all the metabolic pathway intermediates. The experimental approaches used in the
identification of the pacemaker, key enzymes, “bottlenecks.” limiting steps, or
regulatory enzymes [1, 2] were(i)
inspection of the metabolic pathway architecture: due to cell
economy and for reaching the highest efficiency, pathway control must
reside in the enzymes localized at the beginning of a pathway or after a
branch (teleological approach);(ii)
determination of nonequilibrium reactions: those reactions in which
the quotient between the mass action ratio (Γ) and its equilibrium constant (Keq) is low, Γ/Keq≪1 (thermodynamic
approach);(iii)
identification of the steps with the lowest maximal rates (Vmax) in cellular extracts: the key
enzyme of the pathway is the one that has the lowest rate (kinetic
approach);(iv)
enzymes with sigmoidal kinetics: steps that are susceptible to
alteration in their kinetic properties by compounds different from
substrates and products and which may coordinate the entire metabolism
(NADH/NAD+; NADPH/NADP+, ATP/ADP; acetyl CoA/CoA; Ca2+/Mg2+;
high pH/low pH) or at least two metabolic pathways (citrate, Pi, AMP,
malonyl-CoA);(v)
crossover theorem. Comparing the intermediary concentrations
between a basal and an active steady-state pathway flux, the rate-limiting
step in the basal condition will be that for which its substrate
concentration diminishes and its product concentration increases when the
system changes from the basal to the active state or vice versa (crossover
point on a histogram of each intermediary versus its normalized variation in concentration);(vi)
the shape of the metabolic flux inhibition curve: a sigmoidal curve
on a plot of inhibitor concentration versus flux shows that the sensitive
step to the inhibitor exerts no control, that is, there is not proportionality between enzyme
activity inhibition and pathway flux inhibition because there is an
“excess” of enzyme. On the other
hand, a hyperbolic curve indicates that the enzyme susceptible to the
inhibitor controls the flux.


## 2. Controlling Sites in a Metabolic Pathway

Once a site in a metabolic
pathway has been identified with at least one of the criteria described above
as “the rate-limiting step,” researchers have frequently concluded that such
enzyme or transporter is the only limiting step of the metabolic flux and
extend this conclusion to all cell types and to all conditions.For example, inspection of the glycolytic pathway (teleological approach) suggests that
hexokinase (HK) and phosphofructokinase-1 (PFK-1) (which are at the beginning
and after a branch of the pathway) are the key steps of glycolysis. However, all studies on glycolysis in the 60s,
70s, and 80s were performed by taking into account only the intracellular
reactions from HK to LDH (i.e., without including the glucose transport
reaction through the plasma membrane) and by considering glycolysis as a linear
pathway without branches. To this regard,
it is recalled that the glucose transporter (GLUT) includes a family of
proteins and genes that are susceptible of regulation. Thus, if the extracellular glucose is
considered as the initial glycolytic substrate, then another potential key step
would be GLUT. Hence, if all the
branches of the pathway are considered (Figure1), then according to the
teleological approach there will be additional potential rate-limiting sites.Figure 1
Glycolytic pathway and principal branches. GLUT, glucose transporter; HK, hexokinase; PFK-1,
phosphofructokinase-1; G6P, glucose-6-phosphate; F1,6BP, fructose 1,6
bisphosphate; DHAP, dihydroxyacetone phosphate; G3P, glyceraldehyde-3-phosphate; 3PG, 3-phosphoglycerate; PEP, phosphoenolpyruvate; pyr, pyruvate;
PYK, pyruvate kinase; L-lac, L-lactate; acetal, acetaldehyde; AT, alanine
transaminase.S. cerevisiae lacks the LDH gene.Application of the thermodynamic and kinetic approaches to glycolysis reveals that HK,
PFK-1, and pyruvate kinase (PYK) are the rate-limiting steps because in the
living cell they catalyze reactions that are far away from equilibrium (Γ/Keq=10−3–10−4), and they are also the slowest
enzymes in the pathway by at least one order of magnitude (they have the lowest Vmax values).The use of the enzyme cooperativity approach has established that the regulatory
steps of glycolysis are (i) PFK-1 and PYK because they are allosteric enzymes
and (ii) HK because it is inhibited by its products (G6P and ADP, or AMP as an ADP-analogue).
The application of the crossover theorem
(approach no. v) to glycolysis has shown a consistent variation in the PFK-1 substrate
(F6P) and product (F1,6BP). Up to now,
there are few studies on control of glycolysis using the shape of the inhibitor
titrating curve (approach no. vi), due to the lack of specific inhibitors for
any of the three presumed key steps. An exception is iodoacetate which is indeed
a potent inhibitor of GAPDH, but also of other highly reactive
cysteine-containing enzymes [3–5]. By
using iodoacetate as specific inhibitor, both GAPDH activity and flux showed
identical titration curves, leading to the conclusion that GAPDH was the
rate-limiting step of glycolysis in Streptococcus lactis and S. cremoris [6] (see,
however, Section 3.2; Glycolysis in lactobacteria below).All together, these results constitute
the main reason why many intermediary metabolism researchers, including the
authors of biochemistry text books, have proposed HK, PFK-1, and PYK as the
rate-limiting steps of glycolysis. In
consequence, to vary the glycolytic flux, one of these enzymes has to be
modified.Although the above-described experimental approaches are qualitative, full control has
been automatically assigned to the “key” steps because the concept of the rate-limiting
step assumes that there is only one single enzyme controlling the metabolic
pathway flux (and the concentration of the final product of the pathway) and,
in consequence, assigns values of zero to the control exerted by the other
enzymes and transporters. However, as analyzed for glycolysis, researchers have commonly “identified” more than one
limiting step. In the case of oxidative
phosphorylation (OXPHOS), in the 70s and 80s some researchers considered
cytochrome c oxidase as the rate-limiting step, whereas others preferred the
ATP/ADP translocator or the Krebs cycle Ca2+-sensitive
dehydrogenases (for a review, see [7]).Rephrasing the initial question, which could be the aim of manipulating a metabolic
pathway such as glycolysis, knowing its universal distribution in the living
organisms? From a clinical standpoint, the inhibition of glycolysis is relevant for the treatment of human parasitic
or pathological diseases such as cancer. The glycolytic reactions are almost identical in all organisms; in
addition, the enzymes catalyzing these reactions are highly conserved throughout
the evolutionary scale (their amino acid sequences are highly similar). In mammals, the genes of the 12 glycolytic
enzymes are scattered throughout the genome, generally in different chromosomes,
whereas in bacteria many of the glycolytic enzymes are clustered in operons [8].
However, there are organisms (like some
human parasites) that contain enzymes with remarkable differences in their
biochemical properties (substrate selectivity, catalytic capacity, stability,
and oligomeric structure), or in genetic expression regulation in comparison to
the human enzymes, which could be considered as drug targets.Furthermore, some glycolytic products are of commercial interest such as ethanol for wine,
beer, and other alcoholic beverages; CO2 for bread manufacturing; and
lactic acid and other organic acids for cheese production. Thus, from a biotechnological standpoint, it
is convenient to accelerate the pathway flux to diminish the processing time and
it is also desirable to increase the concentration of the metabolite to obtain
robust commercial products. Here, it is important to emphasize that the metabolic pathways are designed to attain
changes in flux with minimal disturbances in the intermediary concentrations. For example, the glycolytic flux in skeletal
muscle can increase from rest to an active state by 100 fold, without large
changes in metabolites. Then, it is physiologically more common to change a metabolic flux and the production of
the final metabolite in the pathway than varying the intermediary concentrations
[2]. However, we will see that, by
using a suitable approach of metabolic control analysis, it is possible to
design strategies to manipulate not only fluxes but also metabolic intermediary
concentrations.


## 3. In Vivo Overexpression Experiments of Enzymes

### 3.1. Glycolysis in Yeasts

When the yeastSaccharomyces
cerevisiae is exposed to high glucose (>2%; 0.11 M), the genes of all
glycolytic enzymes are induced (PDC and ENO increase their expression by 20 fold;
PGK, PYK, and ADH, 3–10 times; and the
others, 2 fold in average) [8–11]. However,
when the methodological development of genetic engineering allowed modulating the
expression of enzymes within cells, researchers turned to the rate-limiting
step concept to manipulate a metabolic pathway to increase flux and/or its
intermediates, hypothesizing that the overexpression of only one, or of a few
key glycolytic genes, should increase the flux.Historically, Heinisch [9] in Germany was the first author to
obtain a 3.5 fold overexpression of PFK-1 in  S. cerevisiae, but
surprisingly he observed that the rate of ethanol production was not modified. Subsequent experiments for increasing the
ethanol production rate by overexpressing either each of the presumed limiting
steps, or in combination with other glycolytic enzymes (Table 1), have been
unsuccessful and, even in some cases, a slight decrease in flux has been
attained. For instance, the simultaneous
overexpression of seven enzymes of the final section of glycolysis induced only
a 21% increase in ethanol production after 2 hours of culture (Table 1) [11]. This was accompanied by a 10–20% decrease in PFK-1
expression, which might have attenuated the flux increase.Table 1
Overexpression of glycolytic enzymes in different cell types.
Cell typeEnzymeActivity  (overexpression fold)Flux (% Control)ReferenceSaccharomyces cerevisiaeHK13.9107[12]PFK-13.5, 3.7,5102[9, 10, 12]PYK8.6107[12]PDC3.785[13]ADH4.889[12]PFK-1 + PYK5.6 + 1.3107[12]GAPDH + PGK + PGAM + ENO + PYK + PDC + ADH1.4 + 1.7 + 16 + 4 + 10.4 + 1.08 + 1.4121[12]GAPDH + PGK + PGAM + ENO + PYK + PDC + ADH1.5 + 1.4 + 3.4 + 1.5 + 2.5 + 1.1 + 1.294[11, 14]EscherichiacoliPFK8.772[15]PYK2.9, 4.291,95[16]Lactococcus lactisGAPDH14-210100[17]Aspergillus nigerPFK3100[18]PYK5100Chinese hamster ovaryPFK2.2, 3.4, 3.7100[19]Flux to ethanol was forS. cerevisiae and E. coli;
flux to citrate was for A. niger; and
flux to L-lactate was for hamster.In yeasts, HK is not product inhibited
by G6P or ADP; instead, it is strongly feedback inhibited by trehalose-6-phosphate
(Tre6P). This metabolite is synthesized from G1P by Tre6P synthase and Tre6P phosphatase. Deletion
of the Tre6P synthase gene does not
bring about an increased ethanol production, but it rather induces a defective cellular
growth on glucose and fructose and a lowered ethanol production, as a result of
a highly active HK that leads to hyperaccumulation of hexose phosphate
metabolites (particularly F1,6BP) and fast depletion of ATP, Pi, and downstream
metabolites. The explanation for this event is that, in the Tre6P synthase
mutants, the rate of glucose phosphorylation exceeds the rate of glycolytic ATP
synthesis (named “turbo effect”). Heterologous expression of a Tre6P-insensitive HK does not recover
completely the wild-type phenotype. Furthermore, deletion of the Tre6P synthase gene in the
Tre6P-insensitive HK strain did affect growth, suggesting other interactions
and functions of Tre6P synthase in the control of sugar metabolism, at
least inSchizosaccharomyces pombe [20].Davies and Brindle [10] obtained a 5-fold overexpression of
PFK-1 in S. cerevisiae, but the increase in ethanol production was not attained
under anaerobic conditions. There was a slight
increase in ethanol production in resting cells in aerobic conditions, under
which the mitochondrial metabolism contributes to the ATP supply. In all these works, it may be noted that
enzyme overexpression indeed affects the concentration of several intermediaries,
but this effect has not been further examined.It is worth noting that the
experiments described in Table1 do not rigorously reproduce the physiological
situation, in which overexpression of all the enzymes should be carried out in
the proportions found in the organisms. The
rationale behind this observation is that overexpression of only one “limiting”
step leads to a flux control redistribution, a condition at which other steps
now become rate limiting. Thus, the
concept of “rate-limiting step” offers no simple answer to the question of
increasing the yeast glycolytic flux, and it rather makes this problem to
appear as a difficult task to solve. In contrast, it seems that all relevant controlling steps
have to be overexpressed, thus reproducing what natural
selection has already successfully accomplished.In addition toS. cerevisiae, overexpression of glycolytic enzymes in other
organisms such as E. coli [15, 16],
lactobacteria [17], tomato [21], potato [22], and
hamster ovary cells [19] has been accomplished, although without increasing
flux (Table 1). It is somewhat surprising to note that in the glycolytic enzyme
overexpression experiments, the strong inhibitory effect of G6P (or Tre6P in S. cerevisiae), and citrate on HK and PFK-1, respectively, have been neglected. This
regulatory mechanism does not disappear in the cells overexpressing the enzymes
but, on the contrary, it is exacerbated. Then, what would be the aim of overexpressing HK, PFK-1 or any other
allosteric, or strongly product-inhibited enzyme if they will be more
inhibited?A successful experiment of increasing
the glycolytic flux was performed in primary cultures of rat hepatocytes [23]. HK and glucokinase (GK) were overexpressed by
using adenovirus as carrier. The transformed
hepatocytes showed higher activity of 18.7- and 7.1-times for HK and GK,
respectively, at 3 mM glucose, and of 6.3- and 7.1-times at 20 mM glucose. However, at 20 mM glucose, the flux to
lactate was not modified in HK-transformed cells, just like the experiments
described above (Table 1). In contrast,
with GK overexpression, a 3-fold increase in flux was achieved. The mechanistic difference is the HK
inhibition by G6P (10 mM G6P inhibits HK activity by 90%), whereas GK is not product inhibited.


### 3.2. Glycolysis in Lactobacteria

Lactococcus lactis is used in cheese production. For this purpose,
L. lactis ferments lactose to lactic acid by glycolysis. The end products, lactate and H+, are
expelled and acidify the external medium which contributes to cheese flavor and
texture and inhibits the growth of other bacteria. Similarly to yeast, the lack of carbon source
in lactobacteria promotes a metabolic change that leads to the production of
formic and acetic acids, ethanol, and, in a lower proportion, L-lactic acid,
altering the product quality. Thus, from a commercial point of view, it does
not seem important to know what controls the flux to lactate (because its rate
of production is adequate), but what controls the branching flux.To understand the process, and to eventually inhibit the production of secondary acids, Andersen et al. [24] constructed LDH mutants,
using a synthetic promoter library for tuning the gene expression. In mutants
lacking this enzyme, most of the pyruvate was transformed into acetic and
formic acids (Figure 1). In turn, flux
to lactate was affected in mutants expressing only 10% or less of wild-type LDH
levels, which indicated that LDH exerts no control of the glycolytic flux in
wild-type bacteria. Only with a normal content of this enzyme (100%), flux
toward secondary acids was prevented. Therefore, the flux to formic and acetic
acids is negatively controlled by LDH, and positively by PYK [17, 25]. As in S. cerevisiae, overexpression of
PFK-1, PYK, or GAPDH in lactobacteria did not increase the flux to L-lactic
acid [17, 25]. Similarly to E. coli glycolysis [26], glycolysis in L. lactis was controlled by the ATP
demand when working below its maximum capacity [27, 28], whereas, under high-rate
conditions, the glucose and lactate transporters exerted the main flux control [28]. Furthermore, this kind of observations indicates
that the flux control may reside outside the pathway [27–29], and it also supports the proposal
by Hofmeyr and Cornish-Bowden [30] that the end-product demand (which is
usually overlooked in studies of metabolism because these metabolites are
frequently not considered as part of the pathway) might be essential in flux
control.


### 3.3. Glutathione and Phytochelatin Synthesis in Plants

Glutathione (γ-Glu-Cys-Gly; GSH) is the most abundant nonproteinaceous
thiol compound (1–10 mM)
in almost all living cells. GSH is
involved in the oxidative stress processing, xenobiotic detoxification, and, in
some plants and yeasts, in the inactivation of toxic heavy metals (for a recent
revision see [31]). GSH is synthesized by two enzymes: γ-glutamylcysteine synthetase
(γ-ECS) and glutathione synthetase (GS) (Figure 2),
which catalyze reactions with high-equilibrium constants (Keq > 1000). Under a low GSH demand (unstressed
conditions), the producing block of enzymes has to receive information from the
last part of the pathway to (i) avoid the excessive and toxic accumulation of
the intermediary γ-EC and (ii) reach a stable steady state [32]. This information transfer is mediated by GSH,
which exerts strong competitive inhibition of γ-ECS [33] (Figure 2). GSH and Cys also exert inhibition on the
ATP-sulfurylase (ATPS) and on sulfate transporters (Figure 2) (for a review,
see [31]). The feedback inhibition of γ-ECS has led several researchers to propose
that this enzyme is the rate-limiting step of GSH synthesis [33–35]. Although there are no studies about the
pathway’s behavior under stressed conditions, which means under a high GSH
demand, the proposal that γ-ECS is the key enzyme has been automatically
extended to any environmental condition such as heavy metal exposure.Figure 2
Sulfur assimilation and glutathione and phytochelatins synthesis in plants ATPS, ATP sulfurylase; APS, adenosine5′ phosphosulphate;
γ-ECS, γ-glutamyl cysteine synthetase; γ-EC, γ-glutamyl
cysteine; GS, glutathione synthetase; GSH, reduced glutathione; GSSG, oxidized
glutathione; GPx, GSH peroxidase; GR, GSH reductase; PCS, phytochelatin synthase;
PCs, phytochelatins; GT, GSH-S-transferases; Xe, xenobiotic; GS-Xe, glutathione-xenobiotic
complex. The reactions are not shown
stochiometrically. GR uses the cofactor
NADPH. The Cd2+-GSH complex formation (cadmium bis-glutathionate) is fast and spontaneous and
does not require enzyme catalysis. Modified
from [31].By assuming thatγ-ECS is the rate-limiting step, many research groups
have tried to increase, in plants and yeasts, the rate of synthesis and the
concentration of GSH and phytochelatins (PCs) with the aim of fortifying their
heavy metal resistance and storage capacity, mainly toward Cd2+. The development of organisms able to grow in
soils and water systems contaminated with heavy metals, which may have the
ability of accumulating toxic metal ions, is of biotechnological interest for
bioremediation strategies.With this goal in mind,
researchers have then overexpressedγ-ECS and other pathway enzymes, including
phytochelatin synthase (PCS) (Table 2). Some of these experiments have been
partially successful in increasing GSH levels, although this has been rather
marginal with no correlation between enzyme levels and GSH concentration. Unfortunately, these overexpression experiments
have not been accompanied by determinations of fluxes or other relevant metabolite
concentrations such as PCs or Cys. On
the other hand, the overexpression of PCS has surprisingly induced oxidative stress
and necrosis instead of increasing Cd2+ accumulation and resistance
[36]. This result suggests that, under high
GSH demand (i.e., for PCs synthesis and for direct heavy metal
sequestration by GSH), the GSH concentration does not suffice for maintaining
the other essential GSH functions such as oxidative stress management and
xenobiotic detoxification.Table 2
GSH and phytochelatin synthesis enzymes overexpression in plants and yeasts.
Overexpressed enzyme (activity fold)Organism (experimental condition)MetaboliteReference(increment fold)ATP sulfurylase (2.1)Brassica juncea2.1 [GSH][37]ATP sulfurylase (4.8)Tobacco (unstressed)1.3 [SO42−][38]O-acetyl-serine thiol-lyase (2.5)Tobacco (unstressed)2 [Cys][39]0 [GSH]Serine acetyl transferase
(>10)Potato chloroplasts (unstressed)2 [Cys][40]0 [GSH]E. coli GS (90)Populus tremula (unstressed)0 [GSH][34]GS (3)S. cerevisiae (unstressed)0 [GSH][41]E. coliγ-ECS (>2)Brassica juncea (unstressed)0 [GSH][35]B. juncea
(+100 μM C d2+)4 [GSH](a)γ-ECS (2.1)S. cerevisiae (unstressed))1.3 [GSH][42]E. coliγ-ECS (50)Populus tremula (unstressed)4.6 [GSH][34]E. coliγ-ECS (4.9)Brassica juncea (unstressed)3.5 [GSH](b)[43]B. juncea (+200 μM C d2+)1.5 [GSH](b)E. coliγ-ECS (40)Tobacco (unstressed)>4 [GSH][44]γ-ECS (9.1) + GS (18)S. cerevisiae (unstressed)1.8 [GSH][45]PCS (>2)Arabidopsis thaliana  (+85 μM C d2+)0 [GSH][36]Vacuolar transporter of PC-Cd complexes (>2)S. pombeHigher Cd2+[46]resistance(a)The
increase was only in roots with no effect on shoots. (b)The increase was only in shoots with
no effect on roots.Another problem in the study
of GSH biosynthesis for its eventual manipulation is that the pathway has been
analyzed considering only the GSH-synthetic reactions without taking into
account the GSH-consuming reactions (Figure2), [31]. The analysis of an incomplete pathway leads to
misleading conclusions about the control of flux. Metabolic modeling has shown that only with
the incorporation of the consuming reactions of the pathway end products, a true
steady state can be established [30]. In
conclusion, without a solid theoretical framework, the overexpression of only
one enzyme (the “rate-limiting step”), or of many arbitrarily selected enzymes
(Tables 1 and 2), the problem of increasing the flux or metabolite
concentrations cannot be solved.


### 3.4. Overexpression of Proteins from Other Metabolic Pathways

There are some successful examples of the genetic engineering approach to manipulate
metabolism:(i)
overexpression
(approx. 23 fold) of the five genes of the tryptophan synthesis pathway inS.
cerevisiae, to increase (9-fold) flux [47];(ii)
increase
in amino acids (Trp, Ile, Lys, Val, Thr) and
trehalose production inCorynebacterium glutamicum, in which some proteins of
each metabolic pathway are simultaneously overexpressed, but some of them with
mutations that confer insensitivity to feedback inhibition [48–53]. In these transformed bacteria, the end products
are indeed overproduced and their excretion is accelerated;(iii)
overexpression
of PFK and PyK to increase ethanol production by 35% inE. coli, although lactic acid formation was not modified [16];(iv)
mannitol
1-phosphate dehydrogenase and mannitol 1-phosphatase overexpression to increase
mannitol production by 27–50% in LDH-deficientLactococcus lactis [54];(v)
increase
in sorbitol production (5 fold) in LDH-deficientLactobacillus plantarum through the overexpression of sorbitol
6-phosphate dehydrogenase (activity up to 250 fold in mutants versus wild type) [55];(vi)
overexpression
of PFK (14 fold) or LDH (3.5 times) to increase 2-3 times the homolactic
fermentation flux inLactococcus lactis growing on maltose, and in parallel decrease fluxes toward secondary acids and
ethanol [56].


## 3.1. Glycolysis in Yeasts

When the yeastSaccharomyces
cerevisiae is exposed to high glucose (>2%; 0.11 M), the genes of all
glycolytic enzymes are induced (PDC and ENO increase their expression by 20 fold;
PGK, PYK, and ADH, 3–10 times; and the
others, 2 fold in average) [8–11]. However,
when the methodological development of genetic engineering allowed modulating the
expression of enzymes within cells, researchers turned to the rate-limiting
step concept to manipulate a metabolic pathway to increase flux and/or its
intermediates, hypothesizing that the overexpression of only one, or of a few
key glycolytic genes, should increase the flux.Historically, Heinisch [9] in Germany was the first author to
obtain a 3.5 fold overexpression of PFK-1 in  S. cerevisiae, but
surprisingly he observed that the rate of ethanol production was not modified. Subsequent experiments for increasing the
ethanol production rate by overexpressing either each of the presumed limiting
steps, or in combination with other glycolytic enzymes (Table 1), have been
unsuccessful and, even in some cases, a slight decrease in flux has been
attained. For instance, the simultaneous
overexpression of seven enzymes of the final section of glycolysis induced only
a 21% increase in ethanol production after 2 hours of culture (Table 1) [11]. This was accompanied by a 10–20% decrease in PFK-1
expression, which might have attenuated the flux increase.Table 1
Overexpression of glycolytic enzymes in different cell types.
Cell typeEnzymeActivity  (overexpression fold)Flux (% Control)ReferenceSaccharomyces cerevisiaeHK13.9107[12]PFK-13.5, 3.7,5102[9, 10, 12]PYK8.6107[12]PDC3.785[13]ADH4.889[12]PFK-1 + PYK5.6 + 1.3107[12]GAPDH + PGK + PGAM + ENO + PYK + PDC + ADH1.4 + 1.7 + 16 + 4 + 10.4 + 1.08 + 1.4121[12]GAPDH + PGK + PGAM + ENO + PYK + PDC + ADH1.5 + 1.4 + 3.4 + 1.5 + 2.5 + 1.1 + 1.294[11, 14]EscherichiacoliPFK8.772[15]PYK2.9, 4.291,95[16]Lactococcus lactisGAPDH14-210100[17]Aspergillus nigerPFK3100[18]PYK5100Chinese hamster ovaryPFK2.2, 3.4, 3.7100[19]Flux to ethanol was forS. cerevisiae and E. coli;
flux to citrate was for A. niger; and
flux to L-lactate was for hamster.In yeasts, HK is not product inhibited
by G6P or ADP; instead, it is strongly feedback inhibited by trehalose-6-phosphate
(Tre6P). This metabolite is synthesized from G1P by Tre6P synthase and Tre6P phosphatase. Deletion
of the Tre6P synthase gene does not
bring about an increased ethanol production, but it rather induces a defective cellular
growth on glucose and fructose and a lowered ethanol production, as a result of
a highly active HK that leads to hyperaccumulation of hexose phosphate
metabolites (particularly F1,6BP) and fast depletion of ATP, Pi, and downstream
metabolites. The explanation for this event is that, in the Tre6P synthase
mutants, the rate of glucose phosphorylation exceeds the rate of glycolytic ATP
synthesis (named “turbo effect”). Heterologous expression of a Tre6P-insensitive HK does not recover
completely the wild-type phenotype. Furthermore, deletion of the Tre6P synthase gene in the
Tre6P-insensitive HK strain did affect growth, suggesting other interactions
and functions of Tre6P synthase in the control of sugar metabolism, at
least inSchizosaccharomyces pombe [20].Davies and Brindle [10] obtained a 5-fold overexpression of
PFK-1 in S. cerevisiae, but the increase in ethanol production was not attained
under anaerobic conditions. There was a slight
increase in ethanol production in resting cells in aerobic conditions, under
which the mitochondrial metabolism contributes to the ATP supply. In all these works, it may be noted that
enzyme overexpression indeed affects the concentration of several intermediaries,
but this effect has not been further examined.It is worth noting that the
experiments described in Table1 do not rigorously reproduce the physiological
situation, in which overexpression of all the enzymes should be carried out in
the proportions found in the organisms. The
rationale behind this observation is that overexpression of only one “limiting”
step leads to a flux control redistribution, a condition at which other steps
now become rate limiting. Thus, the
concept of “rate-limiting step” offers no simple answer to the question of
increasing the yeast glycolytic flux, and it rather makes this problem to
appear as a difficult task to solve. In contrast, it seems that all relevant controlling steps
have to be overexpressed, thus reproducing what natural
selection has already successfully accomplished.In addition toS. cerevisiae, overexpression of glycolytic enzymes in other
organisms such as E. coli [15, 16],
lactobacteria [17], tomato [21], potato [22], and
hamster ovary cells [19] has been accomplished, although without increasing
flux (Table 1). It is somewhat surprising to note that in the glycolytic enzyme
overexpression experiments, the strong inhibitory effect of G6P (or Tre6P in S. cerevisiae), and citrate on HK and PFK-1, respectively, have been neglected. This
regulatory mechanism does not disappear in the cells overexpressing the enzymes
but, on the contrary, it is exacerbated. Then, what would be the aim of overexpressing HK, PFK-1 or any other
allosteric, or strongly product-inhibited enzyme if they will be more
inhibited?A successful experiment of increasing
the glycolytic flux was performed in primary cultures of rat hepatocytes [23]. HK and glucokinase (GK) were overexpressed by
using adenovirus as carrier. The transformed
hepatocytes showed higher activity of 18.7- and 7.1-times for HK and GK,
respectively, at 3 mM glucose, and of 6.3- and 7.1-times at 20 mM glucose. However, at 20 mM glucose, the flux to
lactate was not modified in HK-transformed cells, just like the experiments
described above (Table 1). In contrast,
with GK overexpression, a 3-fold increase in flux was achieved. The mechanistic difference is the HK
inhibition by G6P (10 mM G6P inhibits HK activity by 90%), whereas GK is not product inhibited.


## 3.2. Glycolysis in Lactobacteria

Lactococcus lactis is used in cheese production. For this purpose,
L. lactis ferments lactose to lactic acid by glycolysis. The end products, lactate and H+, are
expelled and acidify the external medium which contributes to cheese flavor and
texture and inhibits the growth of other bacteria. Similarly to yeast, the lack of carbon source
in lactobacteria promotes a metabolic change that leads to the production of
formic and acetic acids, ethanol, and, in a lower proportion, L-lactic acid,
altering the product quality. Thus, from a commercial point of view, it does
not seem important to know what controls the flux to lactate (because its rate
of production is adequate), but what controls the branching flux.To understand the process, and to eventually inhibit the production of secondary acids, Andersen et al. [24] constructed LDH mutants,
using a synthetic promoter library for tuning the gene expression. In mutants
lacking this enzyme, most of the pyruvate was transformed into acetic and
formic acids (Figure 1). In turn, flux
to lactate was affected in mutants expressing only 10% or less of wild-type LDH
levels, which indicated that LDH exerts no control of the glycolytic flux in
wild-type bacteria. Only with a normal content of this enzyme (100%), flux
toward secondary acids was prevented. Therefore, the flux to formic and acetic
acids is negatively controlled by LDH, and positively by PYK [17, 25]. As in S. cerevisiae, overexpression of
PFK-1, PYK, or GAPDH in lactobacteria did not increase the flux to L-lactic
acid [17, 25]. Similarly to E. coli glycolysis [26], glycolysis in L. lactis was controlled by the ATP
demand when working below its maximum capacity [27, 28], whereas, under high-rate
conditions, the glucose and lactate transporters exerted the main flux control [28]. Furthermore, this kind of observations indicates
that the flux control may reside outside the pathway [27–29], and it also supports the proposal
by Hofmeyr and Cornish-Bowden [30] that the end-product demand (which is
usually overlooked in studies of metabolism because these metabolites are
frequently not considered as part of the pathway) might be essential in flux
control.


## 3.3. Glutathione and Phytochelatin Synthesis in Plants

Glutathione (γ-Glu-Cys-Gly; GSH) is the most abundant nonproteinaceous
thiol compound (1–10 mM)
in almost all living cells. GSH is
involved in the oxidative stress processing, xenobiotic detoxification, and, in
some plants and yeasts, in the inactivation of toxic heavy metals (for a recent
revision see [31]). GSH is synthesized by two enzymes: γ-glutamylcysteine synthetase
(γ-ECS) and glutathione synthetase (GS) (Figure 2),
which catalyze reactions with high-equilibrium constants (Keq > 1000). Under a low GSH demand (unstressed
conditions), the producing block of enzymes has to receive information from the
last part of the pathway to (i) avoid the excessive and toxic accumulation of
the intermediary γ-EC and (ii) reach a stable steady state [32]. This information transfer is mediated by GSH,
which exerts strong competitive inhibition of γ-ECS [33] (Figure 2). GSH and Cys also exert inhibition on the
ATP-sulfurylase (ATPS) and on sulfate transporters (Figure 2) (for a review,
see [31]). The feedback inhibition of γ-ECS has led several researchers to propose
that this enzyme is the rate-limiting step of GSH synthesis [33–35]. Although there are no studies about the
pathway’s behavior under stressed conditions, which means under a high GSH
demand, the proposal that γ-ECS is the key enzyme has been automatically
extended to any environmental condition such as heavy metal exposure.Figure 2
Sulfur assimilation and glutathione and phytochelatins synthesis in plants ATPS, ATP sulfurylase; APS, adenosine5′ phosphosulphate;
γ-ECS, γ-glutamyl cysteine synthetase; γ-EC, γ-glutamyl
cysteine; GS, glutathione synthetase; GSH, reduced glutathione; GSSG, oxidized
glutathione; GPx, GSH peroxidase; GR, GSH reductase; PCS, phytochelatin synthase;
PCs, phytochelatins; GT, GSH-S-transferases; Xe, xenobiotic; GS-Xe, glutathione-xenobiotic
complex. The reactions are not shown
stochiometrically. GR uses the cofactor
NADPH. The Cd2+-GSH complex formation (cadmium bis-glutathionate) is fast and spontaneous and
does not require enzyme catalysis. Modified
from [31].By assuming thatγ-ECS is the rate-limiting step, many research groups
have tried to increase, in plants and yeasts, the rate of synthesis and the
concentration of GSH and phytochelatins (PCs) with the aim of fortifying their
heavy metal resistance and storage capacity, mainly toward Cd2+. The development of organisms able to grow in
soils and water systems contaminated with heavy metals, which may have the
ability of accumulating toxic metal ions, is of biotechnological interest for
bioremediation strategies.With this goal in mind,
researchers have then overexpressedγ-ECS and other pathway enzymes, including
phytochelatin synthase (PCS) (Table 2). Some of these experiments have been
partially successful in increasing GSH levels, although this has been rather
marginal with no correlation between enzyme levels and GSH concentration. Unfortunately, these overexpression experiments
have not been accompanied by determinations of fluxes or other relevant metabolite
concentrations such as PCs or Cys. On
the other hand, the overexpression of PCS has surprisingly induced oxidative stress
and necrosis instead of increasing Cd2+ accumulation and resistance
[36]. This result suggests that, under high
GSH demand (i.e., for PCs synthesis and for direct heavy metal
sequestration by GSH), the GSH concentration does not suffice for maintaining
the other essential GSH functions such as oxidative stress management and
xenobiotic detoxification.Table 2
GSH and phytochelatin synthesis enzymes overexpression in plants and yeasts.
Overexpressed enzyme (activity fold)Organism (experimental condition)MetaboliteReference(increment fold)ATP sulfurylase (2.1)Brassica juncea2.1 [GSH][37]ATP sulfurylase (4.8)Tobacco (unstressed)1.3 [SO42−][38]O-acetyl-serine thiol-lyase (2.5)Tobacco (unstressed)2 [Cys][39]0 [GSH]Serine acetyl transferase
(>10)Potato chloroplasts (unstressed)2 [Cys][40]0 [GSH]E. coli GS (90)Populus tremula (unstressed)0 [GSH][34]GS (3)S. cerevisiae (unstressed)0 [GSH][41]E. coliγ-ECS (>2)Brassica juncea (unstressed)0 [GSH][35]B. juncea
(+100 μM C d2+)4 [GSH](a)γ-ECS (2.1)S. cerevisiae (unstressed))1.3 [GSH][42]E. coliγ-ECS (50)Populus tremula (unstressed)4.6 [GSH][34]E. coliγ-ECS (4.9)Brassica juncea (unstressed)3.5 [GSH](b)[43]B. juncea (+200 μM C d2+)1.5 [GSH](b)E. coliγ-ECS (40)Tobacco (unstressed)>4 [GSH][44]γ-ECS (9.1) + GS (18)S. cerevisiae (unstressed)1.8 [GSH][45]PCS (>2)Arabidopsis thaliana  (+85 μM C d2+)0 [GSH][36]Vacuolar transporter of PC-Cd complexes (>2)S. pombeHigher Cd2+[46]resistance(a)The
increase was only in roots with no effect on shoots. (b)The increase was only in shoots with
no effect on roots.Another problem in the study
of GSH biosynthesis for its eventual manipulation is that the pathway has been
analyzed considering only the GSH-synthetic reactions without taking into
account the GSH-consuming reactions (Figure2), [31]. The analysis of an incomplete pathway leads to
misleading conclusions about the control of flux. Metabolic modeling has shown that only with
the incorporation of the consuming reactions of the pathway end products, a true
steady state can be established [30]. In
conclusion, without a solid theoretical framework, the overexpression of only
one enzyme (the “rate-limiting step”), or of many arbitrarily selected enzymes
(Tables 1 and 2), the problem of increasing the flux or metabolite
concentrations cannot be solved.


## 3.4. Overexpression of Proteins from Other Metabolic Pathways

There are some successful examples of the genetic engineering approach to manipulate
metabolism:(i)
overexpression
(approx. 23 fold) of the five genes of the tryptophan synthesis pathway inS.
cerevisiae, to increase (9-fold) flux [47];(ii)
increase
in amino acids (Trp, Ile, Lys, Val, Thr) and
trehalose production inCorynebacterium glutamicum, in which some proteins of
each metabolic pathway are simultaneously overexpressed, but some of them with
mutations that confer insensitivity to feedback inhibition [48–53]. In these transformed bacteria, the end products
are indeed overproduced and their excretion is accelerated;(iii)
overexpression
of PFK and PyK to increase ethanol production by 35% inE. coli, although lactic acid formation was not modified [16];(iv)
mannitol
1-phosphate dehydrogenase and mannitol 1-phosphatase overexpression to increase
mannitol production by 27–50% in LDH-deficientLactococcus lactis [54];(v)
increase
in sorbitol production (5 fold) in LDH-deficientLactobacillus plantarum through the overexpression of sorbitol
6-phosphate dehydrogenase (activity up to 250 fold in mutants versus wild type) [55];(vi)
overexpression
of PFK (14 fold) or LDH (3.5 times) to increase 2-3 times the homolactic
fermentation flux inLactococcus lactis growing on maltose, and in parallel decrease fluxes toward secondary acids and
ethanol [56].


## 4. Downregulation of Enzymes to Manipulate Metabolism

### 4.1. Glycolysis in Tumor Cells

Glycolysis is enhanced in human and animal cancer cells (reviewed in [57]). Several glycolytic enzymes are overexpressed in
at least 70% of human cancers [58]. Except
for glucose transporter 1 (GLUT-1), the other 11 glycolytic enzymes (HK to LDH)
are overexpressed in brain and nervous system cancers. Prostate and lymphatic nodule cancers (Hodgkin
and non-Hodgkin lymphomas; myelomas) overexpress 10 glycolytic enzymes (except
for HK; in prostate cancer GLUT1 is also overexpressed). There is a second group of cancers that overexpresses 6–8 glycolytic
genes (skin, kidney, stomach, testicles, lung, liver, placenta, pancreas,
uterus, ovary, eye, head and neck, and mammary gland). A third group includes those cancers overexpressing
1 or 2 glycolytic genes (bone, bone marrow, cervix, and cartilage) [58].In animals, gene expression of glycolytic enzymes is regulated (both coordinately
and individually) under hypoxic conditions by hypoxia-responsive transcription
factors such as HIF-1α (hypoxia-inducible factor 1α), SP family factors, AP-1, and possibly MRE
(metal response elements) [8, 59–61]. HIF-1α is probably the principal coordinator in gene
induction. There are binding sites (consensus sequence ACGT) for HIF-1α in the promoters of genes for HK [62], PFK-1,
ALDO, GAPDH, PGK, ENO, PYK, and LDH (reviewed in [8]). TPI and perhaps HPI and PGAM are also induced
by hypoxia, but it is not clear whether HIF-1α mediates this induction [8], and whether this
factor regulates other metabolic pathways associated with glucose
catabolism. For example, although
glycogen phosphorylase is overexpressed under hypoxia in human tissues [63],
the role of HIF-1 has not been demonstrated.If direct manipulation of
pathway genes becomes difficult, then the overexpression or repression of
transcription factors such as HIF-1α, AP1, and MREs might solve the problem of changing
flux, although overexpression of transcription factors may also be difficult
due to the numerous upstream and downstream factors involved.


### 4.2. Glycolysis inTrypanosoma brucei

The kinetoplastid parasitesTrypanosoma
cruzi, Trypanosoma brucei, and Leishmania are the causative agents of
Chagas disease, African trypanosomiasis, and leishmaniasis, respectively. The
available drugs to treat these diseases are highly toxic for humans. Moreover, the
parasites may become resistant, and hence the search for new drugs and drug
targets is relevant for solving these public health problems.In these parasites, the
metabolism is organized in a peculiar way; they have a subcellular structure
called glycosome in which several metabolic pathways take place:
gluconeogenesis, reactions of the pentose phosphate pathway, purine salvage and
pyrimidine biosynthesis,β-oxidation
of fatty acids, fatty acid elongation, biosynthesis of ether lipids, and the
first seven steps of glycolysis. In fact, approximately 90% of glycosome enzyme content
corresponds to glycolytic enzymes [64]. Glycosomal glycolytic enzymes have unique structural, kinetic, and
regulatory features not found in their human counterparts, and therefore have
been the subject of extensive biochemical studies to use them as drug targets [65]. The rationale behind this is to synthesize
inhibitors that affect mainly the parasitic enzymes with relatively low effect
on the human enzymes since the infective parasite stages rely mostly on
glycolysis for ATP supply.There are reports on the
design of presumed specific inhibitors for some of theT. brucei glycolytic
enzymes: GLUT (bromoacetyl-2-glucose) [66], HK, HPI, PFK, ALDO, TPI, GAPDH,
PGK, PYK, and glycerol-3-phosphate dehydrogenase [67]. Although the purified enzymes display
very low Ki values for these
inhibitors and some of them inhibit
parasite growth or infective capabilities, their effect on inhibiting the
glycolytic flux has not been explored. Therefore, it is not yet possible to
directly ascribe the effects seen in parasite culture with the in vitro effects
on the isolated enzymes. To identify the
best drug targets, determination of the flux control steps of glycolysis
in T. brucei has been recently initiated [68].


### 4.3. Trypanothione Synthesis in Kinetoplastid Parasites

Trypanothione (TSH2)
is a reducing agent present in trypanosomatids that is synthesized from one
spermidine and two GSH molecules by TSH2 synthetase (TryS)
(Figure 3). This metabolite and its reducing enzyme,
TSH2 reductase (TryR), replace the antioxidant and metabolic
functions of the more common GSH/GSH reductase system present in mammals. In
fact, most of the antioxidant metabolism of these parasites depend on TSH2 (Figure 3) [69, 70]. Thus, the enzymes of this metabolic pathway have been
proposed as drug targets for killing the parasites.Figure 3
Trypanothione synthesis in trypanosomatids. The trypanothione producing enzymes areγ-ECS, GS, ODC, aminopropyl transferase (PAT), and TryS. The trypanothione consuming enzymes are
ascorbate peroxidase (APX); tryparedoxin peroxidases (TXNPx); trypanothione-glutathione thiol transferase (thiol transferase); and glutathione peroxidases
I (GPX I) and II (GPX II). The regenerating enzyme is TryR. APX, thiol
transferase, and GPX II have only been described in T. cruzi. This last parasite lacks ODC activity, but it
has developed high-affinity transporters for putrescine, cadaverine, and
spermidine [71].Several studies have focused in assessing TryR as drug target. Diminution in its gene transcription yields a
loss of activity between 56–90%, depending on
the genetic technique [72–75]. In
knockdown T. brucei cells (i.e., when TryR activity has diminished
to less than 10% of the wild-type level), the parasites show growth diminution
and higher sensitivity to H2O2 in culture and loss of
infectiveness in mice. However, TSH2 and thiol compound contents
were not affected [75]. TryR
downregulation by >85% in Leishmania species causes inability to survive under
oxidative stress inside macrophages [72–74]. In contrast, when TryR is 14- and 10 fold
overexpressed in Leishmania and T. cruzi, respectively, there are no
significant differences in H2O2 susceptibility between
control and transfected cells; both types of cells are also equally resistant
to the oxidative stress-inducers gentian violet, and nitrofurans [76]. Intriguingly, the cellular levels of TSH2,
GSH, and glutathionyl-spermidine, determined in both types of experiments (TryR
suppression and overexpression) were similar in control and transformed cells.Other studies have proposed TryS as an alternative drug target. Knockdown
of TryS by siRNA in procyclicT. brucei causes (i) viability impairment and arrest of proliferation when TSH2 levels decrease to 15% of the wild-type level, (ii) increased sensitivity to H2O2 and alkyl hydroperoxides, (iii) damage to the plasma membrane, and (iv)
diminution of the TSH2 content and accumulation of GSH and
glutathionyl-spermidine [77]. A similar metabolite variation (lower TSH2;
higher GSH) was attained with a TryS knockdown induced by siRNA in the
bloodstream form of T. brucei [78]. This
TryS knockdown also induced an increased sensitivity to different compounds
that affect TSH2 metabolism such as arsenicals, melarsen oxide,
trivalent antimonials, and nifurtimox [78]. Indeed, western blot analysis showed,
in addition to the expected (10-fold) decrease in TryS protein, a 2-3-folds increase in γ-ECS and TryR. The changes in expression of
other enzymes suggest unveiled compensatory or pleiotropic effects on TSH2 metabolism.Other researchers have selectedγ-glutamylcysteine synthetase (γ-ECS), the presumed rate-limiting step of GSH
synthesis, as an alternative drug target of TSH2 synthesis in T. brucei (Figure 3). Knockdown of γ-ECS gene in the parasite induces cell death
and depletion of GSH and TSH2 only after 80% decrease in the enzyme
content [79]. The γ-ECS knockdown cells are rescued from death by
adding external GSH, which elevates the cellular GSH and TSH2 levels
[79].Glutathione synthetase (GS) has not been manipulated in trypanosomatids, or in any other organism, perhaps
because it has been considered as a nonrate-limiting step of GSH and TSH2 biosynthesis. However, DNA microarray
analysis of antimonite-resistant Leishmania tarentolae shows increased
transcription of γ-ECS, GS, and P-glycoprotein A RNAs [80].
Although it was not evaluated whether increase in gene transcription correlated
with an increase in enzyme activity, it may be possible that under high GSH
demand (i.e., under oxidative stress conditions) GS might exert control of TSH2 synthesis. On the other hand, ornithine
decarboxylase (ODC) overexpression in T. brucei (the presumed limiting
step of spermidine synthesis) causes no change in TSH2 levels
[81]. Therefore, ODC does not seem to be
a controlling step of TSH2 synthesis.Although almost full inhibition (>80%) of gene transcription or activity of any of
these enzymes results in parasite death, the question remains of how TSH2 metabolism is affected when the enzymes are less inhibited. For example, in the therapeutic treatment of
patients it is certain that drugs have to be administered for long periods of
time. If the parasites are not
completely cleared from the patient, disease recurrence and generation of drug-resistant
parasites are possible. The results described
above indicate that each enzyme by itself has low control on TSH2 synthesis and concentration; therefore, highly specific and very potent
inhibitors have to be designed in order to attain the required full activity blockade
to affect TSH2 metabolism in these parasites.


## 4.1. Glycolysis in Tumor Cells

Glycolysis is enhanced in human and animal cancer cells (reviewed in [57]). Several glycolytic enzymes are overexpressed in
at least 70% of human cancers [58]. Except
for glucose transporter 1 (GLUT-1), the other 11 glycolytic enzymes (HK to LDH)
are overexpressed in brain and nervous system cancers. Prostate and lymphatic nodule cancers (Hodgkin
and non-Hodgkin lymphomas; myelomas) overexpress 10 glycolytic enzymes (except
for HK; in prostate cancer GLUT1 is also overexpressed). There is a second group of cancers that overexpresses 6–8 glycolytic
genes (skin, kidney, stomach, testicles, lung, liver, placenta, pancreas,
uterus, ovary, eye, head and neck, and mammary gland). A third group includes those cancers overexpressing
1 or 2 glycolytic genes (bone, bone marrow, cervix, and cartilage) [58].In animals, gene expression of glycolytic enzymes is regulated (both coordinately
and individually) under hypoxic conditions by hypoxia-responsive transcription
factors such as HIF-1α (hypoxia-inducible factor 1α), SP family factors, AP-1, and possibly MRE
(metal response elements) [8, 59–61]. HIF-1α is probably the principal coordinator in gene
induction. There are binding sites (consensus sequence ACGT) for HIF-1α in the promoters of genes for HK [62], PFK-1,
ALDO, GAPDH, PGK, ENO, PYK, and LDH (reviewed in [8]). TPI and perhaps HPI and PGAM are also induced
by hypoxia, but it is not clear whether HIF-1α mediates this induction [8], and whether this
factor regulates other metabolic pathways associated with glucose
catabolism. For example, although
glycogen phosphorylase is overexpressed under hypoxia in human tissues [63],
the role of HIF-1 has not been demonstrated.If direct manipulation of
pathway genes becomes difficult, then the overexpression or repression of
transcription factors such as HIF-1α, AP1, and MREs might solve the problem of changing
flux, although overexpression of transcription factors may also be difficult
due to the numerous upstream and downstream factors involved.


## 4.2. Glycolysis inTrypanosoma brucei

The kinetoplastid parasitesTrypanosoma
cruzi, Trypanosoma brucei, and Leishmania are the causative agents of
Chagas disease, African trypanosomiasis, and leishmaniasis, respectively. The
available drugs to treat these diseases are highly toxic for humans. Moreover, the
parasites may become resistant, and hence the search for new drugs and drug
targets is relevant for solving these public health problems.In these parasites, the
metabolism is organized in a peculiar way; they have a subcellular structure
called glycosome in which several metabolic pathways take place:
gluconeogenesis, reactions of the pentose phosphate pathway, purine salvage and
pyrimidine biosynthesis,β-oxidation
of fatty acids, fatty acid elongation, biosynthesis of ether lipids, and the
first seven steps of glycolysis. In fact, approximately 90% of glycosome enzyme content
corresponds to glycolytic enzymes [64]. Glycosomal glycolytic enzymes have unique structural, kinetic, and
regulatory features not found in their human counterparts, and therefore have
been the subject of extensive biochemical studies to use them as drug targets [65]. The rationale behind this is to synthesize
inhibitors that affect mainly the parasitic enzymes with relatively low effect
on the human enzymes since the infective parasite stages rely mostly on
glycolysis for ATP supply.There are reports on the
design of presumed specific inhibitors for some of theT. brucei glycolytic
enzymes: GLUT (bromoacetyl-2-glucose) [66], HK, HPI, PFK, ALDO, TPI, GAPDH,
PGK, PYK, and glycerol-3-phosphate dehydrogenase [67]. Although the purified enzymes display
very low Ki values for these
inhibitors and some of them inhibit
parasite growth or infective capabilities, their effect on inhibiting the
glycolytic flux has not been explored. Therefore, it is not yet possible to
directly ascribe the effects seen in parasite culture with the in vitro effects
on the isolated enzymes. To identify the
best drug targets, determination of the flux control steps of glycolysis
in T. brucei has been recently initiated [68].


## 4.3. Trypanothione Synthesis in Kinetoplastid Parasites

Trypanothione (TSH2)
is a reducing agent present in trypanosomatids that is synthesized from one
spermidine and two GSH molecules by TSH2 synthetase (TryS)
(Figure 3). This metabolite and its reducing enzyme,
TSH2 reductase (TryR), replace the antioxidant and metabolic
functions of the more common GSH/GSH reductase system present in mammals. In
fact, most of the antioxidant metabolism of these parasites depend on TSH2 (Figure 3) [69, 70]. Thus, the enzymes of this metabolic pathway have been
proposed as drug targets for killing the parasites.Figure 3
Trypanothione synthesis in trypanosomatids. The trypanothione producing enzymes areγ-ECS, GS, ODC, aminopropyl transferase (PAT), and TryS. The trypanothione consuming enzymes are
ascorbate peroxidase (APX); tryparedoxin peroxidases (TXNPx); trypanothione-glutathione thiol transferase (thiol transferase); and glutathione peroxidases
I (GPX I) and II (GPX II). The regenerating enzyme is TryR. APX, thiol
transferase, and GPX II have only been described in T. cruzi. This last parasite lacks ODC activity, but it
has developed high-affinity transporters for putrescine, cadaverine, and
spermidine [71].Several studies have focused in assessing TryR as drug target. Diminution in its gene transcription yields a
loss of activity between 56–90%, depending on
the genetic technique [72–75]. In
knockdown T. brucei cells (i.e., when TryR activity has diminished
to less than 10% of the wild-type level), the parasites show growth diminution
and higher sensitivity to H2O2 in culture and loss of
infectiveness in mice. However, TSH2 and thiol compound contents
were not affected [75]. TryR
downregulation by >85% in Leishmania species causes inability to survive under
oxidative stress inside macrophages [72–74]. In contrast, when TryR is 14- and 10 fold
overexpressed in Leishmania and T. cruzi, respectively, there are no
significant differences in H2O2 susceptibility between
control and transfected cells; both types of cells are also equally resistant
to the oxidative stress-inducers gentian violet, and nitrofurans [76]. Intriguingly, the cellular levels of TSH2,
GSH, and glutathionyl-spermidine, determined in both types of experiments (TryR
suppression and overexpression) were similar in control and transformed cells.Other studies have proposed TryS as an alternative drug target. Knockdown
of TryS by siRNA in procyclicT. brucei causes (i) viability impairment and arrest of proliferation when TSH2 levels decrease to 15% of the wild-type level, (ii) increased sensitivity to H2O2 and alkyl hydroperoxides, (iii) damage to the plasma membrane, and (iv)
diminution of the TSH2 content and accumulation of GSH and
glutathionyl-spermidine [77]. A similar metabolite variation (lower TSH2;
higher GSH) was attained with a TryS knockdown induced by siRNA in the
bloodstream form of T. brucei [78]. This
TryS knockdown also induced an increased sensitivity to different compounds
that affect TSH2 metabolism such as arsenicals, melarsen oxide,
trivalent antimonials, and nifurtimox [78]. Indeed, western blot analysis showed,
in addition to the expected (10-fold) decrease in TryS protein, a 2-3-folds increase in γ-ECS and TryR. The changes in expression of
other enzymes suggest unveiled compensatory or pleiotropic effects on TSH2 metabolism.Other researchers have selectedγ-glutamylcysteine synthetase (γ-ECS), the presumed rate-limiting step of GSH
synthesis, as an alternative drug target of TSH2 synthesis in T. brucei (Figure 3). Knockdown of γ-ECS gene in the parasite induces cell death
and depletion of GSH and TSH2 only after 80% decrease in the enzyme
content [79]. The γ-ECS knockdown cells are rescued from death by
adding external GSH, which elevates the cellular GSH and TSH2 levels
[79].Glutathione synthetase (GS) has not been manipulated in trypanosomatids, or in any other organism, perhaps
because it has been considered as a nonrate-limiting step of GSH and TSH2 biosynthesis. However, DNA microarray
analysis of antimonite-resistant Leishmania tarentolae shows increased
transcription of γ-ECS, GS, and P-glycoprotein A RNAs [80].
Although it was not evaluated whether increase in gene transcription correlated
with an increase in enzyme activity, it may be possible that under high GSH
demand (i.e., under oxidative stress conditions) GS might exert control of TSH2 synthesis. On the other hand, ornithine
decarboxylase (ODC) overexpression in T. brucei (the presumed limiting
step of spermidine synthesis) causes no change in TSH2 levels
[81]. Therefore, ODC does not seem to be
a controlling step of TSH2 synthesis.Although almost full inhibition (>80%) of gene transcription or activity of any of
these enzymes results in parasite death, the question remains of how TSH2 metabolism is affected when the enzymes are less inhibited. For example, in the therapeutic treatment of
patients it is certain that drugs have to be administered for long periods of
time. If the parasites are not
completely cleared from the patient, disease recurrence and generation of drug-resistant
parasites are possible. The results described
above indicate that each enzyme by itself has low control on TSH2 synthesis and concentration; therefore, highly specific and very potent
inhibitors have to be designed in order to attain the required full activity blockade
to affect TSH2 metabolism in these parasites.


## 5. Theory of Metabolic Control Analysis

The metabolic
control analysis (MCA) was initially developed by Kacser and Burns in Scotland [82, 83] and by Heinrich and Rapoport
in East Germany
[84, 85]. This analysis establishes a
theoretical framework that explains the results observed with the enzyme
overexpression and downregulation experiments. In addition, it helps to identify and design
experimental strategies for the manipulation of a given process in an organism
(heavy metal hyperaccumulation; increased production of ethanol, CO2,
lactate or acetate; or inhibition of a metabolic pathway flux with therapeutic
purposes). MCA rationalizes the quantitative
determination of the degree of control that a given enzyme exerts on flux and
on the concentration of metabolites. Different
experimental approaches have been developed to detect and direct what has to be
done and measured, in order to identify and understand why an enzyme exerts a
significant or a negligible control on flux and metabolite concentration in a
metabolic pathway. Thus, the application of this analysis avoids the “trial and
error” experiments for identifying and manipulating the conceptually wrong “rate-limiting
step.”To
understand how a metabolic pathway is controlled and could be manipulated, its
control structure has to be evaluated. The
control structure of a pathway is constituted by the flux control coefficient (CviJ), which is the degree of control that the rate (v) of a given enzyme i exerts
on flux J; the concentration control coefficient (CviX), which is the degree of control that a given enzyme i exerts on the concentration of a metabolite
(X); and the elasticity coefficients. The control coefficients are systemic
properties of the pathway that are mechanistically determined by the elasticity
coefficients (εXvi), which are defined as the degree of sensitivity
of a given enzyme vi
(i.e., the enzyme’s ability to change
its rate) when any of its ligands (X: substrate, products or allosteric
modulators) is varied.The flux control coefficient
is defined as(1)CviJ=dJdvi•vioJo, in which the expression dJ/dvi describes
the variation in flux (J) when an infinitesimal change is done in the enzyme i concentration or activity. In practice,
the infinitesimal changes in vi
are undetectable, and hence measurable noninfinitesimal changes are undertaken.
If a small change in vi
promotes a significant
variation in J, then this enzyme exerts an elevated flux control (Figure 4,
position 1). In contrast, if a rather small
or negligible change in flux is observed when vi
is greatly varied, then the enzyme does not exert
significant flux control (Figure 4, position 2). To obtain dimensionless and normalized values
of CviJ the scaling factor vio/Jo is applied, which represents the ratio between the initial values from which
the slope dJ/dvi
is
calculated. If all CviJ of the pathway enzymes and transporters are added up, the sum comes to
one (summation theorem).Figure 4
Experimental determination
of flux control coefficient.The MCA clearly distinguishes
between the control exerted by a given enzyme on flux (flux control
coefficient) and on the metabolite concentration (concentration control
coefficient). Thus, an enzyme can have significant control on a metabolite
concentration but not on the pathway flux. This distinction is important for
biotechnology purposes. On one hand, the use of the rate-limiting step concept
for manipulating metabolic pathways does not make such differentiation, which
probably has contributed to the many unsuccessful experiments reported in the
literature; on the other hand, it should be clearly defined whether the aim of the
project is to increase flux and/or a metabolite concentration since MCA
establishes for each aim a different experimental design.To determine the flux control
coefficient of a given enzyme, small variations in the enzyme content, or
preferentially, in activity are required, without altering the rest of the
pathway, and then the changes in flux are determined. The experimental points are plotted as shown
in Figure4 to calculate the slope at the reference point vio/Jo. This experiment, apparently easy to perform,
has demanded great intellectual and experimental effort. Several experimental strategies have been
developed to determine CviJ:(i)
formation of heterokarionts and heterocygots (classical genetics),(ii)
titration of flux with specific inhibitors,(iii)
elasticity analysis,(iv)
mathematical modeling (in
silico biology),(v)
in vitro reconstitution of metabolic pathways,(vi)
genetic engineering to manipulate in vivo protein levels.


### 5.1. Classical Mendelian Genetics

The arginine biosynthesis inNeurospora crassa was the first metabolic
pathway in which flux control coefficients were experimentally determined by
Kacser’s laboratory [86]. This fungus
forms multinucleated mycelia that facilitate the generation of polyploid cells.
By mixing different ratios of spores containing
genes encoding wild (active) and mutant (inactive) enzymes of this pathway, it
was possible to generate heterokaryont mycelia with different content, and
activity, of four pathway enzymes. The authors built plots of enzyme activity versus
flux (see Figure 4) for acetyl-ornithine aminotransferase, ornithine
transcarbamoylase, arginine-succinate synthetase, and arginine-succinate lyase.
All the experimental points of these
heterokaryonts localized near to position 2 of Figure 4 with CviJarg= 0.02–0.2 (flux control by these enzymes was
only 2–20%), which indicated that none of these enzymes exerted significant
control on arginine synthesis. The authors did not determine the remaining flux
control (75%), which might reside in carbamoyl-phosphate synthetase I (this mitochondrial
ammonium-dependent isoform can be bound to the mitochondrial inner membrane or
form complexes with ornithine transcarbamoylase [87, 88]) and in mitochondrial citruline/ornithine
transporter, both of which have been proposed as limiting steps, or might be in
the arginine demand for protein synthesis.Organisms
with many alleles of one enzyme may form homo-and heterozygotes expressing
different activity levels.Drosophila
melanogaster has three ADH alleles encoding for isoforms with different Vmax. When three natural homozygotes, a null mutant, and
some heterozygotes were generated, different ADH activities were attained but
the ethanol consuming rate did not change (Figure 4, position 2). It was concluded that the ADH flux control was
near zero [89].


### 5.2. Titration of Flux with Inhibitors (Control of Oxidative Phosphorylation)

Oxidative phosphorylation (OXPHOS) is
the only pathway for which specific and potent inhibitors for many enzymes and
transporters are available. OXPHOS is divided in two segments (Figure5): the
oxidative system (OS) formed by substrate transporters (pyruvate,
2-oxoglutarate, glutamate, glutamate/aspartate, dicarboxylates), Krebs cycle
enzymes, and the respiratory chain complexes; and the phosphorylating system
(PS) constituted by the ATP/ADP (ANT) and Pi (PiT) transporters, and ATP
synthase. The proton electrochemical
gradient (Δμ−H+) connects the two systems.Figure 5
Mitochondrial oxidative phosphorylation. ST, oxidizable substrate transporter; KC, Krebs cycle;
RC, respiratory chain;(Δμ∼H+),
proton electrochemical
gradient; ANT, adenine nucleotide translocator; PiT, phosphate transporter; ATP
Sint, ATP synthase.When the flux (ATP synthesis)
is titrated by adding increasing concentrations of each specific inhibitor,
plots are generated in which the enzyme activity is progressively diminished by
increasing inhibitor concentration. Hence, theCviJ value depends on the type of
inhibitor used(a)
for irreversible inhibition,(2)CviJ=(−ImaxJo)(dJdI)[I]→0,(b)
for simple noncompetitive inhibition,(3)CviJ=(−KiJo)(dJdI)[I]→0,(c)
for simple competitive inhibition,(4)CviJ=(-Ki[(1+S)/Km]Jo)(dJdI)[I]→0, where Jo is the pathway flux in the absence
of inhibitor; Imax, minimal
inhibitor concentration to reach maximal flux inhibition; Ki, inhibition constant; S,
substrate concentration; Km,
Michaelis-Menten constant; and dJ/dI,
initial slope ([I]=0) of inhibition titration curve.To estimate flux control
coefficients from inhibitor titration of ADP-stimulated (state 3) respiratory
rates (i.e., mitochondrialO2 consumption coupled to ATP synthesis), (2) for irreversible inhibitors was used
because researchers assumed that mitochondrial inhibitors such as rotenone,
antimycin, carboxyatractyloside, and oligomycin were “pseudoirreversible,” due
to the enzyme’s high affinity for them. However, under this assumption flux control coefficients were usually
overestimated [90, 91]. To solve this
problem, Gellerich et al. [92] developed (5) for noncompetitive
tightly-bound inhibitors and, by using nonlinear regression analysis, it was
possible to include all experimental points from the titration curve thus
increasing accuracy in calculating CviJ:(5)J=[n(Jo−Ji)2•EnCo•Jo•Eon[(n−Co)•Jo−(n•Ji)•En]]+JiE2+(Kd+I−Eo)•E−Kd•Eo=0, in which Jo and Ji are the
respiration fluxes in the noninhibited (E=Eo) and inhibited (E=0) states; Kd is the dissociation constant of
the enzyme-inhibitor complex, and n is an empirical component that expresses the relationship between substrate
concentration and the reaction catalyzed by the enzyme E.The analysis of data in Table3 shows that OXPHOS is not controlled by only one
limiting step, but the flux control is rather distributed among several enzymes
and transporters. It is worth noting
that the value of the flux control coefficient depends on the content of enzyme
or transporter, which varies from tissue to tissue. Perhaps the ATP/ADP translocase in AS-30D hepatoma mitochondria
might reach the status of being the “OXPHOS limiting step” with a CANTJOxPhos=0.70, or the Pi transporter in kidney mitochondria [93], or the
ATP/ADP translocase and the respiratory chain complex 3 in liver mitochondria [94], but
it should be noted that other steps also exert significant control (Table 3). Although the distribution of control varies
between tissues, the flux control mainly resides in the PS of organs with high ATP
demand such as the heart  (CPT+ANT+ATPsynthaseJOxPhos=CPSJOxPhos=0.73), kidney (CPSJOxPhos=0.75; COSJOxPhos=0.31), and  fast-growing tumors (CPSJOxPhos=0.98). In contrast, in the
liver  (COSJOxPhos=0.80; CPSJOxPhos=0.65) and brain (COSJOxPhos=0.35; CPSJOxPhos=0.41), the control is shared by both systems.Table 3
Control distribution of oxidative phosphorylation.
EnzymeCviJATPRat organ mitochondriaSpecific inhibitorInhibition mechanismReferenceNADH-CoQ-oxidoreductase
(Site 1 of energy conservation or Complex I of respiratory chain)0.15Heart
(0.5 mM pyr + 0.2μM Ca2+)RotenoneNoncompetitive
tightly bound[93]0.26Heart
(10 mM pyr + 10 mM mal)[95]0.31Kidney
(0.5 mM pyr + 0.2μM Ca2+)[93]0.06Kidney (10 mM pyr + 10 mM mal)[95]0.06–0.10Brain (0.05 mM pyr + 0.4μM Ca2+)[91]0.25Brain (10 mM pyr + 10 mM mal)[95]0Tumor (10 mM glut + 3 mM mal)[96]0.27Liver (10 mM pyr + 10 mM mal)[95]0.13Skeletal muscle (10 mM pyr + 10 mM mal)[95]CoQ.cytochrome
c oxidoreductase (Site 2 of energy conservation or Complex III of respiratory
chain)0.01HeartAntimycinNoncompetitive
tightly bound[93]0.19Heart[95]0.02Kidney[95]0.05–0.11Brain[91]0.02Brain[95]0Tumor[96]0.43Liver (5 mM Succ + 1μM Ca2+)[94]0.07Liver[95]0.22Skeletal muscle[95]Cytochrome
c oxidase (Site 3 of energy conservation or Complex IV of respiratory chain)0.11HeartCyanide
or azideNoncompetitive
simple[93]0.13Heart[95]0.04Kidney[95]0.02–0.07Brain[91]0.02Brain[95]0.04Tumor[96]0.23Liver[94]0.03Liver[95]0.20Skeletal
muscle[95]ATP/ADP
transporter (adenine-nucleotides or ATP/ADP transporter, carrier or exchanger)0.24HeartCarboxy-atractyloside (CAT)Noncompetitive
tightly bound[93]0.04Heart[95]0Kidney[93]0.07Kidney[95]0.08Brain[91]0.08Brain[95]0.60–0.70Tumor[96]0.48Liver[93]0.01Liver[93]0.37Skeletal
muscle (10 mM Glut + 3 mM mal)[97]0.08Skeletal
muscle[95]ATP synthase0.34HeartOligomycinNoncompetitive tightly bound[93]0.12Heart[95]0.32Kidney[93]0.27Kidney[95]0.09–0.20Brain[91]0.26Brain[95]0.28Tumor[96]0.05Liver[94]0.20Liver[95]0.10Skeletal muscle[97]0.10Skeletal muscle[95]Pi transporter0.15HeartMersalylNoncompetitive simple[93]0.14Heart[95]0.43Kidney[93]0.28Kidney[95]0.13Brain[91]0.26Brain[95]0Tumor[96]0.05–0.12Liver[94]0.26Liver[95]0.15Skeletal muscle[97]0.08Skeletal muscle[95]Pyruvate transporter0.15Heartα-cyano-4-hydroxy-cinnamateNoncompetitive simple[95]0.03Kidney[95]0.08Brain[91]0.26Brain[95]0.21Liver[95]0.20Skeletal muscle[95]Dicarboxylates transporter0.05–0.14LiverMalate or butyl-malonateCompetitive simple[94]External ATPase0.40Skeletal musclePurified ATPase addition[94]The situation
in skeletal muscle appears controversial. Wisniewski et al. [97] determined that the OXPHOS
control was shared by the PS (CPSJOxPhos=0.62) and the ATP demand (purified ATPase). In turn, Rossignol et al. [95] concluded that
the OS exerted the main control (COSJOxPhos=0.68), but these authors apparently used low-quality mitochondria
(low respiratory control values that lead to low rates of ATP synthesis
associated with high rates of respiration) that were not incubated under near physiological
conditions (10 mM pyruvate, 10 mM malate, 10 mM Pi, pH 7.4 in Tris buffer), and the authors incorrectly assumed that rotenone and antimycin
were irreversible inhibitors. It is notorious
that in all works shown in Table 3 at least one of these mistakes is evident.There are some inhibitors for enzymes and transporters from other pathways, but they
are not quite specific and may affect other sites. Due to the fact that there are no inhibitors
for every step in these pathways, only one flux control coefficient has been
determined by inhibitor titration. Examples
of these inhibitors are 6-chloro-6-deoxyglucose for glucose transporters in
bacteria, 2-deoxyglucose for HPI, iodoacetate for GAPDH [6], 1,4-dideoxy-1,4-imino-D-arabinitol
for glycogen phosphorylase [98], oxalate and oxamate for LDH, 6-amino
nicotinamide for the phosphate pentose pathway [99], amino-oxyacetate for
aminotransferases and kirureninase (tryptophan synthesis), norvaline for
ornithine transcarbamylase, mercaptopycolinate for PEP carboxykinase, acetazolamide
for carbonic anhydrase, and isobutyramide for ADH (compiled by
Fell [2]).Potential Uses of the Experimental Approach
Mitochondrial
pathologies are a heterogeneous group of metabolic perturbations characterized
by morphological abnormalities and/or OXPHOS dysfunction [100]. Mitochondrial DNA analysis has revealed specific
mutations for some mitochondriopathies. Although the specific OXPHOS mutations causing
the disease may appear in all tissues, the functioning of only some of them is
altered. The organ’s sensitivity might be related to the different flux control
coefficients of the mutated enzyme in the different tissues (Table 3) and to
their ATP supply dependence from OXPHOS versus
glycolysis.
MCA allows for the analysis of a metabolic flux or intermediate concentration by focusing
either on one step or by grouping enzymes in blocks or in pathways. Thus, a comparative analysis of OXPHOS control
distribution reveals that heart, kidney, some fast growing tumors (rat AS-30D
hepatoma, mouse fibrosarcoma, human breast, lung, thyroid carcinoma, melanoma)
[101], and perhaps skeletal muscle are more susceptible to mitochondrial mutations
in ATP synthase, which is the only PS site with subunits encoded in the mitochondrial
genome. On the other side, liver and
brain might be more susceptible to mitochondrial mutations of the respiratory
chain enzymes (see Table 3). Considering that the brain is a fully aerobic
organ [102], whereas the liver depends on both OXPHOS (70–80%) and glycolysis
(20–30%) for ATP supply [103], then it can be postulated that the brain is more
sensitive to mutations in the mitochondrial genome than the liver because subunits
of complexes I, III, and IV are encoded by the mitochondrial genome.
Titration of flux with
specific inhibitors to determine the flux control coefficients of OXPHOS has been
applied to intact tumor cells [90]. The results showed that the flux control
resided mainly in site 1 of the respiratory chain (CSitelJOxPhos=0.30), whereas the other evaluated sites exerted a marginal
control [90]. This observation could
have therapeutic application if site 1 does not exert control in healthy cells,
leading to less severe side effects.
The use of inhibitors in
intact cells to determine control coefficients might pose two problems: hydrophilic
inhibitors such as carboxyatractyloside (for ANT) andα-cyano-4-hydroxy-cinammate (for pyruvate transporter)
cannot readily enter the cell due to the presence of the plasma membrane
barrier; the other problem is that hydrophobic but slow inhibitors, such as
oligomycin, require long incubation times to ensure the interaction with the
specific sites. These problems can be
solved by incubating the cells for long periods of time and taking care of cell
viability, for instance, AS-30D hepatoma cells are fairly resistant to this
mechanical manipulation as they maintain high viability after a lengthy
incubation under smooth orbital agitation of 1 h at 37°C
[90].


### 5.3. Elasticity Analysis

MCA defines the elasticity coefficients as(6)εXvi=dvidX•Xovio, which is a dimensionless number that show the rate variation v of a given enzyme or transporter i when the concentration of a ligand X (substrate S, product P or allosteric modulator) is varied in infinitesimal
proportions. The elasticity coefficients are positive for those metabolites
that increase the enzyme or transporter rate (substrate or activator), and they
are negative for the metabolites that decrease the enzyme or transporter rates
(product or inhibitor). An enzyme working, under a steady-state metabolic flux, at saturating conditions of S or P,
is no longer sensitive to changes in these metabolites. Thus, its elasticity is close to zero (Figure 6, εXvi=0).
In turn, an enzyme working at S or P
concentrations well below the Michaelis constant (KmS or KmP)
is expected to be highly sensitive to small variations in these metabolites (Figure
6, εXvi=1).Elasticity coefficients.
(a)(b)The elasticities are intrinsically linked to the actual enzyme kinetics. If the kinetic parameters of an enzyme are
known (Vmf, Vmr,  KmS, and KmP), then the enzyme elasticity for any given metabolite
concentration may be calculated as shown in the following equations.For substrate,(7)εsvi=−S/Kms1+S/Kms+P/Kmp+11−Γ/Keq, and
for product,(8)εpvi=−P/KmP1+S/Kms+P/KmP−Γ/Keq1−Γ/Keq, in which Γ is the mass
action ratio, and Keq is the equilibrium constant preferentially determined
under physiological conditions.An enzyme with low elasticity cannot increase (or decrease) its rate despite large
variations inS (or P) concentration; in consequence, such enzyme exerts a high
flux control. In turn, an enzyme with a
high elasticity can adjust its rate to the variation in S or P concentrations,
and thus it does not interfere with the metabolic flux, exerting a low flux control. This inverse relationship between the
elasticity and the flux control coefficients is expressed in a formal equation
denominated connectivity theorem. A
metabolic pathway can be divided in two blocks around an intermediary X: the
producing (synthetic, supply) and the consuming (demand) enzyme blocks of X are i1 and i2, respectively. Thus, the connectivity theorem for this two-block system is(9)Cv1JCv2J=−εXv2εXv1. The negative sign of the right part of the equation
cancels with εXvi1, which is negative because X
is a product of enzyme block i1 (Figure 6).To obtain the flux control coefficients, this approach requires experimental
determination of the elasticity coefficients. How can this be done? Many strategies have been designed [90, 103–108], but the most
used and probably more trustworthy is that in which the initial pathway metabolite
(So) concentration is varied to increase the X concentration (any intermediary
in the pathway), and measuring in parallel the variation in flux. Under steady-state conditions, the flux rate
is equal to the rate of end-product formation (i.e., lactate or alcohol for
glycolysis; oxygen consumption for OXPHOS) and to the rate of any partial
reaction. Then, plots of X versus
flux (Figure 7) are generated. The slope, calculated at the reference
coordinate (Xo, Jo) that is
equivalent to (So, vio), yields
the elasticity coefficient of the consuming block of X. In another set of experiments, an inhibitor is
added to block one or more enzymes after X. The X concentration and flux are determined and
plotted as shown in Figure 7, from which the elasticity coefficient of the
producing block is calculated.Figure 7
Experimental determination of the elasticity coefficients for substrates and products.The flux
control coefficients are determined by using the connectivity theorem and
considering that the sum of the control coefficients comes to 1,C1+C2=1 (summation theorem):(10)Cv1J=εXv2εXv2−εXv1,Cv2J=−εXv1εXv2−εXv1.This method for determiningCviJ using the elasticities of the two blocks was called double
modulation by Kacser and Burns [83]. Years
later, Brand and his group [103, 104] renamed this method as top-down approach. By applying the procedure shown in Figure 7
and using (10) for different metabolites along the metabolic pathway, it
is possible to identify those sites that exert a higher control (which may be
the sites for therapeutic use or biotechnological manipulation) and those that
exert a negligible control under a given physiological or pathological
situation.Elasticity analysis has been used to evaluate the OXPHOS control distribution
in tumor cells [90]. Almost all studies on
this subject have been carried out with isolated mitochondria incubated in
sucrose-based medium at 25 or 30°C or with the more physiological KCl-based medium but
still at 30°C (Table 3). Furthermore,
these studies did not consider that the product, ATP, never accumulates in the
living cells, which does occur in experiments with isolated mitochondria. Under such a condition, a steady state in ATP production can
never be reached as in living cells. In
other words, the distribution of control in mitochondria (Table 3) has been
determined in the absence of an ATP-consuming system. A remarkable exception to this incomplete
experimental design was the work done by Wanders et al. [105], in which isolated liver mitochondria were incubated
with two different ATP-consuming systems (or ADP-regenerating systems): HK +
glucose and creatine kinase (CK) + creatine. Under this more physiological setting, the OXPHOS
flux control distributed between ANT and the ATP-consuming system; however, flux
control by the other pathway components was not examined. Therefore, to accurately evaluate OXPHOS control
distribution, mitochondria should be incubated in the presence of an
ATP-consuming system or in their natural environment (i.e., inside the cell).The rate of OXPHOS in intact
cells is determined from the rate of oligomycin-sensitive respiration: in the
steady state, the enzyme rates are the same and constant; in branched pathways
the sum of the branched fluxes equals the flux that supplies the branches. The global elasticity of the ATP-consuming processes
(e.g., synthesis of protein,
nucleic acid, and other biomolecules, as well as ion ATPases to maintain the
ionic gradients, mechanical activity such as muscular contraction or flagellum
and cilium movement, and secretion of hormones, digestive enzymes and
neurotransmitters) is estimated by inhibiting flux with low concentrations of
oligomycin or a respiratory chain inhibitor. To determine the elasticity of the
ATP-producing block, flux, and [ATP] are varied with streptomycin, an inhibitor
of protein synthesis (Figure7). The
elasticity coefficients are calculated from the initial coordinate slopes
(without inhibitors) of each titration. With
this procedure, it has been determined that the ATP-consuming block exerts a
significant flux control of 34% [90]. Remarkably,
this flux control value obtained in cells is quite similar to the flux control
coefficients of the ATP-consuming system (HK or CK) reported by Wanders
et al. [105] with isolated
mitochondria.Elasticity analysis by enzyme
blocks allows the inclusion of the end-product demand as another pathway block.
The conclusions obtained from this
analysis have formulated the supply-demand theory [30], which proposes that when
flux is controlled by one block (demand), the concentration of the end-product
is determined by the other block (supply). The ratio of elasticities determines the distribution of flux control
between supply and demand blocks. For
instance, if εXSupply>εXDemand (i.e., demand becomes saturated by the end-product X,
and hence its elasticity is near zero), then the demand block exerts the main
flux control. For concentration control,
at larger εXDemand−εXSupply,  smaller absolute values of both CSupplyX and CDemandX are attained; hence, under demand saturation,
the supply elasticity fully governs the magnitude of the variation in the
end-product concentration. On the other
hand, when demand increases, it loses flux control and induces a diminution in
the end-product concentration. In turn, supply gains flux control and loses
concentration control. In the presence of feed-back inhibition, the system can
maintain the end-product concentration orders of magnitude away from
equilibrium (at a concentration around the K0.5 of the allosteric enzyme).As mentioned before, the
demand is not usually included in the pathway because it is erroneously thought
that it is not part of it. But then, is
it valid to analyze the control of a metabolite synthesis if its demand is not
considered? When the demand block is not
included, it is assumed that the metabolic pathway produces a metabolite at the
same rate regardless whether the metabolite demand is high or low. This reasoning is incorrect because a
metabolic pathway indeed responds to changes in the metabolite demand and, more
importantly, a pathway without end-products consumption reactions is unable to
reach a steady state.Therefore,
a metabolic pathway can be divided in supply and demand blocks. The intermediaryX linking the two blocks is one
of the end-products of the producing block (e.g.,
pyruvate or lactate or ethanol, and ATP for glycolysis). The variation in rate of the two blocks in
response to a variation in X can be theoretical or experimentally determined (Figure 8(a)). It is worth noting that, for this
supply-demand approach, it is not necessary to know the kinetics of each
pathway enzyme because the rate response of each block reflects the global kinetics
of all participating enzymes. When the X
concentration is increased, the rate of the supply block decreases (i) because X
is its product and (ii) because usually an enzyme within this block receives
information from the final part of the pathway, decreasing its rate through
feedback inhibition. In turn, the rate
of the demand block increases as X is its substrate.(a) Kinetics of the synthesis
(supply) and consuming (demand) blocks of the intermediaryX. The kinetic parameters are from enzymes in tobacco
glutathione (GSH) synthesis. X
represents the intermediary concentration, in this case GSH. (b) Rate plots of the supply and demand
blocks in a natural logarithmic scale.
(a)(b)To better
visualize the effect of large rate changes, the kinetics of both blocks are
plotted in a logarithmic scale. Figure8(b) shows the kinetics described in Figure 8(a) converted to natural
logarithm. The intersection point
between kinetic curves, at which the supply and demand rates are identical,
represents the pathway steady-state flux (in the Y axis) and end-product
concentration (in the X axis). Since the
elasticity is also defined as εXvi=dlnvi/dlnX, the slope at the intersection point represents the elasticity of each
block towards the intermediary X. Here,
the use of the scalar factor is not necessary because it is included in the
logarithmic equation. With the elasticity
coefficients calculated from plots like those shown in Figure 8, and the
connectivity theorem, the flux control coefficient of each block is determined.
The example in Figure 8(b) shows that
the demand exerts a high flux control (and has low elasticity) and the supply
block exerts low control (and has high elasticity).The
fact that the demand may exert a high flux control in metabolite pathways has
at least three important implications: (a) the supply block responds to variations
in the demand (high elasticity); (b) the demand block has information transfer
mechanisms towards the supply block that avoid the unrestricted intermediary accumulation under a low demand,
particularly when the supply block has reactions with large Keq (>100;ΔG°′>3 Kcal mol-1 at 37°C); and (c)
if the main flux control resides in the demand block, then the supply block may
only exert control on the intermediary concentration but not on the flux [30, 32]. This last conclusion explains why it
is incorrect to consider that an enzyme that controls flux must also control
the intermediary concentration.Regulatory mechanisms of
enzyme activity are modulation of protein concentration by synthesis and
degradation, as well as covalent modification and variation in the substrate or
product concentrations (which are components of the pathway). In addition, another regulatory mechanism is the
modulation by molecules that are not part of the pathway, that is, through allosteric interaction with cooperative (sigmoidal
kinetics) or noncooperative enzymes (hyperbolic kinetics) (e.g., Ca2+ activates some Krebs cycle dehydrogenases; citrate inhibits PFK-1; malonyl-CoA inhibits
the mitochondrial transporter of acyl-carnitine/carnitine; or the initial
substrate of a pathway that has not entered the system). For these last cases, Kacser and Burns [83]
proposed the use of the response coefficient R which is defined by the
following expression:(11)RMJ=CviJ•εMvi, where M is the external modulator of the i enzyme. The response coefficient is dJ/dM•Mo/Jo.
If the elasticity of the sensitive
enzyme toward the external effector is also determined, then it is possible to
calculate CviJ by using (11). Unfortunately, due to the experimental complexity for determining the
elasticity coefficient, this coefficient is often calculated in a theoretical
way by using the respective rate equation (Michaelis-Menten or Hill equations)
and the kinetic parameters Km and Vmax determined by someone else under optimal
assay conditions, which are commonly far away from the physiological ones. Therefore, for this theoretical determination
of elasticity only the value of the external modulator concentration is required. It is convenient to emphasize that the determination
of the flux control coefficients becomes more reliable when they are calculated
from several experimental points (Figure 7), instead of only one, as occurs
with the theoretical elasticity analysis.Groen et al. [106] determined the flux control distribution of gluconeogenesis
from lactate in hepatocytes by using both theoretical and experimental elasticity
analysis and the response coefficient. These authors concluded that gluconeogenesis
stimulated by glucagon was controlled by the pyruvate carboxylase (CPCJglucose=0.83); in the absence of this hormone, the
control was shared by PC, PYK, ENO-PGK segment, and TPI-fructose-1,6-biphosphatase
segment [106].Elasticity
analysis has been applied to elucidate the flux control of ATP-producing
pathways in fast-growing tumor cells. For OXPHOS, this approach showed that respiratory chain complex I and
the ATP-consuming pathways were the enzymes with higher control (CviJ=0.7) [90]. For glycolysis, the main flux control (CviJ=0.71) resided in GLUT + HK reactions because
HK is strongly inhibited by its product G6P despite extensive enzyme overexpression
[107]. Examples of elasticity analysis on
other pathways are photosynthesis [108], ketogenesis [109], serine [110] and
threonine synthesis in E. coli [111], glycolysis in yeast [112], glucose
transport in yeast [113], DNA supercoiling [114], glycogen synthesis in muscle [115],
and galactose synthesis in yeast [116].In conclusion, the elasticity
analysis is the most frequently used method for determining flux control
coefficients because it does not need a group of specific inhibitors for all
the enzymes and transporters of the pathway, neither does it require knowledge
of the inhibitory mechanisms or kinetic constants. It is only necessary to produce a variation in
the intermediary concentrationX by using an inhibitor of either block or by
directly varying the X concentration.


### 5.4. Pathway Modeling

In agreement with Fell [2], it seems impossible for a researcher to analyze one by
one the rate equation of each enzyme in a metabolic pathway to predict and
explain the system behavior as a whole. To deal with this problem, in the last three
decades some scientists have constructed mathematical models for some metabolic
pathways using several software programs. Thus, the specific variation of a single enzyme
activity without altering the rest of the pathway (Figure 4), which has been an
experimentally difficult task for applying MCA, becomes easier to achieve with
reliable computing models. The term “in
silico biology” has been coined for this approach.There are two basic types of modeling: (a) structural modeling and (b) kinetic
modeling. The former is related to the pathway chemical reaction structure and
does not involve kinetic information. The use of reactions is based on their
stoichiometries. The information obtained with structural modeling is the
description of the following:(i)
the exact determination of which reactions and
metabolites interact among them;(ii)
the conservation reactions. There are metabolites for
which their sum is always constant or conserved (e.g., NADH + NAD+; NADPH + NADP+;
ubiquinol + ubiquinone; ATP + ADP + AMP; CoA + acetyl-CoA). The identification of
conserved metabolites might not be obvious;(iii)
enzyme groups catalyzing reactions in a given relationship
with another group of enzymes;(iv)
elemental modules, which are defined as the minimal
number of enzymes required to reach a steady state, which can be isolated from the
system (for a review about structural modeling; see [117]).Kinetic
modeling is more frequently used. In addition to an appropriate computing
program, this approach requires the knowledge of the stoichiometries, rate
equations, and Keq values of each reaction in the pathway (or theVmax in the forward and reverse
reactions), as well as the intermediary concentrations reached under a given
steady state. Some currently used
softwares are Copasi (http://www.copasi.org/tiki-index.php)
based on Gepasi (http://www.gepasi.org/; [118]); Metamodel [119]; WinScamp [120]
and Jarnac [121] (both available at http://www.sys-bio.org/); and PySCeS
(http://pysces.sourceforge.net/; [122]). For other programs and links, go to http://sbml.org/index.psp. To reach a steady-state flux, it is necessary
to fix the initial metabolite concentration to a constant value and the
irreversible and constant removal of the end products. Except for the final reactions in which their
products have to be removed from the system, all pathway reactions have to be
considered as reversible, notwithstanding whether they have large Keq (if there
is an irreversible reaction under physiological conditions, then a reversible rate
equation that includes the Keq suffices to maintain the reaction as practically
irreversible). Care should be taken to include the enzyme’s sensitivity toward
its products because this property is related with the enzyme elasticity and hence
with its flux control; omission of this parameter may very likely lead to
erroneous conclusions.It
should be pointed out that the purpose of kinetic modeling is not merely to
replicate experimental data but also to explain them [117]. Thus, pathway modeling is a powerful tool
that allows for (i) the detection of those properties of the pathway that are
not so obvious to visualize when the individual kinetic characteristics of the
participating enzymes are examined; and (ii) the understanding of the biochemical
mechanisms involved in flux and intermediary concentration control. Modeling requires the consideration of all
reported experimental data and interactions that have been described for the
components of a specific pathway, thus allowing for the integration of disperse
data, discarding irrelevant facts [84]. Although all models are oversimplifications of complex cellular
processes, they are useful for the deduction of essential relationships, for
the design of experimental strategies that evaluate the control of a metabolic
pathway, and for the detection of incompatibilities in the kinetic parameters
of the participating enzymes and transporters, which may prompt the
experimental revision of the most critical uncertainties.With
the model initially constructed, the simulation results do not usually concur
with the experimental results; in consequence, the model normally requires
refinement, a point at which the researcher’s thinking and knowledge of biology
plays a fundamental role in modifying the structure and parameters of the model.
The discrepancies observed between modeling
and experimentation unequivocally pinpoint what elements or factors have to be re-evaluated
or incorporated so that the model approximates more closely reality (i.e., experimental data). The comparison of the experimentally obtained
intermediary concentrations and fluxes with those obtained by simulation is an
appropriate validating index of the model; this index indicates whether the
model approximation to the physiological situation is acceptable or whether
re-evaluation of the kinetic properties of some enzymes and transporters and/or
incorporation of other reactions or factors is required.A reason to why the results obtained by modeling may substantially differ from the
experimental results is that the kinetic parameters of the pathway enzyme and
transporters and the Keq values used
were determined by different research groups, under different experimental
conditions and in different cell types. Moreover,
enzyme kinetic assays are carried out at low, diluted enzyme
concentrations (thus discarding or ignoring relevant protein-protein
interactions), and at optimal (but not physiological) pH and “room temperature”
(which may be far away from the physiological values). In addition, no experimental information is
usually available regarding the reactions reversibility and the product
inhibition of the enzymes and transporters (particularly for physiological
irreversible reactions, i.e., reactions with large Keq). With worrisome
frequency, the researcher has to adjust the experimentally determinedVm and Km values to achieve a model behavior that acceptably resembles
that observed in the biological system. Apparently,
this type of limitations as well as the sometimes overwhelming amount of
kinetic data necessary for the construction of a kinetic model has restricted
the number of reliable models that can be used for the prediction of the
pathway control structure.Once the kinetic model stability, robustness, structural and dynamic properties have
been evaluated, and experimentally validated, the model may become a virtual
laboratory in which any parameter or component can be modified or replaced and
any aspect of the pathway behavior can be explored within a wide diversity of
circumstances or limits [117]. At this
stage, the model is suitable for examining the pathway regulatory properties
and control structure.Glycolysis
inS. bayanus, S. cerevisiae [113, 123, 124], and Trypanosoma brucei [125, 126] is the
metabolic pathway that has been more extensively modeled. Both cell types
have a very active glycolysis and are fully dependent on this metabolic pathway
for ATP supply, under anaerobiosis and aerobiosis, respectively. One advantage
of modeling glycolysis in these cell types is that most of the kinetic
parameters used have been experimentally determined by the same groups under
the same experimental conditions. However,
the kinetics of the reverse reactions has not been determined and thus these
authors used KmP and Keq
values reported by others and obtained in other cell types under rather different
experimental conditions, or they were adjusted to improve model fitting.Nevertheless, the simulation
results yielded relevant information on the control of the glycolytic flux. In both cases, the enzymes traditionally considered
the rate-limiting steps, HK, ATP-PFK-1, and PYK did not contribute to the flux
control, whereas the main control resided in GLUT (54% in the parasite and 85–100% in yeast). Under some conditions, HK may exert some
control (15%) inS. cerevisiae and some nonallosteric enzymes such as
ALDO, GAPDH, and PGK may also exert some flux control in T. brucei.MCA
through kinetic modeling has been applied to several pathways:(i)
glycolysis in
erythrocytes [84] in which flux control distributes between HK (71%) and PFK-1
(29%);(ii)
carbohydrate
metabolism during differentiation inDictyostelium discoideum [127] with
cellulose synthase (86%) as the main controlling step;(iii)
sucrose accumulation
in sugar cane with HK, invertase, fructose uptake, glucose uptake, and vacuolar
sucrose transporter having the most significant flux control [128];(iv)
glycerol
synthesis inS. cerevisiae with GAPDH
(85%) as the main control step [129];(v)
penicillin
synthesis inPenicillium chrysogenum controlled
(75–98%) either by d-(a-aminoadipyl) cysteinylvaline synthetase (short
incubation times <30 hour) or isopenicillin N. synthetase (long incubation
times > 100 h) [130];(vi)
Calvin cycle
[131] controlled by GAPDH (50%) and sedoheptulose-1,7-bisphosphatase (50%);(vii)
threonine
synthesis inE. coli controlled by homoserine dehydrogenase (46%),
aspartate kinase (28%), and aspartate semialdehyde dehydrogenase (25%) [111];(viii)
lysine
production inCorynebacterium glutamicum mainly
controlled by aspartate kinase and permease [132];(ix)
nonoxidative
pentose pathway in erythrocytes mainly controlled by transketolase (74%) [133];(x)
EGF-induced MAPK
signaling in tumor cells controlled by Ras-activation by EGF (21%), Ras
dephosphorylation (43%), ERK phosphorylation by MEK (44%), and MEK
phosphorylation by RAS (143%) [13];(xi)
Aspergillus niger arabinose utilization with
flux control shared by arabinose reductase (68%), arabitol dehydrogenase (17%),
and xylulose reductase (14%) [134];(xii)
glycolysis inL. lactis in which several end products are generated (lactate,
organic acids, ethanol, acetoin) [135]. Model predictions indicated that flux toward diacetyl and acetoin
(important flavor compounds) was mainly controlled by LDH but not by
acetolactate synthetase, the first enzyme of this branch.We modeled
the GSH and PCs biosynthesis (Figure2) to determine and understand the control
structure of the pathway and thus be able to identify potential sites for genetic
engineering manipulation that might lead to the generation of improved species
in heavy metal resistance and accumulation. Two models were constructed, one
for higher plants and the other for yeast, both exposed to high concentrations
of Cd2+ [136]. Due to the
similarity in the results, only the plant results are analyzed below.An interesting conclusion from the GSH-PCs synthesis modeling is that control of flux
(and GSH concentration) is shared between the GSH supply and demand under both unstressed
and Cd2+ exposure
conditions (Table 4). This observation strongly differs from the
idea that γ-ECS is the rate-limiting step [33–35]. For many researchers, the concept of γ-ECS being the key controlling step has seemed to be
correct because (a) γ-ECS receives information from the final part
of the pathway, as it is potently inhibited by GSH, the pathway end-product;
and (b) γ-ECS is localized in the first part of the
pathway (Figure 2). In addition, GS is
usually more abundant and efficient than γ-ECS [137].Table 4
Control of GSH and PC synthesis in plants exposed to Cd2+.
Enzyme1xγ-ECS + PCS2.5xγ-ECS + PCSCviJGSHCviJPCCviGSHCviPCCviJGSHCviJPCCviGSHCviPCγ-ECS0.580.600.680.760.450.610.700.60GS<0.01<0.010.010.010.19<0.01<0.010.97GS-transferase0.01−0.06−0.07−0.07<0.01<0.01<−0.01−0.05PCS0.400.44−0.63−0.560.330.44−0.620.57vacuole
PC-Cd transporter<0.01<0.01<0.01−1.2<0.01<0.01<0.01−2.1CviJGSH, control coefficient of
enzyme i in GSH synthesis; CviJPC, control coefficient of enzyme Ei on PCs
synthesis; CviGSH, control coefficient of enzyme i on GSH concentration; CviPC, control coefficient of enzyme i on PCs concentration. An enzyme with a negative
flux control indicates that it is localized in a branch, turning aside the
principal flux; an enzyme with a negative concentration control indicates that
an increase in its activity decreases metabolite concentration.However, in most of the
studies on the control of GSH synthesis, the GSH demand has not been
considered. The GSH synthesis modeling shows that under a physiological feedback
inhibition ofγ-ECS by GSH a small increase in demand increases
flux because the GSH concentration decreases and the γ-ECS inhibition attenuates. In contrast, if the demand remains constant, then
an increase in γ-ECS activity or content (by overexpression) does
not increase flux because the GSH inhibition is still there and operates on
both new and old enzymes. The same pattern is also observed when HK is
overexpressed to increase
glycolytic flux since it is still inhibited by G6P (see Section 3). On the other hand, γ-ECS indeed exerts significant concentration control
on GSH, which means that a γ-ECS increase results in higher GSH
concentration (Table 4). This last
observation demonstrates that an enzyme controlling a metabolite concentration does
not necessarily control the flux.Cd2+ exposure promotes a high GSH demand because significant oxidative stress surges,
thus causing oxidation of GSH through GSH peroxidases, and because GSH and PCs
are used for sequestering the toxic metal ion; hence, a higher GSH consuming
rate sets up. Under this condition,
modeling predicted that control was almost equally shared between the supply
and demand blocks, but particularly between γ-ECS and PCS (see Figure 2). Modeling was also able to explain why PCS overexpression
can have toxic effects on the cell [36]. An increase in the GSH demand (PCS
overexpression) under high-demand conditions (Cd2+ stress) leads to
GSH depletion that severely compromises other processes such as the oxidative
stress control and xenobiotic detoxification.The
conclusions drawn by this model led us to propose that, to significantly increase
the Cd2+ resistance and accumulation, γ-ECS and PCS should be simultaneously overexpressed
(Table 4; Figure 9). This particular
manipulation promotes an increase in the rate of GSH and PCs synthesis
(determined by the high-to-low transition of their flux control coefficients)
and in the GSH and PCs concentrations
(determined by their high concentration control coefficients). The model predicts that a 2-fold increase in
the simultaneous overexpression of γ-ECS and PCS brings about a 1.9–2.4-fold
increase in flux to GSH (JGS)
and PCs (JPCS) and in PCs
concentration (Figure 9); a 5-fold overexpression further increases by 4.5–8.1
times the fluxes and PCs concentration.Figure 9
Modeled simultaneous overexpression of two
controlling enzymes, one in the supply (γ-glutamylcisteine synthetase, γ-ECS) and the other in the demand branch
(phytochelatin synthase, PCS), of the glutathione and phytochelatins synthesis
pathway in plants.This proposed enzyme overexpression
should not exceed the GS and the complex PC-Cd (or GS-Cd-GS) vacuolar
transporters’ maximal activities, in order to keep the cell away from a severe
oxidative stress caused by GSH depletion orγ-EC accumulation. Indeed, the concentration of GSH was maintained high and constant although
γ-EC accumulated with the simultaneous overexpression
(Figure 9). Furthermore, this enzyme
manipulation should avoid the increase of the PC-Cd and GS-Cd-GS complexes in
cytosol to toxic levels. In other words,
excessive enzyme overexpression should be avoided, unless this is accompanied
by compensating overexpression of consuming enzymes (GS for γ-ECS overexpression and PCs vacuolar transporters for
that of PCS). In yeasts and plants, Cd2+ is ultimately inactivated by the additional interaction with S2− and
the subsequent formation of stable high molecular weight complexes with PCs, Cd2+,
S2−, and GSH [138, 139]. In
parallel to the γ-ECS and PCS overexpression, moderate repression
of GSH-S-transferases, which compete for the available GSH (Figure 2), may also
promote an increase in GSH concentration and PCs formation flux [136].MCA
is based on infinitesimal changes in an enzyme or metabolite concentration. In contrast, gene overexpression induces large
changes in activity; hence, further theoretical background has been developed for
predicting the effect on flux and metabolite concentrations induced by large
enzyme changes. Such a theoretical background was initially developed by Small
and Kacser [140], who depicted (12) based on the flux control coefficients to
predict the effect promoted by large changes in enzyme activity:(12)fEj−mrJ=11−∑i=jm(Cvi0Jo•(ri−1)/ri), in which f is the amplification factor (the flux increase), and r represents how many times the enzyme is overexpressed. To predict the flux changes, promoted by identical
overexpression of two enzymes (same r value) with different CviJ,
the equation is
(13)fEj−mrJ=11−(CiJ+CjJ)•((r−1)/r).Figure10 shows the effect on flux when one or more enzymes with different CviJ are changed by the same r factor. If the sum of CviJ
of one or more enzymes is less than 0.25, the
impact on flux is discrete when the expression increases 5 folds (which is the
most common variation in the overexpression experiments analyzed in Section
2). But for a 3-fold overexpression of
a group of enzymes, for which their sum of CviJ is more than 0.5, then a significant flux
change is achieved. If the sum of CviJ is 1, the flux varies in a linear proportion
with the degree of overexpression. It
has to be remarked, however, that the predicted change in flux (Figure 10) will
be valid until certain degree, the limits of which being determined by the
other pathway enzymes that should stay as noncontrolling steps.Figure 10
Effect on flux when one or more enzymatic
activities with different control coefficients are varied. This figure represents an enzyme or group of enzymes
in which theirCviJ sum is indicated in parenthesis and is
modified by the same r factor. Number
1 represents the reference control, thus if r<1, there is suppression, whereas r>1 represents overexpression.Figure10 also shows the effect on flux of decreasing an enzyme activity (third
quadrant). This segment plot is useful when inhibition of pathway flux is being
pursued for therapeutic purposes or for understanding the molecular basis of the
genetic dominance and recessivity. Like
in the enzyme overexpression experiment, only a significant effect on flux is
achieved when the enzymes with high CviJ values are inhibited. For an enzyme or group of enzymes with CviJ
of 0.25, greater than 80% inhibition has to be
attained to decrease 50% the pathway flux. In this context, it seems feasible
to explain why knockdown of enzymes involved in TSH2 synthesis has
to be almost total to detect an effect on TSH2 content or to alter
functional or pathogenic properties of the parasites (Section 4.3). The knockdown or knockout experiments in
trypanosomatids suggest that γ-ECS, TryS, and TryR most probably have low flux control
and concentration-control coefficients since their contents or activities have
to be reduced >80% of the normal levels to reach changes in intermediary
levels or in oxidative stress handling.Contrary
to the several unsuccessful overexpression experiments carried out to increase
the flux or metabolites of a metabolic pathway, modeling may allow for a more
focused and appropriate design of experimental strategies of genetic
engineering to increase flux or a given metabolite, and for selecting drug
targets to decrease flux or metabolite concentration. For these predictions, modeling considers
that overexpression of a controlling enzyme or transporter may promote flux or
metabolite control redistributions.
Thus, a low-control step may become a
controlling point when overexpressing another step and, in consequence, the
prediction shown in Figure10 based on (11) and (12) may be inaccurate. By considering the whole pathway components,
modeling is also a powerful tool for predicting the effects on flux and
metabolite concentration of varying an enzyme activity (by overexpression or
drug inhibition).Model Predictions to Inhibit a Pathway Flux
Kinetic modeling has been used to identify the flux controlling steps inTrypanosoma
brucei glycolysis for drug targeting purposes. Interestingly, modeling has predicted
controlling steps for the parasite pathway different from those described for
glycolysis in human host cells [125, 126].
Entamoeba histolytica is the causal agent of human
amebiasis. The parasite lacks functional
mitochondria and has neither Krebs cycle nor OXPHOS enzyme activities. Therefore,
substrate level phosphorylation by glycolysis is the only way to generate ATP
for cellular work [141]. An important
difference in amebal glycolysis in comparison to glycolysis in human cells is
that it contains the pyrophosphate (PPi)-dependent enzymes phosphofructokinase
(PPi-PFK) and pyruvate phosphate dikinase (PPDK), which replace the highly
modulated ATP-PFK and PYK present in human cells. Moreover, both have been
proposed as drug targets by using PPi analogues (bisphosphonates) [141].
We recently described the
construction of a kinetic model ofE. histolytica glycolysis to
determine the control distribution of this energetically important pathway in
the parasite [142]. The model was
constructed using the Gepasi software and was based on the kinetic parameters
determined in the purified recombinant enzymes [143], as well as the enzyme
activities, fluxes, and metabolite concentrations found in the parasite. The results of the
metabolic control analysis
indicated that HK and PGAM are the main flux control steps of the pathway (73
and 65%, resp.) and perhaps GLUT. In
contrast, the PPi-PFK and PPDK displayed low flux control (13 and 0.1%, resp.)
because they have overcapacity over the glycolytic flux [142]. The amebal model allowed evaluating the
effect on flux of “inhibiting” the pathway enzymes. The model predicted that in order to diminish
by 50% the glycolytic flux (and the ATP concentration; data not shown), HK and
PGAM should be inhibited by 24 and 55%, respectively, or both enzymes by 18%
(Figure 11). In contrast, to attain the
same reduction in flux by inhibiting PPi-PFK and PPDK, they should be decreased
>70% (Figure 11). Therefore, the
kinetic model results indicate that HK can be an appropriate drug target
because its specific inhibition can compromise the energy levels in the
parasite. They also indicate that although
PPi-PFK and PPDK remain as promising drug targets because of their divergence
from the human glycolytic enzymes, highly potent and very specific inhibitors
should be designed for these enzymes in order to affect the parasite’s energy
metabolism.Figure 11
Modeled flux behavior when
inhibiting pathway enzymes. The predicted flux when varying the enzyme activity
was obtained using the kinetic model forEntamoeba
histolytica glycolysis [142]. In
this case, 100% enzyme activity is the enzyme activity present in amebal
extracts, and 100% flux is the ethanol flux displayed by amoebae incubated with
glucose. PPi-PFK, PPi-dependent
phosphofructokinase; PPDK, pyruvate phosphate dikinase; PGAM, 2,3
bisphosphoglycerate independent 3-phosphoglycerate mutase.


### 5.5. In Vitro Reconstitution of Metabolic Pathways

Another experimental approach
for determining the enzyme control coefficients is the in vitro reconstitution
of segments of metabolic pathways. It is
recalled that for determining the flux control coefficient exerted by a given
step on a metabolic pathway the enzyme activity has to be varied, without
altering the other components in the system, and the flux variations are to be
measured (Figure4). Such an experiment can be readily made if a pathway is
reconstituted with purified enzymes. Some advantages of this approach are that the
pathway structure is known, in which the components concentration may be
manipulated and analyzed separately, and the enzyme effectors can be assayed. As
the system composition is strictly controlled, the results may be highly
reproducible. The main disadvantage is
that the enzyme concentrations in the assays are diluted and thus the enzyme
interactions are not favored. If this interaction
is important for activity, the in vitro reconstitution may limit the
extrapolation to the metabolic pathway inside the cell.There are not many studies
describing this type of experiments, most probably due to the fact that for
applying MCA the pathway must be working under steady-state conditions. In a reconstituted system, only a quasi steady
state may be reached because there is net substrate, and cofactors consumption,
as well as product accumulation, since it is difficult to attain a constant
substrate supply and release of products.One of the first experimental
reports on control coefficient determination in a reconstituted system was
carried out for the upper glycolytic segment with the commercially available
rabbit muscle HK, HPI, PFK-1, ALDO, and TPI [144]. Each enzyme was separately titrated and the
flux variation to glycerol-3-phosphate (by coupling the reconstituted system to
an excess of α-GPDH) was measured in the presence of CK to maintain
the ATP concentration constant. The flux
control coefficients were determined as described in Figure 4. The results showed that PFK-1 and HK exerted the
main flux control (65% and 20%, resp.), whereas the remaining 15% resided in
the other enzymes. These authors observed that the addition of F1,6BP, a PFK-1
activator slightly diminished the flux control exerted by PFK-1 and increases
that of HK. The validation of the
summation theorem was also demonstrated in this work [144].The lower glycolytic segment
has also been reconstituted with commercial enzymes for determining the flux
control coefficients [145]. The results
showed that flux was mainly controlled by PYK (60–100%), although under some
conditions control was shared with PGAM; ENO did not contribute to the flux
control.Another important limitation
of the reconstitution experiments is that the commercial availability of the
purified enzymes from the same organism is restricted or inexistent. However, by using the information from the
genome sequence projects and the recombinant DNA technology, it is now possible
to access all the enzyme genes from a metabolic pathway in the same organism, thus
facilitating their cloning, overexpression, and purification. With this strategy, we cloned, overexpressed,
and purified the 10 glycolytic enzymes ofEntamoeba histolytica [143] for
studying the flux control distribution in this organism by using kinetic
modeling [142] and pathway reconstitution.The reconstitution
experiments of the lower amebal glycolytic segment, under near physiological
conditions of pH, temperature, and enzyme activity (Figure12) showed that PGAM
and, to a lesser extent, PPDK exert the main flux control (these amebal enzymes
are genetically and kinetically different from their human counterparts) with
ENO exhibiting negligible control [143]. In turn, reconstitution of the upper amebal
glycolytic segment has revealed that HK and, to a much lesser extent HPI,
PPi-PFK, and ALD, exerted the main flux control, with TPI having negligible
control [146]. These results strongly
correlate with the enzyme catalytic efficiencies previously reported [143], in
which HK is highly sensitive to AMP inhibition, ALD, and PGAM have the lowest
catalytic efficiencies among the glycolytic enzymes, leading to high flux control
coefficients and thus becoming suitable candidates for therapeutic
intervention. The reconstitution results
also agree with the pathway modeling predictions previously analyzed (Section
5.4), in which HK and PGAM are two of the main controlling steps [142].Determination of flux control
coefficients in an in vitro
reconstitution of the final section ofEntamoeba histolytica glycolysis.
Enzymatic assay with the three recombinant enzymes from
the ameba: EhPGAM, EhENO, and EhPPDK. LDH, commercial lactate dehydrogenase. The flux control coefficient was determined at
the *marked position. 2PG,
2-phosphoglycerate; 3PG, 3-phosphoglycerate. Modified from [143].
(a)(b)(c)(d)The in vitro reconstitution
experiments are also useful for studying the effect on control redistribution of
an enzyme modulation that is particularly difficult to manage in vivo; the main controlling steps
identified with the reconstitution experiments should be further analyzed with
other experimental strategies such as elasticity analysis in the in vivo
systems.


### 5.6. Genetic Engineering to Manipulate the In Vivo Protein Levels

This experimental approach for determining the control coefficients could be part of
the genetic approach analyzed in Section5.1, but it was separated due to its
recent methodological development and because it actually belongs to the
molecular genetics rather than to the Mendelian genetics.


#### 5.6.1. Repression of Gene Expression

This approach is based on the in vivo modulation of the enzyme levels using the RNA
antisense technology. There are at least
three strategies to
inhibit gene expression: (a) the use of single stranded antisense
oligonucleotides, which form a double stranded RNA that might be degraded by RNAse
H; (b) target RNA degradation with catalytically active oligonucleotides, known
as ribozymes that bind to their specific RNA; and (c) RNA degradation using siRNAs
(21–23 nucleotides) [147].The RNA antisense technology was applied for control coefficient determination of the
ribulose-bisphosphate-carboxylase (Rubisco) that fixes CO2 in the
plant Calvin cycle. This enzyme considered
the rate-limiting step of the Calvin cycle and of the whole photosynthetic
process, despite its high concentration (4 mM) in the chloroplasts stroma that compensates
its low catalytic efficiency.Attempts to make Rubisco a nonlimiting step, either by modifying its catalytic efficiency
or by overexpressing it, have been unsuccessful. Stitt et
al. [148] determined the CrubiscoJphotosynthesis of tobacco plants by decreasing its activity
with DNA antisense. The plants were transformed with DNA antisense against the
mRNA of the enzyme’s small subunit, thus promoting its degradation. For Calvin cycle enzymes, the pleiotropic
effects were minimal. The results showed
that Rubisco may indeed be the photosynthesis limiting step with a CrubiscoJphotosynthesis= 0.69–0.83 when plants are exposed to high
illumination (1050 μmol quanta m-2s-1), high
humidity (85%), and low CO2 concentrations (25 Pa). However, this flux control decreases to
0.05–0.12 under moderate illumination or high CO2 levels [148]. Unfortunately, the authors did not determine
the control coefficients of the other pathway enzymes or the branches fluxes which
may be significant.As described in Section5.4, the results of the T. brucei glycolysis
modeling indicated that GLUT was the main flux control step (CGLUTJ∼ 50%), [125, 126]. This model predicted a large overcapacity for
HK, PFK-1, ALDO, GAPDH, PGAM, ENO, and PYK over the glycolytic flux leading to
low flux control coefficients [125, 126]. To validate the modeling results, the concentrations of HK, PFK-1, PGAM,
ENO, and PYK were changed with siRNAs in growing parasites [149]. These knockdown expression experiments showed
overcapacity of HK and PYK over the flux, although at lower levels than predicted
by the model. A good correlation for
PGAM and ENO was obtained between model predictions and experimental results. However, a large difference (9 folds) was
obtained for PFK-1. This discrepancy is
perhaps related to pleiotropic effects of PFK-1 downregulation, as these mutants
also displayed diminution in the activities of other enzymes (HK, ENO, and PYK).
The combination of these two approaches,
in silico modeling and in vivo experimentation, is complementary: on one
hand, modeling identifies the enzymes (out of 19 that contain the model) that
display the highest flux control coefficients, whereas in vivo experimentation validates the
accuracy of the model to establish predictions about the pathway’s behavior.


#### 5.6.2. Fine Tuning of Cellular Protein Expression

The knockdown experiments described above usually yield only two experimental points
of the plot shown in Figure4: the
wild-type and the knockdown strain protein levels or enzyme activities. Thus, with
such an approach high levels of inhibition (>80%) are mostly analyzed,
whereas intermediate levels of downregulation (if obtained) are generally
overlooked. Therefore, knockdown
experiments are not very useful to obtain the complete set of experimental data
(above and below the wild-type levels of enzyme activity with the corresponding
flux) for determining reliable control coefficients.A strategy to determine flux
control coefficients from several protein levels has been developed by using
adenovirus-mediated glucose-6-phosphatase (G6Pase) overexpression under the
control of the cytomegalovirus promoter in rat hepatocytes. A 2-fold G6Pase overexpression did not alterCG6PaseGlycolysis or CGKGlycolysis (GK, glucokinase). However, if G6Pase is overexpressed by 4 folds, then CGKGlycogen-synthesis
diminished from 2.8 to 1.8 and there was a 35% lowering in glycogen synthesis [150]. However, this approach allows titration of flux only above the basal
enzyme activities found in the cell, but not below.These experimental inconveniences have been circumvented by using inducible gene
expression systems based in thelac,
Lambda, nisin, GAL, tetracycline, and other inducible promoters, in bacteria
and yeast [151, 152]. However, a problem
frequently encountered with inducible promoters is that a steady-state of
protein expression is difficult to attain [151, 152].Recently,
Jensen and Hammer described the design of synthetic promoter libraries (SPL), in
particular forL. lactis metabolic
optimization [153]. These promoters
maintain constant the array of the known consensus sequences for L. lactis gene transcription (−10 and
−35 boxes), while the nucleotide sequence between these boxes (a spacer
sequence of 17 ± 1 bp) is randomized, thus producing a set of promoters with
different transcriptional strength. These promoter libraries allow the transcription and protein expression
several folds above and below the wild-type levels of enzyme activity [153],
thus enhancing the usefulness of this approach for  MCA studies.The
control distribution of glycolysis inE.
coli and  L. lactis, as discussed
in Section 3.2 [17, 24, 27, 151],  has been determined by using the SPL
technology. SPL for  yeast, mammalian and
plant cells are also under  development [151, 152]. Certainly, the advances in genetic
engineering  in combination with MCA allow better experimental  designs for
metabolic optimization of micro-organisms of  biotechnological interest.Concluding Remarks
(1)
The frequently recurred idea of manipulating the key
enzyme or rate-limiting step (a concept based on a qualitative and rather
intuitive background) to change metabolism is incorrect. As MCA has demonstrated, flux control is shared
by multiple steps and it is not usually localized in only one step. MCA determines quantitatively the control that
a given enzyme exerts on the flux and on intermediary concentration and helps
to explain why an enzyme does or does not exert control.(2)
A metabolic pathway is manipulated to change the rate
of the end-product formation (i.e.,
the flux) or the concentration of a relevant intermediary. As it is demonstrated in many unsuccessful
experiments, it is not enough to overexpress one enzyme (the rate-limiting step)
or many arbitrarily selected sites of the pathway. MCA proposes an initial experimental analysis
that determines the structural control of the pathway and identifies the sites
(enzymes and transporters) with higher control coefficients values (i.e., targets to be manipulated). For example, if there is a system composed of
six enzymes and three of them have flux control coefficients with values of 0.2
or higher and the other three with values of 0.1 or lower, the three enzymes
with high control coefficients must be overexpressed (if a flux increase is
desired) or repressed (if flux inhibition is the objective) and not only one of
them. If one of the selected enzymes is
strongly inhibited by its product or has allosteric inhibition, the overexpression
of this enzyme might not be enough to increase the flux, as it may also be
necessary to moderately vary the product and allosteric modulator consuming
enzymes.(3)
If the aim of the researcher is a metabolite
concentration increase, which is not the end product of the pathway, MCA
suggests the overexpression of those enzymes or transporters in the supply
block with the highest control coefficients and/or the repression of those
enzymes in the demand block with the highest control coefficients. These manipulations may become complicated if
the metabolite of interest has allosteric interactions with enzymes and
transporters (inhibition and activation) of both the supply and demand blocks. It is recalled that ethanol production in
yeast and lactate and acetate production in lactobacteria do not increase by
overexpressing PFK-1, an allosteric enzyme and the presumed rate-limiting step
of glycolysis. In fact, the flux was diminished with an excessive PFK-1 overexpression. However, the analysis of these results reveals
that the F1,6BP concentration is indeed increased many times over the control
level. Another strategy for eliminating
the feedback inhibition might be the introduction of mutations on the enzymes
that are closer to the metabolite of interest.


## 5.1. Classical Mendelian Genetics

The arginine biosynthesis inNeurospora crassa was the first metabolic
pathway in which flux control coefficients were experimentally determined by
Kacser’s laboratory [86]. This fungus
forms multinucleated mycelia that facilitate the generation of polyploid cells.
By mixing different ratios of spores containing
genes encoding wild (active) and mutant (inactive) enzymes of this pathway, it
was possible to generate heterokaryont mycelia with different content, and
activity, of four pathway enzymes. The authors built plots of enzyme activity versus
flux (see Figure 4) for acetyl-ornithine aminotransferase, ornithine
transcarbamoylase, arginine-succinate synthetase, and arginine-succinate lyase.
All the experimental points of these
heterokaryonts localized near to position 2 of Figure 4 with CviJarg= 0.02–0.2 (flux control by these enzymes was
only 2–20%), which indicated that none of these enzymes exerted significant
control on arginine synthesis. The authors did not determine the remaining flux
control (75%), which might reside in carbamoyl-phosphate synthetase I (this mitochondrial
ammonium-dependent isoform can be bound to the mitochondrial inner membrane or
form complexes with ornithine transcarbamoylase [87, 88]) and in mitochondrial citruline/ornithine
transporter, both of which have been proposed as limiting steps, or might be in
the arginine demand for protein synthesis.Organisms
with many alleles of one enzyme may form homo-and heterozygotes expressing
different activity levels.Drosophila
melanogaster has three ADH alleles encoding for isoforms with different Vmax. When three natural homozygotes, a null mutant, and
some heterozygotes were generated, different ADH activities were attained but
the ethanol consuming rate did not change (Figure 4, position 2). It was concluded that the ADH flux control was
near zero [89].


## 5.2. Titration of Flux with Inhibitors (Control of Oxidative Phosphorylation)

Oxidative phosphorylation (OXPHOS) is
the only pathway for which specific and potent inhibitors for many enzymes and
transporters are available. OXPHOS is divided in two segments (Figure5): the
oxidative system (OS) formed by substrate transporters (pyruvate,
2-oxoglutarate, glutamate, glutamate/aspartate, dicarboxylates), Krebs cycle
enzymes, and the respiratory chain complexes; and the phosphorylating system
(PS) constituted by the ATP/ADP (ANT) and Pi (PiT) transporters, and ATP
synthase. The proton electrochemical
gradient (Δμ−H+) connects the two systems.Figure 5
Mitochondrial oxidative phosphorylation. ST, oxidizable substrate transporter; KC, Krebs cycle;
RC, respiratory chain;(Δμ∼H+),
proton electrochemical
gradient; ANT, adenine nucleotide translocator; PiT, phosphate transporter; ATP
Sint, ATP synthase.When the flux (ATP synthesis)
is titrated by adding increasing concentrations of each specific inhibitor,
plots are generated in which the enzyme activity is progressively diminished by
increasing inhibitor concentration. Hence, theCviJ value depends on the type of
inhibitor used(a)
for irreversible inhibition,(2)CviJ=(−ImaxJo)(dJdI)[I]→0,(b)
for simple noncompetitive inhibition,(3)CviJ=(−KiJo)(dJdI)[I]→0,(c)
for simple competitive inhibition,(4)CviJ=(-Ki[(1+S)/Km]Jo)(dJdI)[I]→0, where Jo is the pathway flux in the absence
of inhibitor; Imax, minimal
inhibitor concentration to reach maximal flux inhibition; Ki, inhibition constant; S,
substrate concentration; Km,
Michaelis-Menten constant; and dJ/dI,
initial slope ([I]=0) of inhibition titration curve.To estimate flux control
coefficients from inhibitor titration of ADP-stimulated (state 3) respiratory
rates (i.e., mitochondrialO2 consumption coupled to ATP synthesis), (2) for irreversible inhibitors was used
because researchers assumed that mitochondrial inhibitors such as rotenone,
antimycin, carboxyatractyloside, and oligomycin were “pseudoirreversible,” due
to the enzyme’s high affinity for them. However, under this assumption flux control coefficients were usually
overestimated [90, 91]. To solve this
problem, Gellerich et al. [92] developed (5) for noncompetitive
tightly-bound inhibitors and, by using nonlinear regression analysis, it was
possible to include all experimental points from the titration curve thus
increasing accuracy in calculating CviJ:(5)J=[n(Jo−Ji)2•EnCo•Jo•Eon[(n−Co)•Jo−(n•Ji)•En]]+JiE2+(Kd+I−Eo)•E−Kd•Eo=0, in which Jo and Ji are the
respiration fluxes in the noninhibited (E=Eo) and inhibited (E=0) states; Kd is the dissociation constant of
the enzyme-inhibitor complex, and n is an empirical component that expresses the relationship between substrate
concentration and the reaction catalyzed by the enzyme E.The analysis of data in Table3 shows that OXPHOS is not controlled by only one
limiting step, but the flux control is rather distributed among several enzymes
and transporters. It is worth noting
that the value of the flux control coefficient depends on the content of enzyme
or transporter, which varies from tissue to tissue. Perhaps the ATP/ADP translocase in AS-30D hepatoma mitochondria
might reach the status of being the “OXPHOS limiting step” with a CANTJOxPhos=0.70, or the Pi transporter in kidney mitochondria [93], or the
ATP/ADP translocase and the respiratory chain complex 3 in liver mitochondria [94], but
it should be noted that other steps also exert significant control (Table 3). Although the distribution of control varies
between tissues, the flux control mainly resides in the PS of organs with high ATP
demand such as the heart  (CPT+ANT+ATPsynthaseJOxPhos=CPSJOxPhos=0.73), kidney (CPSJOxPhos=0.75; COSJOxPhos=0.31), and  fast-growing tumors (CPSJOxPhos=0.98). In contrast, in the
liver  (COSJOxPhos=0.80; CPSJOxPhos=0.65) and brain (COSJOxPhos=0.35; CPSJOxPhos=0.41), the control is shared by both systems.Table 3
Control distribution of oxidative phosphorylation.
EnzymeCviJATPRat organ mitochondriaSpecific inhibitorInhibition mechanismReferenceNADH-CoQ-oxidoreductase
(Site 1 of energy conservation or Complex I of respiratory chain)0.15Heart
(0.5 mM pyr + 0.2μM Ca2+)RotenoneNoncompetitive
tightly bound[93]0.26Heart
(10 mM pyr + 10 mM mal)[95]0.31Kidney
(0.5 mM pyr + 0.2μM Ca2+)[93]0.06Kidney (10 mM pyr + 10 mM mal)[95]0.06–0.10Brain (0.05 mM pyr + 0.4μM Ca2+)[91]0.25Brain (10 mM pyr + 10 mM mal)[95]0Tumor (10 mM glut + 3 mM mal)[96]0.27Liver (10 mM pyr + 10 mM mal)[95]0.13Skeletal muscle (10 mM pyr + 10 mM mal)[95]CoQ.cytochrome
c oxidoreductase (Site 2 of energy conservation or Complex III of respiratory
chain)0.01HeartAntimycinNoncompetitive
tightly bound[93]0.19Heart[95]0.02Kidney[95]0.05–0.11Brain[91]0.02Brain[95]0Tumor[96]0.43Liver (5 mM Succ + 1μM Ca2+)[94]0.07Liver[95]0.22Skeletal muscle[95]Cytochrome
c oxidase (Site 3 of energy conservation or Complex IV of respiratory chain)0.11HeartCyanide
or azideNoncompetitive
simple[93]0.13Heart[95]0.04Kidney[95]0.02–0.07Brain[91]0.02Brain[95]0.04Tumor[96]0.23Liver[94]0.03Liver[95]0.20Skeletal
muscle[95]ATP/ADP
transporter (adenine-nucleotides or ATP/ADP transporter, carrier or exchanger)0.24HeartCarboxy-atractyloside (CAT)Noncompetitive
tightly bound[93]0.04Heart[95]0Kidney[93]0.07Kidney[95]0.08Brain[91]0.08Brain[95]0.60–0.70Tumor[96]0.48Liver[93]0.01Liver[93]0.37Skeletal
muscle (10 mM Glut + 3 mM mal)[97]0.08Skeletal
muscle[95]ATP synthase0.34HeartOligomycinNoncompetitive tightly bound[93]0.12Heart[95]0.32Kidney[93]0.27Kidney[95]0.09–0.20Brain[91]0.26Brain[95]0.28Tumor[96]0.05Liver[94]0.20Liver[95]0.10Skeletal muscle[97]0.10Skeletal muscle[95]Pi transporter0.15HeartMersalylNoncompetitive simple[93]0.14Heart[95]0.43Kidney[93]0.28Kidney[95]0.13Brain[91]0.26Brain[95]0Tumor[96]0.05–0.12Liver[94]0.26Liver[95]0.15Skeletal muscle[97]0.08Skeletal muscle[95]Pyruvate transporter0.15Heartα-cyano-4-hydroxy-cinnamateNoncompetitive simple[95]0.03Kidney[95]0.08Brain[91]0.26Brain[95]0.21Liver[95]0.20Skeletal muscle[95]Dicarboxylates transporter0.05–0.14LiverMalate or butyl-malonateCompetitive simple[94]External ATPase0.40Skeletal musclePurified ATPase addition[94]The situation
in skeletal muscle appears controversial. Wisniewski et al. [97] determined that the OXPHOS
control was shared by the PS (CPSJOxPhos=0.62) and the ATP demand (purified ATPase). In turn, Rossignol et al. [95] concluded that
the OS exerted the main control (COSJOxPhos=0.68), but these authors apparently used low-quality mitochondria
(low respiratory control values that lead to low rates of ATP synthesis
associated with high rates of respiration) that were not incubated under near physiological
conditions (10 mM pyruvate, 10 mM malate, 10 mM Pi, pH 7.4 in Tris buffer), and the authors incorrectly assumed that rotenone and antimycin
were irreversible inhibitors. It is notorious
that in all works shown in Table 3 at least one of these mistakes is evident.There are some inhibitors for enzymes and transporters from other pathways, but they
are not quite specific and may affect other sites. Due to the fact that there are no inhibitors
for every step in these pathways, only one flux control coefficient has been
determined by inhibitor titration. Examples
of these inhibitors are 6-chloro-6-deoxyglucose for glucose transporters in
bacteria, 2-deoxyglucose for HPI, iodoacetate for GAPDH [6], 1,4-dideoxy-1,4-imino-D-arabinitol
for glycogen phosphorylase [98], oxalate and oxamate for LDH, 6-amino
nicotinamide for the phosphate pentose pathway [99], amino-oxyacetate for
aminotransferases and kirureninase (tryptophan synthesis), norvaline for
ornithine transcarbamylase, mercaptopycolinate for PEP carboxykinase, acetazolamide
for carbonic anhydrase, and isobutyramide for ADH (compiled by
Fell [2]).Potential Uses of the Experimental Approach
Mitochondrial
pathologies are a heterogeneous group of metabolic perturbations characterized
by morphological abnormalities and/or OXPHOS dysfunction [100]. Mitochondrial DNA analysis has revealed specific
mutations for some mitochondriopathies. Although the specific OXPHOS mutations causing
the disease may appear in all tissues, the functioning of only some of them is
altered. The organ’s sensitivity might be related to the different flux control
coefficients of the mutated enzyme in the different tissues (Table 3) and to
their ATP supply dependence from OXPHOS versus
glycolysis.
MCA allows for the analysis of a metabolic flux or intermediate concentration by focusing
either on one step or by grouping enzymes in blocks or in pathways. Thus, a comparative analysis of OXPHOS control
distribution reveals that heart, kidney, some fast growing tumors (rat AS-30D
hepatoma, mouse fibrosarcoma, human breast, lung, thyroid carcinoma, melanoma)
[101], and perhaps skeletal muscle are more susceptible to mitochondrial mutations
in ATP synthase, which is the only PS site with subunits encoded in the mitochondrial
genome. On the other side, liver and
brain might be more susceptible to mitochondrial mutations of the respiratory
chain enzymes (see Table 3). Considering that the brain is a fully aerobic
organ [102], whereas the liver depends on both OXPHOS (70–80%) and glycolysis
(20–30%) for ATP supply [103], then it can be postulated that the brain is more
sensitive to mutations in the mitochondrial genome than the liver because subunits
of complexes I, III, and IV are encoded by the mitochondrial genome.
Titration of flux with
specific inhibitors to determine the flux control coefficients of OXPHOS has been
applied to intact tumor cells [90]. The results showed that the flux control
resided mainly in site 1 of the respiratory chain (CSitelJOxPhos=0.30), whereas the other evaluated sites exerted a marginal
control [90]. This observation could
have therapeutic application if site 1 does not exert control in healthy cells,
leading to less severe side effects.
The use of inhibitors in
intact cells to determine control coefficients might pose two problems: hydrophilic
inhibitors such as carboxyatractyloside (for ANT) andα-cyano-4-hydroxy-cinammate (for pyruvate transporter)
cannot readily enter the cell due to the presence of the plasma membrane
barrier; the other problem is that hydrophobic but slow inhibitors, such as
oligomycin, require long incubation times to ensure the interaction with the
specific sites. These problems can be
solved by incubating the cells for long periods of time and taking care of cell
viability, for instance, AS-30D hepatoma cells are fairly resistant to this
mechanical manipulation as they maintain high viability after a lengthy
incubation under smooth orbital agitation of 1 h at 37°C
[90].


## 5.3. Elasticity Analysis

MCA defines the elasticity coefficients as(6)εXvi=dvidX•Xovio, which is a dimensionless number that show the rate variation v of a given enzyme or transporter i when the concentration of a ligand X (substrate S, product P or allosteric modulator) is varied in infinitesimal
proportions. The elasticity coefficients are positive for those metabolites
that increase the enzyme or transporter rate (substrate or activator), and they
are negative for the metabolites that decrease the enzyme or transporter rates
(product or inhibitor). An enzyme working, under a steady-state metabolic flux, at saturating conditions of S or P,
is no longer sensitive to changes in these metabolites. Thus, its elasticity is close to zero (Figure 6, εXvi=0).
In turn, an enzyme working at S or P
concentrations well below the Michaelis constant (KmS or KmP)
is expected to be highly sensitive to small variations in these metabolites (Figure
6, εXvi=1).Elasticity coefficients.
(a)(b)The elasticities are intrinsically linked to the actual enzyme kinetics. If the kinetic parameters of an enzyme are
known (Vmf, Vmr,  KmS, and KmP), then the enzyme elasticity for any given metabolite
concentration may be calculated as shown in the following equations.For substrate,(7)εsvi=−S/Kms1+S/Kms+P/Kmp+11−Γ/Keq, and
for product,(8)εpvi=−P/KmP1+S/Kms+P/KmP−Γ/Keq1−Γ/Keq, in which Γ is the mass
action ratio, and Keq is the equilibrium constant preferentially determined
under physiological conditions.An enzyme with low elasticity cannot increase (or decrease) its rate despite large
variations inS (or P) concentration; in consequence, such enzyme exerts a high
flux control. In turn, an enzyme with a
high elasticity can adjust its rate to the variation in S or P concentrations,
and thus it does not interfere with the metabolic flux, exerting a low flux control. This inverse relationship between the
elasticity and the flux control coefficients is expressed in a formal equation
denominated connectivity theorem. A
metabolic pathway can be divided in two blocks around an intermediary X: the
producing (synthetic, supply) and the consuming (demand) enzyme blocks of X are i1 and i2, respectively. Thus, the connectivity theorem for this two-block system is(9)Cv1JCv2J=−εXv2εXv1. The negative sign of the right part of the equation
cancels with εXvi1, which is negative because X
is a product of enzyme block i1 (Figure 6).To obtain the flux control coefficients, this approach requires experimental
determination of the elasticity coefficients. How can this be done? Many strategies have been designed [90, 103–108], but the most
used and probably more trustworthy is that in which the initial pathway metabolite
(So) concentration is varied to increase the X concentration (any intermediary
in the pathway), and measuring in parallel the variation in flux. Under steady-state conditions, the flux rate
is equal to the rate of end-product formation (i.e., lactate or alcohol for
glycolysis; oxygen consumption for OXPHOS) and to the rate of any partial
reaction. Then, plots of X versus
flux (Figure 7) are generated. The slope, calculated at the reference
coordinate (Xo, Jo) that is
equivalent to (So, vio), yields
the elasticity coefficient of the consuming block of X. In another set of experiments, an inhibitor is
added to block one or more enzymes after X. The X concentration and flux are determined and
plotted as shown in Figure 7, from which the elasticity coefficient of the
producing block is calculated.Figure 7
Experimental determination of the elasticity coefficients for substrates and products.The flux
control coefficients are determined by using the connectivity theorem and
considering that the sum of the control coefficients comes to 1,C1+C2=1 (summation theorem):(10)Cv1J=εXv2εXv2−εXv1,Cv2J=−εXv1εXv2−εXv1.This method for determiningCviJ using the elasticities of the two blocks was called double
modulation by Kacser and Burns [83]. Years
later, Brand and his group [103, 104] renamed this method as top-down approach. By applying the procedure shown in Figure 7
and using (10) for different metabolites along the metabolic pathway, it
is possible to identify those sites that exert a higher control (which may be
the sites for therapeutic use or biotechnological manipulation) and those that
exert a negligible control under a given physiological or pathological
situation.Elasticity analysis has been used to evaluate the OXPHOS control distribution
in tumor cells [90]. Almost all studies on
this subject have been carried out with isolated mitochondria incubated in
sucrose-based medium at 25 or 30°C or with the more physiological KCl-based medium but
still at 30°C (Table 3). Furthermore,
these studies did not consider that the product, ATP, never accumulates in the
living cells, which does occur in experiments with isolated mitochondria. Under such a condition, a steady state in ATP production can
never be reached as in living cells. In
other words, the distribution of control in mitochondria (Table 3) has been
determined in the absence of an ATP-consuming system. A remarkable exception to this incomplete
experimental design was the work done by Wanders et al. [105], in which isolated liver mitochondria were incubated
with two different ATP-consuming systems (or ADP-regenerating systems): HK +
glucose and creatine kinase (CK) + creatine. Under this more physiological setting, the OXPHOS
flux control distributed between ANT and the ATP-consuming system; however, flux
control by the other pathway components was not examined. Therefore, to accurately evaluate OXPHOS control
distribution, mitochondria should be incubated in the presence of an
ATP-consuming system or in their natural environment (i.e., inside the cell).The rate of OXPHOS in intact
cells is determined from the rate of oligomycin-sensitive respiration: in the
steady state, the enzyme rates are the same and constant; in branched pathways
the sum of the branched fluxes equals the flux that supplies the branches. The global elasticity of the ATP-consuming processes
(e.g., synthesis of protein,
nucleic acid, and other biomolecules, as well as ion ATPases to maintain the
ionic gradients, mechanical activity such as muscular contraction or flagellum
and cilium movement, and secretion of hormones, digestive enzymes and
neurotransmitters) is estimated by inhibiting flux with low concentrations of
oligomycin or a respiratory chain inhibitor. To determine the elasticity of the
ATP-producing block, flux, and [ATP] are varied with streptomycin, an inhibitor
of protein synthesis (Figure7). The
elasticity coefficients are calculated from the initial coordinate slopes
(without inhibitors) of each titration. With
this procedure, it has been determined that the ATP-consuming block exerts a
significant flux control of 34% [90]. Remarkably,
this flux control value obtained in cells is quite similar to the flux control
coefficients of the ATP-consuming system (HK or CK) reported by Wanders
et al. [105] with isolated
mitochondria.Elasticity analysis by enzyme
blocks allows the inclusion of the end-product demand as another pathway block.
The conclusions obtained from this
analysis have formulated the supply-demand theory [30], which proposes that when
flux is controlled by one block (demand), the concentration of the end-product
is determined by the other block (supply). The ratio of elasticities determines the distribution of flux control
between supply and demand blocks. For
instance, if εXSupply>εXDemand (i.e., demand becomes saturated by the end-product X,
and hence its elasticity is near zero), then the demand block exerts the main
flux control. For concentration control,
at larger εXDemand−εXSupply,  smaller absolute values of both CSupplyX and CDemandX are attained; hence, under demand saturation,
the supply elasticity fully governs the magnitude of the variation in the
end-product concentration. On the other
hand, when demand increases, it loses flux control and induces a diminution in
the end-product concentration. In turn, supply gains flux control and loses
concentration control. In the presence of feed-back inhibition, the system can
maintain the end-product concentration orders of magnitude away from
equilibrium (at a concentration around the K0.5 of the allosteric enzyme).As mentioned before, the
demand is not usually included in the pathway because it is erroneously thought
that it is not part of it. But then, is
it valid to analyze the control of a metabolite synthesis if its demand is not
considered? When the demand block is not
included, it is assumed that the metabolic pathway produces a metabolite at the
same rate regardless whether the metabolite demand is high or low. This reasoning is incorrect because a
metabolic pathway indeed responds to changes in the metabolite demand and, more
importantly, a pathway without end-products consumption reactions is unable to
reach a steady state.Therefore,
a metabolic pathway can be divided in supply and demand blocks. The intermediaryX linking the two blocks is one
of the end-products of the producing block (e.g.,
pyruvate or lactate or ethanol, and ATP for glycolysis). The variation in rate of the two blocks in
response to a variation in X can be theoretical or experimentally determined (Figure 8(a)). It is worth noting that, for this
supply-demand approach, it is not necessary to know the kinetics of each
pathway enzyme because the rate response of each block reflects the global kinetics
of all participating enzymes. When the X
concentration is increased, the rate of the supply block decreases (i) because X
is its product and (ii) because usually an enzyme within this block receives
information from the final part of the pathway, decreasing its rate through
feedback inhibition. In turn, the rate
of the demand block increases as X is its substrate.(a) Kinetics of the synthesis
(supply) and consuming (demand) blocks of the intermediaryX. The kinetic parameters are from enzymes in tobacco
glutathione (GSH) synthesis. X
represents the intermediary concentration, in this case GSH. (b) Rate plots of the supply and demand
blocks in a natural logarithmic scale.
(a)(b)To better
visualize the effect of large rate changes, the kinetics of both blocks are
plotted in a logarithmic scale. Figure8(b) shows the kinetics described in Figure 8(a) converted to natural
logarithm. The intersection point
between kinetic curves, at which the supply and demand rates are identical,
represents the pathway steady-state flux (in the Y axis) and end-product
concentration (in the X axis). Since the
elasticity is also defined as εXvi=dlnvi/dlnX, the slope at the intersection point represents the elasticity of each
block towards the intermediary X. Here,
the use of the scalar factor is not necessary because it is included in the
logarithmic equation. With the elasticity
coefficients calculated from plots like those shown in Figure 8, and the
connectivity theorem, the flux control coefficient of each block is determined.
The example in Figure 8(b) shows that
the demand exerts a high flux control (and has low elasticity) and the supply
block exerts low control (and has high elasticity).The
fact that the demand may exert a high flux control in metabolite pathways has
at least three important implications: (a) the supply block responds to variations
in the demand (high elasticity); (b) the demand block has information transfer
mechanisms towards the supply block that avoid the unrestricted intermediary accumulation under a low demand,
particularly when the supply block has reactions with large Keq (>100;ΔG°′>3 Kcal mol-1 at 37°C); and (c)
if the main flux control resides in the demand block, then the supply block may
only exert control on the intermediary concentration but not on the flux [30, 32]. This last conclusion explains why it
is incorrect to consider that an enzyme that controls flux must also control
the intermediary concentration.Regulatory mechanisms of
enzyme activity are modulation of protein concentration by synthesis and
degradation, as well as covalent modification and variation in the substrate or
product concentrations (which are components of the pathway). In addition, another regulatory mechanism is the
modulation by molecules that are not part of the pathway, that is, through allosteric interaction with cooperative (sigmoidal
kinetics) or noncooperative enzymes (hyperbolic kinetics) (e.g., Ca2+ activates some Krebs cycle dehydrogenases; citrate inhibits PFK-1; malonyl-CoA inhibits
the mitochondrial transporter of acyl-carnitine/carnitine; or the initial
substrate of a pathway that has not entered the system). For these last cases, Kacser and Burns [83]
proposed the use of the response coefficient R which is defined by the
following expression:(11)RMJ=CviJ•εMvi, where M is the external modulator of the i enzyme. The response coefficient is dJ/dM•Mo/Jo.
If the elasticity of the sensitive
enzyme toward the external effector is also determined, then it is possible to
calculate CviJ by using (11). Unfortunately, due to the experimental complexity for determining the
elasticity coefficient, this coefficient is often calculated in a theoretical
way by using the respective rate equation (Michaelis-Menten or Hill equations)
and the kinetic parameters Km and Vmax determined by someone else under optimal
assay conditions, which are commonly far away from the physiological ones. Therefore, for this theoretical determination
of elasticity only the value of the external modulator concentration is required. It is convenient to emphasize that the determination
of the flux control coefficients becomes more reliable when they are calculated
from several experimental points (Figure 7), instead of only one, as occurs
with the theoretical elasticity analysis.Groen et al. [106] determined the flux control distribution of gluconeogenesis
from lactate in hepatocytes by using both theoretical and experimental elasticity
analysis and the response coefficient. These authors concluded that gluconeogenesis
stimulated by glucagon was controlled by the pyruvate carboxylase (CPCJglucose=0.83); in the absence of this hormone, the
control was shared by PC, PYK, ENO-PGK segment, and TPI-fructose-1,6-biphosphatase
segment [106].Elasticity
analysis has been applied to elucidate the flux control of ATP-producing
pathways in fast-growing tumor cells. For OXPHOS, this approach showed that respiratory chain complex I and
the ATP-consuming pathways were the enzymes with higher control (CviJ=0.7) [90]. For glycolysis, the main flux control (CviJ=0.71) resided in GLUT + HK reactions because
HK is strongly inhibited by its product G6P despite extensive enzyme overexpression
[107]. Examples of elasticity analysis on
other pathways are photosynthesis [108], ketogenesis [109], serine [110] and
threonine synthesis in E. coli [111], glycolysis in yeast [112], glucose
transport in yeast [113], DNA supercoiling [114], glycogen synthesis in muscle [115],
and galactose synthesis in yeast [116].In conclusion, the elasticity
analysis is the most frequently used method for determining flux control
coefficients because it does not need a group of specific inhibitors for all
the enzymes and transporters of the pathway, neither does it require knowledge
of the inhibitory mechanisms or kinetic constants. It is only necessary to produce a variation in
the intermediary concentrationX by using an inhibitor of either block or by
directly varying the X concentration.


## 5.4. Pathway Modeling

In agreement with Fell [2], it seems impossible for a researcher to analyze one by
one the rate equation of each enzyme in a metabolic pathway to predict and
explain the system behavior as a whole. To deal with this problem, in the last three
decades some scientists have constructed mathematical models for some metabolic
pathways using several software programs. Thus, the specific variation of a single enzyme
activity without altering the rest of the pathway (Figure 4), which has been an
experimentally difficult task for applying MCA, becomes easier to achieve with
reliable computing models. The term “in
silico biology” has been coined for this approach.There are two basic types of modeling: (a) structural modeling and (b) kinetic
modeling. The former is related to the pathway chemical reaction structure and
does not involve kinetic information. The use of reactions is based on their
stoichiometries. The information obtained with structural modeling is the
description of the following:(i)
the exact determination of which reactions and
metabolites interact among them;(ii)
the conservation reactions. There are metabolites for
which their sum is always constant or conserved (e.g., NADH + NAD+; NADPH + NADP+;
ubiquinol + ubiquinone; ATP + ADP + AMP; CoA + acetyl-CoA). The identification of
conserved metabolites might not be obvious;(iii)
enzyme groups catalyzing reactions in a given relationship
with another group of enzymes;(iv)
elemental modules, which are defined as the minimal
number of enzymes required to reach a steady state, which can be isolated from the
system (for a review about structural modeling; see [117]).Kinetic
modeling is more frequently used. In addition to an appropriate computing
program, this approach requires the knowledge of the stoichiometries, rate
equations, and Keq values of each reaction in the pathway (or theVmax in the forward and reverse
reactions), as well as the intermediary concentrations reached under a given
steady state. Some currently used
softwares are Copasi (http://www.copasi.org/tiki-index.php)
based on Gepasi (http://www.gepasi.org/; [118]); Metamodel [119]; WinScamp [120]
and Jarnac [121] (both available at http://www.sys-bio.org/); and PySCeS
(http://pysces.sourceforge.net/; [122]). For other programs and links, go to http://sbml.org/index.psp. To reach a steady-state flux, it is necessary
to fix the initial metabolite concentration to a constant value and the
irreversible and constant removal of the end products. Except for the final reactions in which their
products have to be removed from the system, all pathway reactions have to be
considered as reversible, notwithstanding whether they have large Keq (if there
is an irreversible reaction under physiological conditions, then a reversible rate
equation that includes the Keq suffices to maintain the reaction as practically
irreversible). Care should be taken to include the enzyme’s sensitivity toward
its products because this property is related with the enzyme elasticity and hence
with its flux control; omission of this parameter may very likely lead to
erroneous conclusions.It
should be pointed out that the purpose of kinetic modeling is not merely to
replicate experimental data but also to explain them [117]. Thus, pathway modeling is a powerful tool
that allows for (i) the detection of those properties of the pathway that are
not so obvious to visualize when the individual kinetic characteristics of the
participating enzymes are examined; and (ii) the understanding of the biochemical
mechanisms involved in flux and intermediary concentration control. Modeling requires the consideration of all
reported experimental data and interactions that have been described for the
components of a specific pathway, thus allowing for the integration of disperse
data, discarding irrelevant facts [84]. Although all models are oversimplifications of complex cellular
processes, they are useful for the deduction of essential relationships, for
the design of experimental strategies that evaluate the control of a metabolic
pathway, and for the detection of incompatibilities in the kinetic parameters
of the participating enzymes and transporters, which may prompt the
experimental revision of the most critical uncertainties.With
the model initially constructed, the simulation results do not usually concur
with the experimental results; in consequence, the model normally requires
refinement, a point at which the researcher’s thinking and knowledge of biology
plays a fundamental role in modifying the structure and parameters of the model.
The discrepancies observed between modeling
and experimentation unequivocally pinpoint what elements or factors have to be re-evaluated
or incorporated so that the model approximates more closely reality (i.e., experimental data). The comparison of the experimentally obtained
intermediary concentrations and fluxes with those obtained by simulation is an
appropriate validating index of the model; this index indicates whether the
model approximation to the physiological situation is acceptable or whether
re-evaluation of the kinetic properties of some enzymes and transporters and/or
incorporation of other reactions or factors is required.A reason to why the results obtained by modeling may substantially differ from the
experimental results is that the kinetic parameters of the pathway enzyme and
transporters and the Keq values used
were determined by different research groups, under different experimental
conditions and in different cell types. Moreover,
enzyme kinetic assays are carried out at low, diluted enzyme
concentrations (thus discarding or ignoring relevant protein-protein
interactions), and at optimal (but not physiological) pH and “room temperature”
(which may be far away from the physiological values). In addition, no experimental information is
usually available regarding the reactions reversibility and the product
inhibition of the enzymes and transporters (particularly for physiological
irreversible reactions, i.e., reactions with large Keq). With worrisome
frequency, the researcher has to adjust the experimentally determinedVm and Km values to achieve a model behavior that acceptably resembles
that observed in the biological system. Apparently,
this type of limitations as well as the sometimes overwhelming amount of
kinetic data necessary for the construction of a kinetic model has restricted
the number of reliable models that can be used for the prediction of the
pathway control structure.Once the kinetic model stability, robustness, structural and dynamic properties have
been evaluated, and experimentally validated, the model may become a virtual
laboratory in which any parameter or component can be modified or replaced and
any aspect of the pathway behavior can be explored within a wide diversity of
circumstances or limits [117]. At this
stage, the model is suitable for examining the pathway regulatory properties
and control structure.Glycolysis
inS. bayanus, S. cerevisiae [113, 123, 124], and Trypanosoma brucei [125, 126] is the
metabolic pathway that has been more extensively modeled. Both cell types
have a very active glycolysis and are fully dependent on this metabolic pathway
for ATP supply, under anaerobiosis and aerobiosis, respectively. One advantage
of modeling glycolysis in these cell types is that most of the kinetic
parameters used have been experimentally determined by the same groups under
the same experimental conditions. However,
the kinetics of the reverse reactions has not been determined and thus these
authors used KmP and Keq
values reported by others and obtained in other cell types under rather different
experimental conditions, or they were adjusted to improve model fitting.Nevertheless, the simulation
results yielded relevant information on the control of the glycolytic flux. In both cases, the enzymes traditionally considered
the rate-limiting steps, HK, ATP-PFK-1, and PYK did not contribute to the flux
control, whereas the main control resided in GLUT (54% in the parasite and 85–100% in yeast). Under some conditions, HK may exert some
control (15%) inS. cerevisiae and some nonallosteric enzymes such as
ALDO, GAPDH, and PGK may also exert some flux control in T. brucei.MCA
through kinetic modeling has been applied to several pathways:(i)
glycolysis in
erythrocytes [84] in which flux control distributes between HK (71%) and PFK-1
(29%);(ii)
carbohydrate
metabolism during differentiation inDictyostelium discoideum [127] with
cellulose synthase (86%) as the main controlling step;(iii)
sucrose accumulation
in sugar cane with HK, invertase, fructose uptake, glucose uptake, and vacuolar
sucrose transporter having the most significant flux control [128];(iv)
glycerol
synthesis inS. cerevisiae with GAPDH
(85%) as the main control step [129];(v)
penicillin
synthesis inPenicillium chrysogenum controlled
(75–98%) either by d-(a-aminoadipyl) cysteinylvaline synthetase (short
incubation times <30 hour) or isopenicillin N. synthetase (long incubation
times > 100 h) [130];(vi)
Calvin cycle
[131] controlled by GAPDH (50%) and sedoheptulose-1,7-bisphosphatase (50%);(vii)
threonine
synthesis inE. coli controlled by homoserine dehydrogenase (46%),
aspartate kinase (28%), and aspartate semialdehyde dehydrogenase (25%) [111];(viii)
lysine
production inCorynebacterium glutamicum mainly
controlled by aspartate kinase and permease [132];(ix)
nonoxidative
pentose pathway in erythrocytes mainly controlled by transketolase (74%) [133];(x)
EGF-induced MAPK
signaling in tumor cells controlled by Ras-activation by EGF (21%), Ras
dephosphorylation (43%), ERK phosphorylation by MEK (44%), and MEK
phosphorylation by RAS (143%) [13];(xi)
Aspergillus niger arabinose utilization with
flux control shared by arabinose reductase (68%), arabitol dehydrogenase (17%),
and xylulose reductase (14%) [134];(xii)
glycolysis inL. lactis in which several end products are generated (lactate,
organic acids, ethanol, acetoin) [135]. Model predictions indicated that flux toward diacetyl and acetoin
(important flavor compounds) was mainly controlled by LDH but not by
acetolactate synthetase, the first enzyme of this branch.We modeled
the GSH and PCs biosynthesis (Figure2) to determine and understand the control
structure of the pathway and thus be able to identify potential sites for genetic
engineering manipulation that might lead to the generation of improved species
in heavy metal resistance and accumulation. Two models were constructed, one
for higher plants and the other for yeast, both exposed to high concentrations
of Cd2+ [136]. Due to the
similarity in the results, only the plant results are analyzed below.An interesting conclusion from the GSH-PCs synthesis modeling is that control of flux
(and GSH concentration) is shared between the GSH supply and demand under both unstressed
and Cd2+ exposure
conditions (Table 4). This observation strongly differs from the
idea that γ-ECS is the rate-limiting step [33–35]. For many researchers, the concept of γ-ECS being the key controlling step has seemed to be
correct because (a) γ-ECS receives information from the final part
of the pathway, as it is potently inhibited by GSH, the pathway end-product;
and (b) γ-ECS is localized in the first part of the
pathway (Figure 2). In addition, GS is
usually more abundant and efficient than γ-ECS [137].Table 4
Control of GSH and PC synthesis in plants exposed to Cd2+.
Enzyme1xγ-ECS + PCS2.5xγ-ECS + PCSCviJGSHCviJPCCviGSHCviPCCviJGSHCviJPCCviGSHCviPCγ-ECS0.580.600.680.760.450.610.700.60GS<0.01<0.010.010.010.19<0.01<0.010.97GS-transferase0.01−0.06−0.07−0.07<0.01<0.01<−0.01−0.05PCS0.400.44−0.63−0.560.330.44−0.620.57vacuole
PC-Cd transporter<0.01<0.01<0.01−1.2<0.01<0.01<0.01−2.1CviJGSH, control coefficient of
enzyme i in GSH synthesis; CviJPC, control coefficient of enzyme Ei on PCs
synthesis; CviGSH, control coefficient of enzyme i on GSH concentration; CviPC, control coefficient of enzyme i on PCs concentration. An enzyme with a negative
flux control indicates that it is localized in a branch, turning aside the
principal flux; an enzyme with a negative concentration control indicates that
an increase in its activity decreases metabolite concentration.However, in most of the
studies on the control of GSH synthesis, the GSH demand has not been
considered. The GSH synthesis modeling shows that under a physiological feedback
inhibition ofγ-ECS by GSH a small increase in demand increases
flux because the GSH concentration decreases and the γ-ECS inhibition attenuates. In contrast, if the demand remains constant, then
an increase in γ-ECS activity or content (by overexpression) does
not increase flux because the GSH inhibition is still there and operates on
both new and old enzymes. The same pattern is also observed when HK is
overexpressed to increase
glycolytic flux since it is still inhibited by G6P (see Section 3). On the other hand, γ-ECS indeed exerts significant concentration control
on GSH, which means that a γ-ECS increase results in higher GSH
concentration (Table 4). This last
observation demonstrates that an enzyme controlling a metabolite concentration does
not necessarily control the flux.Cd2+ exposure promotes a high GSH demand because significant oxidative stress surges,
thus causing oxidation of GSH through GSH peroxidases, and because GSH and PCs
are used for sequestering the toxic metal ion; hence, a higher GSH consuming
rate sets up. Under this condition,
modeling predicted that control was almost equally shared between the supply
and demand blocks, but particularly between γ-ECS and PCS (see Figure 2). Modeling was also able to explain why PCS overexpression
can have toxic effects on the cell [36]. An increase in the GSH demand (PCS
overexpression) under high-demand conditions (Cd2+ stress) leads to
GSH depletion that severely compromises other processes such as the oxidative
stress control and xenobiotic detoxification.The
conclusions drawn by this model led us to propose that, to significantly increase
the Cd2+ resistance and accumulation, γ-ECS and PCS should be simultaneously overexpressed
(Table 4; Figure 9). This particular
manipulation promotes an increase in the rate of GSH and PCs synthesis
(determined by the high-to-low transition of their flux control coefficients)
and in the GSH and PCs concentrations
(determined by their high concentration control coefficients). The model predicts that a 2-fold increase in
the simultaneous overexpression of γ-ECS and PCS brings about a 1.9–2.4-fold
increase in flux to GSH (JGS)
and PCs (JPCS) and in PCs
concentration (Figure 9); a 5-fold overexpression further increases by 4.5–8.1
times the fluxes and PCs concentration.Figure 9
Modeled simultaneous overexpression of two
controlling enzymes, one in the supply (γ-glutamylcisteine synthetase, γ-ECS) and the other in the demand branch
(phytochelatin synthase, PCS), of the glutathione and phytochelatins synthesis
pathway in plants.This proposed enzyme overexpression
should not exceed the GS and the complex PC-Cd (or GS-Cd-GS) vacuolar
transporters’ maximal activities, in order to keep the cell away from a severe
oxidative stress caused by GSH depletion orγ-EC accumulation. Indeed, the concentration of GSH was maintained high and constant although
γ-EC accumulated with the simultaneous overexpression
(Figure 9). Furthermore, this enzyme
manipulation should avoid the increase of the PC-Cd and GS-Cd-GS complexes in
cytosol to toxic levels. In other words,
excessive enzyme overexpression should be avoided, unless this is accompanied
by compensating overexpression of consuming enzymes (GS for γ-ECS overexpression and PCs vacuolar transporters for
that of PCS). In yeasts and plants, Cd2+ is ultimately inactivated by the additional interaction with S2− and
the subsequent formation of stable high molecular weight complexes with PCs, Cd2+,
S2−, and GSH [138, 139]. In
parallel to the γ-ECS and PCS overexpression, moderate repression
of GSH-S-transferases, which compete for the available GSH (Figure 2), may also
promote an increase in GSH concentration and PCs formation flux [136].MCA
is based on infinitesimal changes in an enzyme or metabolite concentration. In contrast, gene overexpression induces large
changes in activity; hence, further theoretical background has been developed for
predicting the effect on flux and metabolite concentrations induced by large
enzyme changes. Such a theoretical background was initially developed by Small
and Kacser [140], who depicted (12) based on the flux control coefficients to
predict the effect promoted by large changes in enzyme activity:(12)fEj−mrJ=11−∑i=jm(Cvi0Jo•(ri−1)/ri), in which f is the amplification factor (the flux increase), and r represents how many times the enzyme is overexpressed. To predict the flux changes, promoted by identical
overexpression of two enzymes (same r value) with different CviJ,
the equation is
(13)fEj−mrJ=11−(CiJ+CjJ)•((r−1)/r).Figure10 shows the effect on flux when one or more enzymes with different CviJ are changed by the same r factor. If the sum of CviJ
of one or more enzymes is less than 0.25, the
impact on flux is discrete when the expression increases 5 folds (which is the
most common variation in the overexpression experiments analyzed in Section
2). But for a 3-fold overexpression of
a group of enzymes, for which their sum of CviJ is more than 0.5, then a significant flux
change is achieved. If the sum of CviJ is 1, the flux varies in a linear proportion
with the degree of overexpression. It
has to be remarked, however, that the predicted change in flux (Figure 10) will
be valid until certain degree, the limits of which being determined by the
other pathway enzymes that should stay as noncontrolling steps.Figure 10
Effect on flux when one or more enzymatic
activities with different control coefficients are varied. This figure represents an enzyme or group of enzymes
in which theirCviJ sum is indicated in parenthesis and is
modified by the same r factor. Number
1 represents the reference control, thus if r<1, there is suppression, whereas r>1 represents overexpression.Figure10 also shows the effect on flux of decreasing an enzyme activity (third
quadrant). This segment plot is useful when inhibition of pathway flux is being
pursued for therapeutic purposes or for understanding the molecular basis of the
genetic dominance and recessivity. Like
in the enzyme overexpression experiment, only a significant effect on flux is
achieved when the enzymes with high CviJ values are inhibited. For an enzyme or group of enzymes with CviJ
of 0.25, greater than 80% inhibition has to be
attained to decrease 50% the pathway flux. In this context, it seems feasible
to explain why knockdown of enzymes involved in TSH2 synthesis has
to be almost total to detect an effect on TSH2 content or to alter
functional or pathogenic properties of the parasites (Section 4.3). The knockdown or knockout experiments in
trypanosomatids suggest that γ-ECS, TryS, and TryR most probably have low flux control
and concentration-control coefficients since their contents or activities have
to be reduced >80% of the normal levels to reach changes in intermediary
levels or in oxidative stress handling.Contrary
to the several unsuccessful overexpression experiments carried out to increase
the flux or metabolites of a metabolic pathway, modeling may allow for a more
focused and appropriate design of experimental strategies of genetic
engineering to increase flux or a given metabolite, and for selecting drug
targets to decrease flux or metabolite concentration. For these predictions, modeling considers
that overexpression of a controlling enzyme or transporter may promote flux or
metabolite control redistributions.
Thus, a low-control step may become a
controlling point when overexpressing another step and, in consequence, the
prediction shown in Figure10 based on (11) and (12) may be inaccurate. By considering the whole pathway components,
modeling is also a powerful tool for predicting the effects on flux and
metabolite concentration of varying an enzyme activity (by overexpression or
drug inhibition).Model Predictions to Inhibit a Pathway Flux
Kinetic modeling has been used to identify the flux controlling steps inTrypanosoma
brucei glycolysis for drug targeting purposes. Interestingly, modeling has predicted
controlling steps for the parasite pathway different from those described for
glycolysis in human host cells [125, 126].
Entamoeba histolytica is the causal agent of human
amebiasis. The parasite lacks functional
mitochondria and has neither Krebs cycle nor OXPHOS enzyme activities. Therefore,
substrate level phosphorylation by glycolysis is the only way to generate ATP
for cellular work [141]. An important
difference in amebal glycolysis in comparison to glycolysis in human cells is
that it contains the pyrophosphate (PPi)-dependent enzymes phosphofructokinase
(PPi-PFK) and pyruvate phosphate dikinase (PPDK), which replace the highly
modulated ATP-PFK and PYK present in human cells. Moreover, both have been
proposed as drug targets by using PPi analogues (bisphosphonates) [141].
We recently described the
construction of a kinetic model ofE. histolytica glycolysis to
determine the control distribution of this energetically important pathway in
the parasite [142]. The model was
constructed using the Gepasi software and was based on the kinetic parameters
determined in the purified recombinant enzymes [143], as well as the enzyme
activities, fluxes, and metabolite concentrations found in the parasite. The results of the
metabolic control analysis
indicated that HK and PGAM are the main flux control steps of the pathway (73
and 65%, resp.) and perhaps GLUT. In
contrast, the PPi-PFK and PPDK displayed low flux control (13 and 0.1%, resp.)
because they have overcapacity over the glycolytic flux [142]. The amebal model allowed evaluating the
effect on flux of “inhibiting” the pathway enzymes. The model predicted that in order to diminish
by 50% the glycolytic flux (and the ATP concentration; data not shown), HK and
PGAM should be inhibited by 24 and 55%, respectively, or both enzymes by 18%
(Figure 11). In contrast, to attain the
same reduction in flux by inhibiting PPi-PFK and PPDK, they should be decreased
>70% (Figure 11). Therefore, the
kinetic model results indicate that HK can be an appropriate drug target
because its specific inhibition can compromise the energy levels in the
parasite. They also indicate that although
PPi-PFK and PPDK remain as promising drug targets because of their divergence
from the human glycolytic enzymes, highly potent and very specific inhibitors
should be designed for these enzymes in order to affect the parasite’s energy
metabolism.Figure 11
Modeled flux behavior when
inhibiting pathway enzymes. The predicted flux when varying the enzyme activity
was obtained using the kinetic model forEntamoeba
histolytica glycolysis [142]. In
this case, 100% enzyme activity is the enzyme activity present in amebal
extracts, and 100% flux is the ethanol flux displayed by amoebae incubated with
glucose. PPi-PFK, PPi-dependent
phosphofructokinase; PPDK, pyruvate phosphate dikinase; PGAM, 2,3
bisphosphoglycerate independent 3-phosphoglycerate mutase.


## 5.5. In Vitro Reconstitution of Metabolic Pathways

Another experimental approach
for determining the enzyme control coefficients is the in vitro reconstitution
of segments of metabolic pathways. It is
recalled that for determining the flux control coefficient exerted by a given
step on a metabolic pathway the enzyme activity has to be varied, without
altering the other components in the system, and the flux variations are to be
measured (Figure4). Such an experiment can be readily made if a pathway is
reconstituted with purified enzymes. Some advantages of this approach are that the
pathway structure is known, in which the components concentration may be
manipulated and analyzed separately, and the enzyme effectors can be assayed. As
the system composition is strictly controlled, the results may be highly
reproducible. The main disadvantage is
that the enzyme concentrations in the assays are diluted and thus the enzyme
interactions are not favored. If this interaction
is important for activity, the in vitro reconstitution may limit the
extrapolation to the metabolic pathway inside the cell.There are not many studies
describing this type of experiments, most probably due to the fact that for
applying MCA the pathway must be working under steady-state conditions. In a reconstituted system, only a quasi steady
state may be reached because there is net substrate, and cofactors consumption,
as well as product accumulation, since it is difficult to attain a constant
substrate supply and release of products.One of the first experimental
reports on control coefficient determination in a reconstituted system was
carried out for the upper glycolytic segment with the commercially available
rabbit muscle HK, HPI, PFK-1, ALDO, and TPI [144]. Each enzyme was separately titrated and the
flux variation to glycerol-3-phosphate (by coupling the reconstituted system to
an excess of α-GPDH) was measured in the presence of CK to maintain
the ATP concentration constant. The flux
control coefficients were determined as described in Figure 4. The results showed that PFK-1 and HK exerted the
main flux control (65% and 20%, resp.), whereas the remaining 15% resided in
the other enzymes. These authors observed that the addition of F1,6BP, a PFK-1
activator slightly diminished the flux control exerted by PFK-1 and increases
that of HK. The validation of the
summation theorem was also demonstrated in this work [144].The lower glycolytic segment
has also been reconstituted with commercial enzymes for determining the flux
control coefficients [145]. The results
showed that flux was mainly controlled by PYK (60–100%), although under some
conditions control was shared with PGAM; ENO did not contribute to the flux
control.Another important limitation
of the reconstitution experiments is that the commercial availability of the
purified enzymes from the same organism is restricted or inexistent. However, by using the information from the
genome sequence projects and the recombinant DNA technology, it is now possible
to access all the enzyme genes from a metabolic pathway in the same organism, thus
facilitating their cloning, overexpression, and purification. With this strategy, we cloned, overexpressed,
and purified the 10 glycolytic enzymes ofEntamoeba histolytica [143] for
studying the flux control distribution in this organism by using kinetic
modeling [142] and pathway reconstitution.The reconstitution
experiments of the lower amebal glycolytic segment, under near physiological
conditions of pH, temperature, and enzyme activity (Figure12) showed that PGAM
and, to a lesser extent, PPDK exert the main flux control (these amebal enzymes
are genetically and kinetically different from their human counterparts) with
ENO exhibiting negligible control [143]. In turn, reconstitution of the upper amebal
glycolytic segment has revealed that HK and, to a much lesser extent HPI,
PPi-PFK, and ALD, exerted the main flux control, with TPI having negligible
control [146]. These results strongly
correlate with the enzyme catalytic efficiencies previously reported [143], in
which HK is highly sensitive to AMP inhibition, ALD, and PGAM have the lowest
catalytic efficiencies among the glycolytic enzymes, leading to high flux control
coefficients and thus becoming suitable candidates for therapeutic
intervention. The reconstitution results
also agree with the pathway modeling predictions previously analyzed (Section
5.4), in which HK and PGAM are two of the main controlling steps [142].Determination of flux control
coefficients in an in vitro
reconstitution of the final section ofEntamoeba histolytica glycolysis.
Enzymatic assay with the three recombinant enzymes from
the ameba: EhPGAM, EhENO, and EhPPDK. LDH, commercial lactate dehydrogenase. The flux control coefficient was determined at
the *marked position. 2PG,
2-phosphoglycerate; 3PG, 3-phosphoglycerate. Modified from [143].
(a)(b)(c)(d)The in vitro reconstitution
experiments are also useful for studying the effect on control redistribution of
an enzyme modulation that is particularly difficult to manage in vivo; the main controlling steps
identified with the reconstitution experiments should be further analyzed with
other experimental strategies such as elasticity analysis in the in vivo
systems.


## 5.6. Genetic Engineering to Manipulate the In Vivo Protein Levels

This experimental approach for determining the control coefficients could be part of
the genetic approach analyzed in Section5.1, but it was separated due to its
recent methodological development and because it actually belongs to the
molecular genetics rather than to the Mendelian genetics.


### 5.6.1. Repression of Gene Expression

This approach is based on the in vivo modulation of the enzyme levels using the RNA
antisense technology. There are at least
three strategies to
inhibit gene expression: (a) the use of single stranded antisense
oligonucleotides, which form a double stranded RNA that might be degraded by RNAse
H; (b) target RNA degradation with catalytically active oligonucleotides, known
as ribozymes that bind to their specific RNA; and (c) RNA degradation using siRNAs
(21–23 nucleotides) [147].The RNA antisense technology was applied for control coefficient determination of the
ribulose-bisphosphate-carboxylase (Rubisco) that fixes CO2 in the
plant Calvin cycle. This enzyme considered
the rate-limiting step of the Calvin cycle and of the whole photosynthetic
process, despite its high concentration (4 mM) in the chloroplasts stroma that compensates
its low catalytic efficiency.Attempts to make Rubisco a nonlimiting step, either by modifying its catalytic efficiency
or by overexpressing it, have been unsuccessful. Stitt et
al. [148] determined the CrubiscoJphotosynthesis of tobacco plants by decreasing its activity
with DNA antisense. The plants were transformed with DNA antisense against the
mRNA of the enzyme’s small subunit, thus promoting its degradation. For Calvin cycle enzymes, the pleiotropic
effects were minimal. The results showed
that Rubisco may indeed be the photosynthesis limiting step with a CrubiscoJphotosynthesis= 0.69–0.83 when plants are exposed to high
illumination (1050 μmol quanta m-2s-1), high
humidity (85%), and low CO2 concentrations (25 Pa). However, this flux control decreases to
0.05–0.12 under moderate illumination or high CO2 levels [148]. Unfortunately, the authors did not determine
the control coefficients of the other pathway enzymes or the branches fluxes which
may be significant.As described in Section5.4, the results of the T. brucei glycolysis
modeling indicated that GLUT was the main flux control step (CGLUTJ∼ 50%), [125, 126]. This model predicted a large overcapacity for
HK, PFK-1, ALDO, GAPDH, PGAM, ENO, and PYK over the glycolytic flux leading to
low flux control coefficients [125, 126]. To validate the modeling results, the concentrations of HK, PFK-1, PGAM,
ENO, and PYK were changed with siRNAs in growing parasites [149]. These knockdown expression experiments showed
overcapacity of HK and PYK over the flux, although at lower levels than predicted
by the model. A good correlation for
PGAM and ENO was obtained between model predictions and experimental results. However, a large difference (9 folds) was
obtained for PFK-1. This discrepancy is
perhaps related to pleiotropic effects of PFK-1 downregulation, as these mutants
also displayed diminution in the activities of other enzymes (HK, ENO, and PYK).
The combination of these two approaches,
in silico modeling and in vivo experimentation, is complementary: on one
hand, modeling identifies the enzymes (out of 19 that contain the model) that
display the highest flux control coefficients, whereas in vivo experimentation validates the
accuracy of the model to establish predictions about the pathway’s behavior.


### 5.6.2. Fine Tuning of Cellular Protein Expression

The knockdown experiments described above usually yield only two experimental points
of the plot shown in Figure4: the
wild-type and the knockdown strain protein levels or enzyme activities. Thus, with
such an approach high levels of inhibition (>80%) are mostly analyzed,
whereas intermediate levels of downregulation (if obtained) are generally
overlooked. Therefore, knockdown
experiments are not very useful to obtain the complete set of experimental data
(above and below the wild-type levels of enzyme activity with the corresponding
flux) for determining reliable control coefficients.A strategy to determine flux
control coefficients from several protein levels has been developed by using
adenovirus-mediated glucose-6-phosphatase (G6Pase) overexpression under the
control of the cytomegalovirus promoter in rat hepatocytes. A 2-fold G6Pase overexpression did not alterCG6PaseGlycolysis or CGKGlycolysis (GK, glucokinase). However, if G6Pase is overexpressed by 4 folds, then CGKGlycogen-synthesis
diminished from 2.8 to 1.8 and there was a 35% lowering in glycogen synthesis [150]. However, this approach allows titration of flux only above the basal
enzyme activities found in the cell, but not below.These experimental inconveniences have been circumvented by using inducible gene
expression systems based in thelac,
Lambda, nisin, GAL, tetracycline, and other inducible promoters, in bacteria
and yeast [151, 152]. However, a problem
frequently encountered with inducible promoters is that a steady-state of
protein expression is difficult to attain [151, 152].Recently,
Jensen and Hammer described the design of synthetic promoter libraries (SPL), in
particular forL. lactis metabolic
optimization [153]. These promoters
maintain constant the array of the known consensus sequences for L. lactis gene transcription (−10 and
−35 boxes), while the nucleotide sequence between these boxes (a spacer
sequence of 17 ± 1 bp) is randomized, thus producing a set of promoters with
different transcriptional strength. These promoter libraries allow the transcription and protein expression
several folds above and below the wild-type levels of enzyme activity [153],
thus enhancing the usefulness of this approach for  MCA studies.The
control distribution of glycolysis inE.
coli and  L. lactis, as discussed
in Section 3.2 [17, 24, 27, 151],  has been determined by using the SPL
technology. SPL for  yeast, mammalian and
plant cells are also under  development [151, 152]. Certainly, the advances in genetic
engineering  in combination with MCA allow better experimental  designs for
metabolic optimization of micro-organisms of  biotechnological interest.Concluding Remarks
(1)
The frequently recurred idea of manipulating the key
enzyme or rate-limiting step (a concept based on a qualitative and rather
intuitive background) to change metabolism is incorrect. As MCA has demonstrated, flux control is shared
by multiple steps and it is not usually localized in only one step. MCA determines quantitatively the control that
a given enzyme exerts on the flux and on intermediary concentration and helps
to explain why an enzyme does or does not exert control.(2)
A metabolic pathway is manipulated to change the rate
of the end-product formation (i.e.,
the flux) or the concentration of a relevant intermediary. As it is demonstrated in many unsuccessful
experiments, it is not enough to overexpress one enzyme (the rate-limiting step)
or many arbitrarily selected sites of the pathway. MCA proposes an initial experimental analysis
that determines the structural control of the pathway and identifies the sites
(enzymes and transporters) with higher control coefficients values (i.e., targets to be manipulated). For example, if there is a system composed of
six enzymes and three of them have flux control coefficients with values of 0.2
or higher and the other three with values of 0.1 or lower, the three enzymes
with high control coefficients must be overexpressed (if a flux increase is
desired) or repressed (if flux inhibition is the objective) and not only one of
them. If one of the selected enzymes is
strongly inhibited by its product or has allosteric inhibition, the overexpression
of this enzyme might not be enough to increase the flux, as it may also be
necessary to moderately vary the product and allosteric modulator consuming
enzymes.(3)
If the aim of the researcher is a metabolite
concentration increase, which is not the end product of the pathway, MCA
suggests the overexpression of those enzymes or transporters in the supply
block with the highest control coefficients and/or the repression of those
enzymes in the demand block with the highest control coefficients. These manipulations may become complicated if
the metabolite of interest has allosteric interactions with enzymes and
transporters (inhibition and activation) of both the supply and demand blocks. It is recalled that ethanol production in
yeast and lactate and acetate production in lactobacteria do not increase by
overexpressing PFK-1, an allosteric enzyme and the presumed rate-limiting step
of glycolysis. In fact, the flux was diminished with an excessive PFK-1 overexpression. However, the analysis of these results reveals
that the F1,6BP concentration is indeed increased many times over the control
level. Another strategy for eliminating
the feedback inhibition might be the introduction of mutations on the enzymes
that are closer to the metabolite of interest.


## 5.6.1. Repression of Gene Expression

This approach is based on the in vivo modulation of the enzyme levels using the RNA
antisense technology. There are at least
three strategies to
inhibit gene expression: (a) the use of single stranded antisense
oligonucleotides, which form a double stranded RNA that might be degraded by RNAse
H; (b) target RNA degradation with catalytically active oligonucleotides, known
as ribozymes that bind to their specific RNA; and (c) RNA degradation using siRNAs
(21–23 nucleotides) [147].The RNA antisense technology was applied for control coefficient determination of the
ribulose-bisphosphate-carboxylase (Rubisco) that fixes CO2 in the
plant Calvin cycle. This enzyme considered
the rate-limiting step of the Calvin cycle and of the whole photosynthetic
process, despite its high concentration (4 mM) in the chloroplasts stroma that compensates
its low catalytic efficiency.Attempts to make Rubisco a nonlimiting step, either by modifying its catalytic efficiency
or by overexpressing it, have been unsuccessful. Stitt et
al. [148] determined the CrubiscoJphotosynthesis of tobacco plants by decreasing its activity
with DNA antisense. The plants were transformed with DNA antisense against the
mRNA of the enzyme’s small subunit, thus promoting its degradation. For Calvin cycle enzymes, the pleiotropic
effects were minimal. The results showed
that Rubisco may indeed be the photosynthesis limiting step with a CrubiscoJphotosynthesis= 0.69–0.83 when plants are exposed to high
illumination (1050 μmol quanta m-2s-1), high
humidity (85%), and low CO2 concentrations (25 Pa). However, this flux control decreases to
0.05–0.12 under moderate illumination or high CO2 levels [148]. Unfortunately, the authors did not determine
the control coefficients of the other pathway enzymes or the branches fluxes which
may be significant.As described in Section5.4, the results of the T. brucei glycolysis
modeling indicated that GLUT was the main flux control step (CGLUTJ∼ 50%), [125, 126]. This model predicted a large overcapacity for
HK, PFK-1, ALDO, GAPDH, PGAM, ENO, and PYK over the glycolytic flux leading to
low flux control coefficients [125, 126]. To validate the modeling results, the concentrations of HK, PFK-1, PGAM,
ENO, and PYK were changed with siRNAs in growing parasites [149]. These knockdown expression experiments showed
overcapacity of HK and PYK over the flux, although at lower levels than predicted
by the model. A good correlation for
PGAM and ENO was obtained between model predictions and experimental results. However, a large difference (9 folds) was
obtained for PFK-1. This discrepancy is
perhaps related to pleiotropic effects of PFK-1 downregulation, as these mutants
also displayed diminution in the activities of other enzymes (HK, ENO, and PYK).
The combination of these two approaches,
in silico modeling and in vivo experimentation, is complementary: on one
hand, modeling identifies the enzymes (out of 19 that contain the model) that
display the highest flux control coefficients, whereas in vivo experimentation validates the
accuracy of the model to establish predictions about the pathway’s behavior.


## 5.6.2. Fine Tuning of Cellular Protein Expression

The knockdown experiments described above usually yield only two experimental points
of the plot shown in Figure4: the
wild-type and the knockdown strain protein levels or enzyme activities. Thus, with
such an approach high levels of inhibition (>80%) are mostly analyzed,
whereas intermediate levels of downregulation (if obtained) are generally
overlooked. Therefore, knockdown
experiments are not very useful to obtain the complete set of experimental data
(above and below the wild-type levels of enzyme activity with the corresponding
flux) for determining reliable control coefficients.A strategy to determine flux
control coefficients from several protein levels has been developed by using
adenovirus-mediated glucose-6-phosphatase (G6Pase) overexpression under the
control of the cytomegalovirus promoter in rat hepatocytes. A 2-fold G6Pase overexpression did not alterCG6PaseGlycolysis or CGKGlycolysis (GK, glucokinase). However, if G6Pase is overexpressed by 4 folds, then CGKGlycogen-synthesis
diminished from 2.8 to 1.8 and there was a 35% lowering in glycogen synthesis [150]. However, this approach allows titration of flux only above the basal
enzyme activities found in the cell, but not below.These experimental inconveniences have been circumvented by using inducible gene
expression systems based in thelac,
Lambda, nisin, GAL, tetracycline, and other inducible promoters, in bacteria
and yeast [151, 152]. However, a problem
frequently encountered with inducible promoters is that a steady-state of
protein expression is difficult to attain [151, 152].Recently,
Jensen and Hammer described the design of synthetic promoter libraries (SPL), in
particular forL. lactis metabolic
optimization [153]. These promoters
maintain constant the array of the known consensus sequences for L. lactis gene transcription (−10 and
−35 boxes), while the nucleotide sequence between these boxes (a spacer
sequence of 17 ± 1 bp) is randomized, thus producing a set of promoters with
different transcriptional strength. These promoter libraries allow the transcription and protein expression
several folds above and below the wild-type levels of enzyme activity [153],
thus enhancing the usefulness of this approach for  MCA studies.The
control distribution of glycolysis inE.
coli and  L. lactis, as discussed
in Section 3.2 [17, 24, 27, 151],  has been determined by using the SPL
technology. SPL for  yeast, mammalian and
plant cells are also under  development [151, 152]. Certainly, the advances in genetic
engineering  in combination with MCA allow better experimental  designs for
metabolic optimization of micro-organisms of  biotechnological interest.Concluding Remarks
(1)
The frequently recurred idea of manipulating the key
enzyme or rate-limiting step (a concept based on a qualitative and rather
intuitive background) to change metabolism is incorrect. As MCA has demonstrated, flux control is shared
by multiple steps and it is not usually localized in only one step. MCA determines quantitatively the control that
a given enzyme exerts on the flux and on intermediary concentration and helps
to explain why an enzyme does or does not exert control.(2)
A metabolic pathway is manipulated to change the rate
of the end-product formation (i.e.,
the flux) or the concentration of a relevant intermediary. As it is demonstrated in many unsuccessful
experiments, it is not enough to overexpress one enzyme (the rate-limiting step)
or many arbitrarily selected sites of the pathway. MCA proposes an initial experimental analysis
that determines the structural control of the pathway and identifies the sites
(enzymes and transporters) with higher control coefficients values (i.e., targets to be manipulated). For example, if there is a system composed of
six enzymes and three of them have flux control coefficients with values of 0.2
or higher and the other three with values of 0.1 or lower, the three enzymes
with high control coefficients must be overexpressed (if a flux increase is
desired) or repressed (if flux inhibition is the objective) and not only one of
them. If one of the selected enzymes is
strongly inhibited by its product or has allosteric inhibition, the overexpression
of this enzyme might not be enough to increase the flux, as it may also be
necessary to moderately vary the product and allosteric modulator consuming
enzymes.(3)
If the aim of the researcher is a metabolite
concentration increase, which is not the end product of the pathway, MCA
suggests the overexpression of those enzymes or transporters in the supply
block with the highest control coefficients and/or the repression of those
enzymes in the demand block with the highest control coefficients. These manipulations may become complicated if
the metabolite of interest has allosteric interactions with enzymes and
transporters (inhibition and activation) of both the supply and demand blocks. It is recalled that ethanol production in
yeast and lactate and acetate production in lactobacteria do not increase by
overexpressing PFK-1, an allosteric enzyme and the presumed rate-limiting step
of glycolysis. In fact, the flux was diminished with an excessive PFK-1 overexpression. However, the analysis of these results reveals
that the F1,6BP concentration is indeed increased many times over the control
level. Another strategy for eliminating
the feedback inhibition might be the introduction of mutations on the enzymes
that are closer to the metabolite of interest.



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*Source: 597913-2008-07-08.xml*