BACKGROUND
growth and survival of microorganisms is strongly affected by environmental variables such as temperature, nutrient and oxygen availability, ph and osmolarity.
since, in natural environments, these parameters are highly dynamic, microorganisms have to cope with fluctuating, often non-optimal growth conditions.
suboptimal growth temperatures have major impacts on cell physiology including decreasing membrane fluidity and a reduced efficiency of protein synthesis and folding  <cit> .
in addition, the catalytic capacity of each enzyme in the cell decreases when the temperature is lowered.
this temperature impact can, in many cases, be described by an arrhenius equation  <cit> .
in the past decade, the response of the mesophilic yeast saccharomyces cerevisiae to suboptimal temperatures has been the focus of several studies  <cit> .
interest in this subject is motivated by the biotechnological applications of s. cerevisiae.
in particular, brewing and winemaking are two processes in which yeast is subjected to suboptimal temperatures  to obtain specific desired flavour compounds  <cit> .
moreover, its experimental accessibility to genome-scale analysis makes s. cerevisiae an attractive model organism for systems biology studies on temperature responses.
with a few exceptions  <cit> , studies on low temperature responses of s. cerevisiae have focussed on so-called cold shock experiments.
in such experiments, instantaneous exposure to low temperatures triggers a general environmental stress response in addition to temperature-specific responses  <cit> .
to investigate long-term acclimation rather than rapid adaptation to low temperature, thereby preventing a cold shock effect, growth of s. cerevisiae has been studied at  <dig> and 12°c in anaerobic glucose-limited chemostat cultures  <cit> .
since the maximum specific growth rate of s. cerevisiae at 12°c is circa sevenfold lower than at 30°c  <cit> , a low dilution rate of  <dig>  h- <dig> was used for both temperatures in this chemostat study  <cit> .
in anaerobic cultures, substrate-level phosphorylation in glycolysis is the sole mechanism for atp synthesis.
tai et al.
<cit>  observed that, despite substantially lower specific catalytic capacities of the glycolytic enzymes at 12°c as compared to 30°c, chemostat cultures maintained the same glycolytic flux at these two temperatures.
because in these chemostat cultivations the growth rate was set to be the same for both conditions , this indicated that the biomass yield was the same for both temperatures.
moreover, yeast did not compensate for the lower temperature by increased synthesis of glycolytic enzymes.
instead, metabolic regulation, i.e., regulation by changes in the concentrations of substrates, products and effectors  <cit>  was identified as the main strategy for temperature compensation.
especially for highly expressed pathways such as glycolysis, whose enzymes can account for up to 20% of the protein content of s. cerevisiae, repeated cycles of protein degradation and synthesis would represent a substantial burden.
it was therefore hypothesized that the observed dominant role of metabolic regulation represents an evolutionary adaptation to environments with frequent  temperature fluctuations  <cit> .
nevertheless, physiological studies carried out at tightly controlled constant temperatures or during very fast temperature changes  represent artificial conditions, considering that many microorganisms are exposed to circadian and seasonal temperature fluctuations in their natural habitats.
evolution in such habitats is likely to have resulted in regulatory strategies to optimize performance under dynamic temperature regimes.
analysing and understanding such strategies is a typical systems biology challenge, and requires integration of biological experiments with mathematical modelling  <cit> .
the aim of this study is to identify and understand mechanisms employed by s. cerevisiae to control glycolytic flux and intracellular metabolite levels under dynamic temperature regimes.
to this end, we investigated the impact of dynamic temperature regimes with different time constants  using a systems approach, integrating mathematical modelling and experimentation.
our results indicate that if the temperature dependencies of the catalytic capacities of enzymes in a pathway are highly similar, changes in metabolite levels during temperature changes are minimal.
RESULTS
a minimal model to describe temperature dependency of metabolic fluxes
to understand and model the impact of temperature dynamics on metabolic fluxes, it is essential to consider the influence of temperature on the kinetic parameters of enzyme catalyzed reactions.
the in vivo rate of an enzyme-catalyzed reaction depends on the concentration of the enzyme , its specific catalytic capacity , the affinities of the enzyme for substrates, products, co-factors and/or inhibitors  and the thermodynamic equilibrium constant  ).
v=e.kcat.fkp,ks,ke,s,p,e.1−Γkeq
in this rate equation, the specific format of the mechanistic kinetic function f depends on the catalytic mechanism of the reaction.
the mass-action ratio  only depends on the stoichiometry and thermodynamic properties of the reaction  <cit> .
three main questions need to be addressed when modeling the impact of temperature on metabolic networks:
<dig>  which kinetic parameters are temperature dependent?
<dig>  how can temperature dependency be described for those who are?
<dig>  can the same mechanism be applied to all enzymes?
it is well known that each enzyme has an optimum temperature at which its catalytic capacity  is maximal, while kcat decreases at values below and above the optimum temperature .
quantitative relations, describing the impact of temperature on kcat, can be established by in vitro activity measurements at different temperatures and at saturating reactant concentrations.
there are, however, only few data available on in vitro enzyme activity measurements at different temperatures for yeast glycolytic enzymes.
a recent study focused on only two different temperatures , thus precluding the derivation of a proper quantitative relation for the temperature dependency of kcat <cit> .
even when information about in vitro temperature-dependencies of enzymes was available, this would not necessarily provide an accurate reflection of the in vivo situation  <cit> .
analysis of the temperature impact on enzyme levels  needs to be done carefully, since these are intrinsically context dependent.
for example, glycolytic enzyme levels in s. cerevisiae are strongly influenced by specific growth rate  <cit> , nutrient limitation regimes  <cit>  and number of generations  <cit> .
tai et al.
<cit>  minimized these influences by growing s. cerevisiae in anaerobic chemostat cultures at  <dig> and 30°c under otherwise identical conditions.
under these conditions, the glycolytic flux was the same for both temperatures and the levels of glycolytic enzymes were found to be very similar  at both temperatures.
in the same experiments, kcat, estimated from in vitro enzyme assays, was  <dig>  ±  <dig>  fold lower at 12°c than at 30°c.
it was therefore inferred that changes in enzyme levels are not the primary regulation mechanism used by cells to, at equal flux, compensate for the loss of catalytic capacity at lower temperatures.
similar conclusions were drawn by postmus et al.
<cit> , when studying the impact of supra-optimal temperatures on the regulation of glycolytic flux in aerobically grown s. cerevisiae.
changes in temperature might also affect the equilibrium constants of reactions and the binding affinities of enzymes.
the temperature impact on the equilibrium constant keq is described by the van’t hoff equation ).
when applying this equation, it can be found that the changes of the equilibrium constants for the glycolytic reactions differ by less than twofold  for temperatures between  <dig> and 30°c .
lnkeq,2keq,1=Δhr0r1t1−1t <dig>
eq
keq values were calculated from  <cit>  considering a reference condition of  <dig>  k, i =  <dig> m and ph  <dig> .
the fold change refers to the ratio keq 12°c/keq 30°c.
based on a mechanistic description  <cit> , it can be assumed that temperature has a minor impact on the binding affinities of the enzymes, because they are a measure of the equilibrium between the enzyme and the enzyme-substrate complex.
furthermore, temperature changes within the mesophilic range  do not result in major structural alterations of the active sites of enzymes from mesophilic microorganisms  <cit> .
therefore, changes in binding affinities caused by temperature-induced structural changes are expected to be negligible.
in the mesophilic range, temperature induced changes in the glycolytic flux are therefore mainly caused by changes of kcat, because this effect is by far the largest and works in the same direction for all enzymes.
consequently, the temperature sensitivity of kcat for the different enzymes in a network will determine its overall response to dynamic temperature conditions.
this raises the key question whether the catalytic capacities of all enzymes of a pathway would have different or identical temperature dependencies.
consider for instance the following simple linear pathway where a and b are intracellular metabolites, while s and p are extracellular:
s→v1a→v2b→v3p
under steady-state conditions  all fluxes are the same, i.e.
v <dig> = v <dig> = v <dig>  this can be formally written by a system of equations , representing the steady-state balances of intracellular metabolites a and b, where n is the matrix containing the stoichiometric coefficients of the reactions.
10−110−1·v1v2v3=00↔n·v1v2v3= <dig>
taking into account that the fluxes vi can be described by rate equations of the form of equation , the system of two metabolite balances becomes, for a reference temperature :
n·e1·kcat,1t0·fka,s,a,keq,1e2·kcat,2t0·fka,kb,a,b,keq,2e3·kcat,3t0·fkb,b,keq,3= <dig>
when it is furthermore assumed that the pathway is irreversible , the concentration of p plays no role.
this set of algebraic relations can then be solved to obtain the intracellular metabolite levels at the reference temperature, for given values of the extracellular concentration of s, thus yielding relations for the intracellular levels of a and b as a function of the extracellular concentration of substrate s for the reference temperature.
it should be noted here that this conclusion is also valid for pathways containing reversible reactions, as long as the steady-state assumption is fulfilled.
assuming that the catalytic capacity of each enzyme as a function of temperature can be described by the function ri and the rate at the reference temperature, such that kcat,i=kcat,it <dig> rit and that the stoichiometry does not change with temperature  <cit> , the description of the system at a temperature t different from t <dig> becomes:
n·e1·r1t·kcat,1t0·fka,s,a,keq,1e2·r2t·kcat,2t0·fka,kb,a,b,keq,2e3·r3t·kcat,3t0·fkb,b,keq,3= <dig>
if each enzyme has its own temperature dependent function ri, the ratio between a, b and s will be different for each temperature and dependent on the parameters of the corresponding temperature function.
if, on the other hand, the temperature function of the single enzymes follow the same mechanism with the same parameters, e.g.
r <dig> = r <dig> = r <dig>  then eq.
will become equal to eq.
.
this would then imply that the relations describing the intracellular concentrations of a and b as a function of the extracellular substrate concentration are temperature independent.
the differences between these two scenarios can be tested in vivo to provide insight into the temperature dependency of enzymes.
considering the simple network described above, we now assume a dynamic temperature situation in which the concentration of s is high and non-limiting and thus fluxes v <dig> to v <dig> are at their maximum values.
if the catalytic capacities of the enzymes in a pathway or network share the same temperature dependency, changes in temperature will cause all enzyme activities to change with the same factor.
in such a scenario, no changes in intracellular metabolite levels will occur and thus the cells maintain complete homeostasis during temperature changes, without the need to adjust enzyme levels.
if, however, for a substrate-limited system  it is experimentally imposed that the fluxes remain the same even at lower temperature , s as well as the metabolite concentrations a and b will change to compensate for the lower enzymatic capacities.
in silico evaluation of different kcat -temperature relationships in yeast glycolysis
to evaluate the impact of different or identical temperature dependencies of the kcat of the enzymes in yeast glycolysis, simulations were carried out with a detailed kinetic model of this pathway developed by teusink et al.
<cit> .
several modifications were made to the published version of the model to, amongst others, account for biomass growth and to include temperature dependency of enzyme capacities .
using this model different substrate feeding regimes and temperature profiles were simulated to distinguish between the effects of temperature and of extracellular glucose concentration on glycolytic flux.
this distinction is especially important for glucose-limited conditions, where the glycolytic flux is highly correlated with the extracellular glucose concentration because, as shown by  <cit>  and  <cit> , glucose transport is a key growth-rate-controlling process.
therefore, in glucose-limited chemostat cultures, temperature dynamics will affect the extracellular glucose concentration via changes in glycolytic capacity.
these changes in the extracellular glucose concentration will then propagate through all intracellular metabolite levels, yielding temperature-independent relations between intracellular metabolite and extracellular glucose levels.
if, on the other hand, a different relationship between intracellular metabolite levels and extracellular glucose concentrations is observed for different temperature profiles, this would indicate that the temperature impact on kcat differs for the different enzymes in yeast glycolysis .
two distinct rounds of simulations with different substrate feeding regimes were performed to evaluate the impact of the parameters of the temperature-dependent function ri on the intracellular metabolite profiles.
in the first round, the temperature sensitivity of one of the glycolytic enzymes was set to be different from all others.
in the second round, temperature sensitivities were set to be identical for all enzymes, implying that a decrease in temperature resulted in the same relative decrease of kcat for all enzymes.
in both rounds, simulations were performed for circadian temperature cycles, linear temperature shifts starting from 30°c steady-state conditions and batch cultures grown at  <dig>   <dig>   <dig> and 30°c .
all simulations resulted in trends between intracellular metabolite levels and the extracellular glucose concentration.
as expected, different temperature profiles or substrate-feeding regimes caused different trends when at least one of the enzymes was set to have a different temperature sensitivity compared to the others.
for instance, when the temperature sensitivity of the kcat of glyceraldehyde 3-phosphate dehydrogenase  was set to be two fold lower than that of the other glycolytic enzymes, the simulated values of the intracellular g6p, f6p and fbp levels under glucose-excess conditions clearly decreased with decreasing temperature .
differences were less pronounced for the model simulations of glucose-limited conditions, where metabolites upstream of tdh  showed no differences and only fbp was mildly affected by the change in temperature sensitivity.
furthermore fbp levels correlated poorly with the extracellular glucose concentration, especially for the fastest temperature shifts applied .
similar results were obtained when changing the sensitivity of the other glycolytic enzymes , indicating that this observation is not related to the flux towards the reaction, nor to its kinetic mechanism or reversibility.
it was noticed that only metabolites upstream of the reaction with the different temperature sensitivity displayed such deviating trends.
these observations are consistent with experimental and modeling results of  <cit>  on the impact of changes in the abundance of single enzymes in metabolic pathways and with the ‘passive network mechanism’ proposed by these authors.
when temperature sensitivities were assumed to be identical for all glycolytic enzymes, the intracellular concentrations of glycolytic intermediates under glucose-excess conditions were predicted to be temperature independent .
conversely, simulations of glucose-limited conditions revealed strong changes of intracellular metabolite concentrations during the temperature shifts.
the range of intracellular levels was broader than in the previous simulation .
nevertheless, because the temperature sensitivity was set to be identical for all enzymes, intracellular metabolite concentrations showed highly similar correlations with the extracellular glucose concentration, irrespective of the simulated temperature profile.
the results of these simulations agree with the results obtained with the simple example network , thus showing that model predictions are independent of the assumed kinetic mechanisms of the enzymes involved, as long as the assumption of temperature independent ki holds true.
therefore, experimental analysis of the relations between the extracellular glucose concentration and intracellular metabolite levels for different cultivation conditions and temperature regimes should resolve the question whether or not all enzymes in a pathway share the same kcat -temperature relationship.
although based on model simulations the major differences between the two hypotheses are expected in glucose-excess conditions, in vivo there might be more than one enzyme with significantly different temperature dependency.
therefore, the deviating trends of intracellular metabolite levels simulated in glucose-limited conditions compared to glucose-excess conditions might be augmented.
experimental analysis under both conditions is important to decipher and quantify the temperature dependency of the glycolytic enzymes.
experimental evaluation of model predictions
to experimentally investigate kcat -temperature relationships in yeast glycolysis, anaerobic cultures were grown under different substrate feeding regimes and dynamic temperature conditions.
the experimental setups used included batch cultures at  <dig>   <dig>   <dig> and 30°c, to evaluate the temperature impact on intracellular metabolite levels under glucose excess conditions ) and different sets of dynamic temperature shifts between  <dig> and 30°c performed in glucose-limited chemostat cultures.
these dynamic experiments comprised short term  linear temperature shifts  and  applied to steady-state cultures at  <dig> and 30°c  and sinoidal circadian temperature cycles  with  <dig> h frequency .
experiments lts <dig> and lts <dig> aimed at understanding if different pre-cultivation temperatures would affect the metabolic response to temperature shifts.
the different timescale of the temperature perturbations between lts and ctc allowed to better discriminate between impact of temperature and substrate concentration .
the co <dig> production rate was monitored on-line during all experiments since, in anaerobic cultures, it provides an accurate measure for  glycolytic flux.
in vitro enzyme activity assays were performed during ctc cultivation, since this setup had the slowest temperature dynamics and, consequently, the highest chance of hierarchical regulation of the glycolytic flux .
nevertheless, levels of glycolytic enzymes did not significantly change during the temperature cycles .
this observation, together with previous results  <cit> , confirms that temperature changes have negligible impact on glycolytic enzyme levels in s. cerevisiae.
on the other hand, intracellular metabolite levels and extracellular glucose concentrations showed a dynamic behavior in the ctc and lts experiments .
.
in the sbr experiments, glucose was present in excess, and therefore the glycolytic flux depended exclusively on the cultivation temperature, through its impact on kcat.
even though the glycolytic flux in batch cultures was observed to be six-fold lower at 12°c than at 30°c, intracellular metabolite levels were independent of the growth temperature .
when temperature dynamics were applied to anaerobic glucose-limited chemostat cultures , the residual glucose concentration was observed to increase with decreasing temperature as response to a decrease of the glucose transport capacity.
as a result, the metabolite profiles show the inverse dynamics when compared to the temperature profiles applied to the chemostat cultivations .
when the intracellular metabolite levels, measured during the lts and ctc experiments, were plotted in one graph as a function of the residual glucose concentration, a single relation between metabolite level and residual glucose was obtained .
it can be inferred from these results that the metabolic response was independent of the initial steady-state temperature  or the dynamics of the temperature perturbation applied, indicating that hierarchical regulation of yeast glycolytic flux does not play a significant role during temperature dynamics.
furthermore, based on the in silico evaluation of different scenarios, these results support the notion that all glycolytic enzymes in s. cerevisiae share a similar temperature-kcat relationship.
discussion
considering that chemical reactions in aqueous solutions have activation energies between  <dig> and  <dig> kj.mol- <dig>  it can be estimated that reaction rates change by two fold for every 10°c temperature change  <cit> .
however, temperature effects on individual enzyme-catalysed reactions can deviate substantially from this ‘rule of thumb’, for example due to the impact of temperature on protein structure.
as illustrated with a simple linear metabolic pathway , different temperature dependencies of enzyme reactions inevitably result in  changes in concentrations of pathway metabolites.
similar changes in metabolite levels are observed when expression levels of individual enzymes in a pathway are modified  <cit> .
hierarchical regulation, i.e.
regulation at the level of enzyme synthesis  <cit> , would then be needed to restore and maintain homeostasis.
previous in vitro assays in cell extracts, performed at  <dig> and 30°c, suggested large differences in temperature dependency for the ten glycolytic enzymes in s. cerevisiae <cit> .
however, in vitro studies with optimized assays, in which parameters such as ph and concentrations of salts, cofactors and effectors differ for each enzyme, are not representative for the intracellular environment  <cit> .
the differences in, among others, protein content, osmotic pressure, substrate diffusion between the in vitro and in vivo conditions might lead to different flux versus temperature relationships.
to avoid the inherent problems of in vitro studies on enzyme kinetics, we developed a novel systems biology approach for analyzing kinetic regulation strategies under temperature dynamics.
by combining in silico simulation of different strategies with experimental analysis of metabolite and substrate concentrations under various controlled temperature and substrate-feeding regimes, regulation strategies could, for the first time, be analyzed without relying on kinetic parameters derived from in vitro experiments.
the in silico simulations predicted that similar temperature dependencies of the kcat of all glycolytic enzymes should result in a single relation between metabolite level and residual substrate concentration for each metabolite, independent of temperature.
consequently, in batch cultures growing at saturating substrate concentrations, intracellular concentrations of glycolytic intermediates should be independent of the growth temperature.
in glucose-limited chemostat cultures, each metabolite level is then predicted to solely depend on the residual glucose concentration and not on the temperature as such .
experimental results obtained under conditions of glucose excess, were consistent with this scenario and could not be reconciled with the alternative scenario in which temperature dependencies of the kcat values of individual glycolytic enzymes were different.
although the experimental results of metabolite levels versus residual glucose for the glucose limited chemostat experiments  showed similar trends as the model simulations, the experimental errors of the metabolite data did not allow discriminating between the two simulated scenarios .
however, if several glycolytic enzymes have different temperature sensitivities, the differences should be larger.
unfortunately, simulations in which several glycolytic enzymes have different temperature sensitivities did not result in a stable model.
all simulations were carried out using the model parameters published in  <cit> .
it should be realized, however, that different initial conditions, in our case anaerobic glucose-limited chemostat cultures at  <dig> and 30°c, could have resulted in different expression levels of glycolytic isoenzymes, which could have led to differences in enzyme kinetic properties in both conditions.
a genome wide transcriptome analysis of cells cultivated under both conditions  <cit>  did not provide indications for significant differences in the expression of glycolytic isoenzymes.
nevertheless, changes were observed in the expression levels of the different hexose transporters between the  <dig> and 30°c chemostat cultivations.
determination of the glucose transport kinetics for both conditions indeed showed that the glucose transport capacity of cells grown in 12°c chemostats was higher than that of cells grown at 30°c  <cit> .
changes in the kinetics of glucose transport could have had a repercussion on the metabolite profiles as a function of the residual glucose concentration between shifts lts <dig> and lts <dig>  nevertheless, it was measured that the increase in the kcat of glucose transport at 12°c was coupled to an increase in the glucose saturation constant , in such a way that the ratio ks/kcat is not significantly different for the two conditions.
moreover, the increase in glucose transport capacity observed for the 12°c chemostat  is significantly lower than the decrease in glucose transport capacity caused by the temperature decrease .
considering the similar ks/kcat ratio and the limited difference in kcat at 30°c for both conditions, the effect must have been small in our experiments.
although this study was focused on yeast glycolysis, pentose phosphate pathway  metabolites were also found to correlate primarily with extracellular glucose concentration rather than with the temperature.
conversely, tricarboxylic acid pathway  and storage carbohydrate-related metabolites showed a different behavior, as their levels seemed to be primarily dependent on the initial steady-state temperature .
it should be noted that under anaerobic conditions, the tca, ppp and storage metabolism fluxes are generally much lower than the glycolytic flux  <cit> .
therefore, changes in metabolites from these pathways will be slower under dynamic conditions.
in the sbr experiments no significant difference was observed in the tca pathway metabolite levels at different temperatures.
this was likely due to the higher turnover times , rather than different temperature sensitivities.
levels of precursors of storage carbohydrates  were too low in glucose-excess conditions to allow a good analysis of the temperature impact in this pathway.
however, t6p levels under glucose limited conditions indicate a different regulation mechanism of trehalose-6-phosphate synthase or trehalose-6-phosphate phosphatase compared to glycolytic enzymes.
further model developments and experimental investigations should help to determine if the differences observed for the tca and storage carbohydrate metabolism are a consequence of transcriptional regulation , higher turnover times or significantly different temperature sensitivities.
analyzing the correlation between residual substrate levels and intracellular metabolite concentrations in different temperature conditions might enable to pinpoint which metabolic pathways are the most sensible to temperature perturbations and likely to be relevant in the overall response of s. cerevisiae to temperature perturbations.
evolutionary ‘synchronization’ of the temperature dependencies of the catalytic capacities of enzymes in a metabolic pathway, may confer selective advantages to microorganisms that are subjected to frequent temperature changes.
firstly, changes of metabolite levels in response to temperature changes are minimized, thereby avoiding the need for energetically costly cycles of de novo synthesis and degradation of enzymes.
this preservation of homeostasis may be particularly important for central metabolism, of which intermediates serve as precursors for several biosynthetic pathways.
secondly, based on metabolic control analysis, it can be inferred that this minimization of changes in metabolite concentrations causes pathway fluxes to be minimally sensitive to temperature variations .
recent studies on temperature as an evolutionary pressure indicate that temperature optima for growth are a key factor for survival of sympatric strains  <cit> .
our results indicate that, in addition to temperature optima, microbial strategies for kinetic adaptation to temperature dynamics  may play a key role in determining microbial fitness in natural environments.
further research should reveal whether microorganisms evolved in environments with a steady temperature  show a different kinetic regulatory strategy than found for glycolysis in s. cerevisiae.
CONCLUSIONS
in view of their size, microorganisms are intrinsically unable to control their temperature.
temperature dynamics in natural environments therefore force microorganisms to continually adapt to temperature changes.
in the present study, the glycolytic pathway of s. cerevisiae was used as a model to study kinetic regulation strategies of organisms in response to temperature dynamics.
by combining both modeling and experimental results we obtained strong indications that the temperature dependencies of the catalytic capacities of yeast glycolytic enzymes are highly similar under in vivo conditions.
these similarities allow the cells to maintain their homeostasis during circadian temperature cycles, thereby avoiding extensive changes in enzyme levels and minimizing the temperature impact on the growth rate.
these results provide new insights in the robustness of yeast central carbon metabolism and open the gate for new studies on temperature as a key parameter for evolution of sympatric strains.

 growth and survival of microorganisms is strongly affected by environmental variables such as temperature, nutrient and oxygen availability, ph and osmolarity. since, in natural environments, these parameters are highly dynamic, microorganisms have to cope with fluctuating, often non-optimal growth conditions. suboptimal growth temperatures have major impacts on cell physiology including decreasing membrane fluidity and a reduced efficiency of protein synthesis and folding. in addition, the catalytic capacity of each enzyme in the cell decreases when the temperature is lowered. this temperature impact can, in many cases, be described by an arrhenius equation. in the past decade, the response of the mesophilic yeast saccharomyces cerevisiae to suboptimal temperatures has been the focus of several studies. interest in this subject is motivated by the biotechnological applications of s. cerevisiae. in particular, brewing and winemaking are two processes in which yeast is subjected to suboptimal temperatures to obtain specific desired flavour compounds. moreover, its experimental accessibility to genome-scale analysis makes s. cerevisiae an attractive model organism for systems biology studies on temperature responses. with a few exceptions, studies on low temperature responses of s. cerevisiae have focussed on so-called cold shock experiments. in such experiments, instantaneous exposure to low temperatures triggers a general environmental stress response in addition to temperature-specific responses. to investigate long-term acclimation rather than rapid adaptation to low temperature, thereby preventing a cold shock effect, growth of s. cerevisiae has been studied at and 12°c in anaerobic glucose-limited chemostat cultures. since the maximum specific growth rate of s. cerevisiae at 12°c is circa sevenfold lower than at 30°c, a low dilution rate of h- was used for both temperatures in this chemostat study. in anaerobic cultures, substrate-level phosphorylation in glycolysis is the sole mechanism for atp synthesis. tai et al. observed that, despite substantially lower specific catalytic capacities of the glycolytic enzymes at 12°c as compared to 30°c, chemostat cultures maintained the same glycolytic flux at these two temperatures. because in these chemostat cultivations the growth rate was set to be the same for both conditions, this indicated that the biomass yield was the same for both temperatures. moreover, yeast did not compensate for the lower temperature by increased synthesis of glycolytic enzymes. instead, metabolic regulation, i.e., regulation by changes in the concentrations of substrates, products and effectors was identified as the main strategy for temperature compensation. especially for highly expressed pathways such as glycolysis, whose enzymes can account for up to 20% of the protein content of s. cerevisiae, repeated cycles of protein degradation and synthesis would represent a substantial burden. it was therefore hypothesized that the observed dominant role of metabolic regulation represents an evolutionary adaptation to environments with frequent temperature fluctuations. nevertheless, physiological studies carried out at tightly controlled constant temperatures or during very fast temperature changes represent artificial conditions, considering that many microorganisms are exposed to circadian and seasonal temperature fluctuations in their natural habitats. evolution in such habitats is likely to have resulted in regulatory strategies to optimize performance under dynamic temperature regimes. analysing and understanding such strategies is a typical systems biology challenge, and requires integration of biological experiments with mathematical modelling. the aim of this study is to identify and understand mechanisms employed by s. cerevisiae to control glycolytic flux and intracellular metabolite levels under dynamic temperature regimes. to this end, we investigated the impact of dynamic temperature regimes with different time constants using a systems approach, integrating mathematical modelling and experimentation. our results indicate that if the temperature dependencies of the catalytic capacities of enzymes in a pathway are highly similar, changes in metabolite levels during temperature changes are minimal.  a minimal model to describe temperature dependency of metabolic fluxes to understand and model the impact of temperature dynamics on metabolic fluxes, it is essential to consider the influence of temperature on the kinetic parameters of enzyme catalyzed reactions. the in vivo rate of an enzyme-catalyzed reaction depends on the concentration of the enzyme, its specific catalytic capacity, the affinities of the enzyme for substrates, products, co-factors and/or inhibitors and the thermodynamic equilibrium constant ). v=e.kcat.fkp,ks,ke,s,p,e.1−Γkeq in this rate equation, the specific format of the mechanistic kinetic function f depends on the catalytic mechanism of the reaction. the mass-action ratio only depends on the stoichiometry and thermodynamic properties of the reaction. three main questions need to be addressed when modeling the impact of temperature on metabolic networks: which kinetic parameters are temperature dependent? how can temperature dependency be described for those who are? can the same mechanism be applied to all enzymes? it is well known that each enzyme has an optimum temperature at which its catalytic capacity is maximal, while kcat decreases at values below and above the optimum temperature. quantitative relations, describing the impact of temperature on kcat, can be established by in vitro activity measurements at different temperatures and at saturating reactant concentrations. there are, however, only few data available on in vitro enzyme activity measurements at different temperatures for yeast glycolytic enzymes. a recent study focused on only two different temperatures, thus precluding the derivation of a proper quantitative relation for the temperature dependency of kcat. even when information about in vitro temperature-dependencies of enzymes was available, this would not necessarily provide an accurate reflection of the in vivo situation. analysis of the temperature impact on enzyme levels needs to be done carefully, since these are intrinsically context dependent. for example, glycolytic enzyme levels in s. cerevisiae are strongly influenced by specific growth rate, nutrient limitation regimes and number of generations. tai et al. minimized these influences by growing s. cerevisiae in anaerobic chemostat cultures at and 30°c under otherwise identical conditions. under these conditions, the glycolytic flux was the same for both temperatures and the levels of glycolytic enzymes were found to be very similar at both temperatures. in the same experiments, kcat, estimated from in vitro enzyme assays, was ± fold lower at 12°c than at 30°c. it was therefore inferred that changes in enzyme levels are not the primary regulation mechanism used by cells to, at equal flux, compensate for the loss of catalytic capacity at lower temperatures. similar conclusions were drawn by postmus et al., when studying the impact of supra-optimal temperatures on the regulation of glycolytic flux in aerobically grown s. cerevisiae. changes in temperature might also affect the equilibrium constants of reactions and the binding affinities of enzymes. the temperature impact on the equilibrium constant keq is described by the van’t hoff equation ). when applying this equation, it can be found that the changes of the equilibrium constants for the glycolytic reactions differ by less than twofold for temperatures between and 30°c. lnkeq,2keq,1=Δhr0r1t1−1t eq keq values were calculated from considering a reference condition of k, i = m and ph. the fold change refers to the ratio keq 12°c/keq 30°c. based on a mechanistic description, it can be assumed that temperature has a minor impact on the binding affinities of the enzymes, because they are a measure of the equilibrium between the enzyme and the enzyme-substrate complex. furthermore, temperature changes within the mesophilic range do not result in major structural alterations of the active sites of enzymes from mesophilic microorganisms. therefore, changes in binding affinities caused by temperature-induced structural changes are expected to be negligible. in the mesophilic range, temperature induced changes in the glycolytic flux are therefore mainly caused by changes of kcat, because this effect is by far the largest and works in the same direction for all enzymes. consequently, the temperature sensitivity of kcat for the different enzymes in a network will determine its overall response to dynamic temperature conditions. this raises the key question whether the catalytic capacities of all enzymes of a pathway would have different or identical temperature dependencies. consider for instance the following simple linear pathway where a and b are intracellular metabolites, while s and p are extracellular: s→v1a→v2b→v3p under steady-state conditions all fluxes are the same, i.e. v = v = v this can be formally written by a system of equations, representing the steady-state balances of intracellular metabolites a and b, where n is the matrix containing the stoichiometric coefficients of the reactions. 10−110−1·v1v2v3=00↔n·v1v2v3= taking into account that the fluxes vi can be described by rate equations of the form of equation, the system of two metabolite balances becomes, for a reference temperature: n·e1·kcat,1t0·fka,s,a,keq,1e2·kcat,2t0·fka,kb,a,b,keq,2e3·kcat,3t0·fkb,b,keq,3= when it is furthermore assumed that the pathway is irreversible, the concentration of p plays no role. this set of algebraic relations can then be solved to obtain the intracellular metabolite levels at the reference temperature, for given values of the extracellular concentration of s, thus yielding relations for the intracellular levels of a and b as a function of the extracellular concentration of substrate s for the reference temperature. it should be noted here that this conclusion is also valid for pathways containing reversible reactions, as long as the steady-state assumption is fulfilled. assuming that the catalytic capacity of each enzyme as a function of temperature can be described by the function ri and the rate at the reference temperature, such that kcat,i=kcat,it rit and that the stoichiometry does not change with temperature, the description of the system at a temperature t different from t becomes: n·e1·r1t·kcat,1t0·fka,s,a,keq,1e2·r2t·kcat,2t0·fka,kb,a,b,keq,2e3·r3t·kcat,3t0·fkb,b,keq,3= if each enzyme has its own temperature dependent function ri, the ratio between a, b and s will be different for each temperature and dependent on the parameters of the corresponding temperature function. if, on the other hand, the temperature function of the single enzymes follow the same mechanism with the same parameters, e.g. r = r = r then eq. will become equal to eq.. this would then imply that the relations describing the intracellular concentrations of a and b as a function of the extracellular substrate concentration are temperature independent. the differences between these two scenarios can be tested in vivo to provide insight into the temperature dependency of enzymes. considering the simple network described above, we now assume a dynamic temperature situation in which the concentration of s is high and non-limiting and thus fluxes v to v are at their maximum values. if the catalytic capacities of the enzymes in a pathway or network share the same temperature dependency, changes in temperature will cause all enzyme activities to change with the same factor. in such a scenario, no changes in intracellular metabolite levels will occur and thus the cells maintain complete homeostasis during temperature changes, without the need to adjust enzyme levels. if, however, for a substrate-limited system it is experimentally imposed that the fluxes remain the same even at lower temperature, s as well as the metabolite concentrations a and b will change to compensate for the lower enzymatic capacities. in silico evaluation of different kcat -temperature relationships in yeast glycolysis to evaluate the impact of different or identical temperature dependencies of the kcat of the enzymes in yeast glycolysis, simulations were carried out with a detailed kinetic model of this pathway developed by teusink et al.. several modifications were made to the published version of the model to, amongst others, account for biomass growth and to include temperature dependency of enzyme capacities. using this model different substrate feeding regimes and temperature profiles were simulated to distinguish between the effects of temperature and of extracellular glucose concentration on glycolytic flux. this distinction is especially important for glucose-limited conditions, where the glycolytic flux is highly correlated with the extracellular glucose concentration because, as shown by and, glucose transport is a key growth-rate-controlling process. therefore, in glucose-limited chemostat cultures, temperature dynamics will affect the extracellular glucose concentration via changes in glycolytic capacity. these changes in the extracellular glucose concentration will then propagate through all intracellular metabolite levels, yielding temperature-independent relations between intracellular metabolite and extracellular glucose levels. if, on the other hand, a different relationship between intracellular metabolite levels and extracellular glucose concentrations is observed for different temperature profiles, this would indicate that the temperature impact on kcat differs for the different enzymes in yeast glycolysis. two distinct rounds of simulations with different substrate feeding regimes were performed to evaluate the impact of the parameters of the temperature-dependent function ri on the intracellular metabolite profiles. in the first round, the temperature sensitivity of one of the glycolytic enzymes was set to be different from all others. in the second round, temperature sensitivities were set to be identical for all enzymes, implying that a decrease in temperature resulted in the same relative decrease of kcat for all enzymes. in both rounds, simulations were performed for circadian temperature cycles, linear temperature shifts starting from 30°c steady-state conditions and batch cultures grown at and 30°c. all simulations resulted in trends between intracellular metabolite levels and the extracellular glucose concentration. as expected, different temperature profiles or substrate-feeding regimes caused different trends when at least one of the enzymes was set to have a different temperature sensitivity compared to the others. for instance, when the temperature sensitivity of the kcat of glyceraldehyde 3-phosphate dehydrogenase was set to be two fold lower than that of the other glycolytic enzymes, the simulated values of the intracellular g6p, f6p and fbp levels under glucose-excess conditions clearly decreased with decreasing temperature. differences were less pronounced for the model simulations of glucose-limited conditions, where metabolites upstream of tdh showed no differences and only fbp was mildly affected by the change in temperature sensitivity. furthermore fbp levels correlated poorly with the extracellular glucose concentration, especially for the fastest temperature shifts applied. similar results were obtained when changing the sensitivity of the other glycolytic enzymes, indicating that this observation is not related to the flux towards the reaction, nor to its kinetic mechanism or reversibility. it was noticed that only metabolites upstream of the reaction with the different temperature sensitivity displayed such deviating trends. these observations are consistent with experimental and modeling results of on the impact of changes in the abundance of single enzymes in metabolic pathways and with the ‘passive network mechanism’ proposed by these authors. when temperature sensitivities were assumed to be identical for all glycolytic enzymes, the intracellular concentrations of glycolytic intermediates under glucose-excess conditions were predicted to be temperature independent. conversely, simulations of glucose-limited conditions revealed strong changes of intracellular metabolite concentrations during the temperature shifts. the range of intracellular levels was broader than in the previous simulation. nevertheless, because the temperature sensitivity was set to be identical for all enzymes, intracellular metabolite concentrations showed highly similar correlations with the extracellular glucose concentration, irrespective of the simulated temperature profile. the results of these simulations agree with the results obtained with the simple example network, thus showing that model predictions are independent of the assumed kinetic mechanisms of the enzymes involved, as long as the assumption of temperature independent ki holds true. therefore, experimental analysis of the relations between the extracellular glucose concentration and intracellular metabolite levels for different cultivation conditions and temperature regimes should resolve the question whether or not all enzymes in a pathway share the same kcat -temperature relationship. although based on model simulations the major differences between the two hypotheses are expected in glucose-excess conditions, in vivo there might be more than one enzyme with significantly different temperature dependency. therefore, the deviating trends of intracellular metabolite levels simulated in glucose-limited conditions compared to glucose-excess conditions might be augmented. experimental analysis under both conditions is important to decipher and quantify the temperature dependency of the glycolytic enzymes. experimental evaluation of model predictions to experimentally investigate kcat -temperature relationships in yeast glycolysis, anaerobic cultures were grown under different substrate feeding regimes and dynamic temperature conditions. the experimental setups used included batch cultures at and 30°c, to evaluate the temperature impact on intracellular metabolite levels under glucose excess conditions ) and different sets of dynamic temperature shifts between and 30°c performed in glucose-limited chemostat cultures. these dynamic experiments comprised short term linear temperature shifts and applied to steady-state cultures at and 30°c and sinoidal circadian temperature cycles with h frequency. experiments lts and lts aimed at understanding if different pre-cultivation temperatures would affect the metabolic response to temperature shifts. the different timescale of the temperature perturbations between lts and ctc allowed to better discriminate between impact of temperature and substrate concentration. the co production rate was monitored on-line during all experiments since, in anaerobic cultures, it provides an accurate measure for glycolytic flux. in vitro enzyme activity assays were performed during ctc cultivation, since this setup had the slowest temperature dynamics and, consequently, the highest chance of hierarchical regulation of the glycolytic flux. nevertheless, levels of glycolytic enzymes did not significantly change during the temperature cycles. this observation, together with previous results, confirms that temperature changes have negligible impact on glycolytic enzyme levels in s. cerevisiae. on the other hand, intracellular metabolite levels and extracellular glucose concentrations showed a dynamic behavior in the ctc and lts experiments.. in the sbr experiments, glucose was present in excess, and therefore the glycolytic flux depended exclusively on the cultivation temperature, through its impact on kcat. even though the glycolytic flux in batch cultures was observed to be six-fold lower at 12°c than at 30°c, intracellular metabolite levels were independent of the growth temperature. when temperature dynamics were applied to anaerobic glucose-limited chemostat cultures, the residual glucose concentration was observed to increase with decreasing temperature as response to a decrease of the glucose transport capacity. as a result, the metabolite profiles show the inverse dynamics when compared to the temperature profiles applied to the chemostat cultivations. when the intracellular metabolite levels, measured during the lts and ctc experiments, were plotted in one graph as a function of the residual glucose concentration, a single relation between metabolite level and residual glucose was obtained. it can be inferred from these results that the metabolic response was independent of the initial steady-state temperature or the dynamics of the temperature perturbation applied, indicating that hierarchical regulation of yeast glycolytic flux does not play a significant role during temperature dynamics. furthermore, based on the in silico evaluation of different scenarios, these results support the notion that all glycolytic enzymes in s. cerevisiae share a similar temperature-kcat relationship. discussion considering that chemical reactions in aqueous solutions have activation energies between and kj.mol- it can be estimated that reaction rates change by two fold for every 10°c temperature change. however, temperature effects on individual enzyme-catalysed reactions can deviate substantially from this ‘rule of thumb’, for example due to the impact of temperature on protein structure. as illustrated with a simple linear metabolic pathway, different temperature dependencies of enzyme reactions inevitably result in changes in concentrations of pathway metabolites. similar changes in metabolite levels are observed when expression levels of individual enzymes in a pathway are modified. hierarchical regulation, i.e. regulation at the level of enzyme synthesis, would then be needed to restore and maintain homeostasis. previous in vitro assays in cell extracts, performed at and 30°c, suggested large differences in temperature dependency for the ten glycolytic enzymes in s. cerevisiae. however, in vitro studies with optimized assays, in which parameters such as ph and concentrations of salts, cofactors and effectors differ for each enzyme, are not representative for the intracellular environment. the differences in, among others, protein content, osmotic pressure, substrate diffusion between the in vitro and in vivo conditions might lead to different flux versus temperature relationships. to avoid the inherent problems of in vitro studies on enzyme kinetics, we developed a novel systems biology approach for analyzing kinetic regulation strategies under temperature dynamics. by combining in silico simulation of different strategies with experimental analysis of metabolite and substrate concentrations under various controlled temperature and substrate-feeding regimes, regulation strategies could, for the first time, be analyzed without relying on kinetic parameters derived from in vitro experiments. the in silico simulations predicted that similar temperature dependencies of the kcat of all glycolytic enzymes should result in a single relation between metabolite level and residual substrate concentration for each metabolite, independent of temperature. consequently, in batch cultures growing at saturating substrate concentrations, intracellular concentrations of glycolytic intermediates should be independent of the growth temperature. in glucose-limited chemostat cultures, each metabolite level is then predicted to solely depend on the residual glucose concentration and not on the temperature as such. experimental results obtained under conditions of glucose excess, were consistent with this scenario and could not be reconciled with the alternative scenario in which temperature dependencies of the kcat values of individual glycolytic enzymes were different. although the experimental results of metabolite levels versus residual glucose for the glucose limited chemostat experiments showed similar trends as the model simulations, the experimental errors of the metabolite data did not allow discriminating between the two simulated scenarios. however, if several glycolytic enzymes have different temperature sensitivities, the differences should be larger. unfortunately, simulations in which several glycolytic enzymes have different temperature sensitivities did not result in a stable model. all simulations were carried out using the model parameters published in. it should be realized, however, that different initial conditions, in our case anaerobic glucose-limited chemostat cultures at and 30°c, could have resulted in different expression levels of glycolytic isoenzymes, which could have led to differences in enzyme kinetic properties in both conditions. a genome wide transcriptome analysis of cells cultivated under both conditions did not provide indications for significant differences in the expression of glycolytic isoenzymes. nevertheless, changes were observed in the expression levels of the different hexose transporters between the and 30°c chemostat cultivations. determination of the glucose transport kinetics for both conditions indeed showed that the glucose transport capacity of cells grown in 12°c chemostats was higher than that of cells grown at 30°c. changes in the kinetics of glucose transport could have had a repercussion on the metabolite profiles as a function of the residual glucose concentration between shifts lts and lts nevertheless, it was measured that the increase in the kcat of glucose transport at 12°c was coupled to an increase in the glucose saturation constant, in such a way that the ratio ks/kcat is not significantly different for the two conditions. moreover, the increase in glucose transport capacity observed for the 12°c chemostat is significantly lower than the decrease in glucose transport capacity caused by the temperature decrease. considering the similar ks/kcat ratio and the limited difference in kcat at 30°c for both conditions, the effect must have been small in our experiments. although this study was focused on yeast glycolysis, pentose phosphate pathway metabolites were also found to correlate primarily with extracellular glucose concentration rather than with the temperature. conversely, tricarboxylic acid pathway and storage carbohydrate-related metabolites showed a different behavior, as their levels seemed to be primarily dependent on the initial steady-state temperature. it should be noted that under anaerobic conditions, the tca, ppp and storage metabolism fluxes are generally much lower than the glycolytic flux. therefore, changes in metabolites from these pathways will be slower under dynamic conditions. in the sbr experiments no significant difference was observed in the tca pathway metabolite levels at different temperatures. this was likely due to the higher turnover times, rather than different temperature sensitivities. levels of precursors of storage carbohydrates were too low in glucose-excess conditions to allow a good analysis of the temperature impact in this pathway. however, t6p levels under glucose limited conditions indicate a different regulation mechanism of trehalose-6-phosphate synthase or trehalose-6-phosphate phosphatase compared to glycolytic enzymes. further model developments and experimental investigations should help to determine if the differences observed for the tca and storage carbohydrate metabolism are a consequence of transcriptional regulation, higher turnover times or significantly different temperature sensitivities. analyzing the correlation between residual substrate levels and intracellular metabolite concentrations in different temperature conditions might enable to pinpoint which metabolic pathways are the most sensible to temperature perturbations and likely to be relevant in the overall response of s. cerevisiae to temperature perturbations. evolutionary ‘synchronization’ of the temperature dependencies of the catalytic capacities of enzymes in a metabolic pathway, may confer selective advantages to microorganisms that are subjected to frequent temperature changes. firstly, changes of metabolite levels in response to temperature changes are minimized, thereby avoiding the need for energetically costly cycles of de novo synthesis and degradation of enzymes. this preservation of homeostasis may be particularly important for central metabolism, of which intermediates serve as precursors for several biosynthetic pathways. secondly, based on metabolic control analysis, it can be inferred that this minimization of changes in metabolite concentrations causes pathway fluxes to be minimally sensitive to temperature variations. recent studies on temperature as an evolutionary pressure indicate that temperature optima for growth are a key factor for survival of sympatric strains. our results indicate that, in addition to temperature optima, microbial strategies for kinetic adaptation to temperature dynamics may play a key role in determining microbial fitness in natural environments. further research should reveal whether microorganisms evolved in environments with a steady temperature show a different kinetic regulatory strategy than found for glycolysis in s. cerevisiae.  in view of their size, microorganisms are intrinsically unable to control their temperature. temperature dynamics in natural environments therefore force microorganisms to continually adapt to temperature changes. in the present study, the glycolytic pathway of s. cerevisiae was used as a model to study kinetic regulation strategies of organisms in response to temperature dynamics. by combining both modeling and experimental results we obtained strong indications that the temperature dependencies of the catalytic capacities of yeast glycolytic enzymes are highly similar under in vivo conditions. these similarities allow the cells to maintain their homeostasis during circadian temperature cycles, thereby avoiding extensive changes in enzyme levels and minimizing the temperature impact on the growth rate. these results provide new insights in the robustness of yeast central carbon metabolism and open the gate for new studies on temperature as a key parameter for evolution of sympatric strains. 
from an evolutionary perspective, such similar temperature dependencies allow cells to adapt more rapidly to temperature changes, because they result in minimal perturbations of intracellular metabolite levels, thus circumventing the need for extensive modification of enzyme levels. an observed temperature-independent relation between intracellular levels of glycolytic metabolites and residual glucose concentration for all experimental conditions revealed that it is the substrate availability rather than temperature that determines intracellular metabolite profiles. these included glucose-excess batch cultures at different temperatures and glucose-limited chemostat cultures, subjected to fast linear temperature shifts and circadian sinoidal temperature cycles. this observation corresponded with predictions generated in silico with a kinetic model of yeast glycolysis, when the catalytic capacities of all glycolytic enzymes were set to share the same normalized temperature dependency. to understand regulation strategies that underlie microbial temperature responses and adaptation, we studied glycolytic pathway kinetics in saccharomyces cerevisiae during temperature changes.
 temperature strongly affects microbial growth, and many microorganisms have to deal with temperature fluctuations in their natural environment. to understand regulation strategies that underlie microbial temperature responses and adaptation, we studied glycolytic pathway kinetics in saccharomyces cerevisiae during temperature changes.  saccharomyces cerevisiae was grown under different temperature regimes and glucose availability conditions. these included glucose-excess batch cultures at different temperatures and glucose-limited chemostat cultures, subjected to fast linear temperature shifts and circadian sinoidal temperature cycles. an observed temperature-independent relation between intracellular levels of glycolytic metabolites and residual glucose concentration for all experimental conditions revealed that it is the substrate availability rather than temperature that determines intracellular metabolite profiles. this observation corresponded with predictions generated in silico with a kinetic model of yeast glycolysis, when the catalytic capacities of all glycolytic enzymes were set to share the same normalized temperature dependency.  from an evolutionary perspective, such similar temperature dependencies allow cells to adapt more rapidly to temperature changes, because they result in minimal perturbations of intracellular metabolite levels, thus circumventing the need for extensive modification of enzyme levels. glycolysiskinetic modellingmetabolomicssaccharomyces cerevisiaetemperature dynamics 