## Major Accomplishments of Evgeni Selkov

Dr. Selkov has made outstanding contributions to the fields of
mathematical/computational analysis of cellular metabolism,
chronobiology, bioinformatics, and metabolic engineering. He has
demonstrated his ability to generate deep theoretical concepts about the
foundations of the cellular organization, to search the simplest ways of
experimental testing the concepts, to organize, lead and endure
long-term multidisciplinary scientific efforts in the Academia and the
Industries.

# Mathematical Analysis and Simulation of Cellular Metabolism

In the beginning of the 60s, Dr. Selkov discovered theoretically that
all open enzyme reactions could strongly amplify signals just like
transistor amplifiers do.

Starting from this point, it was clear for him that oscillatory, trigger
and other phenomena, well known in electronic networks, should be
observed in metabolic networks too. In the spring of 1963, he met Dr.
Britton Chance, an outstanding biochemist from Pennsylvania University.
Chance, like Selkov, was an electronic engineer in the past. By using a
standard linear approximation technique and matrix analysis, Selkov
convinced him that self-oscillations should be observed experimentally
in metabolic networks.

Within several months after that meeting, Chance and his colleagues have
experimentally demonstrated the existence of damped oscillations in the
glycolytic system of yeast suspensions and cell free extracts.

To study the phenomenon theoretically, Selkov has derived and analyzed a
simple mathematical model \[1\] of two non-linear differential
equations, currently known as Selkov's model. Based on the model
analysis, Selkov predicted that one could make the glycolytic
oscillations sustained if glucose, the initial glycolytic substrate, is
injected with a constant rate below some critical bifurcation value.
German biochemists, L. von Klitzing and A. Betz \[2\] and B. Hess and
coworkers (see monograph \[3\] for general references), have confirmed
this prediction.

In the 70s Selkov himself and in a co-authorship with his coworkers (N.
V. Avseenko, A. Betz, V.V. Dynnik, N.P. Kaimachnikov, I.A. Malkova, V.G.
Nazarenko. S. V. Popova, J.G. Reich, T. Schulmeister) has published a
series of mathematical models to explain experimentally observed
relaxation oscillations, double periodicity, chaotic and trigger
behavior in the glycolytic system (a detailed review of some of these
models can be found in the monograph \[4\]).

Systematic studies of the glycolytic system led Selkov to an important
discovery \[5, 6\] that the stoichiometric skeleton of the glycolytic
system, or any other variant of the cell energy metabolism, can strongly
stabilize the relative ATP concentration (also known as Atkinson's
adenylate energy charge) without any regulatory mechanism. Selkov and
his Russian (N.V. Avseenko, V.A. Dronova, V.V. Dynnik, I.A.Ovchinnikov)
and visiting German scientists (R. Bonensack, T. Geier, M. Glende, R.
Heinrich, J.G. Reich) have shown that the stoichiometric structure of
the cell metabolism is very reach in non-linearities that can produce a
wide range of dynamic phenomena usually ascribed to non-stoichiometric
interactions. The results of these joint international efforts have been
summarized in the book of J. G. Reich and E. Selkov \[6\].

By that time, it was firmly believed that a complex network of
regulatory (allosteric, chemical modification, or genetic) mechanisms
controls the cell metabolism and maintains its homeostasis. There was a
hot discussion in the literature about possible control mechanisms
responsible for the experimentally observed stability of the adenylate
energy charge. The Selkov's discovery that none of such regulatory
mechanisms is necessary for the charge stability was disturbing,
difficult to believe and required experimental proof. A. Boiteux, B.
Hess and E. Selkov have published such proof in \[7\]. The authors have
shown that a glycolytic system of yeast cell-free extracts can stabilize
the energy charge under a complete block of its allosteric mechanisms.

The fact that the fundamental properties of the cell metabolism, like
stabilization of energy charge, originate at the level of stoichiometric
structures allowed Selkov to a conclude that the evolutionary younger
regulatory network can be reconstructed from a very simple stoichiometry
of the cell metabolism \[5\]. He has demonstrated that one can
successfully reconstruct allosteric regulatory mechanisms of a large
metabolic network and to compute optimum parameter values.

### Contributions to Theoretical Chronobiology

Selkov considered his theoretical analysis of biochemical oscillations
as a preparation to attack a tough problem of an elusive cell clock
mechanism.

In 1970, Selkov did his first learning shoot toward the problem. After a
thorough study of literature data, he derived a phenomenological limit
cycle model of the thiol metabolism. According to this model,
self-oscillations in the thiol metabolism gate the cell division cycle.
The fundamental prediction that the cell division cycle is a limit cycle
phenomenon has been experimentally demonstrated by S. Kaufman and
coworkers \[3\]. Other results were delayed for long years and came as
by-products of Selkov's research project totally unrelated to the cell
clock.

Quite unexpectedly, theoretical analysis of the cell energy
stoichiometry, made by Selkov and his coworkers (N.V.Avseenko, S.V.
Dynnik, Yu.B. Kirsta, A.M. Taranenko), has unequivocally demonstrated
that an uncontrolled substrate cycling in the so-called futile cycles of
the cell energy metabolism can result in a negative net ATP production.
Selkov has shown that the only way of preventing the energy collapse is
a temporal organization of the futile cycles as opposed to the spatial
one. In free-living unicellular organisms, such organization has to be
periodical and requires a self-oscillatory mechanism.

This conclusion has led Selkov to a metabolic theory of the cell clock
as a self-oscillatory mechanism that separates in time incompatible
biochemical reactions \[8\]. Computational experiments of Selkov and
coworkers (N.V.Avseenko, I.I. Goryanin, R. Guthke, L. Lisnichuck) with a
mathematical model of the central metabolism have shown that the
metabolism can generate extremely stabile oscillations with a period
about a day. The theory predicts a critical role of depot compounds
(like glycogen or starch) in determining oscillation period about a day.

Selkov (in collaboration with E. Nikolaev and E.E. Shnoll) extended this
study toward bifurcation and computational analysis of a mathematical
model describing a non-growing population cells interacting trough the
common cultivation medium. This analysis has revealed a much more
complicated behavior than it is anticipated by the current theories of
cell synchrony. Stable and unstable synchrony, cascades of bifurcations
leading to a spontaneous (de)synchronization of cells, dramatic
differences between the observable global variables (like rates of total
oxygen consumption and CO2 evolution) and the intracellular state
variables are examples of the complexity.

This study is extremely important for designing experiments with
(auto)synchronous cell populations. Such experiments must be done to
verify the Selkov's cell clock theory since the only way to
experimentally observe intracellular events within a single cell cycle
is to analyze the metabolic changes in many synchronously cultivated
cells.

### Contributions to Bioinformatics

> Selkov pioneered in developing modern Metabolic Bioinformatics by
> creating unique databases and metabolic reconstruction technology
> based on them.
>
> In the beginning of the 80s, Selkov converted his large personal punch
> card file on enzymes and metabolic pathways into a computer database
> DBEMP currently known as EMP (Enzymes and Metabolic Pathways) \[9\].
> The format of the database consists of about 300 subject fields that
> allow professional annotators to encode the entire factual content of
> enzymology publications. Selkov and many of his coworkers spent over
> ten years of intensive everyday annotation work before EMP became
> complete enough to cover enzymology of all known enzymes from over
> 1700 different organisms. Selkov himself encoded about a third of the
> current EMP content of over 30,000 records representing 17,000
> original journal publications.
>
> EMP ([http://emp.mcs.anl.gov](http://emp.mcs.anl.gov/)) is the only
> database allowing a numerical range search combined with Boolean
> queries. This feature and a huge amount of qualitative kinetic data
> encoded make it indispensable for qualitative mathematical modeling of
> metabolic networks.
>
> In the beginning of the 90s, Selkov started a new database called MPW
> (Metabolic PathWays), a computer readable collection of metabolic
> pathways \[10\]. Currently, the database has well over 3000 metabolic
> maps (http://emp.mcs.anl.gov/cgi-bin/map_search.pl,
> <http://www.empproject.com/cgi-bin/map_search.pl>). By contrast to
> many other metabolic databases, followed the MPW project, the MPW maps
> are encoded in the form allowing converting them into stoichiometric
> matrices. This is critically important for automation of compiling and
> debugging mathematical models of large metabolic networks.
>
> ERM, Enzyme Reaction Mechanisms (<http://wit.mcs.anl.gov/ERM/>), is
> the smallest database developed by Selkov (with Gene Selkov and M.
> Galimova). It stores graphs and their matrix representations of the
> most frequently occurring enzyme reaction mechanisms. Although the
> database is under construction still, its importance will quickly
> become evident with advancement of the whole cell simulation projects.
>
> A quite positive web review of EMP/MPW databases has just been
> published
> (<http://fenske.che.psu.edu/Faculty/CMaranas/pub/burgard-maranas01b.pdf>).

**Metabolic Reconstruction Technology**

MPW plays a crucial role in the metabolic reconstruction technology from
sequenced genomes developed by Selkov \[11\] and implemented by Ross
Overbeek and coworkers as public WIT (<http://wit.mcs.anl.gov/WIT2>) or
proprietary ERGO (<http://wit.integratedgenomics.com/IGwit/>)
reconstruction/annotation systems.

Selkov has made metabolic reconstructions of all publicly available
genomes by the end of 1997 under WIT2 system and tens of proprietary
genomes for Integrated Genomics under ERGO systems. The examples of such
reconstructions have been published in \[12, 13\]. This outstanding
scientific performance made Selkov an internationally recognized top
authority in metabolic bioinformatics.

Among the Selkov's reconstructions available or to be available soon
from (<http://wit.integratedgenomics.com/IGwit/>) there is a group of
phototrophic bacteria including five cyanobacteria most ubiquitous in
the world's oceans. Cyanobacteria are of a specific interest of DOE
mission -- these bacteria play a key role in marinating the O2/CO2
balance in the Earth atmosphere. These bacteria have circadian cell
clock that controls periodic O2 evolution and gates cell divisions. The
analysis of the phototrophic reconstructions and genomes has revealed
that all of them have metabolic features predicted by Selkov's metabolic
cell clock theory: a set of futile cycles to be controlled by the cell
clock, glycogen metabolism and an invariant set of enzymes controlling
thiol metabolism.

In 1969, Juergen Aschoff, a pioneer of studying biological rhythms,
challenged Selkov to crack the mystery of the cell clock by saying: "If
not you, Selkov, who else". It is even truer today. Selkov is a
world-class scientist who has a unique combination of ample knowledge
and skills in cell biology and metabolism, biophysics, bioinformatics,
and mathematics.

**References**

1.  Sel'kov E. E. Self-oscillations in glycolysis. 1. A simple
    single-frequency model. Eur. J. Biochem., **1968**, 4, 79-86

2.  Von Klitzing L., Betz. A. Metabolic control in flow systems. I.
    Sustained glycolytic oscillations in yeast suspensions. Arch.
    Mikrobiol., **1970**, 71, 220-225

3.  Goldbetter A. Biochemical oscillations and cellular rhythms.
    Cambridge, Cambridge University Press, **1996**, pp. 605

4.  Gurel D., Gurel O. -- Oscillations in Chemical Reactions. Berlin,
    Springer Verlag, 1983, pp. 111

5.  Sel\'kov E. E. \-- Stabilization of energy charge, generation of
    oscillation and multiple steady states in energy metabolism as a
    result of purely stoichiometric regulation. Eur. J. Biochem.,
    **1975**, 59, 151-157

6.  Reich J.G., Sel'kov E.E. Energy metabolism of the cell: a
    theoretical treatise. N.Y., Acad. Press, **1981**, pp.

7.  Boiteux A., Hess B., Sel'kov E. E. \-- Experimental and theoretical
    studies of the regulatory hierarchy in glycolysis.

8.  Sel\'kov E. E. \-- Instability and self-oscillations in the cell
    energy metabolism. Ber. Bunsenges. Phys. Chem., **1980**, 84,
    399-402

9.  Selkov E., Basmanova S., Gaasterland T., Goryanin I., Grechkin Y.,
    Maltsev N., Nenashev V., Overbeek R., Panyushkina E., Pronevich L,
    Sel\'kov E., Jr., Yunus I. \-- The metabolic pathway collection from
    EMP: the enzymes and metabolic pathways database. Nucleic Acids Res.
    **1996**, 24, 26-28

10. Selkov E Jr, Grechkin Y, Mikhailova N, Selkov E. \-- MPW: the
    Metabolic Pathways Database. *Nucleic Acids Res* **1998** Jan 1
    **26:1** 43-45

11. Gaasterland T., Selkov E. \-- Reconstruction of metabolic networks
    using incomplete information. ISMB, **1995**, 3, 127-135

12. Selkov E., Maltsev N., Olsen G., Overbeek R., Whitman W. B. \-- A
    reconstruction of the metabolism of *Methanococcus jannaschii* from
    sequence data. Gene, **1997**, 197, GC10-25

13. Selkov E., Overbeek R., Kogan Y., Chu L., Vonstein V., Holmes D.,
    Silver S., Haselkorn R., Fonstein M. Functional analysis of gapped
    microbial genomes: amino acid metabolism of *Thiobacillus
    ferrooxidans*. *Proc Natl Acad Sci U S A* **2000** Mar 28 97:7
    3509-3514