Tài liệu Báo cáo khoa học: What makes biochemical networks tick? A graphical tool for the

What makes biochemical networks tick?

A graphical tool for the identification of oscillophores

Boris N. Goldstein1

, Gennady Ermakov1

, Josep J. Centelles3

, Hans V. Westerhoff2 and Marta Cascante3

1

Institute of Theoretical and Experimental Biophysics, Russian Academy of Sciences, Pushchino, Moscow Region, Russia;

2

BioCentrum Amsterdam, Departments of Molecular Cell Physiology (IMC, VUA) and Mathematical Biochemistry (SILS, UvA),

Amsterdam, the Netherlands; 3

Department of Biochemistry and Molecular Biology, Faculty of Chemistry and CeRQT at Barcelona

Scientific Parc, University of Barcelona, Spain

In view of the increasing number of reported concentration

oscillations in living cells, methods are needed that can

identify the causes of these oscillations. These causes always

derive from the influences that concentrations have on

reaction rates. The influences reach over many molecular

reaction steps and are defined by the detailed molecular

topology of the network. So-called
autoinfluence paths,

which quantify the influence of one molecular species upon

itself through a particular path through the network, can

have positive or negative values. The former bring a ten￾dency towards instability. In this molecular context a new

graphical approach is presented that enables the classifica￾tion of network topologies into oscillophoretic and non￾oscillophoretic, i.e. into ones that can and ones that cannot

induce concentration oscillations. The network topologies

are formulated in terms of a set of uni-molecular and

bi-molecular reactions, organized into branched cycles of

directed reactions, and presented as graphs. Subgraphs of

the network topologies are then classified as negative ones

(which can) and positive ones (which cannot) give rise to

oscillations. A subgraph is oscillophoretic (negative) when it

contains more positive than negative autoinfluence paths.

Whether the former generates oscillations depends on the

values of the other subgraphs, which again depend on the

kinetic parameters. An example shows how this can be

established. By following the rules of our new approach,

various oscillatory kinetic models can be constructed and

analyzed, starting from the classified simplest topologies and

then working towards desirable complications. Realistic

biochemical examples are analyzed with the new method,

illustrating two new main classes of oscillophore topologies.

Keywords: graph-theoretic approach; kinetic modelling;

oscillations; system identification; systems biology.

Oscillatory biochemical networks have regained intensive

interest during the past few years because of the importance

of oscillatory signaling for various biological functions.

Oscillations in glycolysis [1,2], oscillations of Ca2+ concen￾trations [3,4], and the cell cycle as such [5] are well known.

Some of these have been predicted and analyzed by using

mathematical models [6,7]. The need for such mathematical

models is appreciated even more when studying biochemical

oscillations and their synchronization [7–13].

The behavior of potential biochemical oscillators may

depend on the kinetic properties of their surroundings,

interacting with the oscillator through common metabolites

(e.g [8,14]). Other systems, such as the cell cycle of tumor

cells may be more autonomous [9]. Most intracellular

oscillations involve more than five components that interact

in a nonlinear manner [8]. This makes them unsuitable for

intuitive analysis, a phenomenon encountered more fre￾quently in Systems Biology [8]. New theoretical approaches

are needed that streamline the study of such cases of

Systems Biology, dissecting the system into various inter￾acting kinetic regimes, whilst relating to molecular mecha￾nisms.

Various types of approach can be helpful here. Graph￾theoretic approaches can help dissect the dynamics of

enzyme reactions [15,16] and this is what made others and

ourselves [20,25,26] examine whether these approaches can

also do this for networks. Earlier we have applied graph

theory in order to simplify the King–Altman–Hill [15,16]

analysis of steady-state enzyme reactions [17,18]. This

approach was later extended to presteady-state enzyme

kinetics [19], to stability analysis of enzyme systems [20],

and to the analysis of concentration oscillations in enzyme

cycles [21].

In this paper, the graph-theoretical stability analysis

developed by Clarke [22] as modified by Ivanova [21,23,24]

is the starting point for a more comprehensive approach

to the analysis of biochemical networks. It enables us to

develop a graph-theoretical identification of networks that

may, and of networks that cannot, serve as oscillophores

(i.e. induce oscillations).

In some aspects our approach is similar to that reported

previously [25,26]. However, we use unimolecular and

bimolecular steps and simple catalytic cycles, rather than

Correspondence to M. Cascante, Department of Biochemistry and

Molecular Biology, Faculty of Chemistry and CERQT-Parc Scientific

of Barcelona, University of Barcelona, c/Martı´ i Franque`s 1, 08028

Barcelona, Spain. Fax: +34 934021219; Tel.: +34 934021593;

E-mail: [email protected] or Hans V.Westerhoff, Faculty of Earth and

Life Sciences, Free University, De Boelelaan 1087, NL-1081 HV

Amsterdam, the Netherlands. Fax: +31 204447229;

E-mail: [email protected]

(Received 6 July 2004, revised 30 July 2004, accepted 4 August 2004)

Eur. J. Biochem. 271, 3877–3887 (2004)
FEBS 2004 doi:10.1111/j.1432-1033.2004.04324.x