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Network dynamics and cell physiology

Nature Reviews Molecular Cell Biology volume 2, pages 908–916 (2001)Cite this article

Key Points

  • The 'last step' of computational molecular biology is to derive the physiological properties of a cell from the wiring diagrams of the protein networks that embody all the capabilities of the cell.

  • These networks are intrinsically dynamical systems, driving the adaptive responses of a cell in space and time.

  • The behaviour of a dynamical system is fully determined by rate equations that specify how each network component will change in the next small increment of time.

  • These rate equations can be visualized as a 'vector field' in 'state space'.

  • A powerful tool for analysing the qualitative behaviour of dynamical systems is bifurcation theory, which tells us how the attractors of a vector field depend on parameter values.

  • For example, bifurcations drive the irreversible transitions of the eukaryotic cell cycle, as illustrated by the physiology of wild-type and mutant fission yeast.

  • To take the last step, from networks to physiology, will require serious collaboration between dynamical systems theorists and experimental molecular biologists.

Abstract

Complex assemblies of interacting proteins carry out most of the interesting jobs in a cell, such as metabolism, DNA synthesis, movement and information processing. These physiological properties play out as a subtle molecular dance, choreographed by underlying regulatory networks. To understand this dance, a new breed of theoretical molecular biologists reproduces these networks in computers and in the mathematical language of dynamical systems.

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Figure 1: Computational molecular biology.
Figure 2: The cell-cycle control system in fission yeast.
Figure 3: Simulated time courses of cdc2 and related proteins during the cell cycle of fission yeast.
Figure 4: A vector field.
Figure 5: Bifurcation diagrams for the three control modules of the cell cycle.
Figure 6: Bifurcation diagram for the full cell-cycle control network.

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Acknowledgements

Our work on cell-cycle modelling has been supported by the National Science Foundations of the United States and Hungary. We are deeply grateful to P. Nurse for introducing us to the molecular mechanisms of cell-cycle regulation.

Author information

Authors and Affiliations

  1. Department of Biology, Virginia Polytechnic Institute and State University, Blacksburg, 24061, Virginia, USA

    John J. Tyson & Kathy Chen

  2. Department of Agricultural Chemical Technology, Budapest University of Technology and Economics, Budapest, 1521, Hungary

    Bela Novak

Authors
  1. John J. Tyson
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  2. Kathy Chen
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  3. Bela Novak
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Correspondence to John J. Tyson.

Related links

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DATABASES

Saccharomyces Genome Database:

cdc2

cdc13

cdc25

CDC28

slp1

ste9

wee1

FURTHER INFORMATION

Berkeley Madonna

Cell cycle

E-CELL

GEPASI

Kohn's interaction maps

Milestones in cell division

Molecular wiring diagrams

Novak lab

Virtual Cell

XPPAUT

Yeast proteome database

Glossary

CYCLIN-DEPENDENT KINASE

An enzyme phosphorylating target proteins that are involved in DNA synthesis and mitosis. It requires a cyclin partner for activity and substrate specificity.

B-TYPE CYCLIN

A family of cyclin proteins that is required for mitosis. In fission yeast and some organisms, B-type cyclins drive DNA synthesis as well.

UBIQUITYLATION

The labelling of proteins for destruction by covalent attachment to a small protein, ubiquitin.

ANAPHASE-PROMOTING COMPLEX

An enzymatic complex that labels specific target proteins for degradation. It often works in conjunction with partners (slp1 and ste9, for example) that provide substrate specificity.

DYNAMICAL SYSTEM

A collection of components (for example, genes, proteins and metabolites) the properties of which change in time of response to interactions among the components and influences from outside the system.

STATE (SPACE)

The set of numbers that quantify each component (state variable) of a dynamical system. If there are n components, then the state can be represented by a point in an n-dimensional state space.

VECTOR FIELD

Assigned to each point in state space is a vector that specifies the magnitude and direction in which the state variables are changing.

STABLE (UNSTABLE)

Refers to steady states or limit cycles that attract (repel) nearby orbits.

STEADY STATE

A point in state space where the vector field vanishes (that is, a point that does not move).

SADDLE POINT

A steady state that attracts some nearby orbits and repels others.

ORBIT

A path through state space, traversed over time, as a dynamical system follows the underlying vector field from an initial state to a final state.

CHECKPOINT

A waiting state of the cell-cycle control system, induced by specific conditions such as DNA damage or spindle abnormalities.

BIFURCATION

A combination of parameter values at which something unusual happens to the attractors of a dynamical system; for example, two steady states annihilate each other, or a stable steady state gives way to a stable limit cycle.

PARAMETER (SPACE)

A number (for example, rate constant or binding constant) that influences the rates of change of state variables. The set of all parameters entailed by a dynamical system can be represented by a point in a p-dimensional parameter space.

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Tyson, J., Chen, K. & Novak, B. Network dynamics and cell physiology. Nat Rev Mol Cell Biol 2, 908–916 (2001). https://doi.org/10.1038/35103078

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