Аннотация
Regulation processes in cells are performed by networks of
interacting genes, which regulate each other's expression.
Recent studies have shown that these networks are typically
sparse and include recurring modules or motifs. To analyze
the function of these networks, one needs to simulate their
dynamics. Since the networks often exhibit strong fluctuations,
stochastic methods, based on the master equation, are required.
In this talk I will consider a class of genetic switch systems,
in which bistability is induced by the fluctuations 1,2. I
will show that in general network modules that include feedback,
fluctuations give rise to crucial quantitative and qualitative
effects.
The stochastic simulation of separate modules is only the first
step in the analysis of genetic networks. More complete
understanding of network function will require to simulate large
complex networks, which consist of many interacting modules.
While direct integration of the master equation is suitable
for the analysis of small network modules, it becomes infeasible
in the case of complex networks, since the number of equations
proliferates exponentially with the number of genes in the network.
To address this problem, I will present the multi-plane method
(originally introduced in the context of stochastic chemical netoworks),
which provides a dramatic reduction in the number of equations 3.
The reduction is obtained by breaking the network into fully connected
sub-networks (cliques), with suitable couplings between them.
This method enables to perform stochastic analysis of genetic
networks of any size and complexity and to analyze their function.
1) A. Lipshtat, A. Loinger, N.Q. Balaban and O. Biham,
Genetic toggle switch without cooperative binding,
Phys. Rev. Lett. 96, 188101 (2006).\\
2) A. Loinger, A. Lipshtat, N.Q. Balaban and O. Biham,
Stochastic simulations of genetic switch systems,
Phys. Rev. E 75, 021904 (2007).\\
3) A. Lipshtat, O. Biham,
Efficient simulations of gas-grain chemistry in interstellar clouds,
Phys. Rev. Lett. 93, 170601 (2004).
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