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 genetic 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 modules such
as the toggle switch [1,2], the mixed feedback loop and the
repressilator. I will show that in such modules, which include
feedback, fluctuations give rise to crucial quantitative and
qualitative effects.
More complete understanding of the function of genetic networks
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 modules, it becomes
infeasible in the case of complex networks, because the number of
equations increases exponentially with the number of genes in the
network.
As a potential solution to this problem, I will present the
multi-plane method [3]. This method has been used for chemical
networks, where it provides a dramatic reduction in the
number of equations and enables to perform stochastic
simulations of complex reaction networks. Current efforts
are aimed at extending the method to the more general
reaction processes and interactions which appear in
genetic networks.
[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).