August 25, 2006
Stochastic dynamics of chemical reactions in a mutually repressing two-gene circuit is numerically simulated. The circuit has a rich variety of different states when the kinetic change of DNA status is slow. The stochastic switching transition between those states are compared with the theoretical estimation of the switching rate derived from the idea similar to the transition state theory. Even though the circuit is kept far from equilibrium, the method gives a consistent explanation of the switching kinetics for a wide range of parameters. The transition state theory-like estimation, however, fails to describe transitions involving the state which has the extremely small numbers of protein molecules.
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October 4, 2004
We study by mean-field analysis and stochastic simulations chemical models for genetic toggle switches formed from pairs of genes that mutually repress each other. In order to determine the stability of the genetic switches, we make a connection with reactive flux theory and transition state theory. The switch stability is characterised by a well defined lifetime $\tau$. We find that $\tau$ grows exponentially with the mean number $\Nmean$ of transcription factor molecules in...
June 2, 2004
Bistable biochemical switches are ubiquitous in gene regulatory networks and signal transduction pathways. Their switching dynamics, however, are difficult to study directly in experiments or conventional computer simulations, because switching events are rapid, yet infrequent. We present a simulation technique that makes it possible to predict the rate and mechanism of flipping of biochemical switches. The method uses a series of interfaces in phase space between the two sta...
July 30, 2004
We present a self-consistent field approximation to the problem of the genetic switch composed of two mutually repressing/activating genes. The protein and DNA state dynamics are treated stochastically and on equal footing. In this approach the mean influence of the proteomic cloud created by one gene on the action of another is self-consistently computed. Within this approximation a broad range of stochastic genetic switches may be solved exactly in terms of finding the prob...
March 13, 2007
We analyze three simple genetic circuits which involve transcriptional regulation and feedback: the autorepressor, the switch and the repressilator, that consist of one, two and three genes, respectively. Such systems are commonly simulated using rate equations, that account for the concentrations of the mRNAs and proteins produced by these genes. Rate equations are suitable when the concentrations of the relevant molecules in a cell are large and fluctuations are negligible....
November 28, 2007
In many stochastic simulations of biochemical reaction networks, it is desirable to ``coarse-grain'' the reaction set, removing fast reactions while retaining the correct system dynamics. Various coarse-graining methods have been proposed, but it remains unclear which methods are reliable and which reactions can safely be eliminated. We address these issues for a model gene regulatory network that is particularly sensitive to dynamical fluctuations: a bistable genetic switch....
November 6, 2011
The stochastic mutual repressor model is analysed using perturbation methods. This simple model of a gene circuit consists of two genes and three promotor states. Either of the two protein products can dimerize, forming a repressor molecule that binds to the promotor of the other gene. When the repressor is bound to a promotor, the corresponding gene is not transcribed and no protein is produced. Either one of the promotors can be repressed at any given time or both can be un...
February 1, 2007
Genetic switch systems with mutual repression of two transcription factors are studied using deterministic methods (rate equations) and stochastic methods (the master equation and Monte Carlo simulations). These systems exhibit bistability, namely two stable states such that spontaneous transitions between them are rare. Induced transitions may take place as a result of an external stimulus. We study several variants of the genetic switch and examine the effects of cooperativ...
June 22, 2011
Within systems biology there is an increasing interest in the stochastic behavior of genetic and biochemical reaction networks. An appropriate stochastic description is provided by the chemical master equation, which represents a continuous time Markov chain (CTMC). In this paper we consider the stochastic properties of a biochemical circuit, known to control eukaryotic cell cycle and possibly involved in oncogenesis, recently proposed in the literature within a deterministic...
February 15, 2011
Cells use genetic switches to shift between alternate gene expression states, e.g., to adapt to new environments or to follow a developmental pathway. Here, we study the dynamics of switching in a generic-feedback on/off switch. Unlike protein-only models, we explicitly account for stochastic fluctuations of mRNA, which have a dramatic impact on switch dynamics. Employing the WKB theory to treat the underlying chemical master equations, we obtain accurate results for the quas...
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For cellular biochemical reaction systems where the numbers of molecules is small, significant noise is associated with chemical reaction events. This molecular noise can give rise to behavior that is very different from the predictions of deterministic rate equation models. Unfortunately, there are few analytic methods for examining the qualitative behavior of stochastic systems. Here we describe such a method that extends deterministic analysis to include leading-order corr...