Related papers: Sampling rare switching events in biochemical netw…
We study a biological autoregulation process, involving a protein that enhances its own transcription, in a parameter region where bistability would be present in the absence of fluctuations. We calculate the rate of fluctuation-induced…
In an experimental study of single enzyme reactions, it has been proposed that the rate constants of the enzymatic reactions fluctuate randomly, according to a given distribution. To quantify the uncertainty arising from random rate…
We present a detailed analysis, based on the Forward Flux Sampling (FFS) simulation method, of the switching dynamics and stability of two models of genetic toggle switches, consisting of two mutually-repressing genes encoding transcription…
Living cells need a constant availability of certain resources to have a sustained gene expression process. Limited availability of cellular resources for gene expression, like ribosomes, along with a variation of resource affinity,…
The phage $\lambda$ infection of an \textit{E. coli} cell has become a paradigm for understanding the molecular processes involved in gene expression and cell signaling. This system provides an example of a genetic switch, as cells with…
Based on the theory of stochastic chemical kinetics, the inherent randomness and stochasticity of biochemical reaction networks can be accurately described by discrete-state continuous-time Markov chains. The analysis of such processes is,…
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…
The atomistic characterization of the transition state is a fundamental step to improve the understanding of the folding mechanism and the function of proteins. From a computational point of view, the identification of the conformations…
We present computer-assisted methods for analyzing stochastic models of gene regulatory networks. The main idea that underlies this equation-free analysis is the design and execution of appropriately-initialized short bursts of stochastic…
The ability to predict accurate thermodynamic and kinetic properties in biomolecular systems is of both scientific and practical utility. While both remain very difficult, predictions of kinetics are particularly difficult because rates, in…
The bistable gene regulatory switch controlling the transition from lysogeny to lysis in bacteriophage lambda presents a unique challenge to quantitative modeling. Despite extensive characterization of this regulatory network, the origin of…
Spontaneous switching events in most characterized genetic switches are rare, resulting in extremely stable epigenetic properties. We show how simple arguments lead to theories of the rate of such events much like the absolute rate theory…
In this paper we develop a perturbation method to predict the rate of occurrence of rare events for singularly perturbed stochastic systems using a probability density function approach. In contrast to a stochastic normal form approach, we…
When a chemical reaction is driven by an external field, the transition state that the system must pass through as it changes from reactant to product -for example, an energy barrier- becomes time-dependent. We show that for periodic…
We briefly review simulation schemes for the investigation of rare transitions and we resume the recently introduced Transition Interface Sampling, a method in which the computation of rate constants is recast into the computation of fluxes…
We present a simple analytical tool which gives an approximate insight into the stationary behavior of nonlinear systems undergoing the influence of a weak and rapid noise from one dominating source, e.g. the kinetic equations describing a…
We discuss the transition paths in a coupled bistable system consisting of interacting multiple identical bistable motifs. We propose a simple model of coupled bistable gene circuits as an example, and show that its transition paths are…
Stochastic simulation is a widely used method for estimating quantities in models of chemical reaction networks where uncertainty plays a crucial role. However, reducing the statistical uncertainty of the corresponding estimators requires…
Across many fields, a problem of interest is to predict the transition rates between nodes of a network, given limited stationary state and dynamical information. We give a solution using the principle of Maximum Caliber. We find the…
An important task in quantitative biology is to understand the role of stochasticity in biochemical regulation. Here, as an extension of our recent work [Phys. Rev. Lett. 107, 148101 (2011)], we study how input fluctuations affect the…