Related papers: Analytical distributions for stochastic gene expre…

We develop an approximate theoretical method to study discrete stochastic birth and death models that include a delay time. We analyze the effect of the delay in the fluctuations of the system and obtain that it can qualitatively alter…

Horizontal gene transfer consists in exchanging genetic materials between microorganisms during their lives. This is a major mechanism of bacterial evolution and is believed to be of main importance in antibiotics resistance. We consider a…

This paper is concerned with classes of models of stochastic reaction dynamics with time-scales separation. We demonstrate that the existence of the time-scale separation naturally leads to the application of the averaging principle and…

The dynamics of stochastic reaction networks within cells are inevitably modulated by factors considered extrinsic to the network such as for instance the fluctuations in ribsome copy numbers for a gene regulatory network. While several…

Using analytical calculations and computer simulations we consider both the lateral diffusion of a membrane protein and the fluctuation spectrum of the membrane in which the protein is embedded. The membrane protein interacts with the…

Homeostasis of protein concentrations in cells is crucial for their proper functioning, and this requires concentrations (at their steady-state levels) to be stable to fluctuations. Since gene expression is regulated by proteins such as…

The production processes of proteins in prokaryotic cells are investigated. Most of the mathematical models in the literature study the production of {\em one} fixed type of proteins. When several classes of proteins are considered, an…

Stochastic fluctuations of molecule numbers are ubiquitous in biological systems. Important examples include gene expression and enzymatic processes in living cells. Such systems are typically modelled as chemical reaction networks whose…

We analyse transcriptional bursting within a stochastic non-equilibrium model which accounts for the coupling between the dynamics of DNA supercoiling and gene transcription. We find a clear signature of bursty transcription when there is a…

RNA-Seq and gene expression microarrays provide comprehensive profiles of gene activity, but lack of reproducibility has hindered their application. A key challenge in the data analysis is the normalization of gene expression levels, which…

We show how to construct a reduced description of interacting genes in noisy, small regulatory networks using coupled binary "spin" variables. Treating both the protein number and gene expression state variables stochastically and on equal…

The recent interest in human dynamics has led researchers to investigate the stochastic processes that explain human behaviour in different contexts. Here we propose a generative model to capture the essential dynamics of survival analysis,…

In the presence of multiscale dynamics in a reaction network, direct simulation methods become inefficient as they can only advance the system on the smallest scale. This work presents stochastic averaging techniques to accelerate…

The common understanding of protein evolution has been that neutral or slightly deleterious mutations are fixed by random drift, and evolutionary rate is determined primarily by the proportion of neutral mutations. However, recent studies…

Describing reaction rates in stochastic bio-circuits is commonly done by directly introducing the deterministically deduced Hill function into the master equation. However, when fluctuations in enzymatic reaction rates are not neglectable,…

Stochastic processes offer a flexible mathematical formalism to model and reason about systems. Most analysis tools, however, start from the premises that models are fully specified, so that any parameters controlling the system's dynamics…

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…

Gene expression is a central process to any form of life. It involves multiple temporal and functional scales that extend from specific protein-DNA interactions to the coordinated regulation of multiple genes in response to intracellular…

In this article, we introduce a novel backward method to model stochastic gene expression and protein level dynamics. The protein amount is regarded as a diffusion process and is described by a backward stochastic differential equation…

Stochastic dynamical systems arise naturally across nearly all areas of science and engineering. Typically, a dynamical system model is based on some prior knowledge about the underlying dynamics of interest in which probabilistic features…