Related papers: Stochastic Modeling in Systems Biology
A reaction network is a chemical system involving multiple reactions and chemical species. Stochastic models of such networks treat the system as a continuous time Markov chain on the number of molecules of each species with reactions as…
We discuss recent developments in the modeling of negative autoregulated genetic networks. In particular, we consider the temporal evolution of the population of mRNA and proteins in simple networks using rate equations. In the limit of low…
Gene expression is a stochastic process in which cells produce biomolecules essential to the function of life. Modern experimental methods allow for the measurement of biomolecules at single-cell and single-molecule resolution over time.…
Discrete-state stochastic models are a popular approach to describe the inherent stochasticity of gene expression in single cells. The analysis of such models is hindered by the fact that the underlying discrete state space is extremely…
We describe a mechanism for pronounced biochemical oscillations, relevant to microscopic systems, such as the intracellular environment. This mechanism operates for reaction schemes which, when modeled using deterministic rate equations,…
Numerical computations have become a pillar of all modern quantitative sciences. Any computation involves modeling--even if often this step is not made explicit--and any model has to neglect details while still being physically accurate.…
Gene expression is significantly stochastic making modeling of genetic networks challenging. We present an approximation that allows the calculation of not only the mean and variance but also the distribution of protein numbers. We assume…
In this chapter we review stochastic modelling methods in climate science. First we provide a conceptual framework for stochastic modelling of deterministic dynamical systems based on the Mori-Zwanzig formalism. The Mori-Zwanzig equations…
The well-known issue of reconstructing regulatory networks from gene expression measurements has been somewhat disrupted by the emergence and rapid development of single-cell data. Indeed, the traditional way of seeing a gene regulatory…
A general formalism is developed to construct a Markov chain model that converges to a one-dimensional map in the infinite population limit. Stochastic fluctuations are therefore internal to the system and not externally specified. For…
We introduce a biologically detailed, stochastic model of gene expression describing the multiple rate-limiting steps of transcription, nuclear pre-mRNA processing, nuclear mRNA export, cytoplasmic mRNA degradation and translation of mRNA…
Motivation: Stochastic reaction networks are a widespread model to describe biological systems where the presence of noise is relevant, such as in cell regulatory processes. Unfortu-nately, in all but simplest models the resulting discrete…
Biochemical processes typically involve many chemical species, some in abundance and some in low molecule numbers. Here we first identify the rate constant limits under which the concentrations of a given set of species will tend to…
100 years after Smoluchowski introduces his approach to stochastic processes, they are now at the basis of mathematical and physical modeling in cellular biology: they are used for example to analyse and to extract features from large…
We introduce a minimal model description for the dynamics of transcriptional regulatory networks. It is studied within a mean-field approximation, i.e., by deterministic ode's representing the reaction kinetics, and by stochastic…
Reaction networks are mathematical models of interacting chemical species that are primarily used in biochemistry. There are two modeling regimes that are typically used, one of which is deterministic and one that is stochastic. In…
This paper deals with the analysis of stochastic systems which can be described by a Langevin equation. By the method presented in this paper drift and diffusion terms of the corresponding Fokker-Planck equation can be extracted from the…
In modern science, computer models are often used to understand complex phenomena, and a thriving statistical community has grown around analyzing them. This review aims to bring a spotlight to the growing prevalence of stochastic computer…
Stochasticity in gene expression gives rise to fluctuations in protein levels across a population of genetically identical cells. Such fluctuations can lead to phenotypic variation in clonal populations, hence there is considerable interest…
The past decade has seen great advances in our understanding of the role of noise in gene regulation and the physical limits to signaling in biological networks. Here we introduce the spectral method for computation of the joint probability…