Related papers: Approximation and inference methods for stochastic…
Stochasticity is a key characteristic of intracellular processes such as gene regulation and chemical signalling. Therefore, characterising stochastic effects in biochemical systems is essential to understand the complex dynamics of living…
Many cellular behaviors are regulated by gene regulation networks, kinetics of which is one of the main subjects in the study of systems biology. Because of the low number molecules in these reacting systems, stochastic effects are…
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…
Stochastic models of biochemical reaction networks are widely used to capture intrinsic noise in cellular systems. The typical formulation of these models are based on Markov processes for which there is extensive research on efficient…
Biochemical reaction networks frequently consist of species evolving on multiple timescales. Stochastic simulations of such networks are often computationally challenging and therefore various methods have been developed to obtain sensible…
Stochastic reaction networks are mathematical models with a wide range of applications in biochemistry, ecology, and epidemiology, and are often complex to analyze. Except for some special cases, it is generally difficult to predict how the…
Simulation of biomolecular networks is now indispensable for studying biological systems, from small reaction networks to large ensembles of cells. Here we present a novel approach for stochastic simulation of networks embedded in the…
Several different methods exist for efficient approximation of paths in multiscale stochastic chemical systems. Another approach is to use bursts of stochastic simulation to estimate the parameters of a stochastic differential equation…
Auto-regulatory feedback loops are one of the most common network motifs. A wide variety of stochastic models have been constructed to understand how the fluctuations in protein numbers in these loops are influenced by the kinetic…
Simplified stochastic models are widely used in the study of frequency-resolved noise propagation in biochemical reaction networks, a common measure being the coherence between random fluctuations in molecule number trajectories. Such…
We present a numerical approximation technique for the analysis of continuous-time Markov chains that describe networks of biochemical reactions and play an important role in the stochastic modeling of biological systems. Our approach is…
Biochemical networks play a crucial role in biological systems, implementing a broad range of vital functions. They normally operate at low copy numbers and in spatial settings, but this is often ignored and well-stirred conditions are…
The existing literature on stochastic simulation of chemical reaction networks has a tendency to move as quickly as possible to the abstract formulation of the stochastic dynamics in terms of probabilities based on the concept of the…
A practical introduction to stochastic modelling of reaction-diffusion processes is presented. No prior knowledge of stochastic simulations is assumed. The methods are explained using illustrative examples. The article starts with the…
Heterogeneity in gene expression across isogenic cell populations can give rise to phenotypic diversity, even when cells are in homogenous environments. This diversity arises from the discrete, stochastic nature of biochemical reactions,…
Fluorescent and luminescent gene reporters allow us to dynamically quantify changes in molecular species concentration over time on the single cell level. The mathematical modeling of their interaction through multivariate dynamical models…
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…
This work reviews deterministic and diffusion approximations of the stochastic chemical reaction networks and explains their applications. We discuss the added value the diffusion approximation provides for systems with different phenomena,…
A new tool for modeling electrochemical kinetics is presented. An extension of the Stochastic Simulation Algorithm framework to electrochemical systems is proposed. The physical justifications and constraints for the derivation of a…
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…