Related papers: Generalizing Gillespie's direct method to enable n…

Many physical and biological processes are stochastic in nature. Computational models and simulations of such processes are a mathematical and computational challenge. The basic stochastic simulation algorithm was published by D. Gillespie…

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…

Continuous-time Markov chains are used to model stochastic systems where transitions can occur at irregular times, e.g., birth-death processes, chemical reaction networks, population dynamics, and gene regulatory networks. We develop a…

In biochemical systems some of the chemical species are present with only small numbers of molecules. In this situation discrete and stochastic simulation approaches are more relevant than continuous and deterministic ones. The fundamental…

The Gillespie algorithm provides statistically exact methods for simulating stochastic dynamics modelled as interacting sequences of discrete events including systems of biochemical reactions or earthquake occurrences, networks of queuing…

We propose a universal approach for analysis and fast simulations of stiff stochastic biochemical kinetics networks, which rests on elimination of fast chemical species without a loss of information about mesoscopic, non-Poissonian…

The development of chemical reaction models aids understanding and prediction in areas ranging from biology to electrochemistry and combustion. A systematic approach to building reaction network models uses observational data not only to…

Chemical reaction systems with a low to moderate number of molecules are typically modeled as discrete jump Markov processes. These systems are oftentimes simulated with methods that produce statistically exact sample paths such as the…

This work considers the method of uniformisation for continuous-time Markov chains in the context of chemical reaction networks. Previous work in the literature has shown that uniformisation can be beneficial in the context of…

We introduce expandable partial propensity direct method (EPDM) - a new exact stochastic simulation algorithm suitable for systems involving many interacting molecular species. The algorithm is especially efficient for sparsely populated…

Regulatory gene networks contain generic modules like those involving feedback loops, which are essential for the regulation of many biological functions. We consider a class of self-regulated genes which are the building blocks of many…

There is a growing trend in molecular and synthetic biology of using mechanistic (non machine learning) models to design biomolecular networks. Once designed, these networks need to be validated by experimental results to ensure the…

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…

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…

Biological systems with intertwined feedback loops pose a challenge to mathematical modeling efforts. Moreover, rare events, such as mutation and extinction, complicate system dynamics. Stochastic simulation algorithms are useful in…

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…

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 present an improvement of the Gillespie Exact Stochastic Simulation Algorithm, which leverages a bitwise representation of variables to perform independent simulations in parallel. We show that the subsequent gain in computational yield…

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…

Biochemical networks are used in computational biology, to model the static and dynamical details of systems involved in cell signaling, metabolism, and regulation of gene expression. Parametric and structural uncertainty, as well as…