Related papers: Stochastic simulation of biochemical systems with …
Multiple phenotypic states often arise in a single cell with different gene-expression states that undergo transcription regulation with positive feedback. Recent experiments have shown that at least in E. coli, the gene state switching can…
We present three algorithms for calculating rate constants and sampling transition paths for rare events in simulations with stochastic dynamics. The methods do not require a priori knowledge of the phase space density and are suitable for…
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…
We have developed a coarse-grained formulation for modeling the dynamic behavior of cells quantitatively, based on stochasticity and heterogeneity, rather than on biochemical reactions. We treat each reaction as a continuous-time stochastic…
Stochastic dynamics of chemical reactions in a mutually repressing two-gene circuit is numerically simulated. The circuit has a rich variety of different states when the kinetic change of DNA status is slow. The stochastic switching…
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…
Complex behaviour in many systems arises from the stochastic interactions of spatially distributed particles or agents. Stochastic reaction-diffusion processes are widely used to model such behaviour in disciplines ranging from biology to…
There is great potential to be explored regarding the use of agent-based modelling and simulation as an alternative paradigm to investigate early-stage cancer interactions with the immune system. It does not suffer from some limitations of…
The simulation of complex stochastic network dynamics arising, for instance, from models of coupled biomolecular processes remains computationally challenging. Often, the necessity to scan a models' dynamics over a large parameter space…
Astrochemical simulations are a powerful tool for revealing chemical evolution in the interstellar medium. Astrochemical calculations require efficient processing of large matrices for the chemical networks. The large chemical reaction…
Stochastic kinetic models of genetic expression are able to describe protein fluctuations. A comparative study of the canonical and a feedback model is given here by using stochastic simulation methods. The feedback model is skeleton model…
This study considers using Metropolis-Hastings algorithm for stochastic simulation of chemical reactions. The proposed method uses SSA (Stochastic Simulation Algorithm) distribution which is a standard method for solving well-stirred…
Stochastic models of chemical systems are often analysed by solving the corresponding Fokker-Planck equation which is a drift-diffusion partial differential equation for the probability distribution function. Efficient numerical solution of…
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 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…
Biochemical reaction networks are subjected to large fluctuations attributable to small molecule numbers, yet underlie reliable biological functions. Most theoretical approaches describe them as purely deterministic or stochastic dynamical…
In this paper we provide a new analysis of the SEM algorithm. Unlike previous work, we focus on the analysis of a single run of the algorithm. First, we discuss the algorithm for general mixture distributions. Second, we consider Gaussian…
Stochastic reaction network models are widely utilized in biology and chemistry to describe the probabilistic dynamics of biochemical systems in general, and gene interaction networks in particular. Most often, statistical analysis and…
Methods are presented to evaluate the entropy production rate in stochastic reactive systems. These methods are shown to be consistent with known results from nonequilibrium chemical thermodynamics. Moreover, it is proved that the time…
Simulation of stochastic spatially-extended systems is a challenging problem. The fundamental quantities in these models are individual entities such as molecules, cells, or animals, which move and react in a random manner. In big systems,…