The multinomial simulation algorithm for discrete stochastic simulation of reaction-diffusion systems

The multinomial simulation algorithm for discrete stochastic simulation of reaction-diffusion systems.

The Inhomogeneous Stochastic Simulation Algorithm (ISSA) is a variant of the stochastic simulation algorithm in which the spatially inhomogeneous volume of the system is divided into homogeneous subvolumes, and the chemical reactions in those subvolumes are augmented by diffusive transfers of molecules between adjacent subvolumes. The ISSA can be prohibitively slow when the system is such that ...

Parallel stochastic reaction-diffusion simulation using Gillespie stochastic simulation algorithm

Spatial stochastic simulation is a valuable method for studying processes of reaction and diffusion in biological systems. This technique requires significant computational efforts, but the availability of high-performance computing made it possible to develop coherent computational models of cells [1]. Several approaches were introduced in order to utilize parallel execution to speed up simula...

Spatial-Stochastic Simulation of Reaction-Diffusion Systems

In biological systems, biochemical networks play a crucial role, implementing a broad range of vital functions from regulation and communication to resource transport and shape alteration. While biochemical networks naturally occur at low copy numbers and in a spatial setting, this fact often is ignored and well-stirred conditions are assumed for simplicity. Yet, it is now increasingly becoming...

Stochastic Simulation of Reaction-Diffusion Systems

Stochastic Simulation of Reaction-Diffusion Systems

Reactiondiffusion systems are mathematical models that describe how the concentration of one or more substances distributed in space changes under the influence of local chemical reactions in which the substances are converted into each other, and diffusion which causes the substances to spread out in space. The classical representation of a reaction-diffusion system is given by semi-linear par...