Stochastic Automata Networks and Tensors with Application to Chemical Kinetics

Stochastic Chemical Kinetics

where k is the rate constant. The stochastic approach to chemical kinetics is concerned with modeling chemical reactions in situations where the assumptions underlying equations of this type break down. In order to illustrate this, suppose that the reaction above is occuring in a drop of water of volume V , which contains only a very small number, say 3, of molecules of I. The kinetic equation ...

Stochastic chemical kinetics and the total quasi-steady-state assumption: application to the stochastic simulation algorithm and chemical master equation.

Recently the application of the quasi-steady-state approximation (QSSA) to the stochastic simulation algorithm (SSA) was suggested for the purpose of speeding up stochastic simulations of chemical systems that involve both relatively fast and slow chemical reactions [Rao and Arkin, J. Chem. Phys. 118, 4999 (2003)] and further work has led to the nested and slow-scale SSA. Improved numerical eff...

Stochastic simulation of chemical kinetics.

Stochastic chemical kinetics describes the time evolution of a well-stirred chemically reacting system in a way that takes into account the fact that molecules come in whole numbers and exhibit some degree of randomness in their dynamical behavior. Researchers are increasingly using this approach to chemical kinetics in the analysis of cellular systems in biology, where the small molecular popu...

Stochastic Automata Networks

Aggregation of stochastic automata networks with replicas

We present techniques for computing the solution of large Markov chain models whose generators can be represented in the form of a generalized tensor algebra, such as Stochastic Automata Networks (SAN). Many large systems include a number of replications of identical components. This paper exploits replication by aggregating similar components. This leads to a state space reduction, based on lu...