Many students are familiar with the idea of modeling chemical reactions in terms of ordinary
differential equations. However, these deterministic reaction rate equations are really a …

Kinetic diagrams are commonly used to represent biochemical systems in order to study
phenomena such as free energy transduction and ion selectivity. While numerical methods …

This chapter reviews the theory of stochastic chemical kinetics and several simulation
methods that are based on that theory. An effort is made to delineate the logical connections …

Abstract The direct simulation Monte Carlo (DSMC) method is widely used for numerical
solutions of the Boltzmann equation. However, the associated computational cost becomes …

After being considered as a nuisance to be filtered out, it became recently clear that
biochemical noise plays a complex role, often fully functional, for a biomolecular network …

Based on the theory of stochastic chemical kinetics, the inherent randomness of biochemical
reaction networks can be described by discrete-state continuous-time Markov chains …

Following its introduction over three decades ago, the cohort model has been used
extensively to model population trajectories over time in decision-analytic modeling studies …

Gene transcription models must take account of intrinsic stochasticity. The Chemical Master
Equation framework is based on modelling assumptions that are highly appropriate for this …

PEPA and its semantics have recently been extended to model biological systems. In order
to cope with massive quantities of processes (as is usually the case when considering …

The direct numerical solution of the chemical master equation (CME) is usually impossible
due to the high dimension of the computational domain. The standard method for solution of …