Modeling and simulation of intracellular dynamics: Choosing an appropriate framework

Systems biology is a reemerging paradigm which, among other things, focuses on mathematical modeling and simulation of biochemical reaction networks in intracellular processes. For most simulation tools and publications, they are usually characterized by either preferring stochastic simulation or rate equation models. The use of stochastic simulation is occasionally accompanied with arguments against rate equations. Motivated by these arguments, we discuss in this paper the relationship between these two forms of representation. Toward this end, we provide a novel compact derivation for the stochastic rate constant that forms the basis of the popular Gillespie algorithm. Comparing the mathematical basis of the two popular conceptual frameworks of generalized mass action models and the chemical master equation, we argue that some of the arguments that have been put forward are ignoring subtle differences and similarities that are important for answering the question in which conceptual framework one should investigate intracellular dynamics.