ABSTRACT
This chapter explains the relationship between rate parameters based on ordinary differential equations (ODEs) and those based on stochastic simulation. Stochastic methods differ from ODEs in a number of ways. In general, ODEs are the best choice when the system contains many molecules. Stochastic methods become important when the number of molecules is very small because the concept of "concentration" breaks down and each molecule needs to be counted individually. The stochastic formulation contains a slew of variables and symbols, so the best way to compare these statements directly is with an example. Stochastic simulations are an extremely useful representation of our genetic system in the context of a single cell. These simulations not only helped us to better understand single-cell measurements, but also recaptured much of the information in the ODE-based models. Stochastic simulations can be computationally expensive, especially as the number of molecules and reactions increases.
