Before revision:  The dynamics of such models is described by the master equation , which provides the time course evolution of the probability distribution across the discrete state space consisting of vectors of population levels of the interacting biochemical species. Since solving the master equation exactly is very difficult in general due to the combinatorial explosion of the state space size , several analytical approximations have been proposed.
After revision:  The dynamics of such models is described by the master equation , which provides the time course evolution of the probability distribution across the discrete state space consisting of vectors of population counts for each species. However, since its exact solution is often elusive , several analytical approximations have been proposed.