The Chemical Master Equation With Respect To Reaction Counts

It is well known that many realistic mathematical models of biological and chemical systems, such as enzyme cascades and gene regulatory networks, need to include stochasticity. These systems can be described as Markov processes and are modeled using the Chemical Master Equation (CME). The CME is a differential-difference equation (continuous in time and discrete in the state space) for the probability of certain state at a given time. The state space is the population count of species in the system. However we can also consider the CME with the state space given by the counts of the number of reactions occurring in the system. This form of CME is not frequently used in the literature. This paper, through new results, gives motivation towards considering computing the CME over the reaction counts rather than species counts.