Simulation of Biochemical Reactions

In 1977, Daniel T. Gillespie published the paper that in essence starts the work in my field. Titled "Exact stochastic simulation of coupled chemical reactions" this work lays the foundation for stochastically simulating chemistry. In a biochemical system, reactions occur at random. In order to properly model this system, we must express it in terms of probabilities. The Stochastic Simulation Algorithm, or SSA, is a simulation technique that involves concepts of Monte Carlo simulation and Markov Chains.

In essence, a set of reactions is expressed as matrix of probabilities. Each reaction is assigned a probability, based on the number of reactants available, the number required for the reaction, and the rate of the reaction. These probabilities are lined up on the zero to one interval. Then, a random number generator is used to "select" which reaction fires. The process repeats until an end condition or when all reactions can no longer occur. Often, the reactions for a system are simulated many times to get a "mean" response.

The formulas for the probability of a reaction occurring is as follows:

We calculate the alpha value for each reaction. Using these values, we can determine the probabilities that each reaction will fire. This system gets very complicated with large numbers of reactants and reactions.

Next blog entry about my research: I will give a basic example using this method.