Stochastic Simulation Algorithm
From PBDN
Introduction
The stochastic simulation algorithm, SSA, is sometimes called the Gillespie algorithm after its inventor, Daniel Gillespie, who first proposed it in 1976.
The general idea of SSA is to directly simulate the probabilistic nature of chemical reactions. For example, imagine a mixture of 4 different chemicals which may react with each other in, say, 10 different ways. If we pick a short enough length of time, we can be sure that only one reaction occurs in that interval. In that short time, one of the reactions might be very unlikely, while another might be much more likely. For example, if the mixture were to include metallic potassium in a dilute solution of hydrogen peroxide in water, the decomposition of hydrogen peroxide into water and oxygen, a relatively slow reaction, would be much less likely than the familiar classroom demonstration reaction of potassium with water: a fast, violent, explosive reaction. Accordingly, each reaction occurs with a different likelihood.
The idea in SSA is to start with some amount of each species at time zero, then advance through time in small random steps, using a random number to decide which reaction should occur at each timestep until we reach whatever stopping time we've decided on. An individual simulation, which tracks the amounts of each species at each timestep, is called a trajectory.
Each individual trajectory represents just one possible way in which the system might have reacted over the timespan from the start-time to the stop-time. To get a representative picture of how the system behaves on the whole, we need many thousands of trajectories. Usually, we're interested in the amounts of each species at the end, the final amounts of each species, and not in the minute details of the history of "how we got there". The picture (above right) shows the distribution of the final amounts of the A and B (metabolite) species in 100,000 100-second trajectories of the metabolite-enzyme model.
The video below shows the A and B species in the metabolite-enzyme model for 4 individual trajectories as they change through time. The amount of each species is shown every second or so for 100 seconds. The amount of metabolite A is indicated by horizontal position (0 to 100), while the amount of metabolite B is indicated by vertical position (0 to 100).
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