Boulder 07: Modelling Stochastic Gene Expression

The whys and wherefores of stochasticity A system evolves stochastically if its dynamics is partly generated by a force of random strength or by a force at random times or by both. For stochastic systems, it is not possible to exactly determine the state of the system at later times given its state at the current time. Instead, to describe a stochastic system, we use the probability that the system is in a certain state and can predict exactly how this probability changes with time. Nevertheless, such a calculation is often dicult, and we usually focus on nding the moments of the probability distribution, such as the mean and variance. These two quantities are commonly measured experimentally. The level of stochasticity in a system is often referred to as its `noise'. Any chemical reaction is stochastic. Reactants come together by diusion, their motion driven by rapid and frequent collisions with other molecules. Once together, these same collisions alter the internal energies of the reactants, and so their propen-sity to react. Both eects cause individual reaction events to occur randomly and drive the overall reaction stochastic. Is stochasticity important in biology? Intu