Stochastic Simulation

Finite State Projection

Motivated by our study of the pap pili stochastic switch, we have developed a new method to compute the probability density function arising in stochastic chemical kinetics, called the Finite State Projection (FSP) method. In stochastic chemical kinetics, the configuration space defines a very large or infinite continuous-time discrete-state Markov chain. The FSP approach relies on a projection that preserves an important subset of the state space (e.g. that supporting the bulk of the probability density) while projecting the remaining states onto a single 'absorbing' state.
Probabilities for the resulting finite state Markov chain can be computed exactly, and can be shown to give an error bound for the corresponding probability for the original full system. These guaranteed error bounds make it possible to study rare events that often play a key role in biology, e.g. low switch rates of genetic switches. The FSP method provides a simple and powerful approach to the sensitivity and robustness analyses—with respect to parameter and initial condition variations—of stochastic systems.

Relevant publications:

• Brian Munsky and Mustafa Khammash, "Finite state projection approaches for stochastic analyses of gene regulatory networks”, IEEE Transactions on Automatic Control and IEEE Transactions on Circuits and Systems I, Joint Special Issue on Systems Biology, in press.
  
• Brian Munsky and Mustafa Khammash, “A Multiple Time Interval Finite State Projection Algorithm for the Solution to the Chemical Master Equation", Journal of Computational Physics, 226, 818-835 (2007).
  
• Slaven Peles, Brian Munsky and Mustafa Khammash, "Reduction and Solution of the Chemical Master Equation Using Time-Scale Separation and Finite State Projection," Journal of Chemical Physics 125 (22), 503646 (December 2006).
  
• Brian Munsky and Mustafa Khammash, "The Finite State Projection Algorithm for the Solution of the Chemical Master Equation," Journal of Chemical Physics 124, 044104 (2006).