The mathematics of randomness inside a single cell

Randomness pervades the biochemical processes that make up life at the cellular level; variations in the dynamic behaviour of cellular processes have been observed even if cells are genetically identical and located in identical environments.   Examples of stochastic phenomena inside the cell are numerous and stochastic modeling plays an important role in the design of novel synthetic cellular networks.  In this talk, I will describe basic mathematical techniques for the modeling, simulating, and analyzing stochastic biocircuits such as Markov processes, the Gillespie algorithm, and master equations.  With this background, I will then introduce some problems on the cutting edge of single-cell analysis and describe methods that scientists and engineers are developing to parsimoniously model biocircuits, estimate their states and parameters, and deal with the inherent uncertainty of the
cellular environment.