Multi-scale stochastic systems motivated by biological models

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The challenge of systems biology is identifying how interactions of the proteome and genome produce the function and behaviour of a cell. Cells are inherently "noisy" systems, and how complex biochemical pathways are affected by intrinsic and extrinsic stochasticity is not well understood. A cellular network can be modelled mathematically using the principles of chemical kinetics. At the cellular level, chemical dynamics are often dominated by the action of regulatory molecules present at levels of only a few copies per cell. Intrinsic noise due to random fluctuations of these components can have significant consequences, and stochastic modelling is necessary in order to fully describe the set of possible outcomes. In many cases reaction rates can also vary over several orders of magnitude, which implies that fluctuations of effective changes in abundances occur on multiple time-scales. Many important intracellular processes, from biochemical signalling to gene regulation, are also greatly affected by the location and motility of the molecular types involved.