Multiscale Numerical Simulation for Biochemical Networks

Linda Petzold and Mustafa Khammash

In microscopic systems formed by living cells, the small numbers of reactant molecules can result in dynamical behavior that is discrete and stochastic rather than continuous and deterministic. The figure shows the heat-shock response in E. Coli, where an estimated 20-30 molecules per cell play a key role in sensing the folding state of the cell and in regulating the production of heat shock proteins.  The system cannot be simulated at the fully stochastic level, due to the presence of an exceedingly large number of molecules and reactions that must be accounted for in the stochastic simulation algorithm, alongside of those that appear in small numbers.  We are working on multiscale simulation algorithms that can handle this type of situation.