Multiscale Numerical Simulation for Biochemical Networks
Linda Petzold and Mustafa Khammash
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 Stochastic Simulation Algorithm
(SSA) of Gillespie has been widely used to treat these problems. However
as a procedure that simulates every reaction event, the SSA is necessarily
inefficient for most realistic problems. There are two main reasons for this, both arising from the underlying multiscale nature of the problem: (a) stiffness, i.e. the presence of multiple time scales; and (b) the need to include in the simulation both species that are present in relatively small quantities and should be modeled by a discrete stochastic process, and species that are present in larger quantities and are more efficiently modeled by a deterministic differential equation (or at some scale in between). The work in Professor Petzold's research group seeks to address both of these issues, with accelerated discrete stochastic methods that are specifically designed to deal with stiffness, and with hybrid methods designed to model each reaction at the appropriate scale. |