Limitation and averaging for deterministic and stochastic biochemical reaction networks

We discuss model reduction of multiscale networks of biochemical reactions used in systems biology as models for cell physiology and pathology. For linear kinetic models, which appear as ”pseudo-monomolecular” subsystems of the nonlinear reaction networks, we obtain a general reduction algorithm based on cycle averaging and surgery. The same algorithm, when applied to stochastic networks, allows to reduce simulation time by many orders of magnitude.