Time dependent solution for acceleration of tau-leaping

The tau-leaping method is often effective for speeding up discrete stochasticsimulation of chemically reacting systems. However, when fast reactions areinvolved, the speed-up for this method can be quite limited. One way to ad-dress this is to apply a stochastic quasi-steady state assumption. However wemust to be careful when using this assumption. If the fast subsystem cannotreach a steady distribution fast enough, the quasi-steady-state assumptionwill propagate error into the simulation. To avoid these errors, we proposeto use the time dependent solution rather than the quasi-steady-state. Gen-erally speaking, the time dependent solution is not easy to derive for anarbitrary network. However, for some common motifs we do have time de-pendent solutions. We derive the time dependent solutions for these motifs,and then show how they can be used with tau-leaping to achieve substantialspeed-ups, including for a realistic model of blood coagulation. Although themethod is complicated, we have automated it. ∗Corresponding authorEmail addresses: [email protected] (Jin Fu), [email protected] (ShengWu), [email protected] (Linda R. Petzold) Preprint submitted to Journal of Computational PhysicsOctober 25, 2012