Hybrid Simulation of Dynamic Reaction Networks in Multi-Level Models

Methods combining deterministic and stochastic concepts present an efficient alternative to a purely stochastic treatment of biochemical models. Traditionally, those methods split biochemical reaction networks into one set of slow reactions that is computed stochastically and one set of fast reactions that is computed deterministically. Applying those methods to multi-level models with dynamic nestings requires coping with dynamic reaction networks changing over time. In addition, in case of large populations of nested entities, stochastic events can still decrease the runtime performance significantly, as reactions of dynamically nested entities are inherently stochastic. In this paper, we apply a hybrid simulation algorithm combining deterministic and stochastic concepts to multi-level models including an approximation control. Further, we present an extension of this simulation algorithm applying an additional approximation by executing multiple independent stochastic events simultaneously in one simulation step. The algorithm has been implemented in the rule-based multi-level modeling language ML-Rules. Its impact on speed and accuracy is evaluated based on simulations performed with a model of Dictyostelium discoideum amoebas.