Semantics and Efficient Simulation Algorithms of an Expressive Multilevel Modeling Language

Abstract

The domain-specific modeling and simulation language ML-Rules is aimed at facilitating the description of cell biological systems at different levels of organization. Model states are chemical solutions that consist of dynamically nested, attributed entities. The model dynamics are described by rules that are constrained by arbitrary functions, which can operate on the entities’ attributes, (nested) solutions, and the reaction kinetics. Thus, ML-Rules supports an expressive hierarchical, variable structure modeling of cell biological systems. The formal syntax and semantics of ML-Rules show that it is firmly rooted in continuous-time Markov chains. In addition to a generic stochastic simulation algorithm for ML-Rules, we introduce several specialized algorithms that are able to handle subclasses of ML-Rules more efficiently. The algorithms are compared in a performance study, leading to conclusions on the relation between expressive power and computational complexity of rule-based modeling languages.