BackgroundProteins, individual cells, and cell populations denote different levels of an organizational hierarchy, each of which with its own dynamics. Multi-level modeling is concerned with describing a system at these different levels and relating their dynamics. Rule-based modeling has increasingly attracted attention due to enabling a concise and compact description of biochemical systems. In addition, it allows different methods for model analysis, since more than one semantics can be defined for the same syntax.ResultsMulti-level modeling implies the hierarchical nesting of model entities and explicit support for downward and upward causation between different levels. Concepts to support multi-level modeling in a rule-based language are identified. To those belong rule schemata, hierarchical nesting of species, assigning attributes and solutions to species at each level and preserving content of nested species while applying rules. Further necessities are the ability to apply rules and flexibly define reaction rate kinetics and constraints on nested species as well as species that are nested within others. An example model is presented that analyses the interplay of an intracellular control circuit with states at cell level, its relation to cell division, and connections to intercellular communication within a population of cells. The example is described in ML-Rules - a rule-based multi-level approach that has been realized within the plug-in-based modeling and simulation framework JAMES II.ConclusionsRule-based languages are a suitable starting point for developing a concise and compact language for multi-level modeling of cell biological systems. The combination of nesting species, assigning attributes, and constraining reactions according to these attributes is crucial in achieving the desired expressiveness. Rule schemata allow a concise and compact description of complex models. As a result, the presented approach facilitates developing and maintaining multi-level models that, for instance, interrelate intracellular and intercellular dynamics.

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.

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With Systems Biology, a promising new application area for modelling and simulation emerges. Today's biologists are facing huge amounts of data delivered at different levels of detail by a multitude of advanced experimentation techniques. The Systems Biology approach copes with this information by cycling through phases of forming hypotheses, constructing models, experimenting with or analysing these models, and validating the findings by wet-lab experiments. A crucial point is therefore the way in which the knowledge about a system is formalized, that is, how a biological system is described, as this constrains the perception of the system as well as the scope of possible answers the model might provide. In this article, we compare different discrete event modelling formalisms (PETRI NETS, Stochastic p-CALCULUS, STATECHARTS, and DEVS) regarding their applicability to a cell biological system of current research interest, the Wnt signalling pathway. We then introduce the popular Gillespie algorithm, which is the foundation of many discrete event simulators for molecular-biological systems, and elaborate on some interesting extensions.