Proteins and other biomolecules interact at the level of domains—structural subunits comprised of tens to hundreds of amino acids—and motifs—short sequences of amino or nucleic acids to which domains may bind, often following phosphorylation or other posttranslational modifications. The catalog of these functional elements and their interactions is continually growing and poses a major barrier to the development of predictive mathematical models, which requires explicit incorporation of these functional network elements. Combinatorial complexity, an explosion in the number of possible chemical species as molecules with multiple interactions are added to a model, means that conventional modeling approaches can consider only a small subset of possible interactions simultaneously, limiting the predictive capability of such models. Here, I will describe a language for precisely describing the functional elements and interactions in biochemical networks, methods for simulating models described in this language, and applications to the modeling of specific systems of biological and clinical relevance. The BioNetGen Language (BNGL) uses graphs to represent proteins and other biomolecules, with nodes representing functional subunits of these molecules (such as domains and motifs) and edges representing binding interactions. Graph rewriting rules describe biochemical transformations, such the formation or dissociation of bonds or state changes. This language enables the construction of precise and comprehensive models. In the near future the widespread use of modeling languages such as BNGL will greatly expand the scope of information that can be incorporated into models of cellular networks. The BioNetGen software (BNG) incorporates a wide range of analytical and simulation tools. In addition, networks generated by BNG can be exported in the Systems Biology Markup Languague, providing access to an even broader range of simulation and analysis toos. Standard methods for simulating reaction networks, such as ODE's and Gillespie-based stochastic algorithms, are not adequate to simulate networks arising from the rule-based description of realistic signaling cascades. These systems require a shift to particle-based methods, in which explicit generation of species and reactions is largely avoided. I will present several applications to the modeling of signal transduction networks, including immune and growth factor receptors, which are the subject on ongoing modeling and experimental efforts.

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