The granularity of a rule is adjustable. Although the rule based modeling framework described above is expressive and sufficiently rich to describe a wide array of molecular interactions involved selleck chemical in cell signaling, the graphs of this framework are not sufficiently expressive to provide a completely natural representation of the substructures of signaling proteins. As discussed in detail below, components of a protein can themselves contain components, and so on. Yet, in the framework described above, the components of a protein, regardless of their structural relationships, are represented in the same way, as the colored vertices of a graph, with a shared color indicating joint membership in the set of components of a particular type of mole cule.

In other words, if a component and a subcompo nent of this component are both included in a model, the structural relationship between the component and subcomponent is lost. This representational limitation may not prevent a modeler from specifying a model with desired properties, but it may prevent others from easily connecting the formal elements of the model to the underlying biology and easily interpreting the model as intended. Here, mainly to enable better annotation of rule based models, we introduce the concept of using hierarchical graphs to represent molecules, such as proteins, for which there are structural relationships among compo nent parts. We also present an algorithm and software, which we have called HNauty, for assigning canonical labels to hierarchical graphs.

Canonical labeling enables one to determine if two graphs are the same or different simply by comparing their labels. This task, which is essentially equivalent to the solution of a graph iso morphism problem, is a routine part of network genera tion, the process of enumerating the reactions implied by a set of rules. Network generation, which is not always practical, is an essential ingredient in the gener ate first and on the fly approaches to simulation of a rule based model. Thus, this report not only lays groundwork for using hierarchical graphs to anno tate rule based models but also lays groundwork for making such graphs elements of executable models. In the remainder of this section, we provide additional background on the graphical formalism underlying BNGL, on the hierarchical substructures of proteins, and on graph isomorphism and Nauty, a software tool for canonical labeling of colored graphs. We then provide examples of how hierarchical graphs can be used to represent proteins more naturally than the graphs of the BNGL formalism, and we present a simple extension of the Entinostat method implemented in Nauty that allows for canonical labeling of hierarchical graphs.