Access to unified datasets of protein and genetic interactions is critical for interrogation of gene/ protein function and analysis of global network properties. BioGRID is a freely accessible database of physical and genetic interactions available at

Abstract. Modelling is becoming a necessity in studying biological signalling pathways, because the combinatorial complexity of such systems rapidly overwhelms intuitive and qualitative forms of reasoning. Yet, this same combinatorial explosion makes the traditional modelling paradigm based on systems of differential equations impractical. In contrast, agentbased or concurrent languages, such as κ [1–3] or the closely related BioNetGen language [4–10], describe biological interactions in terms of rules, thereby avoiding the combinatorial explosion besetting differential equations. Rules are expressed in an intuitive graphical form that transparently represents biological knowledge. In this way, rules become a natural unit of model building, modification, and discussion. We illustrate this with a sizeable example obtained from refactoring two models of EGF receptor signalling that are based on differential equations [11, 12]. An exciting aspect of the agent-based approach is that it naturally lends itself to the identification and analysis of the causal structures that deeply shape the dynamical, and perhaps even evolutionary, characteristics of complex distributed biological systems. In particular, one can adapt the notions of causality and conflict, familiar from concurrency theory, to κ, our representation language of choice. Using the EGF receptor model as an example, we show how causality enables the formalization of the colloquial concept of pathway and, perhaps more surprisingly, how conflict can be used to dissect the signalling dynamics to obtain a qualitative handle on the range of system behaviours. By taming the combinatorial explosion, and exposing the causal structures and key kinetic junctures in a model, agent- and rule-based representations hold promise for making modelling more powerful, more perspicuous, and of appeal to a wider audience. 1

Abstract. Given the combinatorial nature of cellular signalling pathways, where biological agents can bind and modify each other in a large number of ways, concurrent or agent-based languages seem particularly suitable for their representation and simulation [1–4]. Graphical modelling languages such as κ [5–8], or the closely related BNG language [9– 14], seem to afford particular ease of expression. It is unclear however how such models can be implemented. 6 Even a simple model of the EGF receptor signalling network can generate more than 10 23 non-isomorphic species [5], and therefore no approach to simulation based on enumerating species (beforehand, or even on-the-fly) can handle such models without sampling down the number of potential generated species. We present in this paper a radically different method which does not attempt to count species. The proposed algorothm uses a representation of the system together with a super-approximation of its ‘event horizon ’ (all events that may happen next), and a specific correction scheme to obtain exact timings. Being completely local and not based on any kind of enumeration, this algorithm has a per event time cost which is independent of (i) the size of the set of generable species (which can even be infinite), and (ii) independent of the size of the system (ie, the number of agent instances). We show how to refine this algorithm, using concepts derived from the classical notion of causality, so that in addition to the above one also has that the even cost is depending (iii) only logarithmically on the size of the model (ie, the number of rules). Such complexity properties reflect in our implementation which, on a current computer, generates about 10 6 events per minute in the case of the simple EGF receptor model mentioned above, using a system with 10 5 agents. 1

Formalized rules for protein-protein interactions have recently been introduced to represent the binding and enzymatic activities of proteins in cellular signaling. Rules encode an understanding of how a system works in terms of the biomolecules in the system and their possible states and interactions. A set of rules can be as easy to read as a diagrammatic interaction map, but unlike most such maps, rules have precise interpretations. Rules can be processed to automatically generate a mathematical or computational model for a system, which enables explanatory and predictive insights into the system’s behavior. Rules are independent units of a model specification that facilitate model revision. Instead of changing a large number of equations or lines of code, as may be required in the case of a conventional mathematical model, a protein interaction can be introduced or modified simply by adding or changing a single rule that represents the interaction of interest. Rules can be defined and visualized by using graphs, so no specialized training in mathematics or computer science is necessary to create models or to take advantage of the representational precision of rules. Rules can be encoded in a machine-readable format to enable electronic storage and exchange of models, as well as basic knowledge about protein-protein interactions. Here, we review the motivation for rule-based modeling; applications of the approach; and issues that arise in model specification, simulation, and testing. We also discuss rule visualization and exchange and the software available for rule-based modeling.

The process by which a cell senses and responds to its environment, as in signal transduction, is often mediated by a network of protein-protein interactions, in which proteins combine to form complexes and undergo post-translational modifications, which regulate their enzymatic and binding activities. A typical signaling protein contains multiple sites of protein interaction and modification and may contain catalytic domains. As a result, interactions of signaling proteins have the potential to generate a combinatorially large number of complexes and modified states, and representing signal-transduction networks can be challenging. Representation, in the form of a diagram or model, usually involves a tradeoff between comprehensibility and precision: comprehensible representations tend to be ambiguous or incomplete, whereas precise representations, such as a long list of chemical species and reactions in a network, tend to be incomprehensible. Here, we develop conventions for representing signal-transduction networks that are both comprehensible and precise. Labeled nodes represent components of proteins and their states, and edges represent bonds between components. Binding and enzymatic reactions are described by reaction rules, in which left graphs define the properties of reactants and right graphs define the products that result from transformations of reactants. The reaction rules can be evaluated to derive a mathematical model.

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Abstract. We present an algorithm, called BioLab, for verifying temporal properties of rule-based models of cellular signalling networks. BioLab models are encoded in the BioNetGen language, and properties are expressed as formulae in probabilistic bounded linear temporal logic. Temporal logic is a formalism for representing and reasoning about propositions qualified in terms of time. Properties are then verified using sequential hypothesis testing on executions generated using stochastic simulation. BioLab is optimal, in the sense that it generates the minimum number of executions necessary to verify the given property. Bio-Lab also provides guarantees on the probability of it generating Type-I (i.e., false-positive) and Type-II (i.e., false-negative) errors. Moreover, these error bounds are pre-specified by the user. We demonstrate Bio-Lab by verifying stochastic effects and bistability in the dynamics of the T-cell receptor signaling network. 1

We present a method for generating a biochemical reaction network from a description of the interactions of components of biomolecules. The interactions are specified in the form of reaction rules, each of which defines a class of reaction associated with a type of interaction. Reactants within a class have shared properties, which are specified in the rule defining the class. A rule also provides a rate law, which governs each reaction in a class, and a template for transforming reactants into products. A set of reaction rules can be applied to a seed set of chemical species and, subsequently, any new species that are found as products of reactions to generate a list of reactions and a list of the chemical species that participate in these reactions, i.e., a reaction network, which can be translated into a mathematical model. © 2005 Wiley Periodicals, Inc. Complexity 10: 22–41, 2005 Key Words: local rules; automatic model generation; networks; signal transduction; combinatorial complexity; systems biology The cell is a complex adaptive system whose emergent behavior we understand only poorly. One reason for our lack of understanding is the complexity of cellular decision making, which is often mediated by a system of interacting proteins. Systems of interacting proteins are particularly prominent in signal transduction [1], 1 the focus Correspondence to: William S. Hlavacek,

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Biological networks can be broken down into modules, groups of interacting molecules. To uncover these functional modules and study their evolution, our research groups are developing graphtheory based strategies for the analysis of gene expression data. We are looking for groups of completely connected subgraphs (e.g. cliques) in which corresponding members have the same combination of protein domains in co-expression networks. The common pattern shown by a group of similar cliques is a “network motif ” that may be reused multiple times within organisms. We have developed algorithms for constructing gene co-expression networks labeled with corresponding protein sequence domain combinations, and then detected recurring network motifs with similar protein domain memberships within these labeled networks. The statistical significance of detected