Abstract
Rule-based modeling frameworks provide a specification format in which kinetic interactions are modeled as “reaction rules”. These rules are specified on phosphorylation motifs, domains, binding sites and other sub-molecular structures, and have proved useful for modeling signal transduction. Visual representations are necessary to understand individual rules as well as analyze interactions of hundreds of rules, which motivates the need for automated diagramming tools for rule-based models. Here, we present a theoretical framework that unifies the layers of information in a rule-based model and enables automated visualization of (i) the mechanism encoded in a rule, (ii) the regulatory interaction of two or more rules, and (iii) the emergent network architecture of a large rule set. Specifically, we present a compact rule visualization that conveys the action of a rule explicitly (unlike conventional visualizations), a regulatory graph visualization that conveys regulatory interactions between rules, and a set of graph compression methods that synthesize informative pathway diagrams from complex regulatory graphs. These methods enable inference of network motifs (such as feedback and feed-forward loops), automated generation of signal flow diagrams for hundreds of rules, and tunable network compression using heuristics and graph analysis, all of which are advances over the state of the art for rule-based models. These methods also produce more readable diagrams than currently available tools as we show with an empirical comparison across 27 published rule-based models of various sizes. We provide an implementation in the open source and freely available BioNetGen framework, but the underlying methods are applicable to all current rule-based models in BioNetGen, Kappa and Simmune frameworks. We expect that these tools will promote communication and analysis of rule-based models and their eventual integration into whole cell models.
Author Summary Signaling in living cells is mediated through a complex network of chemical interactions. Current predictive models of signal pathways have hundreds of reaction rules that specify chemical interactions, and a comprehensive model of a stem cell or cancer cell would be expected to have many more. Visualizations of rules and their interactions are needed to navigate, organize, communicate and analyze large signaling models. In this work, we have developed: (i) a novel visualization for individual rules that compactly conveys what each rule does, (ii) a comprehensive visualization of a set of rules as a network of regulatory interactions called a regulatory graph, and (iii) a set of procedures for compressing the regulatory graph into a pathway diagram that highlights underlying signaling motifs such as feedback and feedforward loops. We show that these visualizations are compact and informative across models of widely varying sizes. The methods developed here not only improve the understandability of current models, but also establish principles for organizing the much larger models of the future.
