Concretizing the Process Hitting into Biological Regulatory Networks

Abstract

Abstract. The Process Hitting (PH) is a recently introduced framework to model concurrent processes. Its major originality lies in a specific restriction on the causality of actions, which makes the formal analysis of very large systems tractable. PH is suitable to model Biological Regulatory Networks (BRNs) with complete or partial knowledge of cooperations between regulators by defining the most permissive dynamics with respect to these constraints.On the other hand, the qualitative modeling of BRNs has been widely addressed using René Thomas' formalism, leading to numerous theoretical work and practical tools to understand emerging behaviors.Given a PH model of a BRN, we first tackle the inference of the underlying Interaction Graph between components. Then the inference of corresponding Thomas' models is provided using Answer Set Programming, which allows notably an efficient enumeration of (possibly numerous) compatible parametrizations.In addition to giving a formal link between different approaches for qualitative BRNs modeling, this work emphasizes the ability of PH to deal with large BRNs with incomplete knowledge on cooperations, where Thomas' approach fails because of the combinatorics of parameters. IntroductionAs regulatory phenomena play a crucial role in biological systems, they need to be studied accurately. Biological Regulatory Networks (BRNs) consist in sets of either positive or negative mutual effects between the components. With the purpose of analyzing these systems, they are often modeled as graphs which make it possible to determine the possible evolutions of all the interacting components of the system. Indeed, besides continuous models of physicists, often designed through systems of ordinary differential equations, a discrete modeling approach was initiated by René Thomas in 1973 [1].In this approach, the different levels of a component, such as concentration or expression levels, are abstractly represented by (positive) integer values and transitions between these levels may be considered as instantaneous. Hence, qualitative state graphs may be derived from which we are able to formally find out all the possible behaviors expressed as sequences of transitions between these states. Nevertheless, these dynamics can be precisely established only with regard to some discrete parameters which stand for a kind of "focal points", i.e. the evolutionary tendency from each state and depending of the set of resources in this very state, that is, the set of the other currently interacting components. Hereafter, we refer to these discrete parameters as Thomas' parameters.Thomas' modeling has motivated numerous works around the link between the Interaction Graph (IG) (summarizing the global influences between components) and the possible dynamics (e.g., [2,3]), model reduction (e.g., [4]), formal checking of dynamics (e.g., [5,6]), and the incorporation of time (e.g., [7,8]) and probability (e.g., [9]) dimensions, to name but a few. While the formal checking of dynamical properties is often limite...

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