Identification of Biological Regulatory Networks from Process Hitting models

International audienceQualitative formalisms offer a well-established alternative to the more tradi-tionally used differential equation models of Biological Regulatory Networks (BRNs). These formalisms led to numerous theoretical works and practical tools to understand emerging behaviors. The analysis of the dynamics of very large models is however a rather hard problem, which led us to previously in-troduce the Process Hitting framework (PH), which is a particular class of non-deterministic asynchronous automata network (or safe Petri nets). Its major advantage lies in the efficiency of several static analyses recently designed to assess dynamical properties, making it possible to tackle very large models. In this paper, we address the formal identification of qualitative models of BRNs from PH models. First, the inference of the Interaction Graph from a PH model summarizes the signed influences between the components that are effective for the dynamics. Second, we provide the inference of all René-Thomas models of BRNs that are compatible with a given PH. As the PH allows the specification of nondeterministic interactions between components, our inference emphasizes the ability of PH to deal with large BRNs with incomplete knowledge on interactions, where Thomas's approach fails because of the combinatorics of parameters. The inference of corresponding Thomas models is implemented using An-swer Set Programming, which allows in particular an efficient enumeration of (possibly numerous) compatible parametrizations

Under-approximating Cut Sets for Reachability in Large Scale Automata Networks

In the scope of discrete finite-state models of interacting components, we present a novel algorithm for identifying sets of local states of components whose activity is necessary for the reachability of a given local state. If all the local states from such a set are disabled in the model, the concerned reachability is impossible. Those sets are referred to as cut sets and are computed from a particular abstract causality structure, so-called Graph of Local Causality, inspired from previous work and generalised here to finite automata networks. The extracted sets of local states form an under-approximation of the complete minimal cut sets of the dynamics: there may exist smaller or additional cut sets for the given reachability. Applied to qualitative models of biological systems, such cut sets provide potential therapeutic targets that are proven to prevent molecules of interest to become active, up to the correctness of the model. Our new method makes tractable the formal analysis of very large scale networks, as illustrated by the computation of cut sets within a Boolean model of biological pathways interactions gathering more than 9000 components

Cell death and life in cancer: mathematical modeling of cell fate decisions

Tumor development is characterized by a compromised balance between cell life and death decision mechanisms, which are tighly regulated in normal cells. Understanding this process provides insights for developing new treatments for fighting with cancer. We present a study of a mathematical model describing cellular choice between survival and two alternative cell death modalities: apoptosis and necrosis. The model is implemented in discrete modeling formalism and allows to predict probabilities of having a particular cellular phenotype in response to engagement of cell death receptors. Using an original parameter sensitivity analysis developed for discrete dynamic systems, we determine the critical parameters affecting cellular fate decision variables that appear to be critical in the cellular fate decision and discuss how they are exploited by existing cancer therapies

Analyzing Large Network Dynamics with Process Hitting

In this chapter, we introduce the Process Hitting framework, which provides the methodology of constructing the most permissive dynamics and then using successive refinements to fine tune the model. We present static analysis methods designed to identify fixed points or answer successive reachability questions, and introduce the stochastic semantics of Process Hitting too

Quantification of reachable attractors in asynchronous discrete dynamics

Motivation: Models of discrete concurrent systems often lead to huge and complex state transition graphs that represent their dynamics. This makes difficult to analyse dynamical properties. In particular, for logical models of biological regulatory networks, it is of real interest to study attractors and their reachability from specific initial conditions, i.e. to assess the potential asymptotical behaviours of the system. Beyond the identification of the reachable attractors, we propose to quantify this reachability. Results: Relying on the structure of the state transition graph, we estimate the probability of each attractor reachable from a given initial condition or from a portion of the state space. First, we present a quasi-exact solution with an original algorithm called Firefront, based on the exhaustive exploration of the reachable state space. Then, we introduce an adapted version of Monte Carlo simulation algorithm, termed Avatar, better suited to larger models. Firefront and Avatar methods are validated and compared to other related approaches, using as test cases logical models of synthetic and biological networks. Availability: Both algorithms are implemented as Perl scripts that can be freely downloaded from http://compbio.igc.gulbenkian.pt/nmd/node/59 along with Supplementary Material.Comment: 19 pages, 2 figures, 2 algorithms and 2 table

Exhaustive analysis of dynamical properties of Biological Regulatory Networks with Answer Set Programming

International audienceThe combination of numerous simple influences between the components of a Biological Regulatory Network (BRN) often leads to behaviors that cannot be grasped intuitively. They thus call for the development of proper mathematical methods to delineate their dynamical properties. As a consequence , formal methods and computer tools for the modeling and simulation of BRNs become essential. Our recently introduced discrete formalism called the Process Hitting (PH), a restriction of synchronous automata networks, is notably suitable to such study. In this paper, we propose a new logical approach to perform model-checking of dynamical properties of BRNs modeled in PH. Our work here focuses on state reachability properties on the one hand, and on the identification of fixed points on the other hand. The originality of our model-checking approach relies in the exhaustive enumeration of all possible simulations verifying the dynamical properties thanks to the use of Answer Set Programming

Abducing Biological Regulatory Networks from Process Hitting models

International audienceThe Process Hitting (PH) is a recently introduced framework to model concurrent processes. It is notably suitable to model Biological Regulatory Networks (BRNs) with partial knowledge of cooperations by defining the most permissive dynamics. On the other hand, the qualitative modeling of BRNs has been widely addressed using René Thomas' formalism. 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 by inferring some parameters and abducing the compatible parametrizations