Logical modeling of the mammalian cell cycle

Proper understanding of the behavior of complex biological regulatory networks requires the integration of heterogeneous data into predictive mathematical models. Logical modeling focuses on qualitative data and offers a flexible framework to delineate the main dynamical properties of such networks. However, formal analysis faces a combinatorial explosion as the number of regulatory components and interactions increases. Here, we show how model-checking techniques can be used to verify sophisticated dynamical properties resulting from model regulatory structure. We demonstrate the power of this approach through the updating of a model of the molecular network controlling mammalian cell cycle. We use model-checking to progressively refine this model in order to fit recent experimental observations. The resulting model accounts for the sequential activation of cyclins, the role of Skp2, and emphasizes a multifunctional role for the cell cycle inhibitor Rb

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

Model Checking to Assess T-Helper Cell Plasticity

Computational modeling constitutes a crucial step toward the functional understanding of complex cellular networks. In particular, logical modeling has proven suitable for the dynamical analysis of large signaling and transcriptional regulatory networks. In this context, signaling input components are generally meant to convey external stimuli, or environmental cues. In response to such external signals, cells acquire specific gene expression patterns modeled in terms of attractors (e.g., stable states). The capacity for cells to alter or reprogram their differentiated states upon changes in environmental conditions is referred to as cell plasticity. In this article, we present a multivalued logical framework along with computational methods recently developed to efficiently analyze large models. We mainly focus on a symbolic model checking approach to investigate switches between attractors subsequent to changes of input conditions. As a case study, we consider the cellular network regulating the differentiation of T-helper (Th) cells, which orchestrate many physiological and pathological immune responses. To account for novel cellular subtypes, we present an extended version of a published model of Th cell differentiation. We then use symbolic model checking to analyze reachability properties between Th subtypes upon changes of environmental cues. This allows for the construction of a synthetic view of Th cell plasticity in terms of a graph connecting subtypes with arcs labeled by input conditions. Finally, we explore novel strategies enabling specific Th cell polarizing or reprograming events.LabEx MemoLife, Ecole Normale Supérieure, FCT grants: (PEst-OE/EEI/LA0021/2013, IF/01333/2013), Ph.D.program of the Agence National de Recherche sur Le Sida (ANRS), European Research Council consolidator grant

Basins of Attraction, Commitment Sets and Phenotypes of Boolean Networks

The attractors of Boolean networks and their basins have been shown to be highly relevant for model validation and predictive modelling, e.g., in systems biology. Yet there are currently very few tools available that are able to compute and visualise not only attractors but also their basins. In the realm of asynchronous, non-deterministic modeling not only is the repertoire of software even more limited, but also the formal notions for basins of attraction are often lacking. In this setting, the difficulty both for theory and computation arises from the fact that states may be ele- ments of several distinct basins. In this paper we address this topic by partitioning the state space into sets that are committed to the same attractors. These commitment sets can easily be generalised to sets that are equivalent w.r.t. the long-term behaviours of pre-selected nodes which leads us to the notions of markers and phenotypes which we illustrate in a case study on bladder tumorigenesis. For every concept we propose equivalent CTL model checking queries and an extension of the state of the art model checking software NuSMV is made available that is capa- ble of computing the respective sets. All notions are fully integrated as three new modules in our Python package PyBoolNet, including functions for visualising the basins, commitment sets and phenotypes as quotient graphs and pie charts

Abstracting Asynchronous Multi-Valued Networks: An Initial Investigation

Multi-valued networks provide a simple yet expressive qualitative state based modelling approach for biological systems. In this paper we develop an abstraction theory for asynchronous multi-valued network models that allows the state space of a model to be reduced while preserving key properties of the model. The abstraction theory therefore provides a mechanism for coping with the state space explosion problem and supports the analysis and comparison of multi-valued networks. We take as our starting point the abstraction theory for synchronous multi-valued networks which is based on the finite set of traces that represent the behaviour of such a model. The problem with extending this approach to the asynchronous case is that we can now have an infinite set of traces associated with a model making a simple trace inclusion test infeasible. To address this we develop a decision procedure for checking asynchronous abstractions based on using the finite state graph of an asynchronous multi-valued network to reason about its trace semantics. We illustrate the abstraction techniques developed by considering a detailed case study based on a multi-valued network model of the regulation of tryptophan biosynthesis in Escherichia coli.Comment: Presented at MeCBIC 201

Efficient parameter search for qualitative models of regulatory networks using symbolic model checking

Investigating the relation between the structure and behavior of complex biological networks often involves posing the following two questions: Is a hypothesized structure of a regulatory network consistent with the observed behavior? And can a proposed structure generate a desired behavior? Answering these questions presupposes that we are able to test the compatibility of network structure and behavior. We cast these questions into a parameter search problem for qualitative models of regulatory networks, in particular piecewise-affine differential equation models. We develop a method based on symbolic model checking that avoids enumerating all possible parametrizations, and show that this method performs well on real biological problems, using the IRMA synthetic network and benchmark experimental data sets. We test the consistency between the IRMA network structure and the time-series data, and search for parameter modifications that would improve the robustness of the external control of the system behavior

Qualitative modelling and analysis of regulations in multi-cellular systems using Petri nets and topological collections

In this paper, we aim at modelling and analyzing the regulation processes in multi-cellular biological systems, in particular tissues. The modelling framework is based on interconnected logical regulatory networks a la Rene Thomas equipped with information about their spatial relationships. The semantics of such models is expressed through colored Petri nets to implement regulation rules, combined with topological collections to implement the spatial information. Some constraints are put on the the representation of spatial information in order to preserve the possibility of an enumerative and exhaustive state space exploration. This paper presents the modelling framework, its semantics, as well as a prototype implementation that allowed preliminary experimentation on some applications.Comment: In Proceedings MeCBIC 2010, arXiv:1011.005

A Method to Identify and Analyze Biological Programs through Automated Reasoning.

Predictive biology is elusive because rigorous, data-constrained, mechanistic models of complex biological systems are difficult to derive and validate. Current approaches tend to construct and examine static interaction network models, which are descriptively rich but often lack explanatory and predictive power, or dynamic models that can be simulated to reproduce known behavior. However, in such approaches implicit assumptions are introduced as typically only one mechanism is considered, and exhaustively investigating all scenarios is impractical using simulation. To address these limitations, we present a methodology based on automated formal reasoning, which permits the synthesis and analysis of the complete set of logical models consistent with experimental observations. We test hypotheses against all candidate models, and remove the need for simulation by characterizing and simultaneously analyzing all mechanistic explanations of observed behavior. Our methodology transforms knowledge of complex biological processes from sets of possible interactions and experimental observations to precise, predictive biological programs governing cell function

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