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

Marker and source-marker reprogramming of Most Permissive Boolean networks and ensembles with BoNesis

Boolean networks (BNs) are discrete dynamical systems with applications to the modeling of cellular behaviors. In this paper, we demonstrate how the software BoNesis can be employed to exhaustively identify combinations of perturbations which enforce properties on their fixed points and attractors. We consider marker properties, which specify that some components are fixed to a specific value. We study 4 variants of the marker reprogramming problem: the reprogramming of fixed points, of minimal trap spaces, and of fixed points and minimal trap spaces reachable from a given initial configuration with the most permissive update mode. The perturbations consist of fixing a set of components to a fixed value. They can destroy and create new attractors. In each case, we give an upper bound on their theoretical computational complexity, and give an implementation of the resolution using the BoNesis Python framework. Finally, we lift the reprogramming problems to ensembles of BNs, as supported by BoNesis, bringing insight on possible and universal reprogramming strategies. This paper can be executed and modified interactively.Comment: Notebook available at https://nbviewer.org/github/bnediction/reprogramming-with-bonesis/blob/release/paper.ipyn

Identification of control targets in Boolean molecular network models via computational algebra

Motivation: Many problems in biomedicine and other areas of the life sciences can be characterized as control problems, with the goal of finding strategies to change a disease or otherwise undesirable state of a biological system into another, more desirable, state through an intervention, such as a drug or other therapeutic treatment. The identification of such strategies is typically based on a mathematical model of the process to be altered through targeted control inputs. This paper focuses on processes at the molecular level that determine the state of an individual cell, involving signaling or gene regulation. The mathematical model type considered is that of Boolean networks. The potential control targets can be represented by a set of nodes and edges that can be manipulated to produce a desired effect on the system. Experimentally, node manipulation requires technology to completely repress or fully activate a particular gene product while edge manipulations only require a drug that inactivates the interaction between two gene products. Results: This paper presents a method for the identification of potential intervention targets in Boolean molecular network models using algebraic techniques. The approach exploits an algebraic representation of Boolean networks to encode the control candidates in the network wiring diagram as the solutions of a system of polynomials equations, and then uses computational algebra techniques to find such controllers. The control methods in this paper are validated through the identification of combinatorial interventions in the signaling pathways of previously reported control targets in two well studied systems, a p53-mdm2 network and a blood T cell lymphocyte granular leukemia survival signaling network.Comment: 12 pages, 4 figures, 2 table

Synthesis of Boolean Networks from Biological Dynamical Constraints using Answer-Set Programming

International audienceBoolean networks model finite discrete dynamical systems with complex behaviours. The state of each component is determined by a Boolean function of the state of (a subset of) the components of the network. This paper addresses the synthesis of these Boolean functions from constraints on their domain and emerging dynamical properties of the resulting network. The dynamical properties relate to the existence and absence of trajectories between partially observed configurations, and to the stable behaviours (fixpoints and cyclic attractors). The synthesis is expressed as a Boolean satisfiability problem relying on Answer-Set Programming with a parametrized complexity, and leads to a complete non-redundant characterization of the set of solutions. Considered constraints are particularly suited to address the synthesis of models of cellular differentiation processes, as illustrated on a case study. The scalability of the approach is demonstrated on random networks with scale-free structures up to 100 to 1,000 nodes depending on the type of constraints

Boolean analysis of lateral inhibition

We study Boolean networks which are simple spatial models of the highly conserved Delta–Notch system. The models assume the inhibition of Delta in each cell by Notch in the same cell, and the activation of Notch in presence of Delta in surrounding cells. We consider fully asynchronous dynamics over undirected graphs representing the neighbour relation between cells. In this framework, one can show that all attractors are fixed points for the system, independently of the neighbour relation, for instance by using known properties of simplified versions of the models, where only one species per cell is defined. The fixed points correspond to the so-called fine-grained “patterns” that emerge in discrete and continuous modelling of lateral inhibition. We study the reachability of fixed points, giving a characterisation of the trap spaces and the basins of attraction for both the full and the simplified models. In addition, we use a characterisation of the trap spaces to investigate the robustness of patterns to perturbations. The results of this qualitative analysis can complement and guide simulation-based approaches, and serve as a basis for the investigation of more complex mechanisms

Random Walks on Stochastic Temporal Networks

In the study of dynamical processes on networks, there has been intense focus on network structure -- i.e., the arrangement of edges and their associated weights -- but the effects of the temporal patterns of edges remains poorly understood. In this chapter, we develop a mathematical framework for random walks on temporal networks using an approach that provides a compromise between abstract but unrealistic models and data-driven but non-mathematical approaches. To do this, we introduce a stochastic model for temporal networks in which we summarize the temporal and structural organization of a system using a matrix of waiting-time distributions. We show that random walks on stochastic temporal networks can be described exactly by an integro-differential master equation and derive an analytical expression for its asymptotic steady state. We also discuss how our work might be useful to help build centrality measures for temporal networks.Comment: Chapter in Temporal Networks (Petter Holme and Jari Saramaki editors). Springer. Berlin, Heidelberg 2013. The book chapter contains minor corrections and modifications. This chapter is based on arXiv:1112.3324, which contains additional calculations and numerical simulation