Uncovering operational interactions in genetic networks using asynchronous boolean dynamics

To analyze and gain intuition on the mechanisms of complex systems of large dimensions, one strategy is to simplify the model by identifying a reduced system, in the form of a smaller set of variables and interactions that still capture specific properties of the system. For large models of biological networks, the diagram of interactions is often well represented by a Boolean model with a family of logical rules. The state space of a Boolean model is finite, and its asynchronous dynamics are fully described by a transition graph in the state space. In this context, a method will be developed for identifying the active or operational interactions responsible for a given dynamic behaviour. The first step in this procedure is the decomposition of the asynchronous transition graph into its strongly connected components, to obtain a ``reduced'' and hierarchically organized graph of transitions. The second step consists of the identification of a partial graph of interactions and a sub-family of logical rules that remain operational in a given region of the state space. This model reduction method and its usefulness are illustrated by an application to a model of programmed cell death. The method identifies two mechanisms used by the cell to respond to death-receptor stimulation and decide between the survival or apoptotic pathways

Dynamical and Structural Modularity of Discrete Regulatory Networks

A biological regulatory network can be modeled as a discrete function that contains all available information on network component interactions. From this function we can derive a graph representation of the network structure as well as of the dynamics of the system. In this paper we introduce a method to identify modules of the network that allow us to construct the behavior of the given function from the dynamics of the modules. Here, it proves useful to distinguish between dynamical and structural modules, and to define network modules combining aspects of both. As a key concept we establish the notion of symbolic steady state, which basically represents a set of states where the behavior of the given function is in some sense predictable, and which gives rise to suitable network modules. We apply the method to a regulatory network involved in T helper cell differentiation

Uncovering operational interactions in genetic networks using asynchronous boolean dynamics

To analyze and gain intuition on the mechanisms of complex systems of large dimensions, one strategy is to simplify the model by identifying a reduced system, in the form of a smaller set of variables and interactions that still capture specific properties of the system. For large models of biological networks, the diagram of interactions is often well represented by a Boolean model with a family of logical rules. The state space of a Boolean model is finite, and its asynchronous dynamics are fully described by a transition graph in the state space. In this context, a method will be developed for identifying the active or operational interactions responsible for a given dynamic behaviour. The first step in this procedure is the decomposition of the asynchronous transition graph into its strongly connected components, to obtain a ``reduced'' and hierarchically organized graph of transitions. The second step consists of the identification of a partial graph of interactions and a sub-family of logical rules that remain operational in a given region of the state space. This model reduction method and its usefulness are illustrated by an application to a model of programmed cell death. The method identifies two mechanisms used by the cell to respond to death-receptor stimulation and decide between the survival or apoptotic pathways

A review of modelling and verification approaches for computational biology

This paper reviews most frequently used computational modelling approaches and formal verification techniques in computational biology. The paper also compares a number of model checking tools and software suits used in analysing biological systems and biochemical networks and verifiying a wide range of biological properties

Decoding the regulatory network of early blood development from single-cell gene expression measurements.

Reconstruction of the molecular pathways controlling organ development has been hampered by a lack of methods to resolve embryonic progenitor cells. Here we describe a strategy to address this problem that combines gene expression profiling of large numbers of single cells with data analysis based on diffusion maps for dimensionality reduction and network synthesis from state transition graphs. Applying the approach to hematopoietic development in the mouse embryo, we map the progression of mesoderm toward blood using single-cell gene expression analysis of 3,934 cells with blood-forming potential captured at four time points between E7.0 and E8.5. Transitions between individual cellular states are then used as input to develop a single-cell network synthesis toolkit to generate a computationally executable transcriptional regulatory network model of blood development. Several model predictions concerning the roles of Sox and Hox factors are validated experimentally. Our results demonstrate that single-cell analysis of a developing organ coupled with computational approaches can reveal the transcriptional programs that underpin organogenesis.We thank J. Downing (St. Jude Children's Research Hospital, Memphis, TN, USA) for the Runx1-ires-GFP mouse. Research in the authors' laboratory is supported by the Medical Research Council, Biotechnology and Biological Sciences Research Council, Leukaemia and Lymphoma Research, the Leukemia and Lymphoma Society, Microsoft Research and core support grants by the Wellcome Trust to the Cambridge Institute for Medical Research and Wellcome Trust - MRC Cambridge Stem Cell Institute. V.M. is supported by a Medical Research Council Studentship and Centenary Award and S.W. by a Microsoft Research PhD Scholarship.This is the accepted manuscript for a paper published in Nature Biotechnology 33, 269–276 (2015) doi:10.1038/nbt.315

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

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

Hub-Centered Gene Network Reconstruction Using Automatic Relevance Determination

Network inference deals with the reconstruction of biological networks from experimental data. A variety of different reverse engineering techniques are available; they differ in the underlying assumptions and mathematical models used. One common problem for all approaches stems from the complexity of the task, due to the combinatorial explosion of different network topologies for increasing network size. To handle this problem, constraints are frequently used, for example on the node degree, number of edges, or constraints on regulation functions between network components. We propose to exploit topological considerations in the inference of gene regulatory networks. Such systems are often controlled by a small number of hub genes, while most other genes have only limited influence on the network's dynamic. We model gene regulation using a Bayesian network with discrete, Boolean nodes. A hierarchical prior is employed to identify hub genes. The first layer of the prior is used to regularize weights on edges emanating from one specific node. A second prior on hyperparameters controls the magnitude of the former regularization for different nodes. The net effect is that central nodes tend to form in reconstructed networks. Network reconstruction is then performed by maximization of or sampling from the posterior distribution. We evaluate our approach on simulated and real experimental data, indicating that we can reconstruct main regulatory interactions from the data. We furthermore compare our approach to other state-of-the art methods, showing superior performance in identifying hubs. Using a large publicly available dataset of over 800 cell cycle regulated genes, we are able to identify several main hub genes. Our method may thus provide a valuable tool to identify interesting candidate genes for further study. Furthermore, the approach presented may stimulate further developments in regularization methods for network reconstruction from data