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

A module of inflammatory cytokines defines resistance of colorectal cancer to EGFR inhibitors

Epidermal Growth Factor Receptor (EGFR) activates a robust signalling network to which colon cancer tumours often become addicted. Cetuximab, one of the monoclonal antibodies targeting this pathway, is employed to treat patients with colorectal cancer. However, many patients are intrinsically refractory to this treatment, and those who respond develop secondary resistance along time. Mechanisms of cancer cell resistance include either acquisition of new mutations or non genomic activation of alternative signalling routes. In this study, we employed a colon cancer model to assess potential mechanisms driving resistance to cetuximab. Resistant cells displayed increased ability to grow in suspension as colonspheres and this phenotype was associated with poorly organized structures. Factors secreted from resistant cells were causally involved in sustaining resistance, indeed administration to parental cells of conditioned medium collected from resistant cells was sufficient to reduce cetuximab efficacy. Among secreted factors, we report herein that a signature of inflammatory cytokines, including IL1A, IL1B and IL8, which are produced following EGFR pathway activation, was associated with the acquisition of an unresponsive phenotype to cetuximab in vitro. This signature correlated with lack of response to EGFR targeting also in patient-derived tumour xenografts. Collectively, these results highlight the contribution of inflammatory cytokines to reduced sensitivity to EGFR blockade and suggest that inhibition of this panel of cytokines in combination with cetuximab might yield an effective treatment strategy for CRC patients refractory to anti-EGFR targeting

Therapeutic target discovery using Boolean network attractors: avoiding pathological phenotypes

Target identification, one of the steps of drug discovery, aims at identifying biomolecules whose function should be therapeutically altered in order to cure the considered pathology. This work proposes an algorithm for in silico target identification using Boolean network attractors. It assumes that attractors of dynamical systems, such as Boolean networks, correspond to phenotypes produced by the modeled biological system. Under this assumption, and given a Boolean network modeling a pathophysiology, the algorithm identifies target combinations able to remove attractors associated with pathological phenotypes. It is tested on a Boolean model of the mammalian cell cycle bearing a constitutive inactivation of the retinoblastoma protein, as seen in cancers, and its applications are illustrated on a Boolean model of Fanconi anemia. The results show that the algorithm returns target combinations able to remove attractors associated with pathological phenotypes and then succeeds in performing the proposed in silico target identification. However, as with any in silico evidence, there is a bridge to cross between theory and practice, thus requiring it to be used in combination with wet lab experiments. Nevertheless, it is expected that the algorithm is of interest for target identification, notably by exploiting the inexpensiveness and predictive power of computational approaches to optimize the efficiency of costly wet lab experiments.Comment: Since the publication of this article and among the possible improvements mentioned in the Conclusion, two improvements have been done: extending the algorithm for multivalued logic and considering the basins of attraction of the pathological attractors for selecting the therapeutic bullet

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

Influence Systems vs Reaction Systems

International audienceIn Systems Biology, modelers develop more and more reaction-based models to describe the mechanistic biochemical reactions underlying cell processes. They may also work, however, with a simpler formalism of influence graphs, to merely describe the positive and negative influences between molecular species. The first approach is promoted by reaction model exchange formats such as SBML, and tools like CellDesigner, while the second is supported by other tools that have been historically developed to reason about boolean gene regulatory networks. In practice, modelers often reason with both kinds of formalisms, and may find an influence model useful in the process of building a reaction model. In this paper, we introduce a formalism of influence systems with forces, and put it in parallel with reaction systems with kinetics, in order to develop a similar hierarchy of boolean, discrete, stochastic and differential semantics. We show that the expressive power of influence systems is the same as that of reaction systems under the differential semantics, but weaker under the other interpretations, in the sense that some discrete behaviours of reaction systems cannot be expressed by influence systems. This approach leads us to consider a positive boolean semantics which we compare to the asynchronous semantics of gene regulatory networks à la Thomas. We study the monotonicity properties of the positive boolean semantics and derive from them an efficient algorithm to compute attractors

Logical model specification aided by model- checking techniques: application to the mammalian cell cycle regulation

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Enhancing Boolean networks with fuzzy operators and edge tuning

Quantitative modeling in systems biology can be difficult due to the scarcity of quantitative details about biological phenomenons, especially at the subcellular scale. An alternative to escape this difficulty is qualitative modeling since it requires few to no quantitative information. Among the qualitative modeling approaches, the Boolean network formalism is one of the most popular. However, Boolean models allow variables to be valued at only true or false, which can appear too simplistic when modeling biological processes. Consequently, this work proposes a modeling approach derived from Boolean networks where fuzzy operators are used and where edges are tuned. Fuzzy operators allow variables to be continuous and then to be more finely valued than with discrete modeling approaches, such as Boolean networks, while remaining qualitative. Moreover, to consider that in a given biological network some interactions are slower and/or weaker relative to other ones, edge states are computed in order to modulate in speed and strength the signal they convey. The proposed formalism is illustrated through its implementation on a tiny sample of the epidermal growth factor receptor signaling pathway. The obtained simulations show that continuous results are produced, thus allowing finer analysis, and that modulating the signal conveyed by the edges allows their tuning according to knowledge about the modeled interactions, thus incorporating more knowledge. The proposed modeling approach is expected to bring enhancements in the ability of qualitative models to simulate the dynamics of biological networks while not requiring quantitative information