Algorithms and Complexity Analyses for Control of Singleton Attractors in Boolean Networks

A Boolean network (BN) is a mathematical model of genetic networks. We propose several algorithms for control of singleton attractors in BN. We theoretically estimate the average-case time complexities of the proposed algorithms, and confirm them by computer experiments. The results suggest the importance of gene ordering. Especially, setting internal nodes ahead yields shorter computational time than setting external nodes ahead in various types of algorithms. We also present a heuristic algorithm which does not look for the optimal solution but for the solution whose computational time is shorter than that of the exact algorithms

On control of singleton attractors in multiple Boolean networks: integer programming-based method

published_or_final_versionThe Twelfth Asia Pacific Bioinformatics Conference (APBC 2014), Shanghai, China. 17-19 January 2014. In BMC Systems Biology, 2014, v. 8, Suppl. 1, article no. S

Control of complex networks requires both structure and dynamics

The study of network structure has uncovered signatures of the organization of complex systems. However, there is also a need to understand how to control them; for example, identifying strategies to revert a diseased cell to a healthy state, or a mature cell to a pluripotent state. Two recent methodologies suggest that the controllability of complex systems can be predicted solely from the graph of interactions between variables, without considering their dynamics: structural controllability and minimum dominating sets. We demonstrate that such structure-only methods fail to characterize controllability when dynamics are introduced. We study Boolean network ensembles of network motifs as well as three models of biochemical regulation: the segment polarity network in Drosophila melanogaster, the cell cycle of budding yeast Saccharomyces cerevisiae, and the floral organ arrangement in Arabidopsis thaliana. We demonstrate that structure-only methods both undershoot and overshoot the number and which sets of critical variables best control the dynamics of these models, highlighting the importance of the actual system dynamics in determining control. Our analysis further shows that the logic of automata transition functions, namely how canalizing they are, plays an important role in the extent to which structure predicts dynamics.Comment: 15 pages, 6 figure

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

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

Revisiting the Training of Logic Models of Protein Signaling Networks with a Formal Approach based on Answer Set Programming

A fundamental question in systems biology is the construction and training to data of mathematical models. Logic formalisms have become very popular to model signaling networks because their simplicity allows us to model large systems encompassing hundreds of proteins. An approach to train (Boolean) logic models to high-throughput phospho-proteomics data was recently introduced and solved using optimization heuristics based on stochastic methods. Here we demonstrate how this problem can be solved using Answer Set Programming (ASP), a declarative problem solving paradigm, in which a problem is encoded as a logical program such that its answer sets represent solutions to the problem. ASP has significant improvements over heuristic methods in terms of efficiency and scalability, it guarantees global optimality of solutions as well as provides a complete set of solutions. We illustrate the application of ASP with in silico cases based on realistic networks and data

Modular organisation of interaction networks based on asymptotic dynamics

This paper investigates questions related to the modularity in discrete models of biological interaction networks. We develop a theoretical framework based on the analysis of their asymptotic dynamics. More precisely, we exhibit formal conditions under which agents of interaction networks can be grouped into modules. As a main result, we show that the usual decomposition in strongly connected components fulfils the conditions of being a modular organisation. Furthermore, we point out that our framework enables a finer analysis providing a decomposition in elementary modules

Gene Regulatory Networks: Modeling, Intervention and Context

abstract: Biological systems are complex in many dimensions as endless transportation and communication networks all function simultaneously. Our ability to intervene within both healthy and diseased systems is tied directly to our ability to understand and model core functionality. The progress in increasingly accurate and thorough high-throughput measurement technologies has provided a deluge of data from which we may attempt to infer a representation of the true genetic regulatory system. A gene regulatory network model, if accurate enough, may allow us to perform hypothesis testing in the form of computational experiments. Of great importance to modeling accuracy is the acknowledgment of biological contexts within the models -- i.e. recognizing the heterogeneous nature of the true biological system and the data it generates. This marriage of engineering, mathematics and computer science with systems biology creates a cycle of progress between computer simulation and lab experimentation, rapidly translating interventions and treatments for patients from the bench to the bedside. This dissertation will first discuss the landscape for modeling the biological system, explore the identification of targets for intervention in Boolean network models of biological interactions, and explore context specificity both in new graphical depictions of models embodying context-specific genomic regulation and in novel analysis approaches designed to reveal embedded contextual information. Overall, the dissertation will explore a spectrum of biological modeling with a goal towards therapeutic intervention, with both formal and informal notions of biological context, in such a way that will enable future work to have an even greater impact in terms of direct patient benefit on an individualized level.Dissertation/ThesisPh.D. Computer Science 201