A Decomposition-based Approach towards the Control of Boolean Networks

We study the problem of computing a minimal subset of nodes of a given asynchronous Boolean network that need to be controlled to drive its dynamics from an initial steady state (or attractor) to a target steady state. Due to the phenomenon of state-space explosion, a simple global approach that performs computations on the entire network, may not scale well for large networks. We believe that efficient algorithms for such networks must exploit the structure of the networks together with their dynamics. Taking such an approach, we derive a decomposition-based solution to the minimal control problem which can be significantly faster than the existing approaches on large networks. We apply our solution to both real-life biological networks and randomly generated networks, demonstrating promising results.

[1]  Gang Yang,et al.  Structure-based control of complex networks with nonlinear dynamics , 2016, Proceedings of the National Academy of Sciences.

[2]  S. Kauffman.  Homeostasis and Differentiation in Random Genetic Control Networks , 1969, Nature.

[3]  Réka Albert,et al.  Cell Fate Reprogramming by Control of Intracellular Network Dynamics , 2014, PLoS Comput. Biol..

[4]  Ion Petre,et al.  Target Controllability of Linear Networks , 2016, CMSB.

[5]  Hugues Mandon,et al.  Relationship Between the Reprogramming Determinants of Boolean Networks and Their Interaction Graph , 2016, HSB.

[6]  Oliver Sawodny,et al.  ON/OFF and Beyond - A Boolean Model of Apoptosis , 2009, PLoS Comput. Biol..

[7]  Jun Pang,et al.  Recent development and biomedical applications of probabilistic Boolean networks , 2013, Cell Communication and Signaling.

[8]  Hugues Mandon,et al.  Temporal Reprogramming of Boolean Networks , 2017, CMSB.

[9]  Albert-László Barabási,et al.  Target control of complex networks , 2014, Nature Communications.

[10]  S. Huang,et al.  Genomics, complexity and drug discovery: insights from Boolean network models of cellular regulation. , 2001, Pharmacogenomics.

[11]  Alessio Lomuscio,et al.  MCMAS: an open-source model checker for the verification of multi-agent systems , 2017, International Journal on Software Tools for Technology Transfer.

[12]  Jun Pang,et al.  ASSA-PBN 2.0: A Software Tool for Probabilistic Boolean Networks , 2016, CMSB.

[13]  Controlling complex , non-linear dynamical networks , 2014 .

[14]  A. Sol,et al.  Concise Review: A Population Shift View of Cellular Reprogramming , 2014, Stem cells.

[15]  Luis Mateus Rocha,et al.  Control of complex networks requires both structure and dynamics , 2015, Scientific Reports.

[16]  B. Fiedler,et al.  Dynamics and control at feedback vertex sets. II: a faithful monitor to determine the diversity of molecular activities in regulatory networks. , 2013, Journal of theoretical biology.

[17]  T. Enver,et al.  Forcing cells to change lineages , 2009, Nature.

[18]  Jun Pang,et al.  Taming Asynchrony for Attractor Detection in Large Boolean Networks , 2017, IEEE/ACM Transactions on Computational Biology and Bioinformatics.

[19]  Albert-László Barabási,et al.  Controllability of complex networks , 2011, Nature.

[20]  Edward R. Dougherty,et al.  Probabilistic Boolean Networks - The Modeling and Control of Gene Regulatory Networks , 2010 .

[21]  M. Boerries,et al.  Boolean Modeling Reveals the Necessity of Transcriptional Regulation for Bistability in PC12 Cell Differentiation , 2016, Front. Genet..

[22]  Wen-Xu Wang,et al.  A geometrical approach to control and controllability of nonlinear dynamical networks , 2016, Nature Communications.

[23]  B. Fiedler,et al.  Dynamics and Control at Feedback Vertex Sets. I: Informative and Determining Nodes in Regulatory Networks , 2013, Journal of Dynamics and Differential Equations.

[24]  Luis Mateus Rocha,et al.  Canalization and Control in Automata Networks: Body Segmentation in Drosophila melanogaster , 2013, PloS one.