Target Control in Logical Models Using the Domain of Influence of Nodes

Dynamical models of biomolecular networks are successfully used to understand the mechanisms underlying complex diseases and to design therapeutic strategies. Network control, and its special case of target control, is a promising avenue toward developing disease therapies. In target control it is assumed that a small subset of nodes is most relevant to the system’s state and the goal is to drive the target nodes into their desired states. An example of target control would be driving a cell to commit to apoptosis (programmed cell death). From the experimental perspective, gene knockout, pharmacological inhibition of proteins and providing sustained external signals are among practical intervention techniques. We identify methodologies to use the stabilizing effect of sustained interventions for target control in logical models of biomolecular networks. Specifically, we define the domain of influence of a node (in a certain state) to be the nodes (and their corresponding states) that will be ultimately stabilized by the sustained state of this node regardless of the initial state of the system. We also define the related concept of the logical domain of influence of a node, and develop an algorithm for its identification using an auxiliary network that incorporates the regulatory logic. This way a solution to the target control problem is a set of nodes whose domain of influence can cover the desired target node states. We perform greedy randomized adaptive search in state space to find such solutions. We apply our strategy to several biological networks to demonstrate its effectiveness.

[1]  Assieh Saadatpour,et al.  Boolean modeling of biological regulatory networks: a methodology tutorial. , 2013, Methods.

[2]  L. Glass,et al.  The logical analysis of continuous, non-linear biochemical control networks. , 1973, Journal of theoretical biology.

[3]  Ching-tai Lin.  Structural controllability , 1974 .

[4]  Albert-László Barabási,et al.  Control Principles of Complex Networks , 2015, ArXiv.

[5]  Réka Albert,et al.  A network modeling approach to elucidate drug resistance mechanisms and predict combinatorial drug treatments in breast cancer , 2017, bioRxiv.

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

[7]  S. P. Cornelius,et al.  Realistic control of network dynamics , 2013, Nature Communications.

[8]  Yuan Li,et al.  Boolean nested canalizing functions: A comprehensive analysis , 2012, Theor. Comput. Sci..

[9]  L. Glass.  Classification of biological networks by their qualitative dynamics. , 1975, Journal of theoretical biology.

[10]  On the robustness of NK-Kauffman networks against changes in their connections and Boolean functions , 2009, 0903.4161.

[11]  Réka Albert,et al.  A framework to find the logic backbone of a biological network , 2017, BMC Systems Biology.

[12]  Réka Albert,et al.  Elementary signaling modes predict the essentiality of signal transduction network components , 2011, BMC Systems Biology.

[13]  Chris Arney.  Algebraic and Discrete Mathematical Methods for Modern Biology , 2016 .

[14]  Rui-Sheng Wang,et al.  Boolean modeling in systems biology: an overview of methodology and applications , 2012, Physical biology.

[15]  U. Alon.  An introduction to systems biology : design principles of biological circuits , 2019 .

[16]  R. Albert,et al.  Chapter 4 Signaling Networks : Asynchronous Boolean Models , 2015 .

[17]  Carsten Peterson,et al.  Random Boolean network models and the yeast transcriptional network , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[18]  Réka Albert,et al.  Minimal functional routes in directed graphs with dependent edges , 2013, Int. Trans. Oper. Res..

[19]  David Murrugarra,et al.  Molecular network control through boolean canalization , 2015, EURASIP J. Bioinform. Syst. Biol..

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

[21]  Adilson E Motter,et al.  Control of Stochastic and Induced Switching in Biophysical Networks. , 2015, Physical review. X.

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

[23]  Jersey Chen,et al.  An Introduction to Genetic Engineering , 1994, The Yale Journal of Biology and Medicine.

[24]  Réka Albert,et al.  An effective network reduction approach to find the dynamical repertoire of discrete dynamic networks. , 2013, Chaos.

[25]  Nripendra N. Biswas,et al.  Minimization of Boolean Functions , 1971, IEEE Transactions on Computers.

[26]  Diana Marculescu,et al.  Dynamic behavior of cell signaling networks - Model design and analysis automation , 2013, 2013 50th ACM/EDAC/IEEE Design Automation Conference (DAC).

[27]  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.

[28]  Stefan Bornholdt,et al.  Boolean network models of cellular regulation: prospects and limitations , 2008, Journal of The Royal Society Interface.

[29]  Panos M. Pardalos,et al.  A Greedy Randomized Adaptive Search Procedure for the Feedback Vertex Set Problem , 1998, J. Comb. Optim..

[30]  Mark Newman,et al.  Networks: An Introduction , 2010 .

[31]  Panos M. Pardalos,et al.  Algorithm 815: FORTRAN subroutines for computing approximate solutions of feedback set problems using GRASP , 2001, TOMS.

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

[33]  Alan Veliz-Cuba,et al.  Identification of control targets in Boolean molecular network models via computational algebra , 2015, BMC Systems Biology.

[34]  Réka Albert,et al.  Node-independent elementary signaling modes: A measure of redundancy in Boolean signaling transduction networks , 2016, Network Science.

[35]  B. Palsson.  Systems Biology: Properties of Reconstructed Networks , 2006 .

[36]  Byeong Wook Jeon,et al.  A new discrete dynamic model of ABA-induced stomatal closure predicts key feedback loops , 2017, PLoS biology.

[37]  Stefan Bornholdt,et al.  Stable and unstable attractors in Boolean networks. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[39]  Reka Albert,et al.  Network modeling of TGFβ signaling in hepatocellular carcinoma epithelial-to-mesenchymal transition reveals joint sonic hedgehog and Wnt pathway activation. , 2014, Cancer research.

[40]  Maarten Kamermans,et al.  A novel mechanism of cone photoreceptor adaptation , 2017, PLoS biology.

[41]  Ulrik Brandes,et al.  What is network science? , 2013, Network Science.

[42]  Colin Campbell,et al.  Compensatory interactions to stabilize multiple steady states or mitigate the effects of multiple deregulations in biological networks. , 2016, Physical review. E.

[43]  R. Albert,et al.  Signaling Networks: Asynchronous Boolean Models , 2015 .

[44]  S. Kauffman.  Metabolic stability and epigenesis in randomly constructed genetic nets. , 1969, Journal of theoretical biology.

[45]  Reka Albert,et al.  Combinatorial interventions inhibit TGFβ-driven epithelial-to-mesenchymal transition and support hybrid cellular phenotypes , 2015, npj Systems Biology and Applications.

[46]  Jason A. Papin,et al.  Reconstruction of cellular signalling networks and analysis of their properties , 2005, Nature Reviews Molecular Cell Biology.