Decompositions of large-scale biological systems based on dynamical properties

MOTIVATION Given a large-scale biological network represented as an influence graph, in this article we investigate possible decompositions of the network aimed at highlighting specific dynamical properties. RESULTS The first decomposition we study consists in finding a maximal directed acyclic subgraph of the network, which dynamically corresponds to searching for a maximal open-loop subsystem of the given system. Another dynamical property investigated is strong monotonicity. We propose two methods to deal with this property, both aimed at decomposing the system into strongly monotone subsystems, but with different structural characteristics: one method tends to produce a single large strongly monotone component, while the other typically generates a set of smaller disjoint strongly monotone subsystems. AVAILABILITY Original heuristics for the methods investigated are described in the article. CONTACT altafini@sissa.it

[1]  N.R. Malik,et al.  Graph theory with applications to engineering and computer science , 1975, Proceedings of the IEEE.

[2]  Robert E. Tarjan,et al.  Depth-First Search and Linear Graph Algorithms , 1972, SIAM J. Comput..

[3]  Robert E. Tarjan,et al.  Depth-First Search and Linear Graph Algorithms (Working Paper) , 1971, SWAT.

[4]  Rolf Niedermeier,et al.  Separator-based data reduction for signed graph balancing , 2010, J. Comb. Optim..

[5]  G Iacono,et al.  Determining the distance to monotonicity of a biological network: a graph-theoretical approach. , 2010, IET systems biology.

[6]  Eduardo D. Sontag,et al.  Algorithmic and Complexity Results for Decompositions of Biological Networks into Monotone Subsystems , 2005, WEA.

[7]  Vincent Danos,et al.  Rule-Based Modelling, Symmetries, Refinements , 2008, FMSB.

[8]  P. Pardalos,et al.  Handbook of Combinatorial Optimization , 1998 .

[9]  Robert Gentleman,et al.  Graphs in molecular biology , 2007, BMC Bioinformatics.

[10]  Ilya V. Kolmanovsky,et al.  Predictive energy management of a power-split hybrid electric vehicle , 2009, 2009 American Control Conference.

[11]  Q. Ouyang,et al.  The yeast cell-cycle network is robustly designed. , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[12]  Denis Thieffry,et al.  Dynamical roles of biological regulatory circuits , 2007, Briefings Bioinform..

[13]  Chris Cosner,et al.  Book Review: Monotone dynamical systems: An introduction to the theory of competitive and cooperative systems , 1996 .

[14]  Berend Hasselman.  Remark on Algorithm 815: FORTRAN subroutines for computing approximate solutions of feedback set problems using GRASP , 2006, TOMS.

[15]  Mikolaj Morzy,et al.  Signed Graphs , 2014, Encyclopedia of Social Network Analysis and Mining.

[16]  Raymond E. Miller,et al.  Complexity of Computer Computations , 1972 .

[17]  Xinzhi Liu.  Comparison methods and stability theory , 1994 .

[18]  H. Kitano,et al.  A comprehensive pathway map of epidermal growth factor receptor signaling , 2005, Molecular systems biology.

[19]  Yukiko Matsuoka,et al.  Molecular Interaction Map of a Macrophage , 2004 .

[20]  François Fages,et al.  From Reaction Models to Influence Graphs and Back: A Theorem , 2008, FMSB.

[21]  Steffen Klamt,et al.  A methodology for the structural and functional analysis of signaling and regulatory networks , 2006, BMC Bioinformatics.

[22]  Eduardo D. Sontag,et al.  Monotone and near-monotone biochemical networks , 2007, Systems and Synthetic Biology.

[23]  S. Shen-Orr,et al.  Network motifs in the transcriptional regulation network of Escherichia coli , 2002, Nature Genetics.

[24]  Sergei Maslov,et al.  Detection of the dominant direction of information flow and feedback links in densely interconnected regulatory networks , 2008, BMC Bioinformatics.

[25]  C. Soulé.  Graphic Requirements for Multistationarity , 2004, Complexus.

[26]  James P. Quirk,et al.  Qualitative Economics and the Stability of Equilibrium , 1965 .

[27]  D. DeAngelis,et al.  Positive Feedback in Natural Systems , 1986 .

[28]  Nicholas Boyd,et al.  Graph-theoretic topological control of biological genetic networks , 2009, 2009 American Control Conference.

[29]  Panos M. Pardalos,et al.  Handbook of combinatorial optimization. Supplement , 2005 .

[30]  Claudio Altafini,et al.  Monotonicity, frustration, and ordered response: an analysis of the energy landscape of perturbed large-scale biological networks , 2010, BMC Systems Biology.

[31]  Richard M. Karp,et al.  Reducibility Among Combinatorial Problems , 1972, 50 Years of Integer Programming.

[32]  H. Kunze,et al.  A graph theoretical approach to monotonicity with respect to initial conditions II , 1999 .

[33]  Panos M. Pardalos,et al.  Feedback Set Problems , 2009, Encyclopedia of Optimization.

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

[35]  H. Kitano,et al.  A comprehensive map of the toll-like receptor signaling network , 2006, Molecular systems biology.

[36]  Eduardo Sontag,et al.  Proximity of intracellular regulatory networks to monotone systems. , 2008, IET systems biology.

[37]  S. Shen-Orr,et al.  Network motifs: simple building blocks of complex networks. , 2002, Science.

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

[39]  Hal L. Smith.  Systems of ordinary differential equations which generate an order preserving flow. A survey of results , 1988 .