Modular Random Boolean Networks1

Random Boolean networks (RBNs) have been a popular model of genetic regulatory networks for more than four decades. However, most RBN studies have been made with random topologies, while real regulatory networks have been found to be modular. In this work, we extend classical RBNs to define modular RBNs. Statistical experiments and analytical results show that modularity has a strong effect on the properties of RBNs. In particular, modular RBNs have more attractors, and are closer to criticality when chaotic dynamics would be expected, than classical RBNs.

[1]  L. Kadanoff,et al.  Boolean Dynamics with Random Couplings , 2002, nlin/0204062.

[2]  James P. Crutchfield.  Critical Computation, Phase Transitions, and Hierarchical Learning , 2001 .

[3]  R. Solé,et al.  Lyapunov exponents in random Boolean networks , 1999, adap-org/9907001.

[4]  Carlos Gershenson,et al.  The Role of Redundancy in the Robustness of Random Boolean Networks , 2005, ArXiv.

[5]  Yao-Chen Hung,et al.  Stochastic coupling of two random Boolean networks , 2005 .

[6]  M. Andrecut,et al.  Mean field dynamics of random Boolean networks , 2005 .

[7]  Carlos Gershenson,et al.  Classification of Random Boolean Networks , 2002, ArXiv.

[8]  S. Huang,et al.  Shape-dependent control of cell growth, differentiation, and apoptosis: switching between attractors in cell regulatory networks. , 2000, Experimental cell research.

[9]  Pau Fernandez,et al.  The Role of Computation in Complex Regulatory Networks , 2003, q-bio/0311012.

[10]  H. Simon,et al.  The sciences of the artificial (3rd ed.) , 1996 .

[11]  D. Pe’er,et al.  Module networks: identifying regulatory modules and their condition-specific regulators from gene expression data , 2003, Nature Genetics.

[12]  Dietrich Stauffer,et al.  Evolution by damage spreading in Kauffman model , 1994 .

[13]  S. Kauffman,et al.  Activities and sensitivities in boolean network models. , 2004, Physical review letters.

[14]  G. Wagner,et al.  The road to modularity , 2007, Nature Reviews Genetics.

[15]  Diego Rasskin-Gutman,et al.  Modularity. Understanding the Development and Evolution of Natural Complex Systems , 2005 .

[16]  Christopher G. Langton,et al.  Computation at the edge of chaos: Phase transitions and emergent computation , 1990 .

[17]  Mariana Benítez,et al.  Dynamic-module redundancy confers robustness to the gene regulatory network involved in hair patterning of Arabidopsis epidermis , 2010, Biosyst..

[18]  Axel Bender,et al.  Degeneracy: a design principle for achieving robustness and evolvability. , 2009, Journal of theoretical biology.

[19]  Andrew Wuensche,et al.  A model of transcriptional regulatory networks based on biases in the observed regulation rules , 2002, Complex..

[20]  R. Seydel.  Practical bifurcation and stability analysis : from equilibrium to chaos , 1994 .

[21]  Mikhail Prokopenko,et al.  A Fisher Information Study of Phase Transitions in Random Boolean Networks , 2010, ALIFE.

[22]  Carlos Gershenson,et al.  Modular Random Boolean Networks , 2010, IEEE Symposium on Artificial Life.

[23]  A. Wagner.  Robustness and Evolvability in Living Systems , 2005 .

[24]  Albert Y. Zomaya,et al.  The Information Dynamics of Phase Transitions in Random Boolean Networks , 2008, ALIFE.

[25]  Róbert Ványi,et al.  Compositional evolution: the impact of sex, symbiosis and modularity on the gradualist framework of evolution , 2008, Genetic Programming and Evolvable Machines.

[26]  Andrew Wuensche,et al.  Discrete Dynamical Networks and Their Attractor Basins , 1998 .

[27]  Eugene V. Koonin,et al.  Power Laws, Scale-Free Networks and Genome Biology , 2006 .

[28]  P. Cluzel,et al.  Effects of topology on network evolution , 2006 .

[29]  Andreas Wagner,et al.  Specialization Can Drive the Evolution of Modularity , 2010, PLoS Comput. Biol..

[30]  Carlos Gershenson,et al.  Guiding the self-organization of random Boolean networks , 2010, Theory in Biosciences.

[31]  Carlos Gershenson,et al.  Updating Schemes in Random Boolean Networks: Do They Really Matter? , 2004, ArXiv.

[32]  Herbert A. Simon,et al.  The Sciences of the Artificial , 1970 .

[33]  Stuart Kau,et al.  The ensemble approach to understand genetic regulatory networks , 2004 .

[34]  Roberto Serra,et al.  Coupled Random Boolean Network Forming an Artificial Tissue , 2006, ACRI.

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

[36]  G. Parisi,et al.  The modular structure of Kauffman networks , 1997, cond-mat/9708214.

[37]  B. Derrida,et al.  Random networks of automata: a simple annealed approximation , 1986 .

[38]  Ricard V. Solé,et al.  PHASE TRANSITIONS IN RANDOM NETWORKS : SIMPLE ANALYTIC DETERMINATION OF CRITICAL POINTS , 1997 .

[39]  Jerrold E. Marsden,et al.  Perspectives and Problems in Nonlinear Science , 2003 .

[40]  Roberto Serra,et al.  Information Transfer among Coupled Random Boolean Networks , 2010, ACRI.

[41]  D. Thieffry,et al.  Modularity in development and evolution. , 2000, BioEssays : news and reviews in molecular, cellular and developmental biology.

[42]  Stuart A. Kauffman,et al.  ORIGINS OF ORDER , 2019, Origins of Order.

[43]  Péter Csermely,et al.  Weak links : stabilizers of complex systems from proteins to social networks , 2006 .

[44]  Roberto Serra,et al.  The Diffusion of Perturbations in a Model of Coupled Random Boolean Networks , 2008, ACRI.

[45]  M. Aldana.  Boolean dynamics of networks with scale-free topology , 2003 .

[46]  S. Kauffman,et al.  Critical Dynamics in Genetic Regulatory Networks: Examples from Four Kingdoms , 2008, PloS one.

[47]  Yao-Chen Hung,et al.  Chaos synchronization of two stochastically coupled random Boolean networks , 2006 .

[48]  Carlos Gershenson,et al.  Introduction to Random Boolean Networks , 2004, ArXiv.

[49]  A. Wagner.  Distributed robustness versus redundancy as causes of mutational robustness. , 2005, BioEssays : news and reviews in molecular, cellular and developmental biology.

[50]  R. Thomas,et al.  Logical analysis of systems comprising feedback loops. , 1978, Journal of theoretical biology.

[51]  P. Cluzel,et al.  A natural class of robust networks , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[52]  S. Kauffman,et al.  Genetic networks with canalyzing Boolean rules are always stable. , 2004, Proceedings of the National Academy of Sciences of the United States of America.