Dynamical Criticality in Gene Regulatory Networks

A well-known hypothesis, with far-reaching implications, is that biological evolution should preferentially lead to states that are dynamically critical. In previous papers, we showed that a well-known model of genetic regulatory networks, namely, that of random Boolean networks, allows one to study in depth the relationship between the dynamical regime of a living being’s gene network and its response to permanent perturbations. In this paper, we analyze a huge set of new experimental data on single gene knockouts in S. cerevisiae, laying down a statistical framework to determine its dynamical regime. We find that the S. cerevisiae network appears to be slightly ordered, but close to the critical region. Since our analysis relies on dichotomizing continuous data, we carefully consider the issue of an optimal threshold choice.

[1]  R. Serraa,et al.  Interacting Random Boolean Networks , 2007 .

[2]  W. Bialek,et al.  Are Biological Systems Poised at Criticality? , 2010, 1012.2242.

[3]  Roberto Serra,et al.  Analysis of attractor distances in Random Boolean Networks , 2010, WIRN.

[4]  Roberto Serra,et al.  Dynamical Properties of a Boolean Model of Gene Regulatory Network with Memory , 2011, J. Comput. Biol..

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

[6]  Nicola J. Rinaldi,et al.  Transcriptional Regulatory Networks in Saccharomyces cerevisiae , 2002, Science.

[7]  Roberto Serra,et al.  Dynamical regimes in non-ergodic random Boolean networks , 2015, Natural Computing.

[8]  Roberto Serra,et al.  Robustness Analysis of a Boolean Model of Gene Regulatory Network with Memory , 2011, J. Comput. Biol..

[9]  Jorge Hidalgo,et al.  Information-based fitness and the emergence of criticality in living systems , 2013, Proceedings of the National Academy of Sciences.

[10]  S. Kauffman,et al.  Measures for information propagation in Boolean networks , 2007 .

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

[12]  Remco van der Hofstad,et al.  An Elementary Proof of the Hitting Time Theorem , 2008, Am. Math. Mon..

[13]  S. Kauffman,et al.  Why a simple model of genetic regulatory networks describes the distribution of avalanches in gene expression data. , 2007, Journal of theoretical biology.

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

[15]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[16]  Roberto Serra,et al.  Identifying Critical States through the Relevance Index , 2017, Entropy.

[17]  A. Califano,et al.  Dialogue on Reverse‐Engineering Assessment and Methods , 2007, Annals of the New York Academy of Sciences.

[18]  B. Efron.  The jackknife, the bootstrap, and other resampling plans , 1987 .

[19]  P. Kemmeren,et al.  De-Novo Learning of Genome-Scale Regulatory Networks in S. cerevisiae , 2014, PloS one.

[20]  Alexandre P. Francisco,et al.  YEASTRACT-DISCOVERER: new tools to improve the analysis of transcriptional regulatory associations in Saccharomyces cerevisiae , 2007, Nucleic Acids Res..

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

[22]  Yudong D. He,et al.  Functional Discovery via a Compendium of Expression Profiles , 2000, Cell.

[23]  M Villani,et al.  Genetic network models and statistical properties of gene expression data in knock-out experiments. , 2004, Journal of theoretical biology.

[24]  D. Noble.  Music of life : biology beyond the genome , 2006 .

[25]  Rupert G. Miller.  The jackknife-a review , 1974 .

[26]  Roberto Serra,et al.  Dynamical Properties of a Gene-Protein Model , 2017, WIVACE.

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

[28]  G. Longo,et al.  EXTENDED CRITICAL SITUATIONS: THE PHYSICAL SINGULARITY OF LIFE PHENOMENA , 2008 .

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

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

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

[32]  Roberto Serra,et al.  The simulation of gene knock-out in scale-free random Boolean models of genetic networks , 2008, Networks Heterog. Media.

[33]  Kunihiko Kaneko,et al.  Life: An Introduction to Complex Systems Biology , 2006 .

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

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

[36]  Christopher G. Langton,et al.  Life at the Edge of Chaos , 1992 .

[37]  Barbara Drossel,et al.  Random Boolean Networks , 2007, 0706.3351.

[38]  Bernard Derrida,et al.  The random map model: a disordered model with deterministic dynamics , 1987 .

[39]  Z. Palková,et al.  The morphology of Saccharomyces cerevisiae colonies is affected by cell adhesion and the budding pattern. , 2005, Research in microbiology.

[40]  Mauro Birattari,et al.  Dynamical regimes and learning properties of evolved Boolean networks , 2013, Neurocomputing.

[41]  S. Kauffman,et al.  Cell-cell interaction and diversity of emergent behaviours. , 2011, IET systems biology.

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

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

[44]  Mehdi M. Kashani,et al.  Large-Scale Genetic Perturbations Reveal Regulatory Networks and an Abundance of Gene-Specific Repressors , 2014, Cell.

[45]  Roberto Serra,et al.  Dynamical Criticality: Overview and Open Questions , 2015, Journal of Systems Science and Complexity.

[46]  X. R. Wang,et al.  Relating Fisher information to order parameters. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[47]  G. Parisi,et al.  Relevant elements, magnetization and dynamical properties in Kauffman networks: a numerical study , 1998 .

[48]  Grégoire Nicolis,et al.  Foundations Of Complex Systems: Nonlinear Dynamics, Statistical Physics, Information And Prediction , 2007 .

[49]  Andreas Wagner,et al.  Estimating coarse gene network structure from large-scale gene perturbation data. , 2002, Genome research.

[50]  Sui Huang,et al.  Criticality Is an Emergent Property of Genetic Networks that Exhibit Evolvability , 2012, PLoS Comput. Biol..

[51]  Ting Wang,et al.  An improved map of conserved regulatory sites for Saccharomyces cerevisiae , 2006, BMC Bioinformatics.

[52]  Roberto Serra,et al.  On the fate of perturbations in critical random Boolean networks , 2009 .

[53]  Diogo M. Camacho,et al.  Wisdom of crowds for robust gene network inference , 2012, Nature Methods.

[54]  Ilya Shmulevich,et al.  Eukaryotic cells are dynamically ordered or critical but not chaotic. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[55]  Roberto Serra,et al.  Dynamically Critical Systems and Power-Law Distributions: Avalanches Revisited , 2015, WIVACE.

[56]  Mark E. J. Newman,et al.  The Structure and Function of Complex Networks , 2003, SIAM Rev..