Evolution of Modular Networks Under Selection for Non-Linearly Denoising
Yusuke Ikemoto* and Kosuke Sekiyama**
*Department of Mechanical Engineering, Meijo University
1-501 Shiogamaguchi, Tempaku, Nagoya, Japan
**Department of Micro-Nano Systems Engineering, Nagoya University
Furo-cho, Chikusa-ku, Nagoya, Japan
Many biological and artifact networks often represent modular structures in which the network can be decomposed into several subnetworks. Here, we propose a simple model for the modular network evolution based on the nonlinear denoising in node activities. This model suggests that modular networks can evolve under certain conditions — if the stipulated goals for the networks or the input and target output pairs involve modular features, or if the signal transfer in a node is carried out in a nonlinear manner with respect to the saturation at the upper and lower bounds. Our model highlights the positive role played by noise in modular network evolution.
-  G. Schlosser and G. P. Wagner (Eds.), “Modularity in Development and Evolution,” Univ of Chicago Pr., 2004.
-  C. Y. Baldwin and K. B. Clark, “Design Rules: The Power of Modularity,” The MIT Press, 2000.
-  G. P. Wagner, M. Pavlicev, and J. M. Cheverud, “The road to modularity,” Nature Reviews Genetics Vol.8, pp. 921-931, 2007.
-  M. Girvan and M. E. J. Newman, “Community structure in social and biological networks,” Proc. Natl. Acad. Sci. U.S.A., Vol.99, pp. 7821, 2002.
-  J. D. J. Han, N. Bertin, T. Hao, D. S. Goldberg, G. F. Berriz, L. V. Zhang, D. Dupuy, A. J. M. Walhout, M. E. Cusick, F. P. Roth, and M. Vidal, “Evidence for dynamically organized modularity in the yeast protein-protein interaction network,” Nature, Vol.430, No.6995, pp. 88-93, 2004.
-  R. D. Leclerc, “Survival of the sparsest: robust gene networks are parsimonious,” Mol. Syst. Biol., Vol.4, pp. 213, 2008.
-  T. H. Oakley, B. Ostman, and A. C. V. Wilson, “Repression and loss of gene expression outpaces activation and gain in recently duplicated fly genes,” Proc. Natl. Acad. Sci. U.S.A., Vol.103, pp. 11637-11641, 2006.
-  E. Levine and T. Hwa, “Stochastic fluctuations in metabolic pathways,” Proc. Natl. Acad. Sci. USA, Vol.104, pp. 9221-9229, 2007.
-  T. Takaguchi, M. Nakamura, N. Sato, K. Yano, and N. Masuda, “Predictability of Conversation Partners,” Phys. Rev. X 1, 011008, 2011.
-  S. Akhshabi and C. Dovrolis, “The evolution of layered protocol stacks leads to an hourglass-shaped architecture,” SIGCOMM-Computer Communication Review, Vol.41, pp. 206, 2011.
-  I. Lestas, G. Vinnicombe, and J. Paulsson, “Fundamental limits on the suppression of molecular fluctuations,” Nature, Vol.467, pp. 174-178, 2010.
-  F. J. Bruggeman, N. Blüthgen, and H. V. Westerhoff, “Noise Management by Molecular Networks,” PLoS Comput. Biol., Vol.5, No.9, 2009.
-  M. B. Elowitz, A. J. Levine, E. D. Siggia, and P. S. Swain, “Stochastic gene expression in a single cell,” Science, Vol.297, pp. 1183-1186, 2002.
-  A. Eldar and M. B. Elowitz, “Functional roles for noise in genetic circuits,” Nature, Vol.467, pp. 167-173, 2010.
-  Y. Ikemoto and K. Sekiyama, “Modular network evolution under selection for robustness to noise,” Phys. Rev. E, Vol.89, pp. 042705, 2014.
-  N. Kashtan, A. E. Mayo, T. Kalisky, and U. Alon, “An Analytically Solvable Model for Rapid Evolution of Modular Structure,” PLoS Comput. Biol., Vol.5, No.4, pp. e1000355, 2009.
-  N. Kashtan and U. Alon, “Spontaneous evolution of modularity and network motifs,” Proc. Natl. Acad. Sci. U.S.A., Vol.102, No.13, pp. 773-778, 2005.
-  J. Clune, J. B. Mouret, and H. Lipson, “The evolutionary origins of modularity,” Proc. R. Soc. B, Vol.280, pp. 20122863, 2013.
-  C. Espinosa-Soto and A. Wagner, “Specialization Can Drive the Evolution of Modularity,” PLoS Comput. Biol., Vol.6, No.3, pp. e1000719, 2010.
-  R. K. Pan and S. Sinha, “Modular networks emerge from multiconstraint optimization,” Phys. Rev. E, Vol.76, pp. 045103(R), 2007.
-  T. Friedlander, A. E. Mayo, T. Tlusty, and U. Alon, “Mutation Rules and the Evolution of Sparseness and Modularity in Biological Systems,” PLoS One 8, 2013.
-  W. C. Stacey and D. M. Durand, “Synaptic noise improves detection of subthreshold signals in hippocampal CA1 neurons,” J. Neurophysiol. Vol.86, pp. 1104-1112, 2001.
-  A. Hyvärinen, J. Karhunen, and E. Oja, “Independent Component Analysis (Adaptive and Learning Systems for Signal Processing, Communications and Control),” Wiley-Interscience, 2001.
-  M. E. J. Newman and M. Girvan, “Finding and evaluating community structure in networks,” Phys. Rev. E, Vol.69, pp. 026113, 2004.
-  G. E. Hinton and R. R. Salakhutdinov, “Reducing the Dimensionality of Data with Neural Networks,” Science, Vol.313, Issue 5786, pp. 504-507, 2006.
This article is published under a Creative Commons Attribution-NoDerivatives 4.0 International License.