NKα - Non-uniform epistatic interactions in an extended NK model

Kauffman’s seminal NK model was introduced to relate the properties of fitness landscapes to the extent and nature of epistasis between genes. The original model considered genomes in which the fitness contribution of each ofN genes was influenced by the value of K other genes located either at random or from the immediately neighbouring loci on the genome. Both schemes ensure that (on average) every gene is as influential as any other. More recently, the epistatic connectivity between genes in natural genomes has begun to be mapped. The topologies of these genetic networks are neither random nor regular, but exhibit interesting structural properties. The model presented here extends the NK model to consider epistatic network topologies derived from a preferential attachment scheme which tends to ensure that some genes are more influential than others. We explore the consequences of this topology for the properties of the associated fitness landscapes.

[1]  Yong Gao,et al.  An Analysis of Phase Transition in NK Landscapes , 2002, J. Artif. Intell. Res..

[2]  Weinberger,et al.  Local properties of Kauffman's N-k model: A tunably rugged energy landscape. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[3]  T. Gisiger.  Scale invariance in biology: coincidence or footprint of a universal mechanism? , 2001, Biological reviews of the Cambridge Philosophical Society.

[4]  Janet Wiles,et al.  A comparison of neutral landscapes - NK, NKp and NKq , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[5]  Stuart A. Kauffman,et al.  The origins of order , 1993 .

[6]  Albert-László Barabási,et al.  Linked - how everything is connected to everything else and what it means for business, science, and everyday life , 2003 .

[7]  Ariel Fernández,et al.  Molecular Basis for Evolving Modularity in the Yeast Protein Interaction Network , 2007, PLoS Comput. Biol..

[8]  Allan Friedman,et al.  The Parable of the Hare and the Tortoise: Small Worlds, Diversity, and System Performance , 2005 .

[9]  A. Barabasi,et al.  Lethality and centrality in protein networks , 2001, Nature.

[10]  Andrey Rzhetsky,et al.  Birth of scale-free molecular networks and the number of distinct DNA and protein domains per genome , 2001, Bioinform..

[11]  G. Caldarelli,et al.  Scale-free Networks without Growth or Preferential Attachment: Good get Richer , 2002 .

[12]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[13]  Elaine B. Barker,et al.  A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications , 2000 .

[14]  R. Rosenfeld.  Nature , 2009, Otolaryngology--head and neck surgery : official journal of American Academy of Otolaryngology-Head and Neck Surgery.

[15]  K. Sneppen,et al.  Specificity and Stability in Topology of Protein Networks , 2002, Science.

[16]  S. Kauffman.  At Home in the Universe: The Search for the Laws of Self-Organization and Complexity , 1995 .

[17]  L. Altenberg.  B2.7.2 NK Fitness Landscapes , 1997 .

[18]  E. Koonin,et al.  Scale-free networks in biology: new insights into the fundamentals of evolution? , 2002, BioEssays : news and reviews in molecular, cellular and developmental biology.

[19]  Sheldon H. Jacobson,et al.  New global optima results for the Kauffman NK model: handling dependency , 2006, Math. Program..

[20]  Sébastien Vérel,et al.  Where are bottlenecks in NK fitness landscapes? , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

[21]  Reka Albert,et al.  Mean-field theory for scale-free random networks , 1999 .

[22]  E. Levanon,et al.  Preferential attachment in the protein network evolution. , 2003, Physical review letters.

[23]  Christoph Adami,et al.  Optimal adaptive performance and delocalization in NK fitness landscapes , 2001, physics/0109020.

[24]  Marco Tomassini,et al.  Effects of Scale-Free and Small-World Topologies on Binary Coded Self-adaptive CEA , 2006, EvoCOP.

[25]  M. Newman.  Clustering and preferential attachment in growing networks. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[26]  Lee Altenberg,et al.  Evolving better representations through selective genome growth , 1994, Proceedings of the First IEEE Conference on Evolutionary Computation. IEEE World Congress on Computational Intelligence.

[27]  L. Barnett.  Ruggedness and neutrality—the NKp family of fitness landscapes , 1998 .

[28]  R. Albert,et al.  The large-scale organization of metabolic networks , 2000, Nature.

[29]  Massimo Marchiori,et al.  Error and attacktolerance of complex network s , 2004 .

[30]  Martin H. Levinson.  Linked: The New Science of Networks , 2004 .

[31]  A. Barabasi,et al.  Evolution of the social network of scientific collaborations , 2001, cond-mat/0104162.

[32]  A. Barabasi,et al.  Network biology: understanding the cell's functional organization , 2004, Nature Reviews Genetics.

[33]  Jan W. Rivkin,et al.  Organizational sticking points on NK Landscapes , 2002, Complex..

[34]  Janet Wiles,et al.  Maximally rugged NK landscapes contain the highest peaks , 2005, GECCO '05.

[35]  M. Newman,et al.  Random graphs with arbitrary degree distributions and their applications. , 2000, Physical review. E, Statistical, nonlinear, and soft matter physics.

[36]  G. Church,et al.  Modular epistasis in yeast metabolism , 2005, Nature Genetics.

[37]  Albert-László Barabási,et al.  Internet: Diameter of the World-Wide Web , 1999, Nature.