title: Punctuated evolution and robustness in morphogenesis.
abstract: This paper presents an analytic approach to the pattern stability and evolution problem in morphogenesis. The approach used here is based on the ideas from the gene and neural network theory. We assume that gene networks contain a number of small groups of genes (called hubs) controlling morphogenesis process. Hub genes represent an important element of gene network architecture and their existence is empirically confirmed. We show that hubs can stabilize morphogenetic pattern and accelerate the morphogenesis. The hub activity exhibits an abrupt change depending on the mutation frequency. When the mutation frequency is small, these hubs suppress all mutations and gene product concentrations do not change, thus, the pattern is stable. When the environmental pressure increases and the population needs new genotypes, the genetic drift and other effects increase the mutation frequency. For the frequencies that are larger than a critical amount the hubs turn off; and as a result, many mutations can affect phenotype. This effect can serve as an engine for evolution. We show that this engine is very effective: the evolution acceleration is an exponential function of gene redundancy. Finally, we show that the Eldredge-Gould concept of punctuated evolution results from the network architecture, which provides fast evolution, control of evolvability, and pattern robustness. To describe analytically the effect of exponential acceleration, we use mathematical methods developed recently for hard combinatorial problems, in particular, for so-called k-SAT problem, and numerical simulations.
authors.affiliation: CNRS, Mathématiques, Université de Lille, Villeneuve d'Ascq 59655, France. Electronic address: dmitry.grigoryev@math.univ-lille1.fr.
authors.forename: D
authors.initials: D
authors.lastname: Grigoriev
authors.affiliation: Department of Statistics, University of Chicago, Chicago, IL 60637, United States; Department of Ecology and Evolution, University of Chicago, United States; Department of Molecular Genetics and Cell Biology, University of Chicago, United States; Institute for Genomics and Systems Biology, University of Chicago, United States. Electronic address: reinitz@galton.uchicago.edu.
authors.forename: J
authors.initials: J
authors.lastname: Reinitz
authors.affiliation: Institute for Mechanical Engineering Problems, Bolshoy pr. V. O.61, Sankt Petersburg, Russia; ITMO University, Sankt Petersburg, Russia. Electronic address: vakulenfr@mail.ru.
authors.forename: S
authors.initials: S
authors.lastname: Vakulenko
authors.affiliation: Computer Science Department, University of Bonn, 53113 Bonn, Germany. Electronic address: weber@cs.uni-bonn.de.
authors.forename: A
authors.initials: A
authors.lastname: Weber
mesh_terms: D000465:Algorithms; D000818:Animals; D017753:Ecosystem; D004777:Environment; D019143:Evolution, Molecular; D053263:Gene Regulatory Networks / Q000235:genetics*; D040961:Genetic Drift; D005838:Genotype; D006801:Humans; D008957:Models, Genetic; D009024:Morphogenesis / Q000235:genetics*; D009154:Mutation; D059645:Mutation Rate; D016571:Neural Networks, Computer; D010641:Phenotype
keywords: Canalization; Evolution; Genetic networks; Hard combinatorial problems; Robustness