Punctuated evolution and robustness in morphogenesis

Dima Grigoriev, Sergey Vakulenko, John Reinitz, and Andreas Weber
In: Bio Systems (2014)
 

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.

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Bibtex

@ARTICLE{GrigorievReinitzVakulenkoWeber2014,
    author = {Grigoriev, Dima and Vakulenko, Sergey and Reinitz, John and Weber, Andreas},
     title = {Punctuated evolution and robustness in morphogenesis},
   journal = {Bio Systems},
      year = {2014},
  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.},
       doi = {10.1016/j.biosystems.2014.06.013}
}