Solution of the quasispecies model for an arbitrary gene network

Emmanuel Tannenbaum and Eugene I. Shakhnovich
Phys. Rev. E 70, 021903 – Published 11 August 2004

Abstract

In this paper, we study the equilibrium behavior of Eigen’s quasispecies equations for an arbitrary gene network. We consider a genome consisting of N genes, so that the full genome sequence σ may be written as σ=σ1σ2σN, where σi are sequences of individual genes. We assume a single fitness peak model for each gene, so that gene i has some “master” sequence σi,0 for which it is functioning. The fitness landscape is then determined by which genes in the genome are functioning and which are not. The equilibrium behavior of this model may be solved in the limit of infinite sequence length. The central result is that, instead of a single error catastrophe, the model exhibits a series of localization to delocalization transitions, which we term an “error cascade.” As the mutation rate is increased, the selective advantage for maintaining functional copies of certain genes in the network disappears, and the population distribution delocalizes over the corresponding sequence spaces. The network goes through a series of such transitions, as more and more genes become inactivated, until eventually delocalization occurs over the entire genome space, resulting in a final error catastrophe. This model provides a criterion for determining the conditions under which certain genes in a genome will lose functionality due to genetic drift. It also provides insight into the response of gene networks to mutagens. In particular, it suggests an approach for determining the relative importance of various genes to the fitness of an organism, in a more accurate manner than the standard “deletion set” method. The results in this paper also have implications for mutational robustness and what C.O. Wilke termed “survival of the flattest.”

  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Received 28 February 2004

DOI:https://doi.org/10.1103/PhysRevE.70.021903

©2004 American Physical Society

Authors & Affiliations

Emmanuel Tannenbaum* and Eugene I. Shakhnovich

  • Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts 02138, USA

  • *Electronic address: etannenb@fas.harvard.edu

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 70, Iss. 2 — August 2004

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review E

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×