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Phys. Rev. E 73, 041913 (2006) [10 pages]

Quasispecies theory for multiple-peak fitness landscapes

David B. Saakian,1,2 E. Muñoz,3 Chin-Kun Hu,1 and M. W. Deem3
1Institute of Physics, Academia Sinica, Nankang, Taipei 11529, Taiwan
2Yerevan Physics Institute, Alikhanian Brothers St. 2, Yerevan 375036, Armenia
3Department of Physics and Astronomy, Rice University, Houston, Texas 77005-1892, USA

Received 15 September 2005; revised 13 December 2005; published 11 April 2006

We use a path integral representation to solve the Eigen and Crow-Kimura molecular evolution models for the case of multiple fitness peaks with arbitrary fitness and degradation functions. In the general case, we find that the solution to these molecular evolution models can be written as the optimum of a fitness function, with constraints enforced by Lagrange multipliers and with a term accounting for the entropy of the spreading population in sequence space. The results for the Eigen model are applied to consider virus or cancer proliferation under the control of drugs or the immune system.

©2006 The American Physical Society

URL: http://link.aps.org/doi/10.1103/PhysRevE.73.041913
DOI: 10.1103/PhysRevE.73.041913
PACS: 87.23.Kg; 02.50.-r; 87.10.+e; 87.15.Aa
  • 87.23.Kg
    Dynamics of evolution
  • 02.50.-r
    Probability theory, stochastic processes, and statistics
  • 87.10.+e
    General theory and mathematical aspects (biological/medical physics)
  • 87.15.Aa
    Theory and modeling in molecular biophysics; computer simulation
  • YEAR: 2006
KEYWORDS: evolution (biological), microorganisms, drugs, cancer, molecular biophysics

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