Exact solution of the Eigen model with general fitness functions and degradation rates

doi:10.1073/pnas.0504924103

Exact solution of the Eigen model with general fitness functions and degradation rates

David B. Saakian*,^† and
Chin-Kun Hu*,^‡

*Institute of Physics, Academia Sinica, Nankang, Taipei 11529, Taiwan; and
^†Yerevan Physics Institute, Alikhanian Brothers Street 2, Yerevan 375036, Armenia

Edited by H. Eugene Stanley, Boston University, Boston, MA, and approved January 18, 2006 (received for review June 13, 2005)

Abstract

We present an exact solution of Eigen’s quasispecies model with a general degradation rate and fitness functions, including a square root decrease of fitness with increasing Hamming distance from the wild type. The found behavior of the model with a degradation rate is analogous to a viral quasispecies under attack by the immune system of the host. Our exact solutions also revise the known results of neutral networks in quasispecies theory. To explain the existence of mutants with large Hamming distances from the wild type, we propose three different modifications of the Eigen model: mutation landscape, multiple adjacent mutations, and frequency-dependent fitness in which the steady-state solution shows a multicenter behavior.

Footnotes

^‡To whom correspondence should be sent at the ∗ address. E-mail: huck{at}phys.sinica.edu.tw
Author contributions: C.-K.H. and D.B.S. designed research, performed research, and wrote the paper.
Conflict of interest statement: No conflicts declared.
This paper was submitted directly (Track II) to the PNAS office.
Abbreviations:

AS,

antiselective;

FM,

ferromagnetic;

HD,

Hamming distance;

PM,

paramagnetic.