Semiconservative replication in the quasispecies model
Abstract
This paper extends Eigen’s quasispecies equations to account for the semiconservative nature of DNA replication. We solve the equations in the limit of infinite sequence length for the simplest case of a static, sharply peaked fitness landscape. We show that the error catastrophe occurs when μ , the product of sequence length and per base pair mismatch probability, exceeds 2 ln [2/ ( 1+1/k ) ] , where k>1 is the firstorder growth rate constant of the viable “master” sequence (with all other sequences having a firstorder growth rate constant of 1 ). This is in contrast to the result of ln k for conservative replication. In particular, as k→∞ , the error catastrophe is never reached for conservative replication, while for semiconservative replication the critical μ approaches 2 ln 2 . Semiconservative replication is therefore considerably less robust than conservative replication to the effect of replication errors. We also show that the mean equilibrium fitness of a semiconservatively replicating system is given by k ( 2 e^{μ/2} 1 ) below the error catastrophe, in contrast to the standard result of k e^{μ} for conservative replication (derived by Kimura and Maruyama in 1966). From this result it is readily shown that semiconservative replication is necessary to account for the observation that, at sufficiently high mutagen concentrations, faster replicating cells will die more quickly than more slowly replicating cells. Thus, in contrast to Eigen’s original model, the semiconservative quasispecies equations are able to provide a mathematical basis for explaining the efficacy of mutagens as chemotherapeutic agents.
 Publication:

Physical Review E
 Pub Date:
 June 2004
 DOI:
 10.1103/PhysRevE.69.061916
 arXiv:
 arXiv:condmat/0309642
 Bibcode:
 2004PhRvE..69f1916T
 Keywords:

 87.23.Kg;
 87.16.Ac;
 64.90.+b;
 Dynamics of evolution;
 Theory and modeling;
 computer simulation;
 Other topics in equations of state phase equilibria and phase transitions;
 Condensed Matter;
 Quantitative Biology  Populations and Evolution
 EPrint:
 15 pages, 7 figures, to be submitted to Phys. Rev. E