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2008 ; 78
(6 Pt 1
): 061921
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Quasispecies theory for horizontal gene transfer and recombination
#MMPMID19256882
Muņoz E
; Park JM
; Deem MW
Phys Rev E Stat Nonlin Soft Matter Phys
2008[Dec]; 78
(6 Pt 1
): 061921
PMID19256882
show ga
We introduce a generalization of the parallel, or Crow-Kimura, and Eigen models
of molecular evolution to represent the exchange of genetic information between
individuals in a population. We study the effect of different schemes of genetic
recombination on the steady-state mean fitness and distribution of individuals in
the population, through an analytic field theoretic mapping. We investigate both
horizontal gene transfer from a population and recombination between pairs of
individuals. Somewhat surprisingly, these nonlinear generalizations of
quasispecies theory to modern biology are analytically solvable. For two-parent
recombination, we find two selected phases, one of which is spectrally rigid. We
present exact analytical formulas for the equilibrium mean fitness of the
population, in terms of a maximum principle, which are generally applicable to
any permutation invariant replication rate function. For smooth fitness
landscapes, we show that when positive epistatic interactions are present,
recombination or horizontal gene transfer introduces a mild load against
selection. Conversely, if the fitness landscape exhibits negative epistasis,
horizontal gene transfer or recombination introduces an advantage by enhancing
selection towards the fittest genotypes. These results prove that the mutational
deterministic hypothesis holds for quasispecies models. For the discontinuous
single sharp peak fitness landscape, we show that horizontal gene transfer has no
effect on the fitness, while recombination decreases the fitness, for both the
parallel and the Eigen models. We present numerical and analytical results as
well as phase diagrams for the different cases.