Solution of the Crow-Kimura and Eigen models for alphabets of arbitrary size by Schwinger spin coherent states

Details Solution of the Crow-Kimura and Eigen models for alphabets of arbitrary size by Schwinger spin coherent states Solution of the Crow-Kimura and Eigen models for alphabets of arbitrary size by Schwinger spin coherent states

2009-03-11

arxiv.org/abs/0903.2004v2

Biology

Quantitative Biology

Populations and Evolution

50 pages, 8 figures, to appear in J. Stat. Phys; some typos fixed

Scientific paper

To represent the evolution of nucleic acid and protein sequence, we express the parallel and Eigen models for molecular evolution in terms of a functional integral representation with an $h$-letter alphabet, lifting the two-state, purine/pyrimidine assumption often made in quasi-species theory. For arbitrary $h$ and a general mutation scheme, we obtain the solution of this model in terms of a maximum principle. Euler's theorem for homogeneous functions is used to derive this `thermodynamic' formulation of evolution. The general result for the parallel model reduces to known results for the purine/pyrimidine $h=2$ alphabet and the nucleic acid $h=4$ alphabet for the Kimura 3 ST mutation scheme. Examples are presented for the $h=4$ and $h=20$ cases. We derive the maximum principle for the Eigen model for general $h$. The general result for the Eigen model reduces to a known result for $h=2$. Examples are presented for the nucleic acid $h=4$ and the amino acid $h=20$ alphabet. An error catastrophe phase transition occurs in these models, and the order of the phase transition changes from second to first order for smooth fitness functions when the alphabet size is increased beyond two letters to the generic case. As examples, we analyze the general analytic solution for sharp peak, linear, quadratic, and quartic fitness functions.

Affiliated with

Also associated with

No associations

Rating

Solution of the Crow-Kimura and Eigen models for alphabets of arbitrary size by Schwinger spin coherent states does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Solution of the Crow-Kimura and Eigen models for alphabets of arbitrary size by Schwinger spin coherent states, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Solution of the Crow-Kimura and Eigen models for alphabets of arbitrary size by Schwinger spin coherent states will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-124201