Modeling Proteins at the Interface of Structure, Evolution, and Population Genetics - Computational Modeling of Biological Systems - page 355

4 Population Genetics and Biophysical Constraints

in Models for Interspecific Evolution

To understand the process of interspecific molecular evolution, the factors which
influence substitution and selection must be recognized and the interplay between
them understood. There exists a broad range of features which can affect substitution
and selection, which may be more or less influential dependent on a given scenario.
To measure selective strength, some models examine the ratio of nonsynonymous
to synonymous changes, where an acceleration of the nonsynonymous substitution
rate is indicative of positive selection. Similar comparisons of the ratio of these
rates can be made to determine if a site is undergoing neutral evolution or purifying
selection. Due to the interest in these ratios, it follows that codon-level models
where synonymous and nonsynonymous changes can be observed have begun
to proliferate. These models allow for formulations of the substitution and the
mutation-selection process to be combined in a single framework which can be
related back to known data from genomes. Measures of selective pressures or
selective strength can then be estimated using maximum likelihood or Bayesian
methods.
A basic implementation of this type of model is given by Halpern and Bruno
[ 33 ]. This model assumes the mutation process (rates) is constant across all codons
but natural selection acts differently depending on the position and the nature of the
amino acid side chain. The model does not explicitly consider structure. Halpern
and Bruno represent the substitution rate between an amino acid i and amino acid
j as

R ij D ij NP.Z ij /;

where is a proportionality constant, ij is the rate at which i mutates to j; N is the
haploid population size, and Z ij is the probability of fixation of the new mutation.
For the mutation-selection portion of their model, they use the probability of fixation
of a new mutation in a haploid population as that given by the classic Kimura [ 34 ]
formulation.

e 2s j

1

e 2N s j :
While conceptually clear, this model does not consider any other forces beside
population size in computing the substitution rate.
As suggested above, the substitution rate may differ depending on the types of
changes made to a codon. A reasonable assumption could be that nonsynonymous
substitutions are more likely to be selected for. Should one be interested in
examining the ratio of nonsynonymous to synonymous changes, the differences in
nonsynonymous transition, nonsynonymous transversion, synonymous transition,
and synonymous transversion can be considered. The first models formulated to
capture these dynamics were outlined by Goldman and Yang [ 35 ] and many models
have built upon this foundation,

P.Z ij / D

1