Modeling Proteins at the Interface of Structure, Evolution, and Population Genetics - Computational Modeling of Biological Systems - page 357

Koshi et al. [ 40 ] extended this approach, examining the influence of some of
the physicochemical properties of the amino acids on the substitution process by
introducing hydrophobicity and bulk as parameters in a suitability function into their
model. Wong et al. [ 41 ] expanded further on this idea by examining the impact of
volume, hydrophobicity, charge, and polarity independently. It is recognized that
these forces are not independent and that detection of selection for one factor does
not imply that the other factors are not influential. To implement this concept, they
expand the Goldman and Yang [ 35 ] model and include a category for the change
of physicochemical properties. While this model represents another step forward
in the inclusion of biophysically relevant parameters and yields interesting results
concerning physicochemical selective pressures, it ignores population-level effects.
Nielsen and Yang [ 42 ] proposed a codon model that would estimate the effective
population size along with selection coefficients. They cast ! in a population genetic
framework

2N j s i
1 e N j s i ;

and substitute this new value of w ij into their familiar 1994 formulation. From their
analysis of mitochondrial protein-coding genes, they found that allowing for the
variation of N among lineages increases model fit.
Huzurbazar et al. [ 43 ] constructed a model which considers both population
size and some basic elements of protein physiochemistry. Building on Kimura's
framework, they explore the probability of fixation of classes of substitutions on
effective population size. These classes of substitution are defined by partitions
based on physicochemical data from the Grantham matrix [ 44 ]. The probability of
fixation is given in a manner easily relatable to Kimura's model as

w ij D

e 2N i S ij /
P j . j S ij /=.1

. j S ij /=.1

F ij D

e 2N i S ij / ;

where j is the relative mutational opportunity, j is the index of partitions,
and i indexes the populations. Applying this model to a set of seven species
with vastly different population sizes, it was found that selective coefficients
decline as population size increases and decline with more radical amino acid
substitutions. This unexpected result could be caused by a number of factors, such
as the complexity of the mechanisms by which positive selection acts, linkage
of substitutions, failure to control for the underlying distribution of protein folds
and corresponding substitution patterns, compensatory processes at a systems
level, failure to account for segregating variation differentially averaged with fixed
changes, or other population-level forces. More than anything, this model suggests
that numerous factors on a broad range of levels influence the substitution and
selection process and should ultimately be considered explicitly.
Though this model includes aspects of physicochemical and population-level
properties, they are both incorporated on a relativity basic level. Future substitution
models will have to consider these factors in a more detailed manner. At a structural