Modeling Proteins at the Interface of Structure, Evolution, and Population Genetics - Computational Modeling of Biological Systems - page 356

8
< 0; if the two codons differ at more that one position;

j ; for synonymous transversion;
k j ; for synonymous transition;
! j ; for nonsynonymous transversion;
!k j ; for nonsynonymous transition;

D

R ij

:

where k is the transition transversion ratio, ! is the ratio of nonsynonymous to
synonymous changes, and j is the equilibrium frequency of codon j .
This initial framework given by Goldman and Yang has been expanded to
incorporate a more complex view of the mutation-selection process taken from the
realm of population genetics, which allows for the consideration of other parameters
influential on selection. Important features of the physical environment such as the
structure of the protein and the solvent accessible surface area of the position can
affect the replacement process. These elements are incorporated into the Robinson
et al. [ 16 ] model, where differences in a solvent accessibility score and pairwise
interaction score are considered in the calculation of nonsynonymous changes. In
order to compute these scores, the 3D structure of a protein must be known and is
assumed to be identical across the set of sequences being analyzed; in this case, it is
inferred using a threading-based approach. Methods like these are novel because
they incorporate the phenotypic property of sequence-structure compatibility in
accounting for the substitution process.
Another extension of codon models involving structure for the detection of
positive selection was the invention of tertiary windowing [ 36 - 38 ]. In this approach,
standard codon models were applied independently in a contact sphere delineated by
protein structure to detect regions of a protein that were co-evolving under positive
selection.
However, neither the Robinson model nor the tertiary windowing approach
captures the whole picture of the substitution process, as both leave out population-
level factors. In fact by relating the Robinson model back to the Halpern-Bruno
model, a 2 Ns j term can be computed. The 2 Ns j term is often referred to as the
scaled selection coefficient. The scaled selection coefficient relates the evolutionary
importance of a trait in a way such that it can be compared to those of other traits
which arose in populations of different sizes.
Amino acid substitution matrices are typically empirical, drawn from existing
data rather than parameterized for use on any one data set. Koshi and Goldstein
[ 39 ] built such matrices explicitly incorporating structural considerations. Assuming
that sequences with the same structural properties have the same substitutional
properties, structural context-specific substitution matrices were created. Properties
considered included secondary structure and solvent accessibility. Interestingly,
it was found that different residue position classes produce different optimal
substitution matrices, suggesting the importance of the incorporation of structural
data in models of the substitution process.