  It is important to understand how protein folding and evolution influences
each other. Several studies based on entropy calculation correlating
experimental measurement of residue participation in folding nucleus and
sequence conservation have reached different conclusions. Here we report
analysis of conservation of folding nucleus using an evolutionary model
alternative to entropy based approaches. We employ a continuous time Markov
model of codon substitution to distinguish mutation fixed by evolution and
mutation fixed by chance. This model takes into account bias in codon
frequency, bias favoring transition over transversion, as well as explicit
phylogenetic information. We measure selection pressure using the ratio
$\omega$ of synonymous vs. non-synonymous substitution at individual residue
site. The $\omega$-values are estimated using the {\sc Paml} method, a
maximum-likelihood estimator. Our results show that there is little correlation
between the extent of kinetic participation in protein folding nucleus as
measured by experimental $\phi$-value and selection pressure as measured by
$\omega$-value. In addition, two randomization tests failed to show that
folding nucleus residues are significantly more conserved than the whole
protein. These results suggest that at the level of codon substitution, there
is no indication that folding nucleus residues are significantly more conserved
than other residues. We further reconstruct candidate ancestral residues of the
folding nucleus and suggest possible test tube mutation studies of ancient
folding nucleus.
