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There is an apparent paradox in our understanding of molecular evolution. Current biochemically based models predict that evolutionary trees should not be recoverable for divergences beyond a few hundred million years. In practice, however, trees often appear to be recovered from much older times. Mathematical models, such as those assuming that sites evolve at different rates [including a Gamma distribution of rates across sites (RAS)] may in theory allow the recovery of some ancient divergences. However, such models require that each site maintain its characteristic rate over the whole evolutionary period. This assumption, however, contradicts the knowledge that tertiary structures diverge with time, invalidating the rate-constancy assumption of purely mathematical models. We report here that a hidden Markov version of the covarion model can meet both biochemical and statistical requirements for the analysis of sequence data. The model was proposed on biochemical grounds and can be implemented with only two additional parameters. The two hidden parts of this model are the proportion of sites free to vary (covarions) and the rate of interchange between fixed sites and these variable sites. Simulation results are consistent with this approach, providing a better framework for understanding anciently diverged sequences than the standard RAS models. However, a Gamma distribution of rates may approximate a covarion model and may possibly be justified on these grounds. The accurate reconstruction of older divergences from sequence data is still a major problem, and molecular evolution still requires mathematical models that also have a sound biochemical basis.
There is an apparent paradox in our understanding of molecular evolution. Current biochemically based models predict that evolutionary trees should not be recoverable for divergences beyond a few hundred million years. In practice, however, trees often appear to be recovered from much older times. Mathematical models, such as those assuming that sites evolve at different rates [including a Gamma distribution of rates across sites (RAS)] may in theory allow the recovery of some ancient divergences. However, such models require that each site maintain its characteristic rate over the whole evolutionary period. This assumption, however, contradicts the knowledge that tertiary structures diverge with time, invalidating the rate-constancy assumption of purely mathematical models. We report here that a hidden Markov version of the covarion model can meet both biochemical and statistical requirements for the analysis of sequence data. The model was proposed on biochemical grounds and can be implemented with only two additional parameters. The two hidden parts of this model are the proportion of sites free to vary (covarions) and the rate of interchange between fixed sites and these variable sites. Simulation results are consistent with this approach, providing a better framework for understanding anciently diverged sequences than the standard RAS models. However, a Gamma distribution of rates may approximate a covarion model and may possibly be justified on these grounds. The accurate reconstruction of older divergences from sequence data is still a major problem, and molecular evolution still requires mathematical models that also have a sound biochemical basis.
SummaryCytochrome c has served as a paradigm for the study of protein stability, folding, and molecular evolution, but it remains unclear how these aspects of the protein are related. For example, while the bovine and equine cytochromes c are known to have different stabilities, and possibly different folding mechanisms, it is not known how these differences arise from just three amino acid substitutions introduced during divergence. Using site-selectively incorporated carbon-deuterium bonds we show that like the equine protein, bovine cytochrome c is induced to unfold by guanidine-hydrochloride via a stepwise mechanism, but it does not populate an intermediate as is observed with the equine protein. The increased stability also results in more similar free energies of unfolding observed at different sites within the protein, giving the appearance of a more concerted mechanism. Furthermore, we show that the differences in stability and folding appear to result from a single amino acid substitution which stabilizes a helix by allowing for increased solvation of its N-terminus.
To gain insight into the role of hydrophobic core-surface charge interactions in stabilizing cytochrome c, we investigated the influence of hydrophobic core residues on phosphate binding by mutating residues in yeast iso-2-cytochrome c to those corresponding to iso-l-cytochrome c in various combinations. Heat transition of ultraviolet CD was followed as a function of pH in the presence and absence of phosphate. Thermodynamic parameters were deduced. It was found that the I20V/V43A/M98L mutation in the hydrophobic core, whose locations are remote from the putative phosphate sites, modulates phosphate interactions. The modulation is pH dependent. The I20V/ M98L and V43A mutation effects are nonadditive. The results lead to a model analogous to that of Tsao, Evans, and Wennerstrom, where a domain associated with the ordered hydrophobic core is sensitive to the fields generated by the surface charges. Such an explanation would be in accord with the observed difference in thermal stability between iso-2 and horse cytochromes c.
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