Statistical mechanics of proteins with ‘‘evolutionary selected’’ sequences

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Abstract
The requirement that the native structure of a protein be stable and kinetically accessible implies that it should correspond to a pronounced energy minimum. Thus we expect the protein sequence not to be random but selected such that this is satisfied. This is achieved in our model by defining a ‘‘selective temperature’’ in sequence space and statistically optimizing the sequence for the target conformation. Mean-field replica calculations are presented for this model and the phase diagram indicating the temperatures and selective temperatures at which the transition to the native conformation occurs is obtained. The transition to the native state is shown to be a first-order one. A temperature range exists in which the target structure of selected sequences is stable and kinetically accessible. It is shown that optimization at very low selective temperature leads to sequences with long-range correlations which appear to be less capable of folding.