Implications of thermodynamics of protein folding for evolution of primary sequences

Natural proteins exhibit essentially two-state thermodynamics, with one stable fold that dominates thermodynamically over a vast number of possible folds, a number that increases exponentially with the size of the protein. Here we address the question of whether this feature of proteins is a rare property selected by evolution or whether it is in fact true of a significant proportion of all possible protein sequences. Using statistical procedures developed to study spin glasses, we show that, given certain assumptions, the probability that a randomly synthesized protein chain will have a dominant fold (which is the global minimum of free energy) is a function of temperature, and that below a critical temperature the probability rapidly increases as the temperature decreases. Our results suggest that a significant proportion of all possible protein sequences could have a thermodynamically dominant fold.