Assessment of the probabilities for evolutionary structural changes in protein folds

Motivation: The evolution of protein sequences can be described by a stepwise process, where each step involves changes of a few amino acids. In a similar manner, the evolution of protein folds can be at least partially described by an analogous process, where each step involves comparatively simple changes affecting few secondary structure elements. A number of such evolution steps, justified by biologically confirmed examples, have previously been proposed by other researchers. However, unlike the situation with sequences, as far as we know there have been no attempts to estimate the comparative probabilities for different kinds of such structural changes. Results: We have tried to assess the comparative probabilities for a number of known structural changes, and to relate the probabilities of such changes with the distance between protein sequences. We have formalized these structural changes using a topological representation of structures (TOPS), and have developed an algorithm for measuring structural distances that involve few evolutionary steps. The probabilities of structural changes then were estimated on the basis of all-against-all comparisons of the sequence and structure of protein domains from the CATH-95 representative set. The results obtained are reasonably consistent for a number of different data subsets and permit the identification of several 'most popular' types of evolutionary changes in protein structure. The results also suggest that alterations in protein structure are more likely to occur when the sequence similarity is ≥10% (the average similarity being ∼6% for the data sets employed in this study), and that the distribution of probabilities of structural changes is fairly uniform within the interval of 15-50% sequence similarity.