It is well known that there are some similarities among various naturally occurring amino acids. Thus, the complexity in protein systems could be reduced by sorting these amino acids with similarities into groups and then protein sequences can be simplified by reduced alphabets. This paper discusses how to group similar amino acids and whether there is a minimal amino acid alphabet by which proteins can be folded. Various reduced alphabets are obtained by reserving the maximal information for the simplified protein sequence compared with the parent sequence using global sequence alignment. With these reduced alphabets and simplified similarity matrices, we achieve recognition of the protein fold based on the similarity score of the sequence alignment. The coverage in dataset SCOP40 for various levels of reduction on the amino acid types is obtained, which is the number of homologous pairs detected by program BLAST to the number marked by SCOP40. For the reduced alphabets containing 10 types of amino acids, the ability to detect distantly related folds remains almost at the same level as that by the alphabet of 20 types of amino acids, which implies that 10 types of amino acids may be the degree of freedom for characterizing the complexity in proteins.
Currently, of the 10(6) known protein sequences, only about 10(4) structures have been solved. Based on homologies and similarities, proteins are grouped into different families in which each has a structural prototype, namely, the fold, and some share the same folds. However, the total number of folds and families, and furthermore, the distribution of folds over families in nature, are still an enigma. Here, we report a study on the distribution of folds over families and the total number of folds in nature, using a maximum probability principle and the moment method of estimation. A quadratic relation between the numbers of families and folds is found for the number of families in an interval from 6000 to 30,000. For example, about 2700 folds for 23,100 families are obtained, among them about 33 superfolds, including more than 100 families each, and the largest superfold comprises about 800 families. Our results suggest that although the majority of folds have only a single family per fold, a considerably larger number of folds include many more families each than in the database, and the distribution of folds over families in nature differs markedly from the sampled distribution. The long tail of fold distribution is first estimated in this article. The results fit the data for different versions of the structural classification of proteins (SCOP) excellently, and the goodness-of-fit tests strongly support the results. In addition, the method of directly "enlarging" the sample to the population may be useful in inferring distributions of species in different fields.
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