Information-theoretic analysis of protein sequences shows that amino acids self-cluster.

We analyse for each of 20 amino acids X the statistics of spacings between consecutive occurrences of X within the well-characterized Saccharomyces cerevisiae genome. The occurrences of amino acids may exhibit near random, clustered or smoothed out behaviour, like one-dimensional stochastic processes along the protein chain. If amino acids are distributed randomly within a sequence, then they follow a Poisson process, and a histogram of the number of observations of each gap size would asymptotically follow a negative exponential distribution. The novelty of the present approach lies in the use of differential geometric methods to quantify information on sequencing of amino acids and groups of amino acids, via the sequences of intervals between their occurrences. The differential geometry arises from an information-theoretic distance function on the two-dimensional space of stochastic processes subordinate to gamma distributions-which latter include the random process as a special case. We find that maximum-likelihood estimates of parametric statistics show that all 20 amino acids tend to cluster, some substantially. In other words, the frequencies of short gap lengths tend to be higher and the variance of the gap lengths is greater than expected by chance. This may be because localizing amino acids with the same properties may favour secondary structure formation or transmembrane domains. Gap sizes of 1 or 2 are generally disfavoured, 1 strongly so. The only exceptions to this are Gln and Ser, as a result of poly(Gln) or poly(Ser) sequences. There are preferences for gaps of 4 and 7 that can be attributed to alpha -helices. In particular, a favoured gap of 7 for Leu is found in coiled coils. Our method contributes to the characterization of whole sequences by extracting and quantifying stable stochastic features.