The Subsequence Composition of Polypeptides

Abstract

The quantitative underpinning of the information content of biosequences represents an elusive goal and yet also an obvious prerequisite to the quantitative modeling and study of biological function and evolution. Several past studies have addressed the question of what distinguishes biosequences from random strings, the latter being clearly unpalatable to the living cell. Such studies typically analyze the organization of biosequences in terms of their constituent characters or substrings and have, in particular, consistently exposed a tenacious lack of compressibility on behalf of biosequences. This article attempts, perhaps for the first time, an assessement of the structure and randomness of polypeptides in terms on newly introduced parameters that relate to the vocabulary of their (suitably constrained) subsequences rather than their substrings. It is shown that such parameters grasp structural/functional information, and are related to each other under a specific set of rules that span biochemically diverse polypeptides. Measures on subsequences separate few amino acid strings from their random permutations, but show that the random permutations of most polypeptides amass along specific linear loci.

Geometric Approach to Biosequence Analysis

“…Our experiments showed that, unlike some other criteria, ours strongly separate random sequences from biosequences, as well as primitive from biologically complex organisms. These results are in accordance with certain earlier interpretations that biosequences have been evolving towards energy minimization in physical terms, as well as of lowering their information complexity [2,10].…”

“…While by its very nature such a goal has been found "quite elusive" [4], there is substantial evidence in support of the argument that biosequences feature properties that are typical of random sequences (for example, near-total incompressibility [6]). Thus, biosequences are regarded as "slightly edited random sequences" [13], and modern proteins are believed to be "memorized" ancestral random polypeptides which have been slightly modified by the evolutionary selection process in order to optimize their stability under specific physiological conditions [2]. Biosequences appear to be hardly distinguishable from their random permutations, although the latter are clearly incongruous with living organisms [5,9,14].…”

Geometric approach to string analysis for biosequence classification

“…Recall also that we distinguish between substrings and subsequences of a given string s, the former being segments of consecutive terms while the latter being ordered subsets of not necessarily consecutive terms of s. Typically, experimental research involving biosequences is based on processing families of substrings rather than subsequences. Only recently, Apostolico and Cunial attempted to assess ("perhaps for the first time," as these authors believe) the structure and randomness of polypeptides in terms of subsequences satisfying certain conditions [3,4]. As the results obtained therein seem interesting and promising, we performed all our experiments both on substrings and subsequences.…”

“…Following the terminology introduced in [3,4], given a string s, a subsequence of s is any string u which can be obtained by removing from s one or more, not necessarily consecutive terms.…”

“…While by its very nature such a goal has been found quite elusive [6], there is substantial evidence in support of the argument that biosequences feature properties that are typical of random sequences (for example, near-total incompressibility [13]). Thus, biosequences are regarded as "slightly edited random sequences" [20], and modern proteins are believed to be "memorized" ancestral random polypeptides which have been slightly modified by the evolutionary selection process in order to optimize their stability under specific physiological conditions [4]. Biosequences appear to be hardly distinguishable from their random permutations, although the latter are clearly incongruous with living organisms [12,16,21].…”