Tables of critical values for examining compositional non-randomness in proteins and nucleic acids

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Abstract
Summary A binomially distributed statisticpχ 2i is defined which in conjunction with a set of critical tables permits, for peptides or proteins of arbitrary lengths, a well-defined answer to the question: Does the proportion of a particular amino acidi present in that protein deviate significantly from random expectation? An analogous statistic is defined for nucleic acids. This statistic is simply related to the classical chi-squared test. The classical χ2 and thepχ 2i are supplementary in that the former permits one to determine that a non-randomness in amino acid composition exists in a protein, while the latter permits one to localize that non-randomness to particular amino acids. Thepχ 2i statistic takes into account explicitly the compositional fluctuations imposed by the finite length of proteins. The tables are more exact than any hitherto existing, and require no intermediate calculations for their use: from the direct experimental measurement of the number of residues of amino acidi, one immediately reads from the tables whether the number observed is within random expectation or not. These statistics are used to analyze eight proteins of diverse length, function, and origin in an accompanying paper.