Methods for assessing the statistical significance of molecular sequence features by using general scoring schemes.

Abstract

An unusual pattern in a nucleic acid or protein sequence or a region of strong similarity shared by two or more sequences may have biological significance. It is therefore desirable to know whether such a pattern can have arisen simply by chance. To identify interesting sequence patterns, appropriate scoring values can be asigned to the individual residues of a single sequence or to sets of residues when several sequences are compared. For single sequences, such scores can reflect biophysical properties such as charge, volume, hydrophobicity, or secondary structure potential; for multiple sequences, they can reflect nucleotide or amino acid similarity measured in a wide variety of ways. Using an appropriate random model, we present a theory that provides precise numerical formulas for assessing the statistical significance of any region with high aggregate score. A second class of results describes the composition of high-scoring segments. In certain contexts, these permit the choice of scoring systems which are "optimal" for distinguishing biologically relevant patterns. Examples are given of applications of the theory to a variety of protein sequences, highlighting segments with unusual biological features. These include distinctive charge regions in transcription factors and protooncogene products, pronounced hydrophobic segments in various receptor and transport proteins, and statistically ignificant subalignments involving the recently characterized cystic fibrosis gene. relationships (e.g., refs. 5, 7, 8, 12). One limitation to the applicability of these results has been their inability to allow for properties or mismatches that vary in degree. For example, in describing the charge or hydrophobicity ofamino acid residues, it would be more informative to use different score levels, and when comparing sequences one may wish to count a mismatch between isoleucine and valine differently than a mismatch between glycine and tryptophan.In this paper we describe a rigorous statistical theory that provides explicit formulas for characterizing significant sequence configurations with reference to a general scoring scheme. In particular, we determine the distribution of high aggregate segment scores and the distribution of the number of separate segments of significantly high score. A second class of results deals with the letter composition of highscoring segments, which in certain contexts provides a method for choosing suitable scoring schemes. We will discuss the theory in two primary contexts: (i) the analysis of a single protein sequence with the objective of identifying segments with statistically significant high scores for hydropathy strength, charge concentration, size profile, phosphorylation potential, or secondary structure propensity; (ii)

Sequence-Specific Sequence Comparison Using Pairwise Statistical Significance

“…random variables tends to an extreme value distribution (EVD) [26,35]. This fact is theoretically well-founded for the ungapped local sequence alignment, where the distribution of Smith-Waterman local alignment score between random, unrelated sequences is known to follow a Gumbel-type EVD [34], as shown in Fig. 1.1.…”

“…Score distribution for ungapped local alignment is known to follow a Gumbel-type EVD [34], as shown in Fig. 1.1 with analytically calculable parameters.…”

“…The above formulae are valid for ungapped alignments [34], and the parameters K and λ can be computed analytically from the substitution scores and sequence compositions.…”

“…For ungapped alignments, rigorous statistical theory for the alignment score distribution is available [34]. However, no precise statistical theory currently exists for the gapped alignment score distribution and for score distributions from alignment programs using additional features like difference blocks [32] or multiple parameter sets [31].…”

“…For ungapped alignments, rigorous statistical theory for the alignment score distribution is available [34]. However, no precise statistical theory currently exists for the simplest extension of ungapped alignment, which is alignment with gaps, although there exist a couple of good starting points for statistically describing gapped alignment score distributions for simple scoring schemes [36,25].…”