KarlinAltschul

Karlin-Altschul refers to a statistical framework for evaluating the significance of local sequence alignments, developed by Samuel Karlin and Stephen F. Altschul. The theory provides a probabilistic model for the distribution of high-scoring segment pairs (HSPs) when two sequences are compared under a random-model assumption, forming the basis for statistical scoring in modern sequence similarity searches.

Central result: under a random background of letters and a scoring system for matches, mismatches, and gaps, the maximum local alignment score follows an approximate Gumbel distribution. The significance of an observed score S is quantified by the E-value, commonly written as E = Kmne^{-λS}, where m and n are the effective lengths of the compared sequences, and λ and K are constants determined by the scoring system and background composition. This enables estimation of how many such results would be expected by chance in a database of size m by n.

Publication and impact: the framework was described in a 1990 paper by Karlin and Altschul and has become foundational for the assessment of sequence similarity, notably underpinning the BLAST and FASTA search algorithms. The approach has been extended to accommodate composition-based statistics and gap penalties, and remains central to computational biology and bioinformatics.

Notes: the model relies on assumptions such as independence of residues and specific scoring schemes; real biological sequences may violate these assumptions, requiring empirical adjustments. The Karlin-Altschul theory continues to influence development of sequence-analysis statistics and related tools.