Exact Asymptotic Results for a Model of Sequence Alignment

Details Exact Asymptotic Results for a Model of Sequence Alignment Exact Asymptotic Results for a Model of Sequence Alignment

2004-10-11

arxiv.org/abs/q-bio/0410012v1

Phys. Rev. E, 72, 020901 (2005)

Biology

Quantitative Biology

Genomics

4 pages Revtex, 2 .eps figures included

Scientific paper

10.1103/PhysRevE.72.020901

Finding analytically the statistics of the longest common subsequence (LCS) of a pair of random sequences drawn from c alphabets is a challenging problem in computational evolutionary biology. We present exact asymptotic results for the distribution of the LCS in a simpler, yet nontrivial, variant of the original model called the Bernoulli matching (BM) model which reduces to the original model in the large c limit. We show that in the BM model, for all c, the distribution of the asymptotic length of the LCS, suitably scaled, is identical to the Tracy-Widom distribution of the largest eigenvalue of a random matrix whose entries are drawn from a Gaussian unitary ensemble. In particular, in the large c limit, this provides an exact expression for the asymptotic length distribution in the original LCS problem.

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