Lecture 7

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Significance of Aligned Sequences

Sequence Alignment
- Inputs:
  - Explicit - Two Sequences {a1, a2,...., am} and {b1, b2,...., bn} (e.g. Query and Database)
  - Implicit - A Scoring Procedure, e.g. Pairwise Scores s(ai,bj) and Gap Costs
- Alignment Algorithm: Global, Local, Gapped, Gapless
- Output: Matching (Sub)sequences with an Overall Score S.
- Significance: What is the Probability of Getting a Score S by Chance?
Statistics of Gapless Local Alignments:
- Random Walks of Scores as a Function of Matching Length (Page 1 (GIF) of Notes)
- Extreme Value Distributions, the Gumbel Distribution, (Page 2 (GIF) of Notes)
- Tails of Distribution in a Gapless Alignment (Page 3 (GIF) of Notes)
Gapped Alignments and Statistical Physics:
- Kardar, Mehran, and Yi-Cheng Zhang. "Scaling of Directed Polymers in Random Media." Physics Review Letters 58, no. 20 (May 18, 1987). (Page 4 (GIF) of Notes)
- Dynamic Programming Method for Sequence Alignment (Example)