DNA Alignment

Dynamic Programming R. Bellman ~ 1950

Bellman’s Optimality Principle States of the system Sequence of decisions to be made Optimality index Optimal decision depends on the present state of the system – does not depend on previous decisions

Example 1 We can go up, right or up-right: Find minimal – cost path

Solution

Cumulative scores matrix Decisions matrix

Example 2 c1c1 c2c2 c3c3 c4c4 c5c5 c i – cost per unit length – find the cheapest way

Remarks Example 1 – cost assigned to states, no cost of decisions Example 2 – cost assigned to decisions no cost of states

Alignments for comparing two DNA sequences For measuring the degree of similarity between them For looking for mutations

Dot matrix plots Formulation DNA alignment as dynamic programming problem

Needleman and Wunsch algorithm 1.Draw dot – matrix plot 2.Alignment = find a path through dot – matrix plot which maximizes cumulative score, s ij score for math-mismatch beteween elements, W k = a+bk – penalty for gap

Smith and Waterman algorithm 1.If a cumulative similarity score becomes negative it is reset to zero. Remote dissimilarities are removed this way 2.The end of an alignment occurs at the largest score in the cumulative score matrix

Software for DNA alignment BLAST, FAST BioEdit BioEdit version Copyright © Tom Hall North Carolina State University, Department of Microbiology so nice