Fundamental Algorithms in Bioinformatics
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Fundamental Algorithms in Bioinformatics
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Fundamental Algorithms in Bioinformatics
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Some suggestions of where the student can get moreexposure to algorithms for bioinformatics and computational biology.
Building evolutionary trees from sequence data. The Maximum Parsimony criteria, the special case of Perfect Phylogeny, and the Fitch-Hartigon dynamic program to minimize mutations when the tree and a sequence alignment are known.
Additive trees and their construction. The Neighbor-Joining algorithm and its use with near-additive data. Bootstrap values and their misuse.
Algorithms for constructing an Ultrametric Tree from an Ultrametric Matrix, and the relationship of ultrametrics to the molecular clock.
lntroduction to trees that represent evolution. We start with the case of perfect data: the Ultrametric tree case.
What the Backwards algorithm computes and why we want it.Profile HMMs and their use. Cleaning up some topics in sequence analysis (running out of time); PSI-BLAST and its dangers.
This class finishes the discussion of the Vitterbi algorithm, its time analysis and the traceback algorithm. Introduction to the Forward algorithm to compute the probability that a given sequence is generate by the HMM.
Finish the discussion of HMMs for CpG islands. Introductionto the Vitterbi algorithm (really dynamic programming)to find the most likely Markov Chain generating a givensequence.
Hidden Markov models to identify CpG islands. Thislecture follows the discussion in Durbin and Eddy.
Finish the discussion of profiles and log-odds ratios. introduction to Markov Modelsand Hidden Markov Models
Use of multiple sequence alignment to build a model of a set of biologically related sequences. Profiles, log-odds ratios.
The center tree method and analysis; progressive alignment, guide trees, CLUSTAL, uses of multiple alignment
Continuation of multiple sequence alignment; sum-of-pairs objective function; tree consistency theorem; factor-of-two approximation.
Start of discussion on Multiple Sequence Alignment. sum-of-pairs objective function. Dynamic program solution for three sequences. Program MSA
Further discussion of probability and database search. Granin and BRCA1 story. Database search used as a filter, not an oracle.
E-values, extreme value distribution, probability of a match
Discussion of hashing kmers, E-values, statistics, BLAST II
Continuation of the topic of probability of matching.Here we look at the probability that a query stringmatches completely, at least once, in a much largerdatabase of strings.
Completion of the analysis of the expected length of the longest common substring in two random strings
We discuss the expected length of the longest common substring(not subsequence) between two random strings of length n each,and show that it grows only logarithmically as a function of n -much slower than the growth of the expected longest c
End-gap-free alignment using dynamic programming. Examplefrom whole-genome shotgun sequencing.
We discuss the expected length of the longest common subsequencebetween two random strings of lengths n each, and show that it grows linearlywith n. This lecture originally contained a discussion both of the expected length of the longestco
In depth treatment of local alignment using dynamicprogramming.
Continuation of the discussion of how to compute similarityand optimal sequence alignment using dynamic programming.Local as well as global alignment.
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