By Richard Durbin, Sean R. Eddy, Anders Krogh, Graeme Mitchison

Probablistic types have gotten more and more vital in studying the large quantity of knowledge being produced via large-scale DNA-sequencing efforts reminiscent of the Human Genome undertaking. for instance, hidden Markov types are used for interpreting organic sequences, linguistic-grammar-based probabilistic types for deciding upon RNA secondary constitution, and probabilistic evolutionary types for inferring phylogenies of sequences from assorted organisms. This publication supplies a unified, up to date and self-contained account, with a Bayesian slant, of such tools, and extra mostly to probabilistic equipment of series research. Written by means of an interdisciplinary staff of authors, it's available to molecular biologists, laptop scientists, and mathematicians without formal wisdom of the opposite fields, and while provides the state-of-the-art during this new and critical box.

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**Extra resources for Biological sequence analysis**

**Example text**

The first is that of obtaining a good random sample of confirmed alignments. Alignments tend not to be independent from each other because protein sequences come in families. The second is more subtle. In truth, different pairs of sequences have diverged by different amounts. When two sequences have diverged from a common ancestor very recently, we expect many of their residues to be identical. The probability pab for a = b should be small, and hence s(a, b) should be strongly negative unless a = b.

This is the typical situation when searching a database. It is clear that if we have a fixed prior odds ratio, then even if all the database sequences are unrelated, as the number of sequences we try to match increases, the probability of one of the matches looking significant by chance will also increase. In fact, given a fixed prior odds ratio, the expected number of (falsely) significant observations will increase linearly. If we want it to stay fixed, then we must set the prior odds ratio in inverse proportion to the number of sequences in the database N .

In the ungapped case, the relevant quantity to consider is the expected value of a fixed length alignment. 10) a,b where qa is the probability of symbol a at any given position in a sequence. 10) is always satisfied. This is because qa qb s(a, b) = − a,b qa qb log a,b qa q b = −H (q 2 || p) pab where H (q 2 || p) is the relative entropy of distribution q 2 = q × q with respect to distribution p, which is always positive unless q 2 = p (see Chapter 11). In fact H (q 2 || p) is a natural measure of how different the two distributions are.