Problems and Solutions in Biological Sequence Analysis

Abstract

This book is the first of its kind to provide a large collection of bioinformatics problems with accompanying solutions. Notably, the problem set includes all of the problems offered in Biological Sequence Analysis (BSA), by Durbin et al., widely adopted as a required text for bioinformatics courses at leading universities worldwide. Although many of the problems included in BSA as exercises for its readers have been repeatedly used for homework and tests, no detailed solutions for the problems were available. Bioinformatics instructors had therefore frequently expressed a need for fully worked solutions and a larger set of problems for use on courses. This book provides just that: following the same structure as BSA and significantly extending the set of workable problems, it will facilitate a better understanding of the contents of the chapters in BSA and will help its readers develop problem-solving skills that are vitally important for conducting successful research in the growing field of bioinformatics. All of the material has been class-tested by the authors at Georgia Tech, where the first ever M.Sc. degree program in Bioinformatics was held.

Uniform Accuracy of the Maximum Likelihood Estimates for Probabilistic Models of Biological Sequences

“…described in Lawrence et al 1993; Borodovsky and McIninch 1993; Burge and Karlin 1997; Durbin et al 1998; Borodovsky and Ekisheva 2006). The bound of the error is obtained in Eq.…”

“…(The logarithms of the ratios of sequence fragment probabilities computed with two alternative models make log-odds scores, the important quantities used in many algorithms of biological sequence analysis; further discussions of the log-odds scores applications are available in Section 2.2 of Durbin et al 1998, and in Sections 4.2 and 5.2.1 of Borodovsky and Ekisheva 2006). The bounds of the error can be estimated from inequality (2.1) for the maximum estimation error Δ.…”

GLProbs

“…These adjusted posterior probabilities will be used to determine the substitution scores in the following step. 1 The double affine pair-HMM is similar to the three-state global model, except that there is an extra pair of gap states for long insertions and deletions.…”

“…To make the alignment process focus on the local conserved regions, we need to remove the "noise" of the flanking regions. To this end, GLProbs applies the standard technique of coupling the local pair-HMM with a random pair-HMM as shown in Figure 1(b), and using the log-odds ratios derived from the two models to determine the posterior probabilities (for details, see [1,8]). …”

GLProbs: Aligning Multiple Sequences Adaptively

“…To make the alignment process focus on the local conserved regions, we need to remove the "noises" of the flanking regions. To this end, GLProbs applies the standard technique of coupling the local pair-HMM with a random pair-HMM as shown in Figure 1(b), and using the log-odds ratios derived from the two models to determine the posterior probabilities (for details, see [1,8]).…”