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Problems And Solutions In Biological Sequence Analysis Pdf

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The Open University has a new and improved website. Get familiar with our new site. Topics include advanced alignment methods, Hidden Markov Models, and next-generation sequencing data analysis methods. The course consists of lectures, study groups, and exercises: Tuesday lecture typically introduces week's topic.

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To learn more, view our Privacy Policy. Log In Sign Up. Download Free PDF. Borodovsky M. MinShuo Li. Download PDF. A short summary of this paper. 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 in courses. This book provides just that: following the same structure as BSA, and signific- antly 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 solv- ing 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. He is the founder of the Georgia Tech M.

His research interests are in bioinformatics and systems biology. He has taught Bioinformatics courses since Her research interests are in bioinformat- ics, applied statistics, and stochastic processes.

Her expertise includes teaching probability theory and statistics at universities in Russia and in the USA. Subject to statutory exception and to the provision of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. These ideas facilitate the conversion of the flood of sequence data unleashed by the recent information explosion in biology into a continuous stream of discoveries.

Not surprisingly, the new biology of the twenty-first century has attracted the interest of many talented university graduates with various backgrounds. Teaching bioinformatics to such a diverse audience presents a well-known challenge. The approach requiring stu- dents to advance their knowledge of computer programming and statistics prior to taking a comprehensive core course in bioinformatics has been accepted by many universities, including the Georgia Institute of Technology, Atlanta, USA.

Eddy, and Graeme Mitchison as a text for the core course in bioinformat- ics. Through the years, BSA, which describes the ideas of the major bioinformatic algorithms in a remarkably concise and consistent manner, has been widely adopted as a required text for bioinformatics courses at leading universities around the globe.

Many problems included in BSA as exercises for its readers have been repeatedly used for homeworks and tests. However, the detailed solutions to these problems have not been available. The absence of such a resource was noticed by students and teachers alike. The goal of this book, Problems and Solutions in Biological Sequence Analysis is to close this gap, extend the set of workable problems, and help its readers develop problem-solving skills that are vitally important for conducting successful research in the growing field of bioinformatics.

We hope that this book will facilitate understanding of the content of the BSA chapters and also will provide an additional perspective for in-depth BSA reading by those who might not be able to take a formal bioinformatics course.

We have augmented the set of original BSA problems with many new problems, primarily those that were offered to the Georgia Tech graduate students. The mainstream bioinformatics algorithms, those for pair- wise and multiple sequence alignment, gene finding, detecting orthologs, and building phylogenetic trees, would not work without rational model selection, parameter estimation, properly justified scoring systems, and assessment of stat- istical significance.

These and many other elements of efficient bioinformatic tools require one to take into account the random nature of DNA and protein sequences.

As it has been illustrated by the BSA authors, probabilistic modeling laid the foundation for the development of powerful methods and algorithms for biolo- gical sequence interpretation and the revelation of its functional meaning and evolutionary connections. Notably, probabilistic modeling is a generalization of strictly deterministic modeling, which has a remarkable tradition in natural science. This tradition could be traced back to the explanation of astronomic observa- tions on the motion of solar system planets by Isaac Newton, who suggested a concise model combining the newly discovered law of gravity and the laws of dynamics.

In studying the processes of inheritance and molecular evolution, where random factors play important roles, fully fledged probabilistic models enter the picture. A classic cycle of experiments, data analysis, and modeling with search for a best fit of the models to data was designed and implemented by Gregor Mendel.

His remarkable long term research endeavor provided proof of the existence of discrete units of inheritance, the genes. When we deal with data coming from a less controllable environment, such as data on natural biological evolution spanning time periods on a scale of millions of years, the problem is even more challenging.

Still, the situation is hopeful. The models of molecular evolution proposed by Dayhoff and co-authors, Jukes and Cantor, and Kimura, are classical examples of fundamental advances in modeling of the complex processes of DNA and protein evolution. Notably these models focus on only a single site of a molecular sequence and require the further simpli- fying assumption that evolution of sequence sites occurs independently from each other.

For instance, amino acid substitution scores are critically important parameters of the optimal global Needleman and Wunsch and local Smith and Waterman sequence alignment algorithms. Biologically sensible derivation of the substitution scores is impossible without models of protein evolution. In the mid s the notion of the hidden Markov model HMM , having been of great practical use in speech recognition, was introduced to bioinformatics and quickly entered the mainstream of the modeling techniques in biological sequence analysis.

Theoretical advances that have occurred since the mid s have shown that the sequence alignment problem has a natural probabilistic interpretation in terms of hidden Markov models. In particular, the dynamic programming DP algorithm for pairwise and multiple sequence alignment has the HMM-based algorithmic equivalent, the Viterbi algorithm.

If the type of probabilistic model for a biological sequence has been chosen, parameters of the model could be inferred by statistical machine learning methods. Two competitive models could be compared to identify the one with the best fit. The events and selective forces of the past, moving the evolution of biological species, have to be reconstructed from the current biological sequence data con- taining significant noise caused by all the changes that have occurred in the lifetime of disappeared generations.

This difficulty can be overcome to some extent by the use of the general concept of self-consistent models with parameters adjusted iteratively to fit the growing collection of sequence data. Subsequently, implement- ation of this concept requires the expectation—maximization type algorithms able to estimate the model parameters simultaneously with rearranging data to pro- duce the data structure such as a multiple alignment that fits the model better.

BSA describes several algorithms of expectation—maximization type, including the self-training algorithm for a profile HMM and the self-training algorithm for a phylogenetic HMM. Given that the practice with many algorithms described in BSA requires significant computer programming, one may expect that describing the solutions would lead us into heavy computer codes, thus moving far away from the initial concepts and ideas. However, the majority of the BSA exercises have analytical solutions.

Finally, we should men- tion that the references in the text to the pages in the BSA book cite the edition. We cordially thank our editor Katrina Halliday for tremendous patience and constant support, without which this book would never have come to fruition. Eddy, and Graeme Mitchison, for encouragement, helpful criticism and suggestions. Finally, we wish to express our particular gratitude to our families for great patience and constant understanding.

The first chapter of BSA contains an introduction to the fundamental notions of biological sequence analysis: sequence similarity, homology, sequence alignment, and the basic concepts of probabilistic modeling.

Finding these distinct concepts described back-to-back is surprising at first glance. However, let us recall several important bioinformatics questions. How could we construct a pairwise sequence alignment? How could we build an align- ment of multiple sequences? How could we create a phylogenetic tree for several biological sequences? How could we predict an RNA secondary structure? None of these questions can be consistently addressed without use of probabilistic methods.

The mathematical complexity of these methods ranges from basic theorems and formulas to sophisticated architectures of hidden Markov models and stochastic grammars able to grasp fine compositional characteristics of empirical biological sequences.

The explosive growth of biological sequence data created an excellent oppor- tunity for the meaningful application of discrete probabilistic models. Perhaps, without much exaggeration, the implications of this new development could be compared with implications of the revolutionary use of calculus and dif- ferential equations for solving problems of classic mechanics in the eighteenth century.

The problems considered in this introductory chapter are concerned with the fun- damental concepts that play an important role in biological sequence analysis: the maximum likelihood and the maximum a posteriori Bayesian estimation of the model parameters.

These concepts are crucial for understanding statistical infer- ence from experimental data and are impossible to introduce without notions of conditional, joint, and marginal probabilities. One may still attempt to use methods suitable for large training sets. But this move may result in overfitting and the generation of biased parameter estimates.

Fortunately, this bias can be eliminated to some degree; the model can be generalized as the training set is augmented by artificially introduced observations, pseudocounts. Necessary definitions of these notions and concepts frequently used in BSA can be found in undergraduate text- books on probability and statistics for example, Meyer , Larson , Hogg and Craig , Casella and Berger , and Hogg and Tanis We pick up a die from a table at random.

What are P six Dloaded and P six Dfair? What are P six, Dloaded and P six, Dfair? What is the probability of rolling a six from the die we picked up?

Solution All possible outcomes of a fair die roll are equally likely, i. Problem 1. Although only one in a million people carry it, you consider getting screened. By how much will the test change this uncertainty? Let us consider two possible outcomes. Thus, taking the test is not worthwhile for practical reasons. We roll a die ten times and observe outcomes of 1, 3, 4, 2, 4, 6, 2, 1, 2, and 2.

What is our maximum likelihood estimate for p2 , the probability of rolling a two? What is the Bayesian estimate if we add one pseudocount per category? What if we add five pseudocounts per category? In any case, it is difficult to assess the validity of these alternative approaches without additional information. The best way to improve the estimate is to collect more data. Our goal here is to help the reader recognize the probabilistic nature of these and similar problems about biological sequences.

Basic probability distributions are used in this section to describe the properties of DNA sequences: a geometric distribution to describe the length distribution of restriction fragments Problem 1.

The independence model is used to describe DNA sequences in Problems 1. The introductory level of Chapter 1 still allows us to deal with the notion of hypotheses testing.

In Problem 1.

[PDF] Problems and Solutions in Biological Sequence Analysis Popular Colection

Course: Algorithms for Biological Sequence Analysis. Fall semester, 20 Prerequisites: Some basic knowledge on algorithms is required. Background in bioinformatics and computational biology is welcome but not required for taking this course. Supporting materials:. Journal of Molecular Biology 48 3 : —

Problems and Solutions in Biological Sequence Analysis

In bioinformatics , a sequence alignment is a way of arranging the sequences of DNA , RNA , or protein to identify regions of similarity that may be a consequence of functional, structural , or evolutionary relationships between the sequences. Gaps are inserted between the residues so that identical or similar characters are aligned in successive columns. Sequence alignments are also used for non-biological sequences, such as calculating the distance cost between strings in a natural language or in financial data. If two sequences in an alignment share a common ancestor, mismatches can be interpreted as point mutations and gaps as indels that is, insertion or deletion mutations introduced in one or both lineages in the time since they diverged from one another.

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Part of the resources offered by BSA to understanding the underlying principles of bioinformatics is a set of workable exercises left to the interested reader to solve. Given the multidisciplinary background of bioinformatics, solving these problems requires integrating knowledge from various fields including genetics and molecular biology as well as mathematics and computer science. This is not an easy challenge for the numerous bioinformatics students who come with different abilities from a wide variety of educational backgrounds.

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Biological Sequence Analysis

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