List of Code Challenges. Meet the Authors Meet the Development Team... xxxii Meet our Adopting Institutions... xxxiv Acknowledgments...
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1 Contents List of Code Challenges xxv Meet the Authors xxxi Meet the Development Team xxxii Meet our Adopting Institutions xxxiv Acknowledgments xxxv 1 Where in the Genome Does DNA Replication Begin? 2 A Journey of a Thousand Miles Hidden Messages in the Replication Origin... 5 DnaA boxes... 5 Hidden messages in The Gold-Bug... 6 Counting words... 7 The Frequent Words Problem... 8 Frequent words in Vibrio cholerae Some Hidden Messages are More Surprising than Others An Explosion of Hidden Messages Looking for hidden messages in multiple genomes The Clump Finding Problem The Simplest Way to Replicate DNA Asymmetry of Replication Peculiar Statistics of the Forward and Reverse Half-Strands Lurking biological phenomenon or statistical fluke? Deamination xi
2 The skew diagram Some Hidden Messages are More Elusive than Others A Final Attempt at Finding DnaA Boxes in E. coli Epilogue: Complications in ori Predictions Open Problems Multiple replication origins in a bacterial genome Finding replication origins in archaea Finding replication origins in yeast Computing probabilities of patterns in a string Charging Stations The frequency array Converting patterns to numbers and vice-versa Finding frequent words by sorting Solving the Clump Finding Problem Solving the Frequent Words with Mismatches Problem Generating the neighborhood of a string Finding frequent words with mismatches by sorting Detours Big-O notation Probabilities of patterns in a string The most beautiful experiment in biology Directionality of DNA strands The Towers of Hanoi The overlapping words paradox Bibliography Notes Which DNA Patterns Play the Role of Molecular Clocks? 66 Do We Have a Clock Gene? Motif Finding Is More Difficult Than You Think Identifying the evening element Hide and seek with motifs A brute force algorithm for motif finding Scoring Motifs From motifs to profile matrices and consensus strings Towards a more adequate motif scoring function Entropy and the motif logo From Motif Finding to Finding a Median String xii
3 The Motif Finding Problem Reformulating the Motif Finding Problem The Median String Problem Why have we reformulated the Motif Finding Problem? Greedy Motif Search Using the profile matrix to roll dice Analyzing greedy motif finding Motif Finding Meets Oliver Cromwell What is the probability that the sun will not rise tomorrow? Laplace s Rule of Succession An improved greedy motif search Randomized Motif Search Rolling dice to find motifs Why randomized motif search works How Can a Randomized Algorithm Perform So Well? Gibbs Sampling Gibbs Sampling in Action Epilogue: How Does Tuberculosis Hibernate to Hide from Antibiotics? Charging Stations Solving the Median String Problem Detours Gene expression DNA arrays Buffon s needle Complications in motif finding Relative entropy Bibliography Notes How Do We Assemble Genomes? 115 Exploding Newspapers The String Reconstruction Problem Genome assembly is more difficult than you think Reconstructing strings from k-mers Repeats complicate genome assembly String Reconstruction as a Walk in the Overlap Graph From a string to a graph The genome vanishes xiii
4 Two graph representations Hamiltonian paths and universal strings Another Graph for String Reconstruction Gluing nodes and de Bruijn graphs Walking in the de Bruijn Graph Eulerian paths Another way to construct de Bruijn graphs Constructing de Bruijn graphs from k-mer composition De Bruijn graphs versus overlap graphs The Seven Bridges of Königsberg Euler s Theorem From Euler s Theorem to an Algorithm for Finding Eulerian Cycles Constructing Eulerian cycles From Eulerian cycles to Eulerian paths Constructing universal strings Assembling Genomes from Read-Pairs From reads to read-pairs Transforming read-pairs into long virtual reads From composition to paired composition Paired de Bruijn graphs A pitfall of paired de Bruijn graphs Epilogue: Genome Assembly Faces Real Sequencing Data Breaking reads into k-mers Splitting the genome into contigs Assembling error-prone reads Inferring multiplicities of edges in de Bruijn graphs Charging Stations The effect of gluing on the adjacency matrix Generating all Eulerian cycles Reconstructing a string spelled by a path in the paired de Bruijn graph. 167 Maximal non-branching paths in a graph Detours A short history of DNA sequencing technologies Repeats in the human genome Graphs The icosian game Tractable and intractable problems xiv
5 From Euler to Hamilton to de Bruijn The seven bridges of Kaliningrad Pitfalls of assembling double-stranded DNA The BEST Theorem Bibliography Notes How Do We Sequence Antibiotics? 184 The Discovery of Antibiotics How Do Bacteria Make Antibiotics? How peptides are encoded by the genome Where is Tyrocidine encoded in the Bacillus brevis genome? From linear to cyclic peptides Dodging the Central Dogma of Molecular Biology Sequencing Antibiotics by Shattering Them into Pieces Introduction to mass spectrometry The Cyclopeptide Sequencing Problem A Brute Force Algorithm for Cyclopeptide Sequencing A Branch-and-Bound Algorithm for Cyclopeptide Sequencing Mass Spectrometry Meets Golf From theoretical to real spectra Adapting cyclopeptide sequencing for spectra with errors From 20 to More than 100 Amino Acids The Spectral Convolution Saves the Day Epilogue: From Simulated to Real Spectra Open Problems The Beltway and Turnpike Problems Sequencing cyclic peptides in primates Charging Stations Generating the theoretical spectrum of a peptide How fast is CYCLOPEPTIDESEQUENCING? Trimming the peptide leaderboard Detours Gause and Lysenkoism Discovery of codons Quorum sensing Molecular mass Selenocysteine and pyrrolysine xv
6 Pseudo-polynomial algorithm for the Turnpike Problem Split genes Bibliography Notes How Do We Compare Biological Sequences? 224 Cracking the Non-Ribosomal Code The RNA Tie Club From protein comparison to the non-ribosomal code What do oncogenes and growth factors have in common? Introduction to Sequence Alignment Sequence alignment as a game Sequence alignment and the longest common subsequence The Manhattan Tourist Problem What is the best sightseeing strategy? Sightseeing in an arbitrary directed graph Sequence Alignment is the Manhattan Tourist Problem in Disguise An Introduction to Dynamic Programming: The Change Problem Changing money greedily Changing money recursively Changing money using dynamic programming The Manhattan Tourist Problem Revisited From Manhattan to an Arbitrary Directed Acyclic Graph Sequence alignment as building a Manhattan-like graph Dynamic programming in an arbitrary DAG Topological orderings Backtracking in the Alignment Graph Scoring Alignments What is wrong with the LCS scoring model? Scoring matrices From Global to Local Alignment Global alignment Limitations of global alignment Free taxi rides in the alignment graph The Changing Faces of Sequence Alignment Edit distance Fitting alignment Overlap alignment xvi
7 Penalizing Insertions and Deletions in Sequence Alignment Affine gap penalties Building Manhattan on three levels Space-Efficient Sequence Alignment Computing alignment score using linear memory The Middle Node Problem A surprisingly fast and memory-efficient alignment algorithm The Middle Edge Problem Epilogue: Multiple Sequence Alignment Building a three-dimensional Manhattan A greedy multiple alignment algorithm Detours Fireflies and the non-ribosomal code Finding a longest common subsequence without building a city Constructing a topological ordering PAM scoring matrices Divide-and-conquer algorithms Scoring multiple alignments Bibliography Notes Are There Fragile Regions in the Human Genome? 296 Of Mice and Men How different are the human and mouse genomes? Synteny blocks Reversals Rearrangement hotspots The Random Breakage Model of Chromosome Evolution Sorting by Reversals A Greedy Heuristic for Sorting by Reversals Breakpoints What are breakpoints? Counting breakpoints Sorting by reversals as breakpoint elimination Rearrangements in Tumor Genomes From Unichromosomal to Multichromosomal Genomes Translocations, fusions, and fissions From a genome to a graph xvii
8 2-breaks Breakpoint Graphs Computing the 2-Break Distance Rearrangement Hotspots in the Human Genome The Random Breakage Model meets the 2-Break Distance Theorem The Fragile Breakage Model Epilogue: Synteny Block Construction Genomic dot-plots Finding shared k-mers Constructing synteny blocks from shared k-mers Synteny blocks as connected components in graphs Open Problem: Can Rearrangements Shed Light on Bacterial Evolution? Charging Stations From genomes to the breakpoint graph Solving the 2-Break Sorting Problem Detours Why is the gene content of mammalian X chromosomes so conserved?. 346 Discovery of genome rearrangements The exponential distribution Bill Gates and David X. Cohen flip pancakes Sorting linear permutations by reversals Bibliography Notes Which Animal Gave Us SARS? 352 The Fastest Outbreak Trouble at the Metropole Hotel The evolution of SARS Transforming Distance Matrices into Evolutionary Trees Constructing a distance matrix from coronavirus genomes Evolutionary trees as graphs Distance-based phylogeny construction Toward An Algorithm for Distance-Based Phylogeny Construction A quest for neighboring leaves Computing limb lengths Additive Phylogeny Trimming the tree Attaching a limb xviii
9 An algorithm for distance-based phylogeny construction Constructing an evolutionary tree of coronaviruses Using Least Squares to Construct Approximate Distance-Based Phylogenies. 372 Ultrametric Evolutionary Trees The Neighbor-Joining Algorithm Transforming a distance matrix into a neighbor-joining matrix Analyzing coronaviruses with the neighbor-joining algorithm Limitations of distance-based approaches to tree construction Character-Based Tree Reconstruction Character tables From anatomical to genetic characters How many times has evolution invented insect wings? The Small Parsimony Problem The Large Parsimony Problem Epilogue: Evolutionary Trees Fight Crime Detours When did HIV jump from primates to humans? Searching for a tree fitting a distance matrix The four point condition Did bats give us SARS? Why does the neighbor-joining algorithm find neighboring leaves? Computing limb lengths in the neighbor-joining algorithm Giant panda: bear or raccoon? Where did humans come from? Bibliography Notes How Did Yeast Become a Wine Maker? 416 An Evolutionary History of Wine Making How long have we been addicted to alcohol? The diauxic shift Identifying Genes Responsible for the Diauxic Shift Two evolutionary hypotheses with different fates Which yeast genes drive the diauxic shift? Introduction to Clustering Gene expression analysis Clustering yeast genes The Good Clustering Principle xix
10 Clustering as an Optimization Problem Farthest First Traversal k-means Clustering Squared error distortion k-means clustering and the center of gravity The Lloyd Algorithm From centers to clusters and back again Initializing the Lloyd algorithm k-means++ Initializer Clustering Genes Implicated in the Diauxic Shift Limitations of k-means Clustering From Coin Flipping to k-means Clustering Flipping coins with unknown biases Where is the computational problem? From coin flipping to the Lloyd algorithm Return to clustering Making Soft Decisions in Coin Flipping Expectation maximization: the E-step Expectation maximization: the M-step The expectation maximization algorithm Soft k-means Clustering Applying expectation maximization to clustering Centers to soft clusters Soft clusters to centers Hierarchical Clustering Introduction to distance-based clustering Inferring clusters from a tree Analyzing the diauxic shift with hierarchical clustering Epilogue: Clustering Tumor Samples Detours Whole genome duplication or a series of duplications? Measuring gene expression Microarrays Proof of the Center of Gravity Theorem Transforming an expression matrix into a distance/similarity matrix Clustering and corrupted cliques Bibliography Notes xx
11 9 How Do We Locate Disease-Causing Mutations? 468 What Causes Ohdo Syndrome? Introduction to Multiple Pattern Matching Herding Patterns into a Trie Constructing a trie Applying the trie to multiple pattern matching Preprocessing the Genome Instead Introduction to suffix tries Using suffix tries for pattern matching Suffix Trees Suffix Arrays Constructing a suffix array Pattern matching with the suffix array The Burrows-Wheeler Transform Genome compression Constructing the Burrows-Wheeler transform From repeats to runs Inverting the Burrows-Wheeler Transform A first attempt at inverting the Burrows-Wheeler transform The First-Last Property Using the First-Last property to invert the Burrows-Wheeler transform. 493 Pattern Matching with the Burrows-Wheeler Transform A first attempt at Burrows-Wheeler pattern matching Moving backward through a pattern The Last-to-First mapping Speeding Up Burrows-Wheeler Pattern Matching Substituting the Last-to-First mapping with count arrays Getting rid of the first column of the Burrows-Wheeler matrix Where are the Matched Patterns? Burrows and Wheeler Set Up Checkpoints Epilogue: Mismatch-Tolerant Read Mapping Reducing approximate pattern matching to exact pattern matching BLAST: Comparing a sequence against a database Approximate pattern matching with the Burrows-Wheeler transform Charging Stations Constructing a suffix tree Solving the Longest Shared Substring Problem xxi
12 Partial suffix array construction Detours The reference human genome Rearrangements, insertions, and deletions in human genomes The Aho-Corasick algorithm From suffix trees to suffix arrays From suffix arrays to suffix trees Binary search Bibliography Notes Why Have Biologists Still Not Developed an HIV Vaccine? 530 Classifying the HIV Phenotype How does HIV evade the human immune system? Limitations of sequence alignment Gambling with Yakuza Two Coins up the Dealer s Sleeve Finding CG-Islands Hidden Markov Models From coin flipping to a Hidden Markov Model The HMM diagram Reformulating the Casino Problem The Decoding Problem The Viterbi graph The Viterbi algorithm How fast is the Viterbi algorithm? Finding the Most Likely Outcome of an HMM Profile HMMs for Sequence Alignment How do HMMs relate to sequence alignment? Building a profile HMM Transition and emission probabilities of a profile HMM Classifying proteins with profile HMMs Aligning a protein against a profile HMM The return of pseudocounts The troublesome silent states Are profile HMMs really all that useful? Learning the Parameters of an HMM Estimating HMM parameters when the hidden path is known xxii
13 Viterbi learning Soft Decisions in Parameter Estimation The Soft Decoding Problem The forward-backward algorithm Baum-Welch Learning The Many Faces of HMMs Epilogue: Nature is a Tinkerer and not an Inventor Detours The Red Queen Effect Glycosylation DNA methylation Conditional probability Bibliography Notes Was T. rex Just a Big Chicken? 586 Paleontology Meets Computing Which Proteins Are Present in This Sample? Decoding an Ideal Spectrum From Ideal to Real Spectra Peptide Sequencing Scoring peptides against spectra Where are the suffix peptides? Peptide sequencing algorithm Peptide Identification The Peptide Identification Problem Identifying peptides in the unknown T. rex proteome Searching for peptide-spectrum matches Peptide Identification and the Infinite Monkey Theorem False discovery rate The monkey and the typewriter Statistical significance of a peptide-spectrum match Spectral Dictionaries T. rex Peptides: Contaminants or Treasure Trove of Ancient Proteins? The hemoglobin riddle The dinosaur DNA controversy Epilogue: From Unmodified to Modified Peptides Post-translational modifications xxiii
14 Searching for modifications as an alignment problem Building a Manhattan grid for spectral alignment Spectral alignment algorithm Detours Gene prediction Finding all paths in a graph The Anti-Symmetric Path Problem Transforming spectra into spectral vectors The infinite monkey theorem The probabilistic space of peptides in a spectral dictionary Are terrestrial dinosaurs really the ancestors of birds? Solving the Most Likely Peptide Vector Problem Selecting parameters for transforming spectra into spectral vectors Bibliography Notes Appendix: Introduction to Pseudocode 639 What is Pseudocode? Nuts and Bolts of Pseudocode The if condition The for loop The while loop Recursive algorithms Arrays Glossary 649 Bibliography 671 Image Courtesies 683 xxiv
List of Code Challenges. About the Textbook Meet the Authors... xix Meet the Development Team... xx Acknowledgments... xxi
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