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Front Matter i-xiv
Chapter 1 The Secrets of Life: A Mathematician's Introduction to Molecular Biology 1-1
BIOCHEMISTRY 2-4
CLASSICAL GENETICS 5-6
MOLECULAR BIOLOGY 7-12
THE RECOMBINANT DNA REVOLUTION 13-15
MOLECULAR GENETICS IN THE 1990S 16-17
THE HUMAN GENOME PROJECT 18-21
COMING ATTRACTIONS 22-23
REFERENCES 24-24
Chapter 2 Mapping Heredity: Using Probabilistic Models and Algorithms to Map Genes and Genomes 25-26
The Concept of Genetic Maps 27-29
Challenges of Genetic Mapping: Human Families and Complex Traits 30-33
MAXIMUM LIKELIHOOD ESTIMATION 34-34
Efficient Algorithms 35-36
Excursion: Susceptibility to Colon Cancer in Mice and the Large Deviation Theory of Diffusion Processes 37-41
Assembling Physical Maps by "Fingerprinting" Random Clones 42-46
Excursion: Designing a Strategy to Map the Human Genome 47-50
CONCLUSION 51-53
REFERENCES 54-55
Chapter 3 Seeing Conserved Signals: Using Algorithms to Detect Similarities between Biosequences 56-57
FINDING GLOBAL SIMILARITIES 58-58
Visualizing Alignments: Edit Graphs 59-59
The Basic Dynamic Programming Algorithm 60-64
FINDING LOCAL SIMILARITIES 65-69
Variations in Gap Cost Penalties 70-71
The Duality Between Similarity and Difference Measures 72-72
Aligning More Than Two Sequences at a Time 73-75
K-Best Alignments 76-77
Approximate Pattern Matching 78-78
Parallel Computing 79-80
COMPARING ONE SEQUENCE AGAINST A DATABASE 81-81
Heuristic Algorithms 82-83
Sublinear Similarity Searches 84-85
OPEN PROBLEMS 86-87
REFERENCES 88-89
Chapter 4 Hearing Distant Echoes: Using Extremal Statistics to Probe Evolutionary Origins 90-93
Sequence Alignment 94-94
Alignment Given 95-95
Alignment Unknown 96-98
Alignment Given 99-104
Alignment Unknown 105-105
APPLICATION TO RNA EVOLUTION 106-107
TWO BEHAVIORS SUFFICE 108-109
RNA EVOLUTION REVISITED 110-111
REFERENCES 112-113
Chapter 5 Calibrating the Clock: Using Stochastic Processes to Measure the Rate of Evolution 114-116
OVERVIEW 117-118
THE COALESCENT AND MUTATION 119-121
The Ewens Sampling Formula 122-123
Top-down 124-124
Bottom-up 125-126
The Infinitely-Many-Sites Model 127-129
K-Allele Models 130-131
The Finitely-Many-Sites Models 132-135
Approximations for the Ewens Sampling Formula 136-138
Combinatorial Assemblies 139-141
Other Combinatorial Structures 142-143
The Large Components 144-144
WHERE TO NEXT? 145-145
Likelihood Methods 146-147
Discussion 148-148
General-Purpose References 149-149
Detailed References 150-152
Chapter 6 Winding the Double Helix: Using Geometry, Topology, and Mechanics of DNA 153-154
DNA GEOMETRY AND TOPOLOGY: LINKING, TWISTING, AND WRITHING 155-162
APPLICATIONS TO DNA TOPOISOMERASE REACTIONS 163-165
DNA ON PROTEIN COMPLEXES 166-166
THE SURFACE LINKING NUMBER 167-170
THE WINDING NUMBER AND HELICAL REPEAT 171-172
RELATIONSHIP BETWEEN LINKING, SURFACE LINKING, AND WINDING 173-173
APPLICATION TO THE STUDY OF THE MINICHROMOSOME 174-176
REFERENCES 177-178
Chapter 7 Unwinding the Double Helix: Using Differential Mechanics to Probe Conformational Changes... 179-180
DNA SUPERHELICITY - MATHEMATICS AND BIOLOGY 181-183
STATEMENT OF THE PROBLEM 184-185
THE ENERGETICS OF A STATE 186-186
ANALYSIS OF SUPERHELICAL EQUILIBRIA 187-191
Evaluation of Free-Energy Parameters 192-193
Accuracy of the Calculated Results 194-194
APPLYING THE METHOD TO STUDY INTERESTING GENES 195-198
DISCUSSION AND OPEN PROBLEMS 199-199
REFERENCES 200-201
Chapter 8 Lifting the Curtain: Using Topology to Probe the Hidden Action of Enzymes 202-202
THE TOPOLOGY OF DNA 203-206
SITE-SPECIFIC RECOMBINATION 207-211
TOPOLOGICAL TOOLS FOR DNA ANALYSIS 212-221
THE TANGLE MODEL FOR SITE-SPECIFIC RECOMBINATION 222-224
THE TOPOLOGY OF TN3 RESOLVASE 225-229
SOME UNSOLVED PROBLEMS 230-231
Application of Geometry and Topology to Biology 232-232
REFERENCES 233-235
Chapter 9 Folding the Sheets: Using Computational Methods to Predict the Structure of Proteins 236-236
A PRIMER ON PROTEIN STRUCTURE 237-240
BASIC INSIGHTS ABOUT PROTEIN STRUCTURE 241-247
THREADING METHODS 248-253
PREDICTING HIV PROTEASE STRUCTURE:AN EXCURSION 254-254
HIERARCHICAL APPROACHES 255-264
PREDICTING MYOGLOBIN STRUCTURE:AN EXCURSION 265-265
ACKNOWLEDGMENTS 266-266
REFERENCES 267-271
Appendix - Chapter Authors 272-276
Index 277-285

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Calculating the Secrets of Life: Contributions of the Mathematical Sciences to Molecular Biology (1995)

Chapter: Approximations for the Ewens Sampling Formula

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Calculating the Secrets of Life: Contributions of the Mathematical Sciences to Molecular Biology (1995)

Chapter: Approximations for the Ewens Sampling Formula