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As researchers have pursued biology's secrets to the molecular level, mathematical and computer sciences have played an increasingly important role—in genome mapping, population genetics, and even the controversial search for "Eve," hypothetical mother of the human race.

In this first-ever survey of the partnership between the two fields, leading experts look at how mathematical research and methods have made possible important discoveries in biology.

The volume explores how differential geometry, topology, and differential mechanics have allowed researchers to "wind" and "unwind" DNA's double helix to understand the phenomenon of supercoiling. It explains how mathematical tools are revealing the workings of enzymes and proteins. And it describes how mathematicians are detecting echoes from the origin of life by applying stochastic and statistical theory to the study of DNA sequences.

This informative and motivational book will be of interest to researchers, research administrators, and educators and students in mathematics, computer sciences, and biology.

Suggested Citation

National Research Council. 1995. Calculating the Secrets of Life: Contributions of the Mathematical Sciences to Molecular Biology. Washington, DC: The National Academies Press. https://doi.org/10.17226/2121.

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Publication Info

300 pages | 6 x 9 | Paperback
ISBN: 978-0-309-07502-2
DOI: https://doi.org/10.17226/2121
Chapters skim
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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