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

National Research Council

doi:10.17226/2121

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Calculating the Secrets of Life

Contributions of the Mathematical Sciences to Molecular Biology

(1995)

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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.

Contributor(s): National Research Council; Division on Engineering and Physical Sciences; Commission on Physical Sciences, Mathematics, and Applications; Committee on the Mathematical Sciences in Genome and Protein Structure Research; Eric S. Lander and Michael S. Waterman, Editors

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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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