Calculating the Secrets of Life -- Copyright -- Preface -- Contents -- Calculating the Secrets of Life -- Chapter 1 The Secrets of Life: A Mathematician's Introduction to Molecular Biology -- BIOCHEMISTRY -- CLASSICAL GENETICS -- MOLECULAR BIOLOGY -- THE RECOMBINANT DNA REVOLUTION -- MOLECULAR GENETICS IN THE 1990S -- THE HUMAN GENOME PROJECT -- COMING ATTRACTIONS -- REFERENCES -- Chapter 2 Mapping Heredity: Using Probabilistic Models and Algorithms to Map Genes and Genomes -- GENETIC MAPPING -- The Concept of Genetic Maps -- Challenges of Genetic Mapping: Human Families and Complex Traits -- MAXIMUM LIKELIHOOD ESTIMATION -- Efficient Algorithms -- Statistical Significance -- Excursion: Susceptibility to Colon Cancer in Mice and the Large Deviation Theory of Diffusion Processes -- PHYSICAL MAPPING -- Assembling Physical Maps by "Fingerprinting" Random Clones -- Excursion: Designing a Strategy to Map the Human Genome -- CONCLUSION -- REFERENCES -- Chapter 3 Seeing Conserved Signals: Using Algorithms to Detect Similarities between Biosequences -- FINDING GLOBAL SIMILARITIES -- Visualizing Alignments: Edit Graphs -- The Basic Dynamic Programming Algorithm -- FINDING LOCAL SIMILARITIES -- VARIATIONS ON SEQUENCE COMPARISON -- Variations in Gap Cost Penalties -- The Duality Between Similarity and Difference Measures -- Aligning More Than Two Sequences at a Time -- K-Best Alignments -- Approximate Pattern Matching -- Parallel Computing -- COMPARING ONE SEQUENCE AGAINST A DATABASE -- Heuristic Algorithms -- Sublinear Similarity Searches -- OPEN PROBLEMS -- REFERENCES -- Chapter 4 Hearing Distant Echoes: Using Extremal Statistics to Probe Evolutionary Origins -- GLOBAL SEQUENCE COMPARISONS -- Sequence Alignment -- Alignment Given -- Alignment Unknown -- LOCAL SEQUENCE COMPARISONS -- Alignment Given -- Alignment Unknown -- APPLICATION TO RNA EVOLUTION.

TWO BEHAVIORS SUFFICE -- RNA EVOLUTION REVISITED -- REFERENCES -- Chapter 5 Calibrating the Clock: Using Stochastic Processes to Measure the Rate of Evolution -- OVERVIEW -- THE COALESCENT AND MUTATION -- The Ewens Sampling Formula -- Forwards and Backwards in the Tree -- Top-down -- Bottom-up -- The Infinitely-Many-Sites Model -- K-Allele Models -- The Finitely-Many-Sites Models -- MATHEMATICAL VIGNETTE: APPROXIMATING COMBINATORIAL STRUCTURES -- Approximations for the Ewens Sampling Formula -- Combinatorial Assemblies -- Other Combinatorial Structures -- The Large Components -- WHERE TO NEXT? -- Likelihood Methods -- Discussion -- REFERENCES -- General-Purpose References -- Detailed References -- Chapter 6 Winding the Double Helix: Using Geometry, Topology, and Mechanics of DNA -- DNA GEOMETRY AND TOPOLOGY: LINKING, TWISTING, AND WRITHING -- APPLICATIONS TO DNA TOPOISOMERASE REACTIONS -- DNA ON PROTEIN COMPLEXES -- THE SURFACE LINKING NUMBER -- THE WINDING NUMBER AND HELICAL REPEAT -- RELATIONSHIP BETWEEN LINKING, SURFACE LINKING, AND WINDING -- APPLICATION TO THE STUDY OF THE MINICHROMOSOME -- REFERENCES -- Chapter 7 Unwinding the Double Helix: Using Differential Mechanics to Probe Conformational Changes... -- DNA SUPERHELICITY-MATHEMATICS AND BIOLOGY -- STATEMENT OF THE PROBLEM -- THE ENERGETICS OF A STATE -- ANALYSIS OF SUPERHELICAL EQUILIBRIA -- Evaluation of Free-Energy Parameters -- Accuracy of the Calculated Results -- APPLYING THE METHOD TO STUDY INTERESTING GENES -- DISCUSSION AND OPEN PROBLEMS -- REFERENCES -- Chapter 8 Lifting the Curtain: Using Topology to Probe the Hidden Action of Enzymes -- THE TOPOLOGY OF DNA -- SITE-SPECIFIC RECOMBINATION -- TOPOLOGICAL TOOLS FOR DNA ANALYSIS -- THE TANGLE MODEL FOR SITE-SPECIFIC RECOMBINATION -- THE TOPOLOGY OF TN3 RESOLVASE -- SOME UNSOLVED PROBLEMS -- ANNOTATED BIBLIOGRAPHY -- Knot Theory.

Application of Geometry and Topology to Biology -- REFERENCES -- Chapter 9 Folding the Sheets: Using Computational Methods to Predict the Structure of Proteins -- A PRIMER ON PROTEIN STRUCTURE -- BASIC INSIGHTS ABOUT PROTEIN STRUCTURE -- THREADING METHODS -- PREDICTING HIV PROTEASE STRUCTURE:AN EXCURSION -- HIERARCHICAL APPROACHES -- PREDICTING MYOGLOBIN STRUCTURE:AN EXCURSION -- CONCLUSION -- ACKNOWLEDGMENTS -- REFERENCES -- Appendix-Chapter Authors -- Index.