Calculating the Secrets of Life

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.Table of ContentsFront MatterChapter 1 The Secrets of Life: A Mathematician's Introduction to Molecular Biology BIOCHEMISTRYCLASSICAL GENETICSMOLECULAR BIOLOGYTHE RECOMBINANT DNA REVOLUTIONMOLECULAR GENETICS IN THE 1990STHE HUMAN GENOME PROJECTCOMING ATTRACTIONSREFERENCESChapter 2 Mapping Heredity: Using Probabilistic Models and Algorithms to Map Genes and Genomes The Concept of Genetic MapsChallenges of Genetic Mapping: Human Families and Complex TraitsMAXIMUM LIKELIHOOD ESTIMATIONEfficient AlgorithmsExcursion: Susceptibility to Colon Cancer in Mice and the Large Deviation Theory of Diffusion ProcessesAssembling Physical Maps by "Fingerprinting" Random ClonesExcursion: Designing a Strategy to Map the Human GenomeCONCLUSIONREFERENCESChapter 3 Seeing Conserved Signals: Using Algorithms to Detect Similarities between Biosequences FINDING GLOBAL SIMILARITIESVisualizing Alignments: Edit GraphsThe Basic Dynamic Programming AlgorithmFINDING LOCAL SIMILARITIESVariations in Gap Cost PenaltiesThe Duality Between Similarity and Difference MeasuresAligning More Than Two Sequences at a TimeK-Best AlignmentsApproximate Pattern MatchingParallel ComputingCOMPARING ONE SEQUENCE AGAINST A DATABASEHeuristic AlgorithmsSublinear Similarity SearchesOPEN PROBLEMSREFERENCESChapter 4 Hearing Distant Echoes: Using Extremal Statistics to Probe Evolutionary Origins Sequence AlignmentAlignment GivenAlignment UnknownAlignment GivenAlignment UnknownAPPLICATION TO RNA EVOLUTIONTWO BEHAVIORS SUFFICERNA EVOLUTION REVISITEDREFERENCESChapter 5 Calibrating the Clock: Using Stochastic Processes to Measure the Rate of Evolution OVERVIEWTHE COALESCENT AND MUTATIONThe Ewens Sampling FormulaTop-downBottom-upThe Infinitely-Many-Sites ModelK-Allele ModelsThe Finitely-Many-Sites ModelsApproximations for the Ewens Sampling FormulaCombinatorial AssembliesOther Combinatorial StructuresThe Large ComponentsWHERE TO NEXT?Likelihood MethodsDiscussionGeneral-Purpose ReferencesDetailed ReferencesChapter 6 Winding the Double Helix: Using Geometry, Topology, and Mechanics of DNA DNA GEOMETRY AND TOPOLOGY: LINKING, TWISTING, AND WRITHINGAPPLICATIONS TO DNA TOPOISOMERASE REACTIONSDNA ON PROTEIN COMPLEXESTHE SURFACE LINKING NUMBERTHE WINDING NUMBER AND HELICAL REPEATRELATIONSHIP BETWEEN LINKING, SURFACE LINKING, AND WINDINGAPPLICATION TO THE STUDY OF THE MINICHROMOSOMEREFERENCESChapter 7 Unwinding the Double Helix: Using Differential Mechanics to Probe Conformational Changes...DNA SUPERHELICITY - MATHEMATICS AND BIOLOGYSTATEMENT OF THE PROBLEMTHE ENERGETICS OF A STATEANALYSIS OF SUPERHELICAL EQUILIBRIAEvaluation of Free-Energy ParametersAccuracy of the Calculated ResultsAPPLYING THE METHOD TO STUDY INTERESTING GENESDISCUSSION AND OPEN PROBLEMSREFERENCESChapter 8 Lifting the Curtain: Using Topology to Probe the Hidden Action of Enzymes THE TOPOLOGY OF DNASITE-SPECIFIC RECOMBINATIONTOPOLOGICAL TOOLS FOR DNA ANALYSISTHE TANGLE MODEL FOR SITE-SPECIFIC RECOMBINATIONTHE TOPOLOGY OF TN3 RESOLVASESOME UNSOLVED PROBLEMSApplication of Geometry and Topology to BiologyREFERENCESChapter 9 Folding the Sheets: Using Computational Methods to Predict the Structure of Proteins A PRIMER ON PROTEIN STRUCTUREBASIC INSIGHTS ABOUT PROTEIN STRUCTURETHREADING METHODSPREDICTING HIV PROTEASE STRUCTURE:AN EXCURSIONHIERARCHICAL APPROACHESPREDICTING MYOGLOBIN STRUCTURE:AN EXCURSIONACKNOWLEDGMENTSREFERENCESAppendix - Chapter AuthorsIndex