Executive Summary p. 1
The Nature of the Field p. 12
Introduction p. 12
The Mathematics-Biology Interface p. 12
What Has Changed in Recent Years? p. 15
What Makes Computational Biology Problems Hard? p. 19
Factors Common to Successful Interactions Between the Mathematical Sciences and the Biosciences p. 20
Preparing the Ground for Improved Synergies of Benefit to Both Fields p. 22
Structure of This Report p. 27
References p. 27
Historical Successes p. 29
The Beginnings of Population Biology p. 29
Inference of Gene Function by Homology p. 30
Evolutionary Processes in Populations p. 32
Modeling p. 33
Medical and Biological Imaging p. 34
Summary p. 35
References p. 36
Understanding Molecules p. 38
Introduction p. 38
The Mathematics-Biology Connection p. 39
Areas of Mathematical Applications for Molecules p. 41
Sequence Analysis p. 41
Structure Analysis p. 43
Dynamics p. 45
Interactions p. 47
Future Directions p. 48
References p. 49
Understanding Cells p. 51
Introduction p. 51
Exemplification of These Issues p. 52
Cellular Structures p. 55
Discovery of Cellular Networks and Their Functions p. 57
From Networks to Cellular Functions p. 60
From Cells to Tissues p. 66
Data Integration p. 68
Biological Considerations p. 70
Future Directions p. 72
References p. 73
Understanding Organisms p. 80
Cardiac Physiology p. 81
Circulatory Physiology p. 84
Respiratory Physiology p. 85
Information Processing p. 86
Endocrine Physiology p. 87
Morphogenesis and Pattern Formation p. 88
Locomotion p. 90
Cancer p. 91
Delivery of Therapy to Target Tumor Cells p. 91
Mechanisms of Drug Action p. 92
Growth and Differentiation of Cell Populations p. 92
Development of Resistance p. 92
In Vivo Dynamics of the HIV-1 Infection p. 93
Future Directions p. 94
References p. 95
Understanding Populations p. 99
Population Genetics p. 99
Ecological Aspects of Populations p. 104
A Synthesis of Ecology and Evolution p. 106
References p. 108
Understanding Communities and Ecosystems p. 110
Computation p. 116
Future Directions p. 117
References p. 122
Crosscutting Themes p. 127
The "Small n, Large P" Problem p. 127
Finding Patterns in Gene-Expression Data p. 128
Supervised Learning p. 131
Unsupervised Learning p. 132
Analysis of Ordered Systems p. 134
Applications of Hidden Markov Models to the Analysis of DNA, RNA, and Protein Sequences p. 134
Profile HMMs p. 135
HMMs in Gene Finding p. 136
Applications of Monte Carlo Methods in Computational Biology p. 138
Gibbs Sampling in Motif Finding p. 139
Inference of Regulatory Networks p. 139
Sampling Protein Conformations p. 140
Lessons from Mathematical Themes of Current Import p. 140
Processing of Low-Level Data p. 142
Epilogue p. 144
References p. 145