of stochastic processes to such evolutionary analysis. The discovery and reading of genetic sequences have breathed new life into the study of the stochastic processes of evolution. The chapter focuses on one of the most exciting new tools, the use of the coalescent to estimate times to the most recent common ancestor.
Geometric methods applied to DNA structure and function are the focus of the next three chapters. Watson and Crick's famous DNA double helix can be thought of as local geometrical structure. There is also much interesting geometry in the more global structure of DNA molecules. Chapter 6 ("Winding the Double Helix") uses methods from geometry to describe the coiling and packing of chromosomes. The chapter describes the supercoiling of the double helix, in terms of key geometric quantitieslink, twist, and writhethat are related by a fundamental theorem. Chapter 7 ("Unwinding the Double Helix") employs differential mechanics to study how stresses on a DNA molecule cause it to unwind in certain areas, thereby allowing access by key enzymes needed for gene expression. Chapter 8 ("Lifting the Curtain") uses topology to infer the mechanism of enzymes that recombine DNA strands, providing a glimpse of details that cannot be seen via experiment.
Finally, Chapter 9 ("Folding the Sheets") discusses one of the hardest open questions in computational biology: the protein-folding problem, which concerns predicting the three-dimensional structure of a protein on the basis of the sequence of its amino acids. Probably no simple solution will ever be given for this central problem, but many useful and interesting approximate approaches have been developed. The concluding chapter surveys various computational approaches for structure prediction.
Together, these chapters provide glimpses of the roles of mathematics, statistics, and computing in some of the most exciting and dynamic areas of molecular biology. If this book tempts some mathematicians, statisticians, and computational scientists to learn more about and to contribute to molecular biology, it will have accomplished one of its goals. Its two other goals are to encourage molecular biologists to be more cognizant of the importance of the mathematical and computational sciences in molecular biology and to encourage scientifically literate people to be aware of the increasing impact of both molecular biology and mathematical and computational sciences on their