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desirable products. Sensitive and reliable diagnostics can be developed for viral diseases such as AIDS, and treatments can be developed for some hereditary diseases, such as cystic fibrosis.

Molecular biology is certain to continue its exciting growth well into the next century. As its frontiers expand, the character of the field is changing. With ever growing databases of DNA and protein sequences and increasingly powerful techniques for investigating structure and function, molecular biology is becoming not just an experimental science, but a theoretical science as well. The role of theory in molecular biology is not likely to resemble the role of theory in physics, in which mathematicians can offer grand unifying theories. In biology, key insights emerge less often from first principles than from interpreting the crazy quilt of solutions that evolution has devised. Interpretation depends on having theoretical tools and frameworks. Sometimes, these constructs are nonmathematical. Increasingly, however, the mathematical sciences—mathematics, statistics, and computational science—are playing an important role.

This book emerged from the recognition of the need to cultivate the interface between molecular biology and the mathematical sciences. In the following chapters, various mathematicians working in molecular biology provide glimpses of that interface. The essays are not intended to be comprehensive up-to-date reviews, but rather vignettes that describe just enough to tempt the reader to learn more about fertile areas for research in molecular biology.

This introductory chapter briefly outlines the intellectual foundations of molecular biology, introduces some key terms and concepts that recur throughout the book, and previews the chapters to follow.

Biochemistry

Historically, molecular biology grew out of two complementary experimental approaches to studying biological function: biochemistry and genetics (Figure 1.1). Biochemistry involves fractionating (breaking up) the molecules in a living organism, with the goal of purifying and characterizing the chemical components responsible for carrying out a particular function. To do this, a biochemist devises an assay for



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