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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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Figure 1.1
 Genetics and biochemistry began as independent ways to study
biological function.

measuring an ''activity" and then tries successive fractionation procedures to isolate a pure fraction having the activity. For example, a biochemist might study an organism's ability to metabolize sugar by purifying a component that could break down sugar in a test tube.

In vitro (literally, in glass) assays were accomplished back in the days when biologists were still grappling with the notion of vitalism. Originally, it was thought that life and biochemical reactions did not obey the known laws of chemistry and physics. Such vitalism held sway until about 1900, when it was shown that material from dead yeast cells could ferment sugar into ethanol, proving that important processes of living organisms were "just chemistry." The catalysts promoting these transformations were called enzymes.

Living organisms are composed principally of carbon, hydrogen, oxygen, and nitrogen; they also contain small amounts of other key elements (such as sodium, potassium, magnesium, sulfur, manganese, and selenium). These elements are combined in a vast array of complex macromolecules that can be classified into a number of major types: proteins, nucleic acids, lipids (fats), and carbohydrates (starches and sugars). Of all the macromolecules, the proteins have the most diverse range of functions. The human body makes about 100,000 distinct proteins, including:

· enzymes, which catalyze chemical reactions, such as digestion of food;

· structural molecules, which make up hair, skin, and cell walls;

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· transporters of substances, such as hemoglobin, which carries oxygen in blood; and

· transporters of information, such as receptors in the surface of cells and insulin and other hormones.

In short, proteins do the work of the cell. From a structural standpoint, a protein is an ordered linear chain made of building blocks known as amino acids (Figures 1.2 and 1.3). There are 20 distinct amino acids, each with its own chemical properties (including size, charge, polarity, and hydrophobicity, or the tendency to avoid packing with water). Each protein is defined by its unique sequence of amino acids; there are typically 50 to 500 amino acids in a protein.

Figure 1.2
Proteins are a linear polymer, assembled from 20
building blocks called amino acids that differ in
their side chains. The diagram shows a highly
stylized view of this linear structure.

Figure 1.3
Examples of different representations of  protein structures focusing
on (left) chemical  bonds and (right) secondary structural features
such as helices and sheet-like elements. Reprinted, by permission,
from Richardson and Richardson (1989). Copyright © 1989 by
the Plenum Publishing Corporation.