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THE SECRETS OF LIFE: A MATHEMATICIAN'S INTRODUCTION TO MOLECULAR BIOLOGY 16 primer is allowed to pair with a base in the complementary region and is then extended to contain the full sequence from the region by using the enzyme DNA polymerase. In this fashion a single copy of the region gives rise to two copies. By iterating this step n times, one might make 2'' copies of the region. In practice, one can start with a small drop of blood or saliva and obtain a millionfold amplification of a region. Not surprisingly, PCR has found myriad applications, especially in genetic diagnostics. MOLECULAR GENETICS IN THE 1990S With the tools of recombinant DNA, the triangle of knowledge (see Figure 1.7) has been transformed, to use a mathematical metaphor, into a commutative diagram (Figure 1.10). It is possible to traverse the diagram in any directionâfor example, to find the genes and proteins underlying a biological function or to find the protein and function associated with a given gene. A good illustration of the power of the techniques is provided by recent studies of the inherited disease cystic fibrosis (CF). CF is a recessive disease, the genetics of which is formally identical to wrinkledness in peas as studied by Mendel: if two non-affected carriers of the recessive CF gene a (that is, heterozygotes with genotype Aa) marry, one fourth of their offspring will be affected (that is, will have genotype aa). The frequency of the disease- causing allele is about 1/42 in the Caucasian population, and so about 1/21 of all Caucasians are carriers. Since a marriage between two carriers produces 1/4 affected children, the disease frequency in the population is about 1/2000 ( 1/4 Ã 1/21 Ã 1/21). Although CF was recognized relatively early in the century, the molecular basis for the disease remained a mystery until 1989. The first breakthrough was the genetic mapping of CF to human chromosome 7 in 1985 (Figure 1.11). Genetic mapping involved showing that the inheritance pattern of the disease in families is closely correlated with the inheritance pattern of a particular DNA polymorphism (that is, a common spelling variation in the DNA), in this case on chromosome 7.
THE SECRETS OF LIFE: A MATHEMATICIAN'S INTRODUCTION TO MOLECULAR BIOLOGY 17 Figure 1.10 Recombinant DNA provided the ability to move freely in any direction among gene, protein, and function, thereby converting the triangle of Figure 1.7 into a commutative diagram. The correlation does not imply that the polymorphism causes the disease, but rather that the polymorphism must be located near the site of the disease gene. Of course, "near" is a relative term. In this case, "near" meant that the CF gene must be within 1 million to 2 million bases of DNA along the chromosome. The next step was the physical mapping and the DNA sequencing of the CF gene itself, which took four more years to accomplish. This involved starting from the nearby polymorphism and sequentially isolating adjacent fragments in a tedious process called chromosomal walking until the disease gene was reached. Once the disease gene was found, its complete DNA sequence was determined. (A description of how one knows that one has found the disease gene is beyond the scope of this introduction.) From the DNA sequence, it became clear that the CF gene encoded a protein of 1,480 amino acids and that the most common misspelling in the population (accounting for about 70 percent of all CF alleles) was a three- letter deletion that removed a single codon specifying an amino acid, a phenylalanine at position 508 of the protein. On the basis of this finding, it became possible to perform DNA diagnostics on individuals to see if they carried the common CF mutation. Even more intriguingly, the sequence gave immediate clues to the structure and function of the gene product. When the protein sequence was compared with the public databases of previous sequences, it was found to show strong similarities to a class of proteins that were membrane-bound transporters-molecules that reside in the cell membrane, bind adenosinetriphosphate (ATP), and transport substances
