Feature Column from the AMS

1. Molecular Biology and Genetics Primer for Mathematicians

Molecular Biology and Genetics Primer for Mathematicians: Genes

2. Genes

Special segments of the DNA are known as genes. In classical Mendelian genetics genes are traditionally thought of as controlling some trait. Variants of the gene, known as alleles are responsible for the different traits observed. Thus, one uses the notation A and a for the alleles that control, say, smooth coat or rough coat in an animal. A specific individual might have genetic makeup AA, Aa (equivalent to aA), or aa. If the physical appearance or phenotype of the animal with AA and Aa is different from the appearance of an animal with aa, then the allele A is known as dominant and the allele a is known as recessive. Furthermore, the phenotype of the animal, smooth coat or rough coat, does not always allow one to determine the genotype of the animal. (In some cases, for example, BB, Bb, and bb, the three genotypes may correspond to three different phenotypes.) The gene responsible for a particular trait will be associated with a particular location, historically called a locus, on a chromosome. The corresponding loci on homologous chromosomes can have identical alleles or different alleles. A group of people might have many alleles at this locus but a specific individual can have at most 2. Genes which are on different chromosomes or which are far apart on the same chromosome usually are inherited independently. However, genes that are in close proximity on a chromosome are subject to linkage.

The modern conception of an allele for a gene is that it is a particular linear section of a DNA molecule. This linear stretch of DNA is associated with the production of a specific protein, by spelling out which amino acids (see below for more detail) make up the protein. (Pioneers in developing the relation between genes and enzymes, which are special proteins that catalyze (accelerate) chemical reactions, were George Beadle, Edward Tatum, and Max Delbrück. However, not all genes make enzymes.) We now understand that sometimes genes have sections that are involved in protein production (exons) and other sections which must be snipped out (introns) before protein production starts. Furthermore, genes have sections that are involved with the regulation process by which the proteins are made, leading to expressions such as genes being turned on or turned off.

Among the most remarkable properties of the DNA molecule is that the sister strands of nucleotides which make up the double helix can be thought of as written in a four-letter alphabet A, C, G, and T which denote specific types of nucleotides. (A nucleotide is a section of a DNA molecule (or RNA molecule, see below) which consists of a sugar, a base containing nitrogen, and a phosphate section.)

A schematic of the DNA showing helical strands and how the the nucleotide are paired.

(This image is used with the permission from the National Human Genome Research Institute (NHGRI))

When A (or T) appears on one strand it is always matched with T (or A) on the other strand. A stands for adenine and G for guanine and as a group, adenine and guanine are known as purines. C stands for cytosine and T for thymine and as a group are known as pyrimidines. When C (or G) appears on one strand, it is always matched with G (or C) on the other. The complementary pairs are known as base pairs (bp) and the length of sections of DNA are customarily measured in base pairs. The diagram above helps one understand how, when the DNA strands separate, each strand can make a copy of itself. The ends of a DNA stretch are known as the 5' and 3' ends, respectively. (The numbers are references to the number used to label the chemical components in the ring structures that make up the nucleotides.) Computing statistics on the number of A's, C's, G's, and T's and purines and pyrimidines in genes (or stretches of DNA) has proved to be useful.