Graphs and Genes

This book is written by a mathematician and a theoretical biologist who have arrived at a good mutual understanding and a well worked-out common notation. The reader need hardly be convinced of the necessity of such a mutual understanding, not only for the two investigators, but also for the sciences they represent. Like Moliere's hero, geneticists are gradually beginning to understand that, unknowingly, they have been speaking in the language of cybernetics. Mathematicians are unexpec tedly discovering that many past and present problems and methods of genetics can be naturally formulated in the language of graph theory. In this way a powerful abstract mathematical theory suddenly finds a productive application. Moreover, in its turn, such an application be gins to "feed" the mathematical theory by presenting it with a number of new problems. The reader may judge for himself the fruitfulness of such mutual interaction. At the same time several important circumstances need to be men tioned. The formalization and rigorous formulation given here embraces not only the older problems, known by geneticists for many decades (the construction of genetic maps, the analysis of complementation, etc. ), but also comparatively new problems: the construction of partial com plementation maps, phylogenetic trees of proteins, etc.

Inhalt

1. Graphs in the Analysis of Gene Structure.- §1. Gene systems and their maps.- §2. The mathematical theory of linear maps: interval graphs.- §3. The mathematical theory of linear maps: interval hypergraphs.- §4. Linear mapping algorithms.- §5. Examples of structural analysis of genetic systems.- 2. Graphs in the Analysis of Gene Semantics.- §1. Interallelic complementation and the functioning of protein multimers.- §2. The approximation of graphs.- §3. Analyzing the spatio-functional organization of specific genetic systems.- 3. Graphs in the Analysis of Gene Evolution.- §1. Trees and phylogenetic trees.- §2. The evolution of families of synonymous proteins.- Epilogue: Cryptographic Problems in Genetics.- Appendix: Some Notions About Graphs.- References.- Index of Genetics Terms.- Index of Mathematical Terms.