Graphs and Genes

ISBN-13: 9783642692826 / Angielski / Miękka / 2011 / 200 str.

B. G. Mirkin; S. N. Rodin; H. L. Beus

Opis

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."

Spis treści

1. Graphs in the Analysis of Gene Structure.- §1. Gene systems and their maps.- 1. Levels of the genetic language.- 2. Mutations, recombination, complementation.- 3. Genetic methods of investigation.- §2. The mathematical theory of linear maps: interval graphs.- 1. Maps and interval orders.- 2. The description of interval graphs.- 3. Graphs of non-covering intervals.- §3. The mathematical theory of linear maps: interval hypergraphs.- 1. Maps and interval hypergraphs.- 2. Minimal hypergraphs and complons.- 3. The construction of fictitious complons.- 4. Non-linear hypergraphs and interval graphs.- §4. Linear mapping algorithms.- 1. The Fulkerson-Gross algorithm.- 2. The uniqueness theorem.- 3. Admissible orderings of linear matrices.- §5. Examples of structural analysis of genetic systems.- 1. The use of deletions and polar mutations.- 2. The complementation maps of multiple mutational defects.- 3. Complex traits and the loci which control them.- 2. Graphs in the Analysis of Gene Semantics.- §1. Interallelic complementation and the functioning of protein multimers.- 1. Interallelic complementation.- 2. The fundamental principles of organization of protein multimers.- 3. The molecular mechanisms of interallelic complementation.- §2. The approximation of graphs.- 1. Approximation problems in a space of relations.- 2. The optimal partition problem.- 3. Detecting macrostructure.- §3. Analyzing the spatio-functional organization of specific genetic systems.- 1. Complex protein organization.- 2. The investigation of genome spatial structure.- 3. Graphs in the Analysis of Gene Evolution.- §1. Trees and phylogenetic trees.- 1. The notion of a phylogenetic tree.- 2. The metric generated by a tree.- 3. The construction of dendrograms.- 4. Reconstructing the probable structure of ancestral successions.- 5. Calculating the internal structure of sequences during tree construction.- §2. The evolution of families of synonymous proteins.- 1. The dendrogram of the globins and its analysis.- 2. Analyzing the evolution of globin sequences from their internal structure.- Epilogue: Cryptographic Problems in Genetics.- Appendix: Some Notions About Graphs.- References.- Index of Genetics Terms.- Index of Mathematical Terms.