Abstract: MATH/CHEM/COMP 2002, Dubrovnik, June 24-29, 2002






Branko BorStnik and Danilo Pumpernik

National Institute of Chemistry, Hajdrihova 19, SI-1001 Ljubljana, Slovenia




Simple thermodynamic systems obey the principle of detailed balance which states that the ratio of the rates of a molecular process versus the inverse process can be expressed in terms of phase space factors and Boltzmann factor. Point mutations, deletions, insertions and other mutational events can not be interpreted by the standard theories of reaction rates because the processes are controlled by the Darwinian principle of survival of the fittest what is not manageable on the microscopic level.

By  analyzing the nucleotide sequences deposited in databanks one can obtain some information about the frequency of  mutational events. Our  interest was devoted to the distributions of lengths of dinucleotide repeats in Human Genome. The results were interpreted in terms of an algebraic formalism which took into account two types of mutational processes: The slippage processes which cause the repeats to be elongated or shortened and point mutations which perform the interruptions in the repeats. The slippage processes were taken to be either symmetric (the elongations being equiprobable to shortening) or asymmetric. The formalism was cast into a form of matrix multiplication of a vector representing the histogram of dinucleotide repeats. A fitting procedure led us to a matrix whose symmetry properties gave us the information about the fulfillment of the principle of detailed balance.