DO MUTATIONAL EVENTS EXHIBIT
THE PRINCIPLE of DETAILED BALANCE?
Branko BorStnik and Danilo Pumpernik
National Institute of Chemistry,
Hajdrihova 19, SI1001 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.
