Non-poissonian Distribution of Point Mutations in DNA

In general, for chemical reactions occurring in systems, where fluctuations are not negligibly small, it is necessary to introduce a master equation for distribution of probability of fluctuations. It has been established that the monomolecular reactions of a type as A↔X are described by the master equation, which leads to the Poisson distribution with the variance equal to the average value N_0. However, the consideration of the Löwdin mechanism as autocatalytic nonlinear chemical reactions such as A+X↔2X and the corresponding master equation lead to the non-Poissonian probability distribution of fluctuations. In the presented work, the first-order autocatalysis has been applied to the Löwdin`s mechanism of spontaneous mutations in DNA. Describing double proton transfers between complimentary nucleotide bases along the chain by first-order autocatalytic chemical reactions, the corresponding master equation for protons in tautomeric states becomes nonlinear, and at non-equlibrium conditions this leads to the non-Poissonian distribution of spontaneous mutations in DNA. It is also suggested that the accumulation of large fluctuations of successive cooperative concerted protons along the chain may produce higher non-linearities which could have a significant impact on some biochemical processes, occurring in DNA.

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