Physics, mathematics, and technology

2021 Issue №4

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The equilibrium states of a mtDNA mutagenesis: an analytics approach



The article is dedicated to the task of construction and analysis of exactly solvable mathematical model for the mutagenesis in mitochondrial DNA (mtDNA). We begin by demonstrating that the average amounts of all four types of nucleotides (adenine A, guanine G, cytosine C and thymine T) is de­ter­mined by a system of four O. D. E.’s of first order, and that this system is fur­ther reducible to a single linear inhomogeneous O. D. E. of third order. Next, we classify all possible solutions to that equation and derive an explicit ge­neral form of equilibrium (i. e. asymptotic) states of mtDNA as a function of a mitochondrial mutational spectrum.