Tamura模型下DNA序列点突变熵性质的研究

Entropy properties of the point mutations in DNA sequence using Tamura model

【目的】研究在较复杂的核苷酸替换模型,即Tamura模型下DNA序列中4种核苷酸频率随世代变化的规律,以得到序列熵的性质,为了解生物进化机理奠定基础。【方法】在Shannon信息熵理论基础上,利用La-grange乘数法进行理论证明,并用Mathematica软件模拟了Tamura模型下DNA序列中4种核苷酸组成的变化规律和序列熵的变化过程。【结果】DNA序列在Tamura模型下发生突变,各核苷酸频率随世代变化逐渐趋于平衡,且序列熵趋于最大值。【结论】核苷酸突变具有保熵性,验证了前人生物是朝着多样性增大的方向发展进化的结论。

[Objective] The changing of the frequencies of 4 nucleotides as the generations changed using Tamura model,which is a more complicated nucleotide substitution model,was studied to obtain the entropy properties of DNA sequences. [Method] Based on Shannon entropy theory,the theoretical demonstration was proved by the Lagrange Multiplier Method,and Mathematica was used to simulate the changing patterns of 4 nucleotides. [Result] If the mutation in the DNA sequence occurs in Tamura model, the frequencies of nucleotides tend to equilibrium,and their entropies tend to the maximum. [Conclusion] The nucleotide mutations can maintain their entropy. It was verified that biodiversity of species increased during evolvement.