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Modeling the Dynamics of Negative Mutations for a Mouse Population and the Inverse Problem of Determining Phenotypic Differences in the First Generation

Author

Listed:
  • Raul Argun

    (Department of Mathematics, Faculty of Physics, Lomonosov Moscow State University, Moscow 119991, Russia)

  • Natalia Levashova

    (Department of Mathematics, Faculty of Physics, Lomonosov Moscow State University, Moscow 119991, Russia)

  • Dmitry Lukyanenko

    (Department of Mathematics, Faculty of Physics, Lomonosov Moscow State University, Moscow 119991, Russia)

  • Alla Sidorova

    (Department of Byophysics, Faculty of Physics, Lomonosov Moscow State University, Moscow 119991, Russia)

  • Maxim Shishlenin

    (Sobolev Insitute of Mathematics, Novosibirsk 630090, Russia
    Institute of Computational Mathematics and Mathematical Geophysics SB RAS, Novosibirsk 630090, Russia)

Abstract

This paper considers a model for the accumulation of mutations in a population of mice with a weakened function of polymerases responsible for correcting DNA copying errors during cell division. The model uses the results of the experiment published by Japanese scientists, which contain data on the accumulation of phenotypic differences in three isolated groups of laboratory mice. We have developed a model for the accumulation of negative mutations. Since the accumulation of phenotypic differences in each of the three groups of mice occurred in its own way, we assumed that these differences were associated with genotypic differences in the zeroth generation and set the inverse problem of determining the initial distribution of these differences. Additional information for solving the inverse problem was a set of experimental data on the number of mutant lines and the number of individuals in each group of mice. The results obtained confirmed our assumption.

Suggested Citation

  • Raul Argun & Natalia Levashova & Dmitry Lukyanenko & Alla Sidorova & Maxim Shishlenin, 2023. "Modeling the Dynamics of Negative Mutations for a Mouse Population and the Inverse Problem of Determining Phenotypic Differences in the First Generation," Mathematics, MDPI, vol. 11(14), pages 1-17, July.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:14:p:3180-:d:1198251
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    References listed on IDEAS

    as
    1. Dmitry Lukyanenko & Tatyana Yeleskina & Igor Prigorniy & Temur Isaev & Andrey Borzunov & Maxim Shishlenin, 2021. "Inverse Problem of Recovering the Initial Condition for a Nonlinear Equation of the Reaction–Diffusion–Advection Type by Data Given on the Position of a Reaction Front with a Time Delay," Mathematics, MDPI, vol. 9(4), pages 1-12, February.
    2. Raul Argun & Alexandr Gorbachev & Dmitry Lukyanenko & Maxim Shishlenin, 2021. "On Some Features of the Numerical Solving of Coefficient Inverse Problems for an Equation of the Reaction-Diffusion-Advection-Type with Data on the Position of a Reaction Front," Mathematics, MDPI, vol. 9(22), pages 1-18, November.
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