Abstract
It is found that the rate of change (kinetics) of the probability of death of representatives of living systems (LS) of different biological species—Drosophila, mice, rats, dogs, horses, and people in natural environments residing in different geographical areas—is described by a kinetic equation with similar values of the parameters. However, the kinetics of the probability of death of young people and rats, starting from birth, is more accurately described by a kinetic equation of a slightly different type, taking into account the prevailing process of development and adaptation of the organism to the environment. On the basis of a single kinetic approach to the description of the probability of death, an analytical model of the intensity of mortality in LS (approximation of the mortality rate—MR) is developed. It is shown that the approximation proposed by Gompertz to MR by an increasing exponent (law of Gompertz) is a special case of the unified mathematical model proposed in this paper.
Similar content being viewed by others
REFERENCES
Anisimov, V.N., Syndrome of accelerated aging under the influence of carcinogenic environmental factors, Ross. Fiziol. Zh. im. I.M. Sechenova, 2010, vol. 96, no. 8, pp. 817–833.
Waisman, N.Ya., Golubovsky, M.D., and Ilinskii, Yu.Yu., Differences in the parameters of longevity and its sexspecificity in human populations and modeling them in drosophila, Adv. Gerontol., 2013, vol. 3, no. 4, pp. 268–276.
Viktorov, A.A. and Kholodnov, V.A., Kinetic theory for aging of living systems, Usp. Gerontol., 2013, vol. 26, no. 1, pp. 58–65.
Viktorov, A.A., Kholodnov, V.A., Gladkikh, V.D., and Alekhnovich, A.V., Influence of environment on aging of living systems: a mathematical model, Usp. Gerontol., 2013, vol. 26, no. 1, pp. 52–57.
Viktorov, A.A., Gladkikh, V.D., Ksenofontov, A.I., and Morozova, E.E., Forecasting environmental health risks based on the kinetic theory of aging of living systems, Adv. Gerontol., 2015, vol. 5, no. 3, pp. 141–146.
Viktorov, A.A., Gladkikh, V.D., and Morozova, E.E., Aging of dogs and Drosophila as described based on the kinetic theory, Adv. Gerontol., 2017, vol. 7, no. 3, pp. 177–183.
Gavrilov, L.A. and Gavrilova, N.S., Biologiya prodolzhitel’nosti zhizni (Biology of Life Expectancy), Moscow: Nauka, 1991.
Gerontologiya in silico. Stanovlenie novoi distsipliny. Matematicheskie modeli, ananliz dannykh i vychislitel’nye eksperimenty (Gerontology in silico. Development of New Science. Mathematical Modeling, Data Analysis, and Computational Experiments), Marchuk, G.I., Eds., Moscow: Binom. Laboratoriya Znanii, 2007.
Grigor’ev, Yu.G., Popov, V.I., Shafirkin, A.V., and Antipenko, Zh.B., Somaticheskie effekty khronicheskogo gamma-oblucheniya (Somatic Effects of Chronic Gamma-Radiation), Moscow: Energoatomizdat, 1986.
Darenskaya, N.G., Uchakov, I.B., Ivanov, I.V., et al., Ekstrapolyatsiya eksperimental’nykh dannykh na cheloveka: printsipy, podkhody, obosnovanie metodov i ikh uspol’zovaniya v fiziologii i radiobiologii (Extrapolation of Experimental Data to Humans: Principles, Approaches, the Substantiation of Methods and Their Use in Physiology and Radiobiology), Moscow: Istoki, 2004.
Urlanis, B.Ts., Evolyutsiya prodolzhitel’nosti zhizni (Evolution of Life Expectation), Moscow: Statistika, 1978.
Butov, A.A., Volkov, M.A., Anisimov, V.N., et al., A model of accelerated aging induced by 5-bromodeoxyuridine biogerontology, Biogerontology, 2002, vol. 3, pp. 175–182.
David, J. and MacKay, C., Consistency of the Mortality of Chronically Irradiated Beagles with the Linear No-Threshold Model, Cambridge: Cavendish Laboratory, 2014.
Demin, V.F., Romanov, V.V., Soloviev, V.Y., and Zakharchenko, I.E., Harmonized approach to the health safety regulation in different areas of human activity, Med. Radiol. Radiat. Bezop., 2013, vol. 58, no. 5, pp. 26–34.
Sacher, G.A., Relation of lifespan to brain weight and body weight in mammals, in The Lifespan Animals, Wolstenholme, G.E.W. and O’Connor, M., Eds., Boston: Little and Brown, 1959, vol. 5, pp. 115–132.
Upton, A.C., Kimball, A.W., Furth, J., et al., Some delayed effects of atom-bomb radiations in mice, Cancer Res., 1960, vol. 20, pp. 1–60.
Viktorov, A.A. and Kholodnov, V.A., Kinetic theory for aging of living systems, Adv. Gerontol., 2013, vol. 3, no. 4, pp. 261–267.
Viktorov, A.A., Kholodnov, V.A., Gladkikh, V.D., and Alekhnovich, A.V., Influence of environment on aging of living systems: a mathematical model, Adv. Gerontol., 2013, vol. 3, no. 4, pp. 255–260.
ACKNOWLEDGMENTS
The authors express their sincere thanks to PhD V.Yu. Solov’ev for his constant interest in the work, valuable advice and discussion, to the graduate student E.E. Morozova and to the student of Moscow Engineering Physics Institute I.S. Zhuravlev for participating in the processing of experimental data, drawing pictures, and discussing the results.
Author information
Authors and Affiliations
Corresponding authors
Ethics declarations
The authors declare that they have no conflict of interest. This article does not contain any studies involving animals or human participants performed by any of the authors.
Additional information
Translated by P. Kuchina
Rights and permissions
About this article
Cite this article
Viktorov, A.A., Kholodnov, V.A. & Anofriev, A.V. Kinetic Model of Aging Biological Species in Natural Habitat. Adv Gerontol 9, 308–316 (2019). https://doi.org/10.1134/S2079057019030044
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S2079057019030044