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Mathematical modeling in biology: Systems capable to live and die

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Abstract

The tendencies in the mathematical modeling of biological systems which under certain conditions are capable of supporting survival were reviewed. Its distinctive features were considered and inherent drawbacks analyzed. Models of limited life span in the animal organism were discussed, and a general scheme of the vital processes in organism, ageing, and death was presented. The oxidative theory-based homeostatic approach to ageing was shown to enable one to combine and generalize the existing theories of ageing. Consideration was given to the biotechnical applications of the homeostatic approach.

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References

  1. Romanovskii, Yu.M., Stepanova, N.V., and Chernavskii, D.S., Matematicheskoc modelirovanie v biofizike (Mathematical Modeling in Biophysics), Moscow: Nauka, 1975.

    Google Scholar 

  2. Nesse, R.M. and Williams, G.C., Evolution by Natural Selection, in Evolution and Healing, Nesse, R.M. and Williams, G.C., Eds., London: Weidenfeld and Nicolson, 1995, pp. 13–25.

    Google Scholar 

  3. Novosel’tsev, V.N. and Yashin, A.I., Horizons of Mathematical Modeling, in Proc. Int. Conf. “Paralel Computations and Problems of Control, RASO-2001”, CD-ROM, Moscow: Inst. Probl. Upravlen., 2001, pp. 214–244.

    Google Scholar 

  4. Inzhenernaya fiziologiya i modelirovanie sistem organizma (Engineering Physiology and Modeling of Organism’s Systems), Novosel’tsev, V.N., Ed., Novosibirsk: Nauka, 1987.

    Google Scholar 

  5. Karr, Ya., Mekhanizmy biologicheskoi zashchity (Mechanisms of Biological Protection), Moscow: Meditsina, 1976.

    Google Scholar 

  6. Ostreikovskii, V.A., Teoriya nadezhnosti (Reliability Theory), Moscow: Vysshaya Shkola, 2003.

    Google Scholar 

  7. Rose, M.R., Evolutionary Biology of Aging, Oxford: Oxford Univ. Press, 1991.

    Google Scholar 

  8. Partridge, L. and Barton, N.H., Optimality, Mutation and the Evolution of Ageing, Nature, 1993, vol. 362, pp. 305–311.

    Article  Google Scholar 

  9. Carey, J.R., Liedo, P., and Müller, H.-G., Relationship of Age Patterns of Fecundity to Mortality, Longevity, and Lifetime Reproduction in a Large Cohort of Mediterranean Fruit Fly Females, J. Geront. Biol. Sci., 1998, vol. 53A, pp. B245–B251.

    Google Scholar 

  10. Kowald, A. and Kirkwood, T.B.L., Accumulation of Defective Mitochondria through Delayed Degradation of Damaged Organelles and Its Possible Role in the Aging of Post-mitotic and Dividing Cells, J. Theor. Biol., 2000, vol. 202, pp. 145–160.

    Article  Google Scholar 

  11. Belotserkovskii, O.M., New Century—New Approaches to Turbulence Based on the Advanced Technologies of Mathematical Modeling and Parallel Computations, in Mat. modelirovanie. Problemy i rezul’taty (Mathematical Modeling. Problems and Results), Moscow: Nauka, 2003.

    Google Scholar 

  12. In silico Simulation of Biological Processes, in Novartis Foundation Symposium, McCulloch, A. and Huber, G., Eds., New York: Wiley, 2003.

  13. Di Stefano, J.J. III, The Modeling Methodology Forum: An Expanded Department. Additional Guidelines, Am. J. Physiol., 1984, no. 1, p. 150.

  14. Samarskii, A.A. and Mikhailov, A.P., Matematicheskoe modelirovanie. Idei. Metody. Primery (Mathematical Modeling. Ideas. Methods. Examples), Moscow: Fizmatlit, 2002.

    Google Scholar 

  15. Pletcher, S.D. and Neuhauser, C., Biological Aging. Criteria for Modeling and a New Mechanistic Model, Int. J. Modern Physics C, 2000, vol. 11, pp. 525–546.

    Google Scholar 

  16. Lande, R., The Response on Major and Minor Mutations Affecting a Metrical Trait, Heredity, 1983, vol. 50, pp. 47–65.

    Google Scholar 

  17. Penna, T.J.P., A Bit-string Model for Biological Aging, J. Statist. Physics, 1995, vol. 78, pp. 1629–1633.

    Article  MATH  Google Scholar 

  18. Larsen, P.L., Albert, P.S., and Riddle, D.L., Interacting Genes Regulate Dauer Larva Development and Adult Life Span in C.elegans, Working Paper in the Library of Max-Planck Inst. of Demographical Studies, Univ. of Missouri, 1994.

  19. Yashin, A.I., Vaupel, J.W., and Iachine, I.A., A Duality in Aging: The Equivalence of Mortality Models Based on Radically Different Concepts, Mech. Aging Dev., 1994, vol. 74, pp. 1–14.

    Article  Google Scholar 

  20. Yashin, A.I., Begun, A.S., Boiko, S.I., Ukraintseva, S.V., and Oeppen, J., The New Trends in Survival Improvement Require a Revision of Traditional Gerontological Concepts, Exp. Gerontol., 2001, vol. 37, pp. 157–167.

    Article  Google Scholar 

  21. Logofet, D.O., Mathematical Model in Ecology: False Toy or Tool of Cognition?, in Matematika, komp’yuter, obrazovanie (Mathematics, Computer, Education), Moscow: Progress-Traditsiya, 2001, vol. 8.

    Google Scholar 

  22. Novosel’tsev, V.N., Upravlenie na organizmennom urovne: biofizika i biokibernetika (Control at the Level of Organism: Biophysics and Biocybernetics), Pushchino: NTS Biologicheskikh Issledovanii, 1982.

    Google Scholar 

  23. Dawkins, R., The Selfish Gene, Oxford: Oxford Univ. Press, 1989.

    Google Scholar 

  24. Novosel’tsev, V.N., Mathematical Modeling of Organism, in Nauka v Rossii (Science in Russia), 2003, no. 1, pp. 52–58.

  25. Wiener, N., Cybernetics, New York: Wiley, 1948. Translated under the title Osnovy kibernetiki, Moscow: Sovetskoe Radio, 1956.

    Google Scholar 

  26. Novosel’tsev, V.N., Teoriya upravleniya i biosistemy. Analiz sokhranitel’nykh svoistv (Theory of Control and Biosystems. Analysis of Preservative Properties), Moscow: Nauka, 1978.

    Google Scholar 

  27. Novosel’tsev, V.N., Analysis of the Aims of Control in Engineering and Natural-technology Systems, in Sb. tr. In-ta probl. upr. (Collections of Work of the Inst. of Control Sciences), 1996, vol. 3, pp. 5–14.

    Google Scholar 

  28. Novosel’tsev, V.N., Modeling of the Natural Technologies of the Organism for Studying the Processes of Control of its Vital Activity, Avtom. Telemekh., 1992, no. 12, pp. 96–105.

  29. Novosel’tsev, V.N., Khal’fin, R.A., and Gribanova, T.N., Modeling of the Human Organism as a Whole for the Problems of Control of the Biosocial and Biotechnical Processes, Prib. Sist. Upravlen., 1998, no. 6, pp. 66–73.

  30. Dagaev, V.N. and Novosel’tsev, V.N., Parametrization of the Pharmacokinetic Models for Studying the Control Processes in Organism, Avtom. Telemekh., 1995, no. 4, pp. 130–144.

  31. Parin, V.V. and Baevskii, R.M., Vvedenie v meditsinskuyu kibernetiku (Introduction to Medical Cybernetics), Moscow: Meditsina, 1966.

    Google Scholar 

  32. Shumakov, V.I., Novosel’tsev, V.N., Sakharov, M.I., and Shtengol’d, E.Sh., Modelirovanie fiziologicleskikh sistem organizma (Modeling of the Physiological Systems of Organism), Moscow: Meditsina, 1971.

    Google Scholar 

  33. Antomonov, Yu.G., Modelirovanie biologicheskikh sistem. Spravochnik (Modeling of Biological Systems. Manual), Kiev: Naukova Dumka, 1977.

    Google Scholar 

  34. Novosel’tsev, V.N., Organizm v mire tekhniki (Organism in the Technical World), Moscow: Nauka, 1989.

    MATH  Google Scholar 

  35. Riznichenko, G.Yu., Lektsii po matematicheskomu modelirovaniyu v biologii. I (Lectures on Mathematical Modeling in Biology. I), Moskva: RKHD, 2002.

    Google Scholar 

  36. Fries, J.F., Aging, Natural Death and the Compression of Morbidity, New England J. Med., 1980, vol. 303, pp. 130–135.

    Article  Google Scholar 

  37. Good, T.P. and Tatar, M., Age-specific Mortality and Reproduction Respond to Adult Dietary Restriction in Drosophila Melanogaster, J. Insect. Physiol., 2001, vol. 47, pp. 1467–1473.

    Article  Google Scholar 

  38. Yashin, A.I. and Manton, K.G., Effects of Unobserved and Partially Observed Covariate Processes on System Failure: A Review of Models and Estimation Strategies, Statist. Sci., 1997, vol. 12, pp. 20–34.

    Article  MathSciNet  MATH  Google Scholar 

  39. Yashin, A.I., Iashine, I.A., and Begun, A.S., Mortality Modeling, Math. Pop. Studies., 2000, vol. 5, pp. 305–332.

    Article  Google Scholar 

  40. Vaupel, J.W., Manton, K.G., and Stallard, E., The Impact of Heterogeneity in Individual Frailty on the Dynamics of Mortality, Demography, 1979, vol. 16, pp. 439–454.

    Google Scholar 

  41. Novosel’tsev, V.N., Interdisciplinary Modeling: A Possible Approach to Analysis of Catastrophes, Avtom. Telemekh., 1998, no. 2, pp. 101–111.

  42. Mashintsov, E.A. and Yakovlev, A.E., Formulation of the Problem of Modeling the Life Cycle of Organism with Regard for the Impact of the External and Internal Factors of Ageing, in Ekologicheskie problemy tul’skogo regiona (Ecological Problems of the Tula Region), Tula, 2002, pp. 116–126.

  43. Vasil’ev, V.P., Kuznetsov, A.A., Mashintsov, E.A., and Yakovlev, A.E., Mathematical Model of the Life Cycle of Human Organism, in Geoinformatsionnye tekhnologii v reshenii regional’nykh problem: sb. nauch. tr. (Geoinformation Technologies to Solve Regional Problems), Tula: Tul. Gos. Univ., 2001, pp. 82–95.

    Google Scholar 

  44. Mashintsov, E.A. and Yakovlev, A.E., Mathematical Modeling of Human Life Cycle and Quality of Population Health, Avtom. Telemekh., 2006, no. 4, pp. 154–168.

  45. Mashintsov, E.A., Novosel’tsev, V.N., and Yakovlev, A.E., Matematicheskoe modelirovanie zhiznennogo tsikla cheloveka i kachestvo zdorov’ya naseleniya (Mathematical Modeling of Human Life Cycle and Quality of Population Health), Moscow: Inst. Probl. Upravlen., 2006.

    Google Scholar 

  46. Casarett, L.J. and Doull, J., Toxicology. The Basic Science of Poisons, New York: McMillan, 1975.

    Google Scholar 

  47. Litvinov, N.N., Novosel’tsev, V.N., Il’yashenko, K.K., and El’kov, A.N., Acute Poisoning by Chlorine—Analysis of Pathogenesis by Mathematical Modeling, Toksikologicheskii Vest., 2002, no. 6, pp. 27–31.

  48. Litvinov, N.N., Novosel’tsev, V.N., Ostapenko, Yu.N., et al., Mathematical Modeling of Acute Actions on Man of the Industrial Chemical Substance (with an Example of Ammonia), Meditsina Katastrof, 1997, no. 3(19), pp. 54–59.

    Google Scholar 

  49. Komfort, A., Biologiya stareniya (Biology of Ageing), Moscow: Nauka, 1967.

    Google Scholar 

  50. Harman, D., Extending Functional Life Span, Exp. Gerontol., 1998, vol. 33, pp. 95–112.

    Article  Google Scholar 

  51. Novosel’tsev, V.N., Novosel’tseva, Zh.A., and Yashin, A.I., Ageing of Insects. I. Experimental Results and Modern Concepts, Uspekhi Gerontologii, 2000, no. 4, pp. 122–131.

  52. Carey, J., How Mediterranean Fruit Flies Resist Aging, Live Long and Remain Fertile, in Paradoxes of Longevity, Robine, J.-M., Forette, B., Franceschi, C., and Allard, M., Eds., New York: Plenum, 1999, pp. 23–34.

    Google Scholar 

  53. Anisimov, V.N.; Molekulyarnye i fiziologicheskie mekhanizmy stareniya (Molecular and Physiological Mechanisms of Ageing), St. Petersburg: Nauka, 2003.

    Google Scholar 

  54. Economos, A.C., Rate of Aging, Rate of Dying and the Mechanism of Mortality, Arch. Geront. Geriatr., 1982, vol. 1, pp. 3–27.

    Article  Google Scholar 

  55. Harman, D., The Free-radical Theory of Aging. in Modern Biological Theories of Aging, Warner, H.R., Sprott, R.L., Butler, R.N., and Shneider, E.L., Eds., New York: Wiley, 1987, pp. 81–87.

    Google Scholar 

  56. Orr, W.C., Senescence: in Search of Casuality, Dev. Genet., 1996, vol. 18, pp. 93–98.

    Article  Google Scholar 

  57. Sohal, R.S. and Weindruch, R., Oxidative Stress, Caloric Restriction, and Aging, Science, 1996, vol. 273, pp. 59–63.

    Google Scholar 

  58. Pearl, R., The Rate of Living, New York: Knopf, 1928.

    Google Scholar 

  59. Miquel, J., Oro, J.L., Bench, K.G., and Johnson, J.E., Jr., Effects of Temperature on the Life Span Vitality and Fine Structure of Drosophila Melanogaster, Mech. Ageing Dev., 1976, vol. 5, pp. 347–370.

    Article  Google Scholar 

  60. Lints, F.A., The Rate of Living Theory Revisited, Gerontology, 1989, vol. 35, pp. 36–57.

    Article  Google Scholar 

  61. Sohal, R.S., The Rate of Living Theory: A Contemporary Interpretation, in Insect Ageing. Strategies and Mechanisms, Collatz, K.-G. and Sohal, R.S., Eds., New York: Springer, 1986, pp. 23–43.

    Google Scholar 

  62. Clarke, J.M. and Maynard Smith, J., Two Phases of Ageing in Drosophila Subobscura, J. Exp. Biol., 1961, vol. 38, pp. 679–684.

    Google Scholar 

  63. Kol’tover, V.K., Free-radical Theory of Ageing: State-of-Art and Outlooks, Uspekhi Gerontologii, 1998, vol. 2, pp. 37–42.

    Google Scholar 

  64. Fleming, J.E., Reveillaud, I., and Niedzwiecki, A., Role of Oxidative Stress in Drosophila Aging, Mutation Res., 1992, vol. 275, pp. 267–279.

    Article  Google Scholar 

  65. Khalyavkin, A.V. and Yashin, A.I., Normal Ageing as the Result of Response of the Organism Control Systems to External Signals Unfavorable to its Full Self-support. I., Probl. Upravlen., 2004, no. 4, pp. 57–61.

  66. Novoseltsev, V.N., Carey, J., Liedo, P., et al., Anticipation of Oxidative Damage Decelerates Aging in Virgin Female Medflies: A Hypothesis Tested by Statistical Modeling, Exp. Gerontol., 2000, vol. 35, pp. 971–987.

    Article  Google Scholar 

  67. Novosel’tsev, V.N., Novosel’tseva, Zh.A., and Yashin, A.I., Ageing of Insects. II. Homeostatic Model, Uspekhi Gerontologii, 2000, no. 4, pp. 132–140.

  68. Exercise: Regulation and Integration of Multiple Systems, in Handbook of Physiology, Rowell, L.B. and Sheperd, J.T., Eds., New York: Oxford Univ. Press, 1996.

  69. Novoseltsev, V.N., Novoseltseva, J.A., Boyko, S.I., and Yashin, A.I., What Fecundity Patterns Indicate about Aging and Longevity: Insights from Drosophila Studies, J. Gerontol., Biological Sci., 2003, vol. 68A, pp. 484–494.

    Google Scholar 

  70. Smidt-Nielsen, K., Animal Physiology, Cambridge: Cambridge Univ. Press, 1997.

    Google Scholar 

  71. Guyton, A., Textbook on Medical Physiology, Philadelphia: Wiley, 1981.

    Google Scholar 

  72. Strehler, B.L. and Mildwan, A.S., General Theory of Mortality and Aging, Science, 1960, vol. 132, pp. 14–21.

    Google Scholar 

  73. Maynard Smith, J., Temperature and the Rate of Aging in Poikiloterms, Nature, 1963, vol. 4891, pp. 400–402.

    Google Scholar 

  74. Novoseltsev, V.N., Novoseltseva, J.A., and Yashin, A.I., A Homeostatic Model of Oxidative Damage Explains Paradoxes Observed in Earlier Aging Experiments: A Fusion and Extension of Older Theories of Aging, Biogerontology, 2001, vol. 2, pp. 127–138.

    Article  Google Scholar 

  75. Novoseltsev, V.N. and Yashin, A.I., Aging of Technological Systems: Analogy between Biological Populations and Human-engineering Systems, in Preprint of IFAC Symposium on Social Stability, Wien, 2001, pp. 261–267.

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  1. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia

    V. N. Novosel’tsev

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Original Russian Text © V.N. Novosel’tsev, 2006, published in Avtomatika i Telemekhanika, 2006, No. 6, pp. 3–26.

This paper was recommended for publication by V.A. Lototskii, a member of the Editorial Board

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Novosel’tsev, V.N. Mathematical modeling in biology: Systems capable to live and die. Autom Remote Control 67, 835–855 (2006). https://doi.org/10.1134/S0005117906060014

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