Skip to main content
SpringerLink
Log in

Contribution of quantitative methods of estimating mortality dynamics to explaining mechanisms of aging

  • Published:
Biochemistry (Moscow) Aims and scope Submit manuscript

Abstract

Accumulation of various types of unrepaired damage of the genome because of increasing production of reactive oxygen species and decreasing efficiency of the antioxidant defense system and repair systems can cause age-related diseases and emergence of phenotypic signs of senescence. This should lead to increasing vulnerability and to mortality monotonously increasing with age independently of the position of the species on the evolutionary tree. In this light, the survival, mortality, and fertility curves for 45 animal and plant species and one alga published by the Max Planck Institute for Demographic Research (Germany/Denmark) are of special interest (Jones, O. R., et al. (2014) Nature, 505, 169-173). We divided all species treated in that study into four groups according to the ratio of mortality at the terminal age (which corresponds to 5% survival) and average mortality during the entire studied period. For animals of group IV (long-lived and senescent), including humans, the Jones method makes it possible to trace mortality during the entire life cycle. The same applies to short-lived animals (e.g. nematodes or the tundra vole), whether they display the Gompertz type of senescence or not. However, in long-lived species with a less pronounced increase in mortality with age (e.g. the freshwater crocodile, hermit crab, or Scots pine), as well as in animals of average lifespan that reach the terminal age earlier than they could have enough time to become senescent, the Jones method is capable of characterizing only a small part of the life cycle and does not allow judging how senescence manifests itself at late stages of the life cycle. Thus, it is known that old trees display signs of biological senescence rather clearly; although Jones et al. consider them non-senescent organisms because less than 5% of sexually mature individuals survive to display the first manifestations of these characters. We have concluded that the classification proposed by Jones et al. makes it possible to approximately divide animals and plants only by their levels of the Gompertz type of senescence (i.e. actuarial senescence), whereas susceptibility to biological senescence can be estimated only when principally different models are applied.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Abbreviations

LS:

lifespan

ROS:

reactive oxygen species

References

  1. Jones, O. R., Scheuerlein, A., Salguero-Gomez, R., Camarda, C. G., Schaible, R., Casper, B. B., Dahlgren, J. P., Ehrlen, J., Garcia, M. B., Menges, E. S., QuintanaAscencio, P. F., Caswell, H., Baudisch, A., and Vaupel, J. W. (2014. Diversity of ageing across the tree of life, Nature, 505, 169–173.

    Article  PubMed Central  CAS  PubMed  Google Scholar 

  2. Harman, D. (1956. Aging: a theory based on free radical and radiation chemistry, J. Gerontol., 11, 298–300.

    Article  CAS  PubMed  Google Scholar 

  3. Emanuel’, N. M. (1982) Biology of Ageing [in Russian], Nauka, Leningrad.

    Google Scholar 

  4. Khokhlov, A. N. (1988) Cell proliferation and aging, in Advances in Science and Technology, General Problems of Physico-Chemical Biology Series [in Russian], Vol. 9, VINITI, Moscow.

    Google Scholar 

  5. Akif’ev, A. P., and Potapenko, A. I. (2001. Nuclear genetic material as an initial substrate of aging in animals, Russ. J. Genet., 37, 1213–1223.

    Article  Google Scholar 

  6. Finkel, T., and Holbrook, N. J. (2000. Oxidants, oxidative stress, and the biology of ageing, Nature, 408, 239–247.

    Article  CAS  PubMed  Google Scholar 

  7. Barja, G. (2004. Aging in vertebrates, and the effect of caloric restriction: a mitochondrial free radical productionDNA damage mechanism? Biol. Rev., 79, 235–251.

    Article  PubMed  Google Scholar 

  8. Stadtman, E. R. (1992. Protein oxidation and aging, Science, 257, 1220–1224.

    Article  CAS  PubMed  Google Scholar 

  9. Hamilton, M. L., Van Remmen, H., Drake, J. A., Yang, H., Guo, Z. M., Kewitt, K., Walter, C. A., and Richardson, A. (2001. Does oxidative damage to DNA increase with age? Proc. Natl. Acad. Sci. USA, 98, 10469–10474.

    Article  PubMed Central  CAS  PubMed  Google Scholar 

  10. Kujoth, G. C., Bradshaw, P. C., Haroon, S., and Prolla, T. A. (2007. The role of mitochondrial DNA mutations in mammalian aging, PLoS Genet., 3, 161–173.

    Article  CAS  Google Scholar 

  11. Skulachev, M. V., and Skulachev, V. P. (2014. New data on programmed aging–slow phenoptosis, Biochemistry (Moscow), 79, 977–993.

    Article  CAS  Google Scholar 

  12. Shilovsky, G. A., Khokhlov, A. N., and Shram, S. I. (2013. The protein poly(ADP-ribosyl)ation system: its role in genome stability and lifespan determination, Biochemistry (Moscow), 78, 433–444.

    Article  CAS  Google Scholar 

  13. Pero, R. W., Holmgren, K., and Persson, L. (1985. ?-Radiation induced ADP-ribosyl transferase activity and mammalian longevity, Mutat. Res., 142, 69–73.

    Article  CAS  PubMed  Google Scholar 

  14. Finch, C. E. (1990) Longevity, Senescence and the Genome, University Chicago Press, Chicago.

    Google Scholar 

  15. Austad, S. N. (1997) Why We Age, John Wiley and Sons, New York.

    Google Scholar 

  16. Anisimov, V. N. (2008) Molecular and Physiological Mechanism of Senescence [in Russian], Nauka, St. Petersburg.

    Google Scholar 

  17. Gavrilov, L. A., Gavrilova, N. S., and Yaguzhinsky, L. S. (1978. Basic patterns of aging and death in animals from the standpoint of reliability theory, Zh. Obshch. Biol., 39, 734–742.

    CAS  PubMed  Google Scholar 

  18. Urlanis, B. Ts. (1978) Evolution of Longevity [in Russian], Statistika, Moscow.

    Google Scholar 

  19. Gavrilov, L. A., and Gavrilova, N. S. (1991) Biology of Longevity [in Russian], Nauka, Moscow.

    Google Scholar 

  20. Mamai, A. V. (2006. Mathematical model for survival of organisms, Trudy ISA RAN, 19, 70–93.

    Google Scholar 

  21. Khalyavkin, A. V., and Yashin, A. I. (2007) in Gerontology in silico: the Emergence of the New Discipline: Mathematical Models, Analysis of Data, and Calculating Experiments (Marchuk, G. I., Anisimov, V. N., Romaniukha, A. A., and Yashin, A. I., eds.) BINOM, Laboratoriya Znanii, Moscow.

  22. Gompertz, B. (1825. On the nature of the function expressive of the law of human mortality and on a new mode of determining life contingencies, Philos. Trans. R. Soc. London, 115, 513–585.

    Article  Google Scholar 

  23. Comfort, A. (1979) The Biology of Senescence, Churchill Livingstone, Edinburgh-London.

    Google Scholar 

  24. McNamara, J. M., and Houston, A. I. (1996. Statedependent life histories, Nature, 380, 215–221.

    Article  CAS  PubMed  Google Scholar 

  25. Finch, C. E. (1998. Variations in senescence and longevity include the possibility of negligible senescence, J. Gerontol. Biol. Sci., 53, 235–239.

    Article  Google Scholar 

  26. Weismann, A. (1889) Essays upon Heredity and Kindred Biological Problems, Clarendon Press, Oxford.

    Book  Google Scholar 

  27. Williams, G. C. (1957. Pleiotropy, natural selection and the evolution of senescence, Evolution, 11, 398–411.

    Article  Google Scholar 

  28. Kirkwood, T. B. L. (1977. Evolution of ageing, Nature, 270, 301–304.

    Article  CAS  PubMed  Google Scholar 

  29. Medvedev, Z. A. (1990. An attempt at a rational classification of theories of ageing, Biol. Rev. Camb. Philos. Soc., 65, 375–398.

    Article  CAS  PubMed  Google Scholar 

  30. Campisi, J. (2005. Aging, tumor suppression and cancer: high wire-act! Mech. Ageing Dev., 126, 51–58.

    Article  CAS  PubMed  Google Scholar 

  31. Kirkwood, T. B. L. (2010. Systems biology of ageing and longevity, Phil. Trans. R. Soc. B, 366, 64–70.

    Article  Google Scholar 

  32. Baudisch, A. (2008) Inevitable Aging? Contributions to Evolutionary-Demographic Theory, Springer-Verlag, BerlinHeidelberg.

    Google Scholar 

  33. Lamb, M. J. (1977) Biology of Aging, John Wiley and Sons, New York.

    Google Scholar 

  34. Grzimek, B. (1990) Grzimek’s Encyclopedia of Mammals, McGraw-Hill, New York.

    Google Scholar 

  35. Carey, J. R., and Judge, D. S. (2001) Monographs on Population Aging, Ser. 8, Odense University Press, Odense, Denmark.

    Google Scholar 

  36. Buffenstein, R. (2005) The naked mole-rat: a new long-living model for human aging research, J. Gerontol., 60, 13691377.

    Article  Google Scholar 

  37. Voituron, Y., De Fraipont, M., Issartel, J., Guillaume, O., and Clobert, J. (2011. Extreme lifespan of the human fish (Proteus anguinus): a challenge for ageing mechanisms, Biol. Lett., 7, 105–107.

    Article  PubMed Central  PubMed  Google Scholar 

  38. Skulachev, V. P. (1997. Aging is a specific biological function rather than the result of a disorder in complex living systems: biochemical evidence in support of Weismann’s hypothesis, Biochemistry (Moscow), 62, 1191–1195.

    CAS  Google Scholar 

  39. Skulachev, V. P. (1999. Phenoptosis: programmed death of an organism? Biochemistry (Moscow), 64, 1418–1426.

    CAS  Google Scholar 

  40. Skulachev, V. P. (2003) Aging and the programmed death phenomena, in Top. Curr. Genet. Model Syst. Aging (Nystrom, T., and Osiewacz, H. D., eds.) Springer-Verlag, Berlin-Heidelberg.

    Google Scholar 

  41. Skulachev, V. P., and Longo, V. D. (2005. Aging as a mitochondria-mediated atavistic program: can aging be switched off? Ann. N. Y. Acad. Sci., 1057, 145–164.

    Article  CAS  PubMed  Google Scholar 

  42. Dawkins, R. (1999) The Extended Phenotype: the Long Reach of the Gene, Oxford University Press, Oxford.

    Google Scholar 

  43. Longo, V. D., Mitteldorf, J., and Skulachev, V. P. (2005. Programmed and altruistic ageing, Nat. Rev. Genet., 6, 866–872.

    Article  CAS  PubMed  Google Scholar 

  44. Libertini, G. (2012. Classification of phenoptotic phenomena, Biochemistry (Moscow), 77, 707–715.

    Article  CAS  Google Scholar 

  45. Libertini, G. (2012. Phenoptosis, another specialized neologism, or the mark of a widespread revolution? Biochemistry (Moscow), 77, 795–798.

    Article  CAS  Google Scholar 

  46. Skulachev, V. P. (2012. What is “phenoptosis” and how to fight it? Biochemistry (Moscow), 77, 689–706.

    Article  CAS  Google Scholar 

  47. Terzibasi, E., Valenzano, D. R., and Cellerino, A. (2007. The short-lived fish Nothobranchius furzeri as a new model system for aging studies, Exp. Gerontol., 42, 81–89.

    Article  CAS  PubMed  Google Scholar 

  48. Weinert, B. T., and Timiras, P. S. (2003. Invited review: theories of aging, J. Appl. Physiol., 95, 1706–1716.

    Article  CAS  PubMed  Google Scholar 

  49. Hoving, H. J., Perez, J. A., Bolstad, K. S., Braid, H. E., Evans, A. B., Fuchs, D., Judkins, H., Kelly, J. T., Marian, J. E., Nakajima, R., Piatkowski, U., Reid, A., Vecchione, M., and Xavier, J. C. (2014. The study of deep-sea cephalopods, Adv. Mar. Biol., 67, 235–239.

    Article  PubMed  Google Scholar 

  50. Bradley, A. J., Mcdonald, I. R., and Lee, A. K. (1980. Stress and mortality in a small marsupial (Antechinus stuartii, Macleay), Gen. Comp. Endocrinol., 40, 188–200.

    Article  CAS  PubMed  Google Scholar 

  51. Lens, F., Smets, E., and Melzer, S. (2012. Stem anatomy supports Arabidopsis thaliana as a model for insular woodiness, New Phytol., 193, 12–17.

    Article  PubMed  Google Scholar 

  52. Melzer, S., Lens, F., Gennen, J., Vanneste, S., Rohde, A., and Beeckman, T. (2008. Flowering-time genes modulate meristem determinacy and growth form in Arabidopsis thaliana, Nat. Genet., 40, 1489–1492.

    Article  CAS  PubMed  Google Scholar 

  53. Lindoo, S. J., and Nooden, L. D. (1977. Studies on behavior of senescence signal in Anoka soybeans, Plant Physiol., 59, 1136–1140.

    Article  PubMed Central  CAS  PubMed  Google Scholar 

  54. Nooden, L. D., and Murray, B. J. (1982. Transmission of the monocarpic senescence signal via the xylem in soybean, Plant Physiol., 69, 754–756.

    Article  PubMed Central  CAS  PubMed  Google Scholar 

  55. Bowles, J. T. (1998. The evolution of aging: a new approach to an old problem of biology, Med. Hypotheses, 51, 179–221.

    Article  CAS  PubMed  Google Scholar 

  56. Ashapkin, V. V., Kutueva, L. I., and Vanyushin, B. F. (2015. Aging epigenetics: accumulation of errors or realization of a specific program? Biochemistry (Moscow), 80, 1406–1417.

    Article  CAS  Google Scholar 

  57. Boyd-Kirkup, J. D., Green, C. D., Wu, G., Wang, D., and Han, J. D. (2013. Epigenomics and the regulation of aging, Epigenomics, 5, 205–227.

    Article  CAS  PubMed  Google Scholar 

  58. Guarente, L., and Kenyon, C. (2000. Genetic pathways that regulate ageing in model organisms, Nature, 408, 255–262.

    Article  CAS  PubMed  Google Scholar 

  59. Vijg, J., and Suh, Y. (2005. Genetics of longevity and aging, Annu. Rev. Med., 56, 193–212.

    Article  CAS  PubMed  Google Scholar 

  60. Vaupel, J. W., Baudisch, A., Dolling, M., Roach, D. A., and Gampe, J. (2004. The case for negative senescence, Theor. Popul. Biol., 65, 339–351.

    Article  PubMed  Google Scholar 

  61. Chiang, C. L. (1984) The Life Table and Its Applications, Robert E. Krieger Publishing Company, Malabar, Florida.

  62. Medawar, P. B. (1952) An Unsolved Problem of Biology, H. C. Lewis and Co. Ltd, London.

    Google Scholar 

  63. Hamilton, W. D. (1966. The moulding of senescence by natural selection, J. Theor. Biol., 12, 12–45.

    Article  CAS  PubMed  Google Scholar 

  64. Pearl, R., and Miner, J. R. (1935. Experimental studies on the duration of life. XIV. The comparative mortality of certain lower organisms, Q. Rev. Biol., 10, 60–79.

    Article  Google Scholar 

  65. Deevey, E. S. (1947. Life tables for natural populations of animals, Q. Rev. Biol., 22, 283–314.

    Article  PubMed  Google Scholar 

  66. Baudisch, A. (2011. The pace and shape of ageing, Methods Ecol. Evol., 2, 375–382.

    Article  Google Scholar 

  67. Oeppen, J., and Vaupel, J. W. (2002. Broken limits to life expectancy, Science, 296, 1029–1031.

    Article  CAS  PubMed  Google Scholar 

  68. Burger, O., Baudisch, A., and Vaupel, J. W. (2012. Human mortality improvement in evolutionary context, Proc. Natl. Acad. Sci. USA, 109, 18210–18214.

    Article  PubMed Central  CAS  PubMed  Google Scholar 

  69. Ricklefs, R. E., Scheuerlein, A., and Cohen, A. (2003. Age-related patterns of fertility in captive populations of birds and mammals, Exp. Gerontol., 38, 741–745.

    Article  CAS  PubMed  Google Scholar 

  70. Cohen, A. A. (2004. Female post-reproductive lifespan: a general mammalian trait, Biol. Rev. Camb. Philos. Soc., 79, 733–750.

    Article  PubMed  Google Scholar 

  71. Brent, L. J., Franks, D. W., Foster, E. A., Balcomb, K. C., Cant, M. A., and Croft, D. P. (2015. Ecological knowledge, leadership, and the evolution of menopause in killer whales, Curr. Biol., 25, 746–750.

    Article  CAS  PubMed  Google Scholar 

  72. Vaupel, J. W., Carey, J. R., Christensen, K., Johnson, T. E., Yashin, A. I., Holm, N. V., Iachine, I. A., Kannisto, V., Khazaeli, A. A., Liedo, P., Longo, V. D., Zeng, Y., Manton, K. G., and Curtsinger, J. W. (1998. Biodemographic trajectories of longevity, Science, 280, 855–860.

    Article  CAS  PubMed  Google Scholar 

  73. Skulachev, M. V., Severin, F. F., and Skulachev, V. P. (2015. Aging as an evolvability-increasing program, which can be switched off by organism to mobilize additional resources for survival, Curr. Aging Sci., 8, 95–109.

    Article  PubMed  Google Scholar 

  74. Khokhlov, A. N. (2010. Does aging need an own program or the existing development program is more than enough, Russ. J. Gen. Chem., 80, 1507–1513.

    Article  CAS  Google Scholar 

  75. Khokhlov, A. N. (2014. On the immortal hydra. Again, Mosc. Univ. Biol. Sci. Bull., 69, 153–157.

    Article  Google Scholar 

  76. Sergeev, A. M. (1937. Materials contributing to the problem of postembryonic growth in reptiles, Zool. Zh., 16, 723.

    Google Scholar 

  77. Miller, J. K. (2001. Escaping senescence: demographic data from the three-toed box turtle (Terrapene carolina triunguis), Exp. Gerontol., 36, 829–832.

    Article  CAS  PubMed  Google Scholar 

  78. Salguero-Gomez, R., Shefferson, R. P., and Hutchings, M. J. (2013. Plants do not count… or do they? New perspectives on the universality of senescence, J. Ecol., 101, 545–554.

    Article  PubMed Central  PubMed  Google Scholar 

  79. Shefferson, R. P., and Roach, D. A. (2013. Longitudinal analysis in Plantago: strength of selection and reverse age analysis reveal age-indeterminate senescence, J. Ecol., 101, 577–584.

    Article  PubMed Central  PubMed  Google Scholar 

  80. Tuomi, J., Crone, E., Gremer, J., Jakalaniemi, A., Lesica, P., Pedersen, B., and Ramula, S. (2013. Prolonged dormancy interacts with senescence for two perennial herbs, J. Ecol., 101, 566–576.

    Article  Google Scholar 

  81. Hayflick, L., and Butler, R. N. (1994) How and Why We Age, Ballantine Books, New York.

    Google Scholar 

  82. Bell, G. (1984. Measuring the cost of reproduction. I. The correlation structure of the life table of a plank rotifer, Evolution, 38, 300–313.

    Article  Google Scholar 

  83. Franco, M., and Silvertown, J. (1996. Life history variation in plants: an exploration of the fast-slow continuum hypothesis, Phil. Trans. R. Soc. B, 351, 1341–1348.

    Article  Google Scholar 

  84. Buss, L. W. (1988. Diversification and germ-line determination, Paleobiology, 14, 313–321.

    Google Scholar 

  85. Martinez, D. E., and Levinton, J. S. (1992. Asexual metazoans undergo senescence, Proc. Natl. Acad. Sci. USA, 89, 9920–9923.

    Article  PubMed Central  CAS  PubMed  Google Scholar 

  86. Baudisch, A., and Vaupel, J. (2010. Senescence vs. sustenance: evolutionary-demographic models of aging, Demogr. Res., 23, 655–668.

    Article  Google Scholar 

  87. Martinez, D. E. (1998. Mortality patterns suggest lack of senescence in hydra, Exp. Gerontol., 33, 217–225.

    Article  CAS  PubMed  Google Scholar 

  88. Markov, A. V. (2012. Can kin selection facilitate the evolution of the genetic program of senescence? Biochemistry (Moscow), 77, 733–741.

    Article  CAS  Google Scholar 

  89. Caswell, H. (2012. Matrix models and sensitivity analysis of populations classified by age and stage: a vec-permutation matrix approach, Theor. Ecol., 5, 403–417.

    Article  Google Scholar 

  90. Gadgil, M., and Bossert, W. H. (1970. Life historical consequences of natural selection, Am. Nat., 104, 1–24.

    Article  Google Scholar 

  91. Ricklefs, R. E. (2010. Life-history connections to rates of aging in terrestrial vertebrates, Proc. Natl. Acad. Sci. USA, 107, 10314–10319.

    Article  PubMed Central  CAS  PubMed  Google Scholar 

  92. Gavrilov, L. A., and Gavrilova, N. S. (2002. Evolutionary theories of aging and longevity, Sci. World J., 2, 339–356.

    Article  Google Scholar 

  93. Khalyavkin, A. V. (2001. Influence of environment on the mortality pattern of potentially non-senescent organisms. General approach and comparison with real populations, Adv. Gerontol., 7, 46–49.

    Google Scholar 

  94. Dubrovitskaya, N. I. (1961) Regeneration and Age-Related Variations in Plants [in Russian], ANSSSR, Moscow.

    Google Scholar 

  95. Markov, M. V. (1986) Population Biology of Plants [in Russian], Kazan University Press, Kazan.

    Google Scholar 

  96. Charmantier, A., Perrins, C., McCleery, R. H., and Sheldon, B. C. (2006. Quantitative genetics of age at reproduction in wild swans: support for antagonistic pleiotropy models of senescence, Proc. Natl. Acad. Sci. USA, 103, 6587–6592.

    Article  PubMed Central  CAS  PubMed  Google Scholar 

  97. Terres, J. (1980) The Audubon Society Encyclopedia of North American Birds, Knopf, New York.

    Google Scholar 

  98. Gillooly, J. F., Brown, J. H., West, G. B., Savage, V. M., and Charnov, E. L. (2001. Effects of size and temperature on metabolic rate, Science, 293, 2248–2251.

    Article  CAS  PubMed  Google Scholar 

  99. Ungvari, Z., Sosnowska, D., Mason, J. B., Gruber, H., Lee, S. W., Schwartz, T. S., Brown, M. K, Storm, N. J., Fortney, K., Sowa, J., Byrne, A. B., Kurz, T., Levy, E., Sonntag, W. E., Austad, S. N., Csiszar, A., and Ridgway, I. (2013. Resistance to genotoxic stresses in Arctica islandica, the longest living noncolonial animal: is extreme longevity associated with a multistress resistance phenotype? J. Gerontol. A Biol. Sci. Med. Sci., 68, 521–529.

    Article  PubMed Central  CAS  PubMed  Google Scholar 

  100. Druffel, E. R., Griffin, M. S., Witter, A., Nelson, E., Southon, J., Kashgarian, M., and Vogel, J. (1995. Gerardia: bristlecone pine of the deep-sea? Geochim. Cosmochim. Acta, 59, 5031–5036.

    Article  CAS  Google Scholar 

  101. Andrews, A. H., Cordes, E. E., Mahoney, M. M., Munk, K., Coale, K. H., Cailliet, G. M., and Heifetz, J. (2002. Age, growth, and radiometric age validation of a deep-sea, habitat-forming gorgonian (Primnoa resedaeformis) from the Gulf of Alaska, Hydrobiologia, 471, 101–110.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Belozersky Institute of Physico-Chemical Biology, Lomonosov Moscow State University, 119991, Moscow, Russia

    G. A. Shilovsky & V. P. Skulachev

  2. Lomonosov Moscow State University, Faculty of Bioengineering and Bioinformatics, 119991, Moscow, Russia

    G. A. Shilovsky & V. P. Skulachev

  3. Lomonosov Moscow State University, Faculty of Biology, 119991, Moscow, Russia

    G. A. Shilovsky, T. S. Putyatina & A. V. Markov

Authors
  1. G. A. Shilovsky
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. T. S. Putyatina
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. V. Markov
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. V. P. Skulachev
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to G. A. Shilovsky.

Additional information

Published in Russian in Biokhimiya, 2015, Vol. 80, No. 12, pp. 1802-1816.

To whom correspondence should be addressed.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Shilovsky, G.A., Putyatina, T.S., Markov, A.V. et al. Contribution of quantitative methods of estimating mortality dynamics to explaining mechanisms of aging. Biochemistry Moscow 80, 1547–1559 (2015). https://doi.org/10.1134/S0006297915120020

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0006297915120020

Keywords

Search

Navigation