Skip to main content
SpringerLink
Log in

Biological Boundaries and Biological Age

  • Regular Article
  • Published:
Acta Biotheoretica Aims and scope Submit manuscript

Abstract

The chronologic age classically used in demography is often unable to give useful information about which exact stage in development or aging processes has reached an organism. Hence, we propose here to explain in some applications for what reason the chronologic age fails in explaining totally the observed state of an organism, which leads to propose a new notion, the biological age. This biological age is essentially determined by the number of divisions before the Hayflick’s limit the tissue or mitochondrion in a critical organ (in the sense where its loss causes the death of the whole organism) has already used for its development and adult phases. We give a precise definition of the biological age of an organ based on the Hayflick’s limit of its cells and we introduce a desynchronization index (the cell entropy) for some critical tissues or membranes, which are mainly skin, intestinal endothelium, alveoli epithelium and mitochondrial inner membrane. In these actively metabolising interface tissues or membranes, there is a rapid turnover of cells, of their cytoplasmic constituents such as proteins, and of membrane lipids. The boundaries corresponding to these tissues, cells or membranes have vital functions of interface with the environment (protection, homeothermy, nutrition and respiration) and have a rapid turnover (the total cell renewal time is in mice equal to 3 weeks for the skin, 1.5 day for the intestine, 4 months for the alveolae and 11 days for mitochondrial inner membrane) conditioning their biological age. The biological age of a tissue is made of two major components: (1) first, its embryonic age based on the distance (in number of divisions) between the birth date of its first differentiated cell and the time until it reaches its final boundary at the end of its development and (2) second, its adult age whose complement until its death is just the lapse of time made of the sum of remaining cell cycle durations authorized by its Hayflick’s limit. From this definition, we calculate the global biological lifespan of an organism and revisit notions like demographic survival curves, duration and synchrony of cell cycles, living boundaries from proto-cells to organs, and embryonic and adult phases duration.

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.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

References

  • Abbas L, Michon F, Cadau S, Gaudart J, Dhouailly D, Demongeot J (2009) Altitude-dependent front waves and zero mean Gaussian curvature lines in reaction-diffusion PDEs. Examples in development (feather morphogenesis) and epidemic spread (black death retroprediction). Philos Trans R Soc A 367:4829–4862

    Google Scholar 

  • Benner SA, Ricardo A, Carrigan MA (2004) Is there a common chemical model for life in the universe? Curr Opin Chem Biol 8:672–689

    Article  Google Scholar 

  • Bourgine P, Stewart J (2004) Autopoiesis and cognition. Artif Life 10:327–345

    Article  Google Scholar 

  • Braeckman BP, Demetrius L, Vanfleteren JR (2006) The dietary restriction effect in C. elegans and humans: is the worm a one-millimeter human? Biogerontology 7:127–133

    Article  Google Scholar 

  • Broderick G, Ru’aini M, Chan E, Ellison MJ (2004) A life-like virtual cell membrane using discrete automata. In Silico Biol 5:0016

    Google Scholar 

  • Brouhns N, Denuit M (2001). Risque de longévité et rente viagère. Institut de Statistique Université Catholique, Louvain, Discussion Paper 0137

  • Caubet JP (1975) Relativistic Brownian motion. Lect Notes Math 451:113–142

    Article  Google Scholar 

  • Cinquin O, Demongeot J (2005) High-dimensional switches and the modeling of cellular differentiation. J Theor Biol 233:391–411

    Article  Google Scholar 

  • De Duve C (1995) The beginnings of life on earth. Am Sci 83:428–437

    Google Scholar 

  • Demetrius L (1979) Relations between demographic parameters. Demography 16:329–338

    Article  Google Scholar 

  • Demetrius L (2005) Of mice and men. EMBO Rep 6:39–44

    Article  Google Scholar 

  • Demetrius L, Demongeot J (1984) A thermodynamic approach in the modelling of the cellular cycle. Biometrics 40:259–260

    Google Scholar 

  • Demongeot J (1983) Thesis. Université J. Fourier, Grenoble

  • Demongeot J (2007) Primitive genome and RNA relics. In: IEEE EMBC’07, IEEE Proceedings, Piscataway, pp 6338–6342

  • Demongeot J, Demetrius L (1989) La dérive démographique et la sélection naturelle: Etude empirique de la France (1850–1965). Population 2:231–248

    Google Scholar 

  • Demongeot J, Moreira A (2007) A circular RNA at the origin of life. J Theor Biol PMID: 17825325

  • Demongeot J, Benaouda D, Jezequel C (1995) Dynamical confinement in neural networks and cell cycle. Chaos 5:167–173

    Article  Google Scholar 

  • Demongeot J, Elena A, Weil G (2006) Potential-Hamiltonian decomposition of cellular automata. Application to degeneracy of genetic code and cyclic codes III. Comptes Rendus Biologies 329:953–962

    Article  Google Scholar 

  • Demongeot J, Glade N, Forest L (2007a) Liénard systems and potential-Hamiltonian decomposition. I methodology. Comptes Rendus Mathématique 344:121–126

    Article  Google Scholar 

  • Demongeot J, Glade N, Forest L (2007b) Liénard systems and potential-Hamiltonian decomposition. II algorithm. Comptes Rendus Mathématique 344:191–194

    Article  Google Scholar 

  • Doliger C (2006) Démographie, fécondité et croissance économique en France, Thesis Université Louis Pasteur, Strasbourg

  • Doumic M (2007) Analysis of a population model structured by the cells molecular content. Math Model Nat Phenom 2:121–152

    Article  Google Scholar 

  • Dworkin JP, Deamer DW, Sandford SA, Allamandola LJ (2001) Self-assembling amphiphilic molecules: synthesis in simulated interstellar/precometary ices. Proc Natl Acad Sci USA 98:815–819

    Article  Google Scholar 

  • Finch CE, Ruvkun G (2001) The genetics of aging. Ann Rev Genomics Hum Genet 2:435–462

    Article  Google Scholar 

  • Forest L, Demongeot J (2006) Cellular modelling of secondary radial growth in conifer trees: application to Pinus radiata. Bull Math Biol 68:753–784

    Article  Google Scholar 

  • Forest L, San Martin J, Padilla F, Chassat F, Giroud F, Demongeot J (2004) Morphogenetic processes: application to cambial growth dynamics. Acta Biotheor 52:415–438

    Article  Google Scholar 

  • Forest L, Martinez S, Padilla F, Demongeot J, San Martin J (2006a) Modelling of auxin transport affected by gravity and differential radial growth. J Theor Biol 241:241–251

    Article  Google Scholar 

  • Forest L, Michon F, Cadau S, Demongeot J, Dhouailly D (2006b) What is the biological basis of pattern formation of skin lesions? Viewpoint 4 skin patterns belong to three main types, determined at three steps of development. Exp Dermatol 12:559–564

    Google Scholar 

  • Forest L, Glade N, Demongeot J (2007) Liénard systems and potential-Hamiltonian decomposition. Applications. C R Acad Sci Biol 330:97–106

    Article  Google Scholar 

  • Glade N, Forest L, Demongeot J (2007) Liénard systems and potential-Hamiltonian decomposition. III applications in biology. Comptes Rendus Mathématique 344:253–258

    Article  Google Scholar 

  • Goetz R, Lipowsky R (1998) Computer simulations of bilayer membranes: self-assembly and interfacial tension. J Chem Phys 108:7397–7409

    Article  Google Scholar 

  • Golubev A, Khrustalev S, Butov A (2003) An in silico investigation into the causes of telomere length heterogeneity and its implications for the Hayflick limit. J Theor Biol 225:153–170

    Article  Google Scholar 

  • Greub G, Raoult D (2003) History of the ADP/ATP-translocase-encoding gene, a parasitism gene transferred from a Chlamydiales ancestor to plants 1 billion years ago. Appl Environ Microbiol 69:5530–5533

    Article  Google Scholar 

  • Griparic L, van der Bliek AM (2001) The many shapes of mitochondrial membranes. Traffic 2:235–244

    Article  Google Scholar 

  • Grover NB, Eward KL, Helmstetter CE (2004) Synchronous cultures from the baby machine A model for animal cells. Math Biosci 190:87–96

    Article  Google Scholar 

  • Hahn GM (1970) Mammalian cell populations. Math Biosci 6:295–315

    Article  Google Scholar 

  • Hare JF, Hodges R (1982) Turnover of mitochondrial inner membrane proteins in hepatoma monolayer cultures. J Biol Chem 257:3575–3580

    Google Scholar 

  • Hayflick L, Moorhead PS (1961) The serial cultivation of human diploid cell strains. Exp Cell Res 25:585–621

    Article  Google Scholar 

  • Hunding A, Kepes F, Lancet D, Minsky A, Norris V, Raine D, Sriram K, Root-Bernstein R (2006) Compositional complementarity and prebiotic ecology in the origin of life. BioEssays 28:399–412. http://umb-www-01.u-strasbg.fr/lexis/2000-01/td-histog-1.htm

    Google Scholar 

  • Johnson TE, Wood WB (1982) Genetic analysis of life-span in Caenorhabditis elegans. Proc Natl Acad Sci USA 79:6603–6607

    Article  Google Scholar 

  • Jolliot A, Prochiantz A (2004) Transduction peptides: from technology to physiology. Nat Cell Biol 6:189–196

    Article  Google Scholar 

  • Kaplan EL, Meier P (1958) Nonparametric estimation from incomplete observations. J Am Stat Assoc 53:457–481

    Article  Google Scholar 

  • Kim NW, Piatyszek MA, Prowse KR, Harley CB, West MD, Ho PL, Coviello GM, Wright WE, Weinrich SL, Shay JW (1994) Specific association of human telomerase activity with immortal cells and cancer. Science 266:2011–2015

    Article  Google Scholar 

  • Klass MR (1977) Aging in the nematode Caenorhabditis elegans: major biological and environmental factors influencing life span. Mech Ageing Dev 6:413–429

    Article  Google Scholar 

  • Knopman DS, Edland SD, Cha RH, Petersen RC, Rocca WA (2007) Incident dementia in women is preceded by weight loss by at least a decade. Neurology 69:739–746

    Article  Google Scholar 

  • Kurland CG, Andersson SGE (2000) Origin and evolution of the mitochondrial proteome. Microbiol Mol Biol Rev 64:786–820

    Article  Google Scholar 

  • Leblond CP, Stevens CE (1948) The constant renewal of the intestinal epithelium in the albino rat. Anat Rec 100:357–371

    Article  Google Scholar 

  • Leslie PH (1945) On the use of matrices in certain population mathematics. Biometrika 33:183–212

    Article  Google Scholar 

  • Levy M, Miller SL (1998) The stability of the RNA bases: implications for the origin of life. Proc Natl Acad Sci USA 95:7933–7938

    Article  Google Scholar 

  • Lindwall G, Hsieh EA, Misell LM, Chai CM, Scott M, Turner SM, Hellerstein MK (2006) Heavy water labeling of keratin as a non-invasive biomarker of skin turnover in vivo in rodents and humans. J Invest Dermatol 126:841–848

    Article  Google Scholar 

  • Malpiece Y, Sharan M, Barbotin JN, Personne P, Thomas D (1980) Theoretical and experimental study of immobilized bienzyme system. J Biol Chem 255:6883–6890

    Google Scholar 

  • Manke T, Demetrius L, Vingron M (2006) An entropic characterization of protein interaction networks and cellular robustness. J R Soc Interface 3:843–850

    Article  Google Scholar 

  • Maturana HR, Varela FJ (1980) Autopoiesis and cognition: the realization of the living. Reidel, Boston

    Google Scholar 

  • Maupertuis PL Moreau de (1745, reed. 1965). Vénus physique, in Oeuvres, Georg Olms, Hildesheim

  • Migliaccio E, Giorgio M, Mele S, Pelicci G, Reboldi P, Pandolfi PP, Lanfrancone L, Pelicci PG (1999) The p66shc adaptor protein controls oxidative stress response and life span in mammals. Nature 402:309–313

    Article  Google Scholar 

  • Miller SL (1953) A production of amino acids under possible primitive earth conditions. Science 117:528–529

    Article  Google Scholar 

  • Nelson KE, Robertson MP, Levy M, Miller SL (2001) Concentration by evaporation and the prebiotic synthesis of cytosine. Orig Life Evol Biosph 31:221–229

    Article  Google Scholar 

  • Ono N, Ikegami T (2000) Self-maintenance and self-reproduction in an abstract cell model. J Theor Biol 206:243–253

    Article  Google Scholar 

  • Ono N, Ikegami T (2001) Artificial chemistry: computational studies on the emergence of self-reproducing units. In: Kelemen J, Sosik S (eds) Proceedings of the 6th European conference on artificial life (ECAL’01), Springer, Berlin, pp 186–195

  • Pilyugin S, Mittler J, Antia R (1997) Modeling T-cell proliferation: an investigation of the consequences of the Hayflick limit. J Theor Biol 186:117–129

    Article  Google Scholar 

  • Pohlmeyer R (2007) The genetic code: a different perspective. http://www.rna-game.org/

  • Porte M (1994) Passion des formes. A René Thom. ENS Editions, Paris

    Google Scholar 

  • Raices M, Maruyama H, Dillin A, Karlseder J (2005) Uncoupling of Longevity and telomere length in C. elegans. Plos Genet 1:e30

    Article  Google Scholar 

  • Ramasamy R, Fazekasova H, Lam EW, Soeiro I, Lombardi G, Dazzi F (2007) Mesenchymal stem cells inhibit dendritic cell differentiation and function by preventing entry into the cell cycle. Transplantation 83:71–76

    Article  Google Scholar 

  • Rensing L, Meyer-Grahle U, Ruoff P (2001) Biological timing and the clock metaphor: oscillatory and hourglass mechanisms. Chronobiol Int 18:329–369

    Article  Google Scholar 

  • Robinson R (2005) Jump-starting a cellular world: investigating the origin of life, from soup to networks. PloS Biol 3:e396

    Article  Google Scholar 

  • Root-Bernstein R (2007) Simultaneous origin of homochirality, the genetic code and its directionality. BioEssays 29:1–10

    Article  Google Scholar 

  • Sciarrino A (2003) A mathematical model accounting for the organization in multiplets of the genetic code. BioSystems 69:1–13

    Article  Google Scholar 

  • Shapiro R (1999) Prebiotic cytosine synthesis: a critical analysis and implications for the origin of life. PNAS 96:4396–4401

    Article  Google Scholar 

  • Shapiro R (2007) A simpler origin for life. Sci Am 296:46–53

    Article  Google Scholar 

  • Shental-Bechor D, Haliloglu T, Ben-Tal N (2007) Interactions of cationic-hydrophobic peptides with lipid bilayers: a Monte Carlo simulation method. Biophys J 93:1858–1871

    Article  Google Scholar 

  • Simons K, Helenius A, Leonard K, Sarvas M, Gething MJ (1978) Formation of protein micelles from amphiphilic membrane proteins. Proc Natl Acad Sci USA 75:5306–5310

    Article  Google Scholar 

  • Sulston JE, Schierenberg E, White JG, Thomson JN (1983) The embryonic cell lineage of the nematode Caenorhabditis elegans. Dev Biol 100:64–119

    Article  Google Scholar 

  • Thom R (1972) Stabilité structurelle et Morphogenèse. Benjamin, New York

    Google Scholar 

  • Tomita M, Hashimoto K, Takahashi K, Shimuzu TS, Matsuzaki Y, Miyoshi F, Saito K, Tanida S, Yugi K, Venter JC, Hutchison CA (1999) E-cell: software environment for whole cell simulation. Bioinformatics 15:72–84

    Article  Google Scholar 

  • Usher MB (1969) A matrix model for forest management. Biometrics 25:309–315

    Article  Google Scholar 

  • Varela FJ (1989) Autonomie et connaissance : essai sur le vivant. Le Seuil, Paris

    Google Scholar 

  • Vogel SR, Deck C, Richert C (2005) Accelerating chemical replication steps of RNA involving activated ribonucleotides and downstream-binding elements. Chem Commun 39:4922–4924

    Article  Google Scholar 

  • Wang J, Tokarz R, Savage-Dunn C (2002) The expression of TGFβ signal transducers in the hypodermis regulates body size in C. elegans. Development 129:4989–4998

    Google Scholar 

  • Wang Y, Aguda BD, Friedman A (2007) A continuum mathematical model of endothelial layer maintenance and senescence. Theor Biol Med Model 4:30

    Article  Google Scholar 

  • Weixlbaumer A, Murphy FV, Dziergowska A, Malkiewicz A, Vendeix FAP, Agris PF, Ramakrishnan V (2007) Mechanism for expanding the decoding capacity of transfer RNAs by modification of uridines. Nat Struct Mol Biol 14:498–502

    Article  Google Scholar 

  • West GB, Brown JH (2005) The origin of allometric scaling laws in biology from genomes to ecosystems: towards a quantitative unifying theory of biological structure and organization. J Exp Biol 208:1575–1592

    Article  Google Scholar 

  • Wyllie FS, Jones CJ, Skinner JW, Haughton MF, Wallis C, Wynford-Thomas D, Faragher RG, Kipling D (2000) Telomerase prevents the accelerated cell aging of Werner syndrome fibroblasts. Nat Genet 24:16–17

    Article  Google Scholar 

  • Yanagi S, Kishimoto H, Kawahara K, Sasaki T, Sasaki M, Nishio M, Yajima N, Hamada K, Horie Y, Kubo H, Whitsett JA, Mak TK, Nakano T, Nakazato M, Suzuki A (2007) Pten controls lung morphogenesis, bronchioalveolar stem cells, and onset of lung adenocarcinomas in mice. J Clin Invest 117:2929–2940. http://www.jci.org

    Google Scholar 

Download references

Acknowledgments

I am indebted to L. Demetrius, N. Glade, A. Moreira and N. Vuillerme for many fruitful suggestions and discussions.

Author information

Authors and Affiliations

  1. TIMC-IMAG, UMR CNRS 5525, Team AGIM³, Faculty of Medicine of Grenoble, University J. Fourier, 38700, La Tronche, France

    Jacques Demongeot

Authors
  1. Jacques Demongeot
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jacques Demongeot.

Additional information

Le corps d’un animal est une espèce de moule intérieur, dans lequel la matière qui sert à son accroissement se modèle et s’assimile au total; de manière que, sans qu’il arrive aucun changement à l’ordre et à la proportion des parties, il en résulte cependant une augmentation dans chaque partie prise séparément, et c’est cette augmentation de volume qu’on appelle développement. Georges-Louis Leclerc de Buffon (1749) Histoire naturelle, générale et particulière, avec la description du cabinet du Roy. Honoré Champion, Paris.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Demongeot, J. Biological Boundaries and Biological Age. Acta Biotheor 57, 397–418 (2009). https://doi.org/10.1007/s10441-009-9087-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10441-009-9087-8

Keywords

Search

Navigation