Biological Scaling and Physiological Time: Biomedical Applications

  • Van M. Savage
  • Geoffrey B. West
Part of the Topics in Biomedical Engineering International Book Series book series (ITBE)


A framework for the development of quantitative theories that capture the body size and body temperature dependence of many cellular and physiological rates and times is presented. These theories rely on basic properties of biological systems, such as the invariance of terminal units, and on fundamental constraints taken from physics and chemistry, such as energy minimization of flow through resource-distribution networks and statistics of biochemical reaction kinetics. The primary postulate of this framework is that metabolic rate—the rate at which organisms take in resources from the environment, distribute these resources throughout their bodies, and process these resources by means of biochemical reactions—is perhaps the most fundamental rate in all of biology and is a major determinant, through both direct and indirect effects, of most cellular and physiological rates. The pervasive effects of metabolic rate are due to the facts that cellular rates work in concert to produce the rates manifested at the whole-organism level, and that the power created by metabolism must be allocated to individual maintenance, ontogenetic growth, and reproduction. Here we outline the derivations of the body size and body temperature dependence of metabolic rate. Using the primacy of metabolic rate, we then describe the ongoing development of theories that connect the theory of biological scaling to several biomedical processes, including ontogenetic growth, nucleotide substitution rates, sleep, and cancer growth. Empirical data are presented that confirm the mass and temperature dependence of metabolic rate as well as predictions for lifespan, ontogenetic growth trajectories, and sleep cycle times. Insights gleaned from these theories could potentially lead to important biomedical applications, such as methods for calculating proper drug dosing or for frustrating processes related to tumor angiogenesis.


Body Size Metabolic Rate Allometric Scaling Genome Length Boltzmann Factor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

6. References

  1. 1.
    Gillooly JF, Brown JH, West GB, Savage VM, Charnov EL. 2001:. Effects of size and temperature on metabolic rate:. Science 293:2248–2251.PubMedCrossRefGoogle Scholar
  2. 2.
    Peters RH. 1983. The ecological implications of body size. Cambridge UP, Cambridge.Google Scholar
  3. 3.
    Savage VM, Gillooly JF, Woodruff WH, West GB, Allen AP, Enquist BJ, Brown JH. 2004. The predominance of quarter-power scaling in biology. Funct Ecol 18:257–282.CrossRefGoogle Scholar
  4. 4.
    Blueweiss L, Fox H, Kudzma V, Nakashima D, Peters R, Sams S. 1978. Relationships between body and size and some life history parameters. Oecologia 37:257–272.CrossRefGoogle Scholar
  5. 5.
    Gillooly JF, Charnov EL, West GB, Savage VM, Brown JH. 2002. Effects of size and temperature on developmental time. Nature 417:70–73.PubMedCrossRefGoogle Scholar
  6. 6.
    Zepelin H, Rechtschaffen A. 1974. Mammalian sleep, longevity, and energy metabolism. Brain Behav Evol 10:425–470.PubMedGoogle Scholar
  7. 7.
    Savage VM, West GB. Paper to be submitted to Science. In progress.Google Scholar
  8. 8.
    Delsanto PP, Guiot C, Degiorgis PG, Condat CA, Mansury Y, Deisboeck TS. A growth model for multicellular tumor spheroids. 2004. arXiv:biological-physics/0307136.Google Scholar
  9. 9.
    Guiot C, Degiorgis PG, Delsanto PP, Gabriele P, Deisboeck TS. 2003. Does tumor growth follow a “universal law”? J Theor Biol 225:147–151.PubMedCrossRefGoogle Scholar
  10. 10.
    Deisboeck TS, Mansury Y, Guiot C, Degiorgis PG, Delsanto PP. 2004. Insights from a novel tumor model: indications for a quantitative link between tumor growth and invasion. arXiv:biological-physics/0309096.Google Scholar
  11. 11.
    Herman AB, Savage VM, West GB. Paper to be submitted to Nature. In progress.Google Scholar
  12. 12.
    West GB, Brown JH, Enquist BJ. 1997. A general model for the origin of allometric scaling laws in biology. Science 276:122–126.PubMedCrossRefGoogle Scholar
  13. 13.
    West GB, Woodruff WH, Brown JH. 2002. Allometric scaling of metabolism from molecules and mitochondria to cells and mammals. Proc Natl Acad Sci USA 99:2473–2478.PubMedCrossRefGoogle Scholar
  14. 14.
    Kozlowski J, Konarzewski M, Gawelczyk AT. 2003. Cell size as a link between noncoding DNA and metabolic rate scaling. Proc Natl Acad Sci USA 100:14080–14085.PubMedCrossRefGoogle Scholar
  15. 15.
    Lynch M, Conery JS. 2003. The origins of genome complexity. Science 302:1401–1404.PubMedCrossRefGoogle Scholar
  16. 16.
    West GB, Brown JH, Enquist BJ. 1999. The fourth dimension of life: fractal geometry and allometric scaling of organisms. Science 284:1677–1679.PubMedCrossRefGoogle Scholar
  17. 17.
    Savage VM, Gillooly JF, Brown JH, West GB, Charnov EL. 2004. Effects of body size and temperature on population growth. Am Naturalist 163:429–441.CrossRefGoogle Scholar
  18. 18.
    Brown JH, Gillooly JF, Allen AP, Savage VM, West GB. 2004. Towards a metabolic theory of ecology. Ecology 85:1771–1789.CrossRefGoogle Scholar
  19. 19.
    Allen AP, Brown JH, Gillooly JF. 2002. Global biodiversity, biochemical kinetics, and the energetic-equivalence rule. Science 297:1545–1548.PubMedCrossRefGoogle Scholar
  20. 20.
    Ernest SKM, Enquist BJ, Brown JH, Charnov EL, Gillooly JF, Savage VM, White EP, Smith FA, Hadly EA, Haskell JP, Lyons SK, Maurer BA, Niklas KJ, Tiffney B. 2003. Statistical mechanics of complex ecological aggregates. Ecol Lett 6:990–995.CrossRefGoogle Scholar
  21. 21.
    Kleiber M. 1932. Body size and metabolism. Hilgardia 6:315–353.Google Scholar
  22. 22.
    Brody, S. 1945. Bioenergetics and growth. Reinhold, New York.Google Scholar
  23. 23.
    Hemmingsen AM. 1960. Energy metabolism as related to body size and respiratory surfaces, and its evolution. Rep Steno Memorial Hospital Nordisk Insulin Laboratorium (Copenhagen), 9:6–110.Google Scholar
  24. 24.
    Enquist BJ, West GB, Charnov EL, Brown JH. 1999. Allometric scaling of production and life history variation in vascular plants. Nature 401:907–911.CrossRefGoogle Scholar
  25. 25.
    West GB, Brown JH, Enquist BJ. 1999. A general model for the structure, and allometry of plant vascular systems. Nature 400:664–667.CrossRefGoogle Scholar
  26. 26.
    Schmidt-Nielsen K. 1984. Scaling: why is animal size so important? Cambridge UP, Cambridge.Google Scholar
  27. 27.
    McMahon TA, Bonner JT. 1983. On size and life. Scientific American Library, New York.Google Scholar
  28. 28.
    Calder WA. 1984. Size, function, and life history. Harvard UP, Cambridge/Google Scholar
  29. 29.
    Cossins AH, Bowler K. 1987. Temperature biology of animals. Chapman and Hall, London.Google Scholar
  30. 30.
    Somero GS. 1997. Temperature relationships: from molecules to biogeography. In Handbook of physiology, Vol. 13, pp. 1391–1444. Ed. WH Dantzler. Oxford UP, New York.Google Scholar
  31. 31.
    Mandelbrot BB. 1982. The fractal geometry of nature. Freeman, San Francisco.Google Scholar
  32. 32.
    Womersley JR. 1955. Oscillatory motion of a viscous liquid in a thin-walled elastic tube, I: the linear approximation for long waves. Philos Mag 46:199–221.Google Scholar
  33. 33.
    Caro CG, Pedley TJ, Schroter RC, Seed WA. 1978. The mechanics of circulation. Oxford UP, Oxford.Google Scholar
  34. 34.
    Fung YC. 1984. Biodynamics. Springer, New York.Google Scholar
  35. 35.
    Landau LD, Lifshitz EM. 1978. Fluid mechanics. Pergamon Press, Oxford.Google Scholar
  36. 36.
    Marion JB, Thornton ST. 1988. Classical dynamics of particles and systems. Harcourt Brace Jovanovich, San Diego.Google Scholar
  37. 37.
    West GB, Brown JH, Enquist BJ. 2000. The origin of universal scaling laws in biology. In Scaling in biology, pp. 87–112. Ed. JH Brown, GB West. Oxford UP, Oxford.Google Scholar
  38. 38.
    Iberall AS. 1967. Anatomy and steady flow characteristics of the arterial system with an introduction to its pulsatile characteristics. Math Biosci 1:375–395.CrossRefGoogle Scholar
  39. 39.
    Sherman TF 1981. On connecting large vessels to small: the meaning of Murray’s law. J Gen Physiol 78:431–453.PubMedCrossRefGoogle Scholar
  40. 40.
    Zamir M, Sinclair P, Wonnacott TH. 1992. Relation between diameter and flow in major branches of the arch of the aorta. J Biomech 25:1303–1310.PubMedCrossRefGoogle Scholar
  41. 41.
    Zamir M. 1999. On fractal properties of arterial trees. J Theor Biol 197:517–526.PubMedCrossRefGoogle Scholar
  42. 42.
    Dodds PS, Rothman DH, Weitz JS. 2001. Re-examination of the “3/4-law” of metabolism. J Theor Biol 209:9–27.PubMedCrossRefGoogle Scholar
  43. 43.
    Arrhenius S. 1889. Über die Reaktionsgeschwindigkeit bei der Inversion von Rohzucker durch Sauren. Z Physik Chem 4:226–248.Google Scholar
  44. 44.
    Glasstone S. 1940. Textbook of physical chemistry. Van Nostrand, New York.Google Scholar
  45. 45.
    Landau LD, Lifshitz EM. 1980. Statistical physics. Pergamon Press, Oxford.Google Scholar
  46. 46.
    Baierlein R. 1999. Thermal physics. Cambridge UP, Cambridge.Google Scholar
  47. 47.
    Westerhoff HV, Dam KV. 1987. Thermodynamics and control of biological free-energy transduction. Elsevier, Amsterdam.Google Scholar
  48. 48.
    Raven JA, Geider RJ. 1988. Temperature and algal growth. New Phytologist 110:441–461.CrossRefGoogle Scholar
  49. 49.
    Vetter RAH. 1995. Ecophysiological studies on citrate-synthase, I: enzyme regulation of selected crustaceans with regard to temperature. J Comp Physiol B 165:46–55.CrossRefGoogle Scholar
  50. 50.
    West GB, Brown JH, Enquist BJ. 2001. A general model for ontogenetic growth. Nature 413:628–631.PubMedCrossRefGoogle Scholar
  51. 51.
    West GB, Enquist BJ, Brown JH. 2002. Ontogenetic growth: modeling universality and scaling [brief communication]. Nature 420:626–627.CrossRefGoogle Scholar
  52. 52.
    Zuckerkandl E, Pauling L. 1965. Evolutionary divergence and convergence in proteins. In Evolving genes and proteins, pp. 97–166. Ed. V Bryson, HJ Vogel. Academic Press, New York.Google Scholar
  53. 53.
    Li WH. 1997. Molecular evolution. Sinauer Associates, Sunderland, MA.Google Scholar
  54. 54.
    Kimura M. 1983. The neutral theory of molecular evolution. Cambridge UP, Cambridge.Google Scholar
  55. 55.
    Gillooly JF, Allen AP, West GB, Brown JH. 2005. The rate of DNA evolution: effects of body size and temperature on the molecular clock. Proc Natl Acad Sci USA 102:140–145.PubMedCrossRefGoogle Scholar
  56. 56.
    Beaton MJ, Cavalier-Smith T. 1999. Eukaryotic non-coding DNA is functional: evidence from the differential scaling of cryptomonad genomes. Proc Roy Soc London B-Biol Sci 266:2053–2059.CrossRefGoogle Scholar
  57. 57.
    Cavalier-Smith T. 1980. r-and K-tactics in the evolution of protist developmental systems: cell and genome size, phenotype diversifying selection, and cell cycle patterns. Biosystems 12(1–2):43–59.PubMedCrossRefGoogle Scholar
  58. 58.
    Gregory TR. 2001. The bigger the C-value, the larger the cell: genome size and red blood cell size in vertebrates [review]. Blood Cells Mol Dis 27:830–843.PubMedCrossRefGoogle Scholar
  59. 59.
    Gregory TR. 2001. Coincidence, coevolution, or causation? DNA content, cell size, and the Cvalue enigma [review]. Biol Rev Camb Philos Soc 76:65–101.PubMedCrossRefGoogle Scholar
  60. 60.
    Olmo E, Capriglione T, Odierna G. 1989. Genome size evolution in vertebrates: trends and constraints [review]. Comp Biochem Physiol B 92:447–453.PubMedCrossRefGoogle Scholar
  61. 61.
    Chandler M, Spain M. 2003. Pitfalls to using small animals in preclinical testing are being eliminated. Preclinica 1:1–2.Google Scholar
  62. 62.
    Jain RK. 1996. Delivery of molecular medicine to solid tumors. Science 271:1079–1080.PubMedCrossRefGoogle Scholar
  63. 63.
    West LJ, Pierce CM. Thomas WD. 1962. Lysergic acid diethylamide: its effect on a male Asiatic elephant. Science 138:1100–1103.CrossRefPubMedGoogle Scholar
  64. 64.
    MacDonald G. 1957. The epidemiology and control of malaria. Oxford UP, London.Google Scholar
  65. 65.
    Ancel LW, Levin BR, Richardson AR, Stojilkovic I. 2001. Two-tiered evolution of Neiserria meningitis: how within-host ecology and between-host epidemiology expedite phase shifting. Santa Fe Institute Working Paper 01-12-079.Google Scholar
  66. 66.
    Ancel LW, Newman MEJ, Martin M, Schrag S. 2002. Applying network theory to epidemic intervention: modelling the spread and control of Mycoplasma pneumoniae. Santa Fe Institute Working Paper 01-12-078.Google Scholar
  67. 67.
    Campbell SS, Tobler I. 1984. Animal sleep: a review of sleep duration across phylogeny. Neurosci Biobehav Rev 8:269–300.PubMedCrossRefGoogle Scholar
  68. 68.
    Mamelak M. 1997. Neurodegeneration, sleep, and cerebral energy metabolism: a testable hypothesis. J Geriat Psychiatry Neurol 10:29–32.Google Scholar
  69. 69.
    Maquet P. 2001. The role of sleep in learning and memory. Science 294:1048–1052.PubMedCrossRefGoogle Scholar
  70. 70.
    Frank MG, Issa NP, Stryker MP. 2001. Sleep enhances plasticity in the developing visual cortex. Neuron 30:275–287.PubMedCrossRefGoogle Scholar
  71. 71.
    Hoffman KL, McNaughton BL. 2002. Sleep on it: cortical reorganization after-the-fact. Trends Neurosci 25:1–2.PubMedCrossRefGoogle Scholar
  72. 72.
    Stickgold R, Hobson JA, Fosse R, Fosse M. 2001. Sleep, learning, and dreams: off-line memory reprocessing. Science 294:1052–1057.PubMedCrossRefGoogle Scholar
  73. 73.
    Tononi G, Cirelli C. 2003. Sleep and synaptic homeostasis: a hypothesis. Brain Res Bull 62:143–150.PubMedCrossRefGoogle Scholar
  74. 74.
    Adam K, Oswald I. 1977. Sleep is for tissue restoration. J Roy Coll Phys London 11:376–388.Google Scholar
  75. 75.
    Inoue S, Honda K, Komoda Y. 1995. Sleep as neuronal detoxification and restitution. Behav Brain Res 69:91–96.PubMedCrossRefGoogle Scholar
  76. 76.
    Moruzzi G. 1966. The functional significance of sleep with particular regard to the brain mechanisms underlying consciousness. In Brain and conscious experience, pp. 345–379. Ed. JC Eccles, Springer, Berlin.Google Scholar
  77. 77.
    Reimund E. 1991. Sleep deprivation-induced neuronal damage may be due to nicotinic acid depletion. J Med Hypo 34:275–277.CrossRefGoogle Scholar
  78. 78.
    Reimund E. 1994. The free radical flux theory of sleep. J Med Hypo 43:231–233.CrossRefGoogle Scholar
  79. 79.
    Siegel JM. 2003. Why we sleep. Sci Am 289:92–97.PubMedGoogle Scholar
  80. 80.
    Cortopassi GA, Wang E. 1996. There is substantial agreement among interspecies estimates of DNA repair activity. Mech Ageing Dev 91:211–218.PubMedCrossRefGoogle Scholar
  81. 81.
    Perez-Campo R, Lopez-Torres M, Cadenas S, Rojas C, Barja G. 1998. The rate of free radical production as a determinant of the rate of aging: evidence from the comparative approach. J Comp Physiol B-Biochem Syst Environ Physiol 168:149–158.CrossRefGoogle Scholar
  82. 82.
    Yu BP. 1993. Free radicals in aging. CRC Press, Boca Raton, FL.Google Scholar
  83. 83.
    Thorbecke GJ. 1975. FASEB Monog, ed. KF Heumann. Plenum Press, New York.Google Scholar
  84. 84.
    Arantes-Oliveira N, Berman JR, Kenyon C. 2003. Healthy animals with extreme longevity. Science 302:611.PubMedCrossRefGoogle Scholar
  85. 85.
    Sohal R, Weindruch R. 1996. Oxidative stress, caloric restriction, and aging. Science 273:59–63.PubMedCrossRefGoogle Scholar
  86. 86.
    Weindruch R. 1996. Caloric restriction and aging. Sci Am 274:46–52.PubMedCrossRefGoogle Scholar
  87. 87.
    Weindruch R, Walford RL. 1988. The retardation of aging and disease by dietary restriction. Charles C. Thomas, Springfield, IL.Google Scholar
  88. 88.
    Mauroy B, Filoche M, Weibel ER, Sapoval B. 2004. An optimal bronchial tree may be dangerous. Nature 427:633–636.PubMedCrossRefGoogle Scholar
  89. 89.
    Zepelin H. 1989. Mammalian sleep. In Principles and practice of sleep medicine, pp. 30–49. Ed. MH Kryger, T Roth, WC Dement. Saunders, Philadelphia.Google Scholar
  90. 90.
    Meddis R. 1983. The evolution of sleep. In Sleep mechanisms and functions in humans and animals, pp. 57–106. Ed. A Mayes. Van Nostrand Reinhold, Cambridge.Google Scholar
  91. 91.
    Smith FA, Lyons SK, Ernest SKM, Jones KE, Kaufman DM, Dayan T, Marquet PA, Haskell JP. 2003. The body mass of late Quaternary mammals. Ecology 84:3403, E084.CrossRefGoogle Scholar
  92. 92.
    Nowak RN. 1991. Walker’s mammals of the world. Johns Hopkins UP, Baltimore.Google Scholar
  93. 93.
    Pagel MD, Harvey PH. 1991. The taxon-level problem in the evolution of mammalian brain size: fact and artifacts. Am Naturalist 132:344–359.Google Scholar

Copyright information

© Springer Inc. 2006

Authors and Affiliations

  • Van M. Savage
    • 1
    • 2
  • Geoffrey B. West
    • 1
    • 2
  1. 1.Bauer Center for Genomics ResearchHarvard UniversityCambridge
  2. 2.Theoretical DivisionLos Alamos National LaboratoryLos Alamos

Personalised recommendations