Quantum statistics and allometric scaling of organisms. (English) Zbl 1022.92001
Summary: This article proposes a mechanism to explain allometric relations between basal metabolic rate and the body size of organisms. The model postulates that energy transduction in biological organisms is constrained by two classes of dynamical processes: The first process has its origin in quantum mechanics and the constraints which the coupling of electron transport and proton translocation impose on metabolic activity. The second derives from evolutionary dynamics and the constraints which ecological and demographic forces impose on the metabolic rate. These two processes are invoked to show that the scaling exponent between basal metabolic rate and body size follows a \({3}/{4}\) rule, in the case of organisms subject to ecological constraints defined by scarce but dependable resources, and a \({2}/{3}\) rule when constraints are defined by ample but only temporarily available resources.
Our conclusions are based on general arguments incorporating the molecular mechanisms that determine metabolic activity at all levels of biological organization. Hence the model applies to uni-cellular organisms, plants and animals.
Our conclusions are based on general arguments incorporating the molecular mechanisms that determine metabolic activity at all levels of biological organization. Hence the model applies to uni-cellular organisms, plants and animals.
MSC:
| 92B05 | General biology and biomathematics |
| 82C10 | Quantum dynamics and nonequilibrium statistical mechanics (general) |
References:
| [1] | Kleiber, M., The Fire of Life. An Introduction to Animal Energetics (1961), Wiley: Wiley New York |
| [2] | S. Brody, Bioenergetics and Growth, Reinhold, New York, 1945.; S. Brody, Bioenergetics and Growth, Reinhold, New York, 1945. |
| [3] | Hemmingsen, A., Energy and metabolism as related to body size and its respiratory surfaces and its evolution, Rep. Steno. Mem. Hosp., 9, 1 (1960) |
| [4] | Bennett, P.; Harvey, P., Active and resting metabolism in birds-allometry, phylogeny and ecology, J. Zool., 213, 324 (1987) |
| [5] | Dodds, P. S.; Rothman, D. H.; Weitz, J. S., Re-examination of the \(34\) law of metabolism, J. Theor. Biol., 209, 9 (2001) |
| [6] | Mc Mahon, T. A., Size and shape in biology, Science, 179, 1201 (1971) |
| [7] | West, G. B.; Brown, T. H.; Enquist, B. J., A general model for the origin of allometric scaling laws in biology, Science, 276, 122 (1997) |
| [8] | Mitchell, P., Chemiosmotic coupling in oxidative and photosynthetic phosphorylation, Biol. Rev., 41, 445 (1966) |
| [9] | Demetrius, L., Directionality principles in thermodynamics and evolution, Proc. Natl. Acad. Sci., 94, 3491 (1997) |
| [10] | Demetrius, L., Directionality theory and the evolution of body size, Proc. Roy. Soc. B, 267, 2385 (2000) |
| [11] | Harold, F., A Study of Bioenergetics (1986), W.H. Freeman and Co: W.H. Freeman and Co New York |
| [12] | Lindstedt, S. L.; Calder, W. A., Body size—physiological time and longevity of homeothermic animals, Q. Rev. Biol., 56, 1 (1976) |
| [13] | Adolph, E., Quantitative relations in the physiological constitutions of mammals, Science, 109, 579 (1949) |
| [14] | Marcus, R. A.; Sutin, N., Electron transfers in chemistry and biology, Biochem. Biophys. Acta, 11, 265 (1985) |
| [15] | Krishtalik, L., The mechanism of the proton transferan outline, Biochem. Biophys. Acta, 1458, 6 (2000) |
| [16] | Silverman, D. N., Marcus rate theory applied to enzymatic proton transfer, Biochem. Biophys. Acta, 1458, 88 (2000) |
| [17] | Demetrius, L., Statistical mechanics and population dynamics, J. Stat. Phys., 30, 709 (1983) · Zbl 0588.60097 |
| [18] | Mandl, F., Statistical Physics (1988), Wiley: Wiley New York |
| [19] | Demetrius, L., Thermodynamics of evolution, Physica A, 43, 257 (1992) |
| [20] | Cramer, W. A.; Knaff, D. B., Energy Transduction in Biological Membranes (1989), Springer: Springer Berlin |
| [21] | West, G.; Woodruff, W. H.; Brown, J. H., Allometric scaling of metabolic rate from molecules and mitochondria to cells and mammals, Proc. Natl. Acad. Sci., 99, 2473 (2002) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
