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Research Article

Sizing Up Allometric Scaling Theory

  • Van M. Savage equal contributor,

    equal contributor Contributed equally to this work with: Van M. Savage, Eric J. Deeds

    Affiliation: Department of Systems Biology, Harvard Medical School, Boston, Massachusetts, United States of America

    X
  • Eric J. Deeds equal contributor,

    equal contributor Contributed equally to this work with: Van M. Savage, Eric J. Deeds

    Affiliation: Department of Systems Biology, Harvard Medical School, Boston, Massachusetts, United States of America

    X
  • Walter Fontana mail

    walter@hms.harvard.edu

    Affiliation: Department of Systems Biology, Harvard Medical School, Boston, Massachusetts, United States of America

    X
  • Published: September 12, 2008
  • DOI: 10.1371/journal.pcbi.1000171

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The correct version of Kleiber that eliminates the deviations

Posted by Gregorio on 19 Jan 2009 at 19:21 GMT

The version of Kleiber that incorporates the term for metabolic efficiency, a ratio of anabolism to catabolism, a redox coupling efficiency ratio, is MR= W^(4ME-1)/4ME where MR is metabolic rate, W is grams biomass of organic chemistry, and ME is metabolic efficiency. The graph of this is MR is the Y axis, ME is the X axis, and there is a different curve for each W. The version favored by WBE and SDF is MR is the X axis, and W is the X axis, where individual Ws occur as points, not line. So far the WBE version has revealed nothing of the secrets WBE suggest can be contained in its complex straight line, like that of aging. In the version containing ME, the sophisticated version, the curves clearly display the energetic nature of biological organization, from small to large, and portray aging as antagonism between BMR and FMR. In addition the curves model not just how life must have begun at submarine volcanic vents, but also how that life had to change to meet the energetic conditions necessary for its drifting from those energy sources to the surface. Those conditions dictated the longevity and replication of the biomass.

The equation models how the question as to the priority of replication and metabolism in the origins of life is a non-issue, that replication is inseparable from metabolism. Thermodynamic pressures for equilibrium in MR trigger changes in W so that it may absorb fluctuations in ME, and these changes occur in some cases as reduction in size of W through division or fragmentation. The value for ME is influenced by environmental energy sources for W, and the structure and organization of W to capture and use these sources. A graph of the equation reveals attractors at 25% ME, and one gram. Equilibration is least drastic around these numbers. At one gram, MR is the same for all ME. At 25% ME, all W converge. This contrasts with the WBE model in which ME is 100% for all W, at all times. It is no wonder that the alleged paradigm shift SDF attribute to the WBE model, is totally without relevance to all of biology.