Quantum metabolism and cancer - power in numbers Gregory O'Kelly, n/a 11 February 2010 The authors describe quantum metabolism as 'an analytic theory of metabolic regulation which exploits the methodology of quantum mechanics to derive allometric rule relating cellular metabolic rate (MR) and cell size." I have no idea what quantum methodology is, or how it differs from scientific methodology. But the allometric scaling rule relating MR and cell mass, as proffered by Dr. Demetrius in his 2004 Journal of Gerontology article, has little if anything to do with quantum mechanics, whatever its alleged methodology. And what little it does have to do, relates to the nature of electrical charge transferred in the redox coupling necessary for the creation of covalent bonds. In fact Dr. Demetrius defines metabolic efficiency (ME) there as a ratio of amperes to amperes. In contrast, in this paper, the authors define ME as: 1. "Metabolic efficiency is the amount of ATP produced per unit of substrate material." 2. "The ratio of the energy stored in the various bio-molecules to the free energy released in redox reactions is the efficiency of the metabolic process, which can be as high as about 95%..." 3. "Metabolic efficiency is the amount of ATP produced per unit of substrate material." Does ME differ from the efficiency of the metabolic process, where the former is an amount, or an amount/unit of substrate, and the latter is a ratio? There is a good deal of looseness to these formulations. The authors make the claim that OxPhos has a higher metabolic efficiency (chose the definition), and thus a higher MR. This conflicts drastically with the Eq. (1) in Dr. Demetrius's 2004 which clearly indicates that for things of mass less than one gram in size, higher ME means lower MR. Problems loom. The authors also claim: "An increased metabolic rate entails an increased efficiency in the acquisition of resources. Hence, when limited resource conditions prevail, types with higher metabolic rates will be favoured," at a time when Demetrius's 2004 clearly shows that higher MR is something determined by the resources and the ability to use them (ME), and not something that exists independently of those resources. That same math also clearly shows, contra the authors' claim that "Cancer cells may be considered as autonomous units which have an impared capacity to maintain the metabolic stability of the organism in which they reside," and "...one cell type replaces a related cell type by natural selection," that all cells share the ME of the host, and that this is the nature of biological organization. The authors seem to think the cells of an organism are instead in competition for energy resources such that ME may vary from once cell to another. And to this Darwinian competition are introduced 'adaptive mechanisms', 'regulatory interventions', and 'anti-tumour defenses', none of which appear in the math. Examination of the definition of MR reveals MR is: 1. Rate of ATP production, and/or 2. "...the totality of chemical reactions in cells carried out by an organism," and/or 3. "...the rate at which an organism transforms nutrients into thermal energy and biological work", and/or 4. "Metabolic rate is the rate of ATP production per unit time..." [surely a redundancy], and/or 5. "... the minimum rate at which the cell uses energy to stay alive," and/or 6. "... determined by the proton conductance and the proton potential of the metabolic system...regulated by the phospholipid composition of the mitochondrial membrane...[that is modifiable by] exercise and diet." The authors don't say how the cells exercise but, instead, seamlessly move between basal and field metabolic rate, and fail to disclose at what scale Darwinian competition for energy is replaced by cooperation of the parts of the organism. But this is not enough. In matters of ME, "...the transformation of nutrients into thermal energy and biological work involves the inter-converson of two forms of energy: the redox potential difference...[and] the phosphorylation potential..." Redox potentials and phosphorylation potentials are not forms of energy. Energy, chemical energy, is expressed in coulombs or amperes, not volts. Amperes are not potentials. The authors assert that thermogenesis is part of metabolism, which conflicts with the idea "Metabolic efficiency is the amount of ATP produced per unit of substrate material." Only when thermogenesis is considered part of metabolism do we find extremely high efficiencies like that the authors claim characterizes the Krebs Cycle - 95%, an efficiency rating characteristic, at best, of mechanical linkages. The authors speak of "two classes of metabolic pathways" - fermentation and respiration - where those two things characterize different 'mode of coupling - chemical and electrical, as if electrochemistry did not include both, at a time when redox coupling efficiency (ME) is a term from electrochemistry. They make this distinction repeatedly through the paper, e.g., MR is "determined by the proton conductance and the proton potential of the metabolic system"; "In OxPhos, the coupling is electrical...In glycolysis, the coupling is chemical..."; "The coupling between the electron transport chain and ADP phosphorylation is generated by the flow of protons across the biomembrane"; "In OxPhos coupling is achieved by a single common intermediate between the oxidation of a variety of substrates and ATP formation. The intermediate is the trans-membrane proton gradient"; "All living systems exist in a steady state relatively far from thermodynamic equilibrium and this state is maintained by sustaining non-equilibrium concentration gradients across membranes"; and "The metabolic rate of normal cells is primarily determined by the proton conductance and the proton potential of the metabolic system." What is problematic with this view of energy is its complete un-relatedness to the quanta of metabolism. Proton gradients, proton pumps, proton conductance, etc., have absolutely nothing to do with quanta. Quanta are the energy states of the electron. They are as discrete as different wavelengths of photons. Use of the word in the favored phrase 'quantum metabolism', in the manner favored by the authors, merely reveals their lack of familiarity with the term. There is a long history to this bit of insular elision that dates to 1902 and Julius Bernstein who sought to explain the electromagnetism of the nervous system in terms of thermodynamics. Bernstein turned to the Nernst equation, a thermodynamic equation of Walter Nernst that spoke of 'elementary particles'. These elementary particles could be any particles in solution or in an ideal gas, i.e., they could be ions, protons, electrons, molecules, whatever. The volts of Nernst were units of osmotic pressure, and had nothing to do with electromagnetism. The claim that there are two modes of energy transduction, one chemical and one electrical, is spurious, because all chemical energy transduction is electrochemical, not osmotic. "Quantum Metabolism predicts that the metabolic rate of cells utilizing OxPhos and cells utilizing glycolysis will have the same scaling exponents but will differ in terms of the proportionality constants"; and "Quantum metabolism, a new bio-energetic theory of metabolic regulation in cells [dating to 1902], shows the proportionality constants in the scaling laws for metabolic rates of cells utilizing OxPhos and glycolysis pathways are contingent on the different modes of coupling..." The proportionality constant depends upon the difference in redox coupling modes (ME), a difference obviated when the quantum world replaces the world of thermodynamic electricity, so that the two modes collapse into one. Proportionality constants are not measured, nor are they calculated. They are disembodied hypotheses meant to rescue a tortured scheme. At the same time when MR is determined entirely by scaling exponents (Demetrius 2004), the authors propose "The evolutionary argument rests on differences in the MR of cells utilizing OxPhos and glycolytic pathways, respectively," Demetrius's 2004 shows that when scaling exponents for cells are the same and there is a difference in MR, the difference is due to the mass of the cell, nothing else. The scaling exponents differ if and only if the value for ME differs from one cell to another, something not likely when ME is determined by the organism, and not the cells which comprise it. The authors are now proposing 'non-invasive' 'regulatory interventions on the basis of quantum metabolism' 'to combat cancer.' "The hypothesis, in its simplest form, asserts that cancer is primarily a disease of metabolic dysregulation..." "...therapeutic strategies based on arresting the transition from normal... to... malignant...may be effective in complementing traditional methods..." Typically, the authors specify no such interventions outside of hints at drugs and pharmaceuticals that might be complementary. They hope to influence MR this way at a time when Demetrius's 2004 shows MR is dependent entirely upon biomass and ME. Presumably ME can be varied for the cell with adequately targeted drugs that act upon modes of energy processing. Demetrius's 2004, which also supports the hypothesis of cancer as due to metabolic dysregulation, does not stoop to this, the idea of modes of energy processing. Instead of hypothesizing regulatory interventions that might complement traditional methods however, the mathematics suggest the traditional methods target the cell but not the cause of the mutation, a matter of ME, and should be rejected outright. The curves suggest the way to act upon MR is to manipulate ME through the application of electrochemistry. The curves model how the cause of mutation is increased ME from the reduced denominator of its redox coupling ratio, and how this drives cells, whose MRs are collapsing, to degenerate by alternately reducing the numerator of the ratio. This allows the cell to survive in an organism of high ME, which the cell shares. John Cairnes called this 'starvation induced mutation'. I will always be disappointed Dr. Demetrius never looked into this equation more thoroughly, but I understand his ability to appreciate its power was limited by his understanding of the quantum nature of chemical energy, and how this understanding's electrophysiology was formulated before the quantum revolution. Competing interests I have no competing interests whatsoever.