Reader Comments
Post a new comment on this article
Post Your Discussion Comment
Please follow our guidelines for comments and review our competing interests policy. Comments that do not conform to our guidelines will be promptly removed and the user account disabled. The following must be avoided:
- Remarks that could be interpreted as allegations of misconduct
- Unsupported assertions or statements
- Inflammatory or insulting language
Thank You!
Thank you for taking the time to flag this posting; we review flagged postings on a regular basis.
closeMetabolic modeling and proliferative adaptation
Posted by Gregorio on 25 Jul 2011 at 02:33 GMT
The mathematical modeling of the metabolic underpinnings of the Warburg Effect and cancer was the subject of a paper by Demetrius and Tuszynski in TBioMed, not cited in this paper. In 2004 [Demetrius, Journal of Gerontology] produced Eq. 1 to account for longevity from caloric restriction. Eq. 1 was essentially Kleiber's Law, with a variable in the exponent of biomass for coupling efficiency, an electrochemical term. It was about the allometric scaling of metabolism.
The authors of this article, as well as Demetrius and Tuszynski, consider high replication either as something 'facilitated' by aerobic glycolysis, or the result of winning a Darwinian struggle for organism energy sources with differentiated cells. In neither case does the metabolic modeling account for the cause of rapid cacerous growth in biomass and replication.
Despite this, Eq.1 of Demetrius, models what is happening, what the cause is, and it turns out to be thermodynamic pressure for metabolic rate stability. The math is impenetrable to the initiate, but Eq.1 yields a numinous array of curves when a range of values are run for biomass and coupling efficiency. The math is covered in part by O'Kelly [2009 TBioMed]. The math supports the idea efficiency is metabolically threatening to the cell (decreasing denominator of the coupling ratio), and can result in mutations that effect energy processing of substrate (decrease in numerator of that ratio through mutation). This effect was presented by Carnes's 1988 paper about bacteria mutating to metabolize lactose (starvation- or stress-induced mutagenesis). When this happens the added energy translates to increase in the denominator of the coupling ratio, seen as lower efficiency in the coupling variable in the exponent of biomass.
The math shows lower efficiency causes biomass less than one gram in size, and this includes the mutated and differentiated cells, to increase metabolic rate. Here's the catch. The cancerous and differentiated cells, when part of a larger organism, are pressured to maintain a metabolic rate based upon a coupling efficiency determined by the larger organism. The O'Kelly paper advances the idea the nature of biological organization is a mathematical construct involving shared coupling ratio at all scales.
Increased metabolic rate of cancer cells engages thermodynamic pressure for those cells to lower metabolic rate to what it was before mutation. This they can do by both increasing mass, and by losing mass, hence tumor growth and replication. Eq. 1 suggests the human organism operates at an efficiency between 30 and 32%, if lifespan is directly related to metabolic rate. At over 25% coupling efficiency cells lose metabolic rate with loss in mass. At under 25% they lose metabolic rate with gain in mass. In both cases the replication and growth of cancerous cells is a response to pressures of those mutated cells to maintain their organizational connection with the host organism by retaining a metabolic rate like that it would have at a coupling ratio determined by the greater organism. Yes. Proliferation is an adaptation, but aerobic glycolysis is not an adaptation that permits or facilitates it. Instead it is a response to aerobic glycolysis.