Mathematics of metabolism's pertinence to understanding origins and
- From: gokelly@xxxxxxxxxxx
- Date: Sat, 22 Mar 2008 00:19:38 -0500 (EST)
In Harvard's Department of Organismic and Evolutionary Biology (DOEB)
can be found the Program for Evolutionary Dynamics, headed by Martin
Nowak. The intent of the program is to put Darwin in mathematical
form. In 2006 Nowak published EVOLUTIONARY DYNAMICS, covered much of
the work of the program. Missing from the book is any discussion of
metabolism.
Lloyd Demetrius, a mathematical biologists in the DOEB, has expanded
upon a power law known as Kleiber's Law, that relates metabolic rate
(MR) to biomass [2004]. Conventionally Kleiber's Law is known as
'quarter power scaling', where the exponent of biomass is 3/4.
Traditional biologists argue the exponent is 2/3. Geoffrey West et
al. assert the exponent is 3/4 because of the efficiency of vascular
delivery to nutrients to the cells of an organism. West et al. also
assert Kleiber with this exponent applies over 27 orders of magnitude,
to organisms that do not have hearts or capillaries.
Demetrius points out that the exponent is actually (4ME-1)/4ME, where
ME is the ratio of the efficiency of redox coupling, a ratio of
amperes of reduction to amperes of oxidation. MR is expressed in
watts, and biomass is expressed in grams. The numbers clearly
indicate that the exponent is 3/4 when ME is 100%, and 2/3 when ME is
89%. Nothing even in the mechanical world is this efficient. The
implication is that West et al. assume the efficiency they claim the
exponent 3/4 models, and, in so doing, remove quarter power scaling
from having any relevance for understanding metabolism.
The reason for this difference is the idea that heat generation is
part of metabolism, rather than ME being measured against loss to heat
of energy otherwise involved in the creation of the covalent bonds
necessary for organic molecules. If thermogenesis is dismissed as
part of metabolism, values for ME are far lower, less than 40%. MR is
actually a measure, in watts, of recharge rate of covalent bonds
necessary to maintain biomass's size, organization and existence.
A graph of the equation MR= W (biomass) ^(4ME-1)/4ME, with MR on the Y
axis and ME on the X axis, and a different curve for each value of
biomass (in grams) over a range of 27 orders of magnitude, reveals a
set of curves that, upon analysis (which will not be included here,
but which is available from me upon request - email
gokelly@xxxxxxxxxxx), reveals that: 1. evolution and the origins of
life is primarily about metabolism, and only secondarily about
genetics; 2. that replication and metabolism are inseparable, with
replication being a response of biomass to perturbations in MR
resulting from fluctuations in ME; that life got started at submarine
volcanic vents where both chemotrophism (hydrogen sulfide oxidizing to
form sulfurous acid and giving off reductive energy) and phototrophism
(UV light from thermal mass) were abundant; that reproduction is
related to food sources; that thermodynamic pressure for stability of
MR acted to reduce MR perturbations by increasing biomass; that only
biomass functioning at over 25% ME was not penalized metabolically by
further increases in biomass; and that therefore for things less than
one gram in mass, division was a response to increase MR lost to mass
increase.
Analysis of the equation given its terms reveals that the nature of
aging, mutation, cancer, exercise, weight loss, and weight regain
after dieting, are clearly modeled as changes in biomass given changes
in ME. ME can change because of changes in the numerator, or the
denominator, that is, because of increased/decreased energy capture
and expenditure, and because of increased/decreased food supply. The
equation models how the MR of the cells of an organism are related to
the MR of the organism (FMR for field metabolic rate). Despite the
claims of West, Savage, et al., the mass of the organism has no affect
on basal cell MR. BMR (basal metabolic rate) changes with the ME of
the organism, which is the same as that for its cells. Note in the
graph how only at one gram does MR remain the same for all MEs. Note
how, at over 25% ME, the MR of the organism increases with further
increases in both mass and ME; but at the basal level MR diminishes
with increases in ME, and can only increase with increases in mass.
This is what drives weight regain after dieting, and portrays aging as
the antagonism between BMR and FMR.
The equation clearly models how reduction in ME from organism activity
in the pursuit of energy, increases BMR while reducing FMR, which then
increases once food has been found. The equation depicts why exercise
then increases BMR, while recovery from exercise increases FMR; but it
also explains why weak muscles impede the conversion of diminished FMR
to BMR, and that if this conversion is to build muscle cell mass then
ME must be reduced to less than 25%, at which point energy delivered
by the nervous system to the muscle is absorbed as mass increase of
muscle cells.
There's a lot more to this. You won't read it anywhere but here, yet.
.
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