magnitude of the differences in vitrowere
relatively small when compared with the
differences in metabolic rates in vivo.
Indeed, in the studies of O 2 consumption
and sodium pump activity referred to
earlier (Gregg and Milligan, 1982; McBride
and Milligan, 1984, 1985a, b), there were
few if any treatment effects on total O 2 con-
sumption of different tissues incubated in
vitro. Coulson (1993) argues that the differ-
ences in metabolic rates in vivoon a per
cell basis are due to differences in the rate
of supply of oxygen to these cells. For
many metabolic pathways, the supply of
oxygen is the rate-limiting step and deliv-
ery of it depends primarily on blood flow
(oxygen extraction rates as tissues are per-
fused are remarkably similar across
species). His argument, which he refers to
as the ‘Flow Theory’, is based on certain
physical constraints imposed on animal
design (Coulson, 1993). Firstly, that blood
pressure has to be maintained within cer-
tain limits (high enough to ensure that red
blood cells can pass through capillary beds
and plasma can perfuse cells, but not so
high as to cause damage to blood vessels).
Secondly, since blood volume is approxi-
mately 6.5% of body weight in animals
(Schmidt-Nielsen, 1984), as animals
increase in size, for blood volume to
remain a fixed proportion of size, the diam-
eter of the major blood vessels must
decrease. As the diameter of blood vessels
decreases, then the rate of flow of blood
through them must also decrease in order
to prevent blood pressure increasing dra-
matically.
Coulson uses the Flow Theory to argue
that the rate of oxygen supply to tissues
thus decreases as animal size increases,
resulting in lower metabolic rates,
expressed on a per cell basis, in larger
animals. He uses this argument to explain
differences between species of differing
mature size and also to explain changes in
the rate of growth as an animal matures. In
this case, the cells within an animal’s body
will have a certain requirement for energy
in order to meet their basal costs. Whilst
oxygen supply is sufficient to ensure rates
of energy production in excess of this fixed
cost, the potential exists for the cells or
tissues to grow. Therefore, as the animal
grows, the diameter of major blood vessels
must decrease in order to maintain blood
volume at a fixed proportion of body
weight. As this happens, so blood flow
rates decrease, and hence the rate of
oxygen supply to the tissues within the
animal’s body also falls. The resting meta-
bolic rate of cells and thus their potential
to produce ATP will decline, reducing the
rate of growth. Additionally, as cells grow,
their surface area increases, causing higher
rates of Na+ leakage. Therefore, as fixed
costs increase and the potential metabolic
rate of the cells decreases, the excess
energy production over the fixed costs
decreases, and hence the potential for
growth reduces. Mature size is reached for
a particular animal when fixed costs and
potential energy supply coincide.
The potential for growth will depend
on the difference between fixed costs of
cells and their metabolic rate. Since fixed
costs are determined in part by cell size
(and this does not vary appreciably across
species) and metabolic rate declines as
mature size increases (as discussed above),
the fractional or proportional rate of
growth also declines across species as
mature size increases. The fractional rate of
growth is effectively the rate of growth on a
per cell basis. Although this is lower in an
animal of larger mature size than it is in a
smaller one, the absolute rate of growth of
the whole animal will be greater as larger
animals contain many more cells than
smaller ones do.Conclusions
Care needs to be taken in the interpretation
of measurements of Na+,K+-ATPase activity
made in vitro. The incubation medium
used, whether it employs CO 2 /HCO 3 as
the main buffer or not (increasing the
potential for cycling of carbonic acid across
the plasma membrane), whether it contains
a single energy substrate or a more
balanced set of nutrients, and how tightly
controlled pH and osmolarity can allAspects of Cellular Energetics 157