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i.e., at zero concentration of nutrient no growth
occurs. If some portion of the energy source were
utilized for functions other than growth, then
one should observe that the addition of very
small amounts of an energy source would not
permit growth. This then would assume that
growth is a secondary feature of energy utiliza-
tion and that energy is preferentially channelled
to maintenance purposes. The concentrations of
the energy source used in these experiments were
such that, although they limited the maximal
population attainable, they did not limit the rate
of growth. Monod also limited the rate of growth
of E. coli by limiting aeration, and although this
doubled the time taken to achieve maximal
density in one culture the cell yield was un-
changed. He concluded that since the rate of
growth did not influence the cell crop any
energy-of-maintenance values were nil.
It seems to us that many of the experiments
designed to test the use of a portion of the exoge-
nous energy source for maintenance rather than
growth are complicated by the fact that the
energy source is also a source of carbon for
growth. More definitive evidence might be ob-
tained with microorganisms which do not in-
corporate their energy source into cell substance;
there are numerous systems available for such
experiments-phototrophs, autotrophs, and the
nutritionally fastidious anaerobes that ferment
carbohydrates almost solely as a source of energy.
Furthermore, experiments designed to show that
some portion of the energy (and carbon) source
is not utilized for growth, and many do demon-
strate this, are not entirely convincing arguments
for the maintenance concept. These experiments
do not show that the energy that is diverted
from growth is utilized specifically for mainte-
It seems feasible that at slower growth rates
the cell yield might be decreased because the cell
physiology with respect to regulatory mecha-
nisms has altered in response to the changed en-
vironment, and that a portion of the energy
source is uncoupled at the enzymatic sites of
phosphor) lation; i.e., the decreased cell yield is
merely a reflection of decreased efficiency of
conversion f the energy source into high-energy
It is perhaps too obvious that the reactions of
energy-yielding metabolism are not always
coupled to the growth of the organism. The more
extreme cases of this are most often observed in
batch cultures that have reached a stationary
population but still consume considerable quan-
tities of substrate. This same feature is seen dur-
ing growth limitation (rate or yield) of some
nutrient other than energy source, and is most
dramatically demonstrated by washed suspen-
sions of nonproliferating cells metabolizing added
carbon or energy substrates.
Where the energy source is also the carbon
source, usage of carbon skeletons occurs without
net growth. In some cases, the carbon skeletons
are removed from the medium and stored within
the cells (assimilation) ready for utilization under
duress. However, uncoupling of assimilation has
also been observed, in that products of metabo-
lism often appear in supernatants, and presum-
ably these are lost to the cell. Further, it has been
suggested that the products of metabolism under
conditions of carbon and energy excess are shunt
products, and that assimilation into reserves
merely reflects this glut. Limitations of the rate of
microbial growth by nutrients other than the
energy source do not control the extent of oxida-
tion of the energy source; e.g., Rosenberger and
Elsden (67) showed that in tryptophan-limited
growth S. faecalis produced large amounts of
A discussion of the theoretical principles of
continuous culture (as controlled by nutrient
limitation), and a comparison of these with results
obtained experimentally, led Herbert (33) to
postulate that A. aerogenes displays a constant
rate of endogenous metabolism during exponen-
tial growth. The curve derived experimentally
relating steady-state bacterial concentration to
dilution rate (growth rate) does not coincide with
the theoretically predicted curve. At low dilution
rates, the cell yield is less than that expected
when the carbon and energy source is the growth-
limiting nutrient. Cultures whose growth is
limited by nutrients other than the carbon and
energy source do not show this phenomenon at
low growth rates, so that the decreased cell yields
observed under these conditions are not simply a
property of the growth rate. The lowered cell
yield recorded during slow growth on a limiting
carbon and energy source was explained by sug-
gesting that, in addition to cell synthesis from
the carbon substrate, there is also a constant oxi-
dation of cell substance to C02, i.e., some turn-
over is occurring during growth. (The experimen-
tal evidence for this is considered later.) The
equation representing the exponential growth of a
bacterial culture can be modified from
dx ds
-= sx = -Y-dt dt
du= _- k)xdt
cohere x = cell concentration; s = substrate
utilized; t = time; A = growth rate; k = a con-
stant representing the endogenous metabolism;
and Y = yield coefficient. Thus, by lowering the
dilution or growth rate, k becomes proportionally
larger in relation to A and, therefore, the cell
density falls; the cell yield is lower because pro-
portionally more cell material is oxidized relative
to the amount of limiting nutrient that is assimi-
lated. In toto, the net result is an uncoupling of
growth from oxidation of carbon substrate, since
proportionally more nutrient is oxidized than is
assimilated per cell. This idea was expanded by
Marr et al. (53), who designed experiments to
determine the value of k (these workers substitute
a for k) which they call the specific maintenance.
Mathematically, the lowered cell yield at low
dilution rates can be expressed as:
dx (u-kx Yds
-Z = (~a-k)x =-Yddt dt
Y ds
x dt
Now Y. x, ds/dt, and At (or D, the dilution rate)
can all be determined experimentally, and, there-
fore, k may be evaluated.
Substitution of k into the continuous culture
equations enables plots of steady-state cell con-
centration versus dilution rate to be made that
correspond exactly with those obtained experi-
mentally (33). Evidence to interpret k as repre-
senting a constant endogenous metabolism that
occurs during growth is demonstrated by com-
paring the rates of respiration of A. aerogenes in
continuous culture at different growth rates.
Extrapolation to zero growth rate of Qo2 and
Qco2 values determined at different growth rates
in media containing limiting glycerol gave values
on the ordinate that were identical to the Qo2
(endogenous) and Qco2 (endogenous) of these
cells. It is suggested that the respiration consists
of (i) substrate oxidation that is proportional to
the growth rate and (ii) a constant rate of oxida-
tion of endogenous material, that occurs at all
growth rates. Carbon balances (details of which
were not recorded) were also claimed to indicate
that proportionally more cell carbon than sub-
strate carbon is oxidized.
The lowered cell yields at low dilution rates
(carbon and energy source limiting) have been
observed for other bacteria and for Torula utilis
(33). Marr et al. (53) noted that E. coli is unable
to maintain cell density at low dilution rates, and
they calculated the specific maintenance as 0.025
The carbon balances of substrate utilization at
different growth rates received attention from
Marr et al. (53) with batch cultures. U-C14-glucose
was (i) added to a batch culture, giving exponen-
tial growth; (ii) fed rapidly to a culture so that
only a small fraction would be used for mainte-
nance, giving linear growth; and (iii) fed slowly
so that a large fraction was used for maintenance,