J. Cell Sci. 4, 645-654 (1969)
Printed in Great Britain
645
THE ENERGETICS OF MAMMALIAN CELL
GROWTH
D. G. KILBURN*, M. D. LILLY AND F. C. WEBB
Biochemical Engineering Section, Department of Chemical Engineering,
University College, London, England
SUMMARY
Data from batch growth curves of mouse LS cells cultivated at controlled dissolved oxygen
partial pressures were used to calculate the weight of cells produced per mole of adenosine
triphosphate generated (YArv). These values agree well with those reported for bacteria.
A theoretical relationship was developed which allowed the biosynthetic and maintenance
energy requirements to be estimated. The biosynthesis of LS cells required i-6 x io" 1 1 moles
of ATP/cell. The maintenance energy, which is a function of growth rate, was 2-9 x io""11
moles ATP/new cell when the mean generation time was 1-15 days. The proportion of the
total energy used for maintenance under these conditions was 65 %. This corresponds to
a value of less than 1 0 % for bacterial maintenance when the organisms are grown at near
their maximum rate. A comparison of biosynthetic energy requirements indicates that bacteria
and moulds require about 4 times as much energy as animal cells to generate the same weight
of cell material. Possible explanations of this difference are discussed.
INTRODUCTION
In recent years attempts have been made to relate the mass of bacterial cells
produced to the number of moles of adenosine triphosphate (ATP) estimated to be
formed by the utilization of the energy-producing substrate (Bauchop & Elsden,
i960; Gunsalus & Shuster, 1961). The rationale behind this approach was outlined
by Senez (1962), who argued that since ATP is apparently used directly or indirectly
in all the major energy-consuming reactions of the cell, it represents the best estimate
of the useful free energy available to the cell. When bacteria were grown in complex
media containing the amino acids and other monomers needed for growth, and the
oxidizable substrate served only as an energy source, it was found that 1 mole of
ATP yielded an average of 10-5 g dry weight of cells.
Some workers have considered ATP yield (YA1:P) t 0 be a biological constant
but in fact it must depend on the conditions of growth. The biosynthetic requirements of the cell are thought to account mainly for Y ATP values and most of the
reported values have been determined under growth conditions in which maintenance
energy has been almost negligible. But Y ATP would be expected to be different if
the maintenance energy (i.e. energy consumption not associated with growth) represented a large proportion of the total energy requirements.
In animal cells the maintenance energy is thought to be substantial; Paul (1965)
• Present address: Department of Microbiology, University of British Columbia, Vancouver
8, B.C., Canada.
646
D. G. Kilburn, M. D. Lilly and F. C. Webb
has estimated that the sodium pump alone consumes 20% of the energy available
to the cell. If bacteria and animal cells have the same efficiency of biosynthesis one
would expect the YATP °f animal cells to be lower than 10 g dry weight per mole
ATP.
Our studies on the growth of mouse LS cells at controlled dissolved oxygen partial
pressures (j>02) have permitted us to estimate independently both YATP and maintenance energy. This has led to the paradoxical conclusion that although the maintenance energy of animal cells is about 10 times that of bacteria (both growing at
maximum rates) the YATP °f these organisms is identical. These results, the methods
used to obtain them and a discussion of the significance of the findings form the
subject of this paper.
THEORY
Determination of A TP yield
The YATF value of 10-5 g cells per mole ATP for bacteria was determined from
anaerobically grown cultures in which the amount of ATP generated by fermentation
of the energy-producing substrate is known (Bauchop & Elsden, i960). For aerobic
growth of bacteria, however, there is some difficulty in calculating Y.KTP because
the phosphorylation ratio (P/O) is not definitely known. This problem does not
prevent an analysis of the energetics of animal cell growth, because oxidative phosphorylation in mammalian mitochondria has been studied extensively and a P/O
ratio of 3 for NADH oxidation seems well documented (Mahler & Cordes, 1966).
In animal cells, ATP is produced primarily in the conversion of glucose to pyruvate
and in the oxidation of pyruvate to CO2 and water via the tricarboxylic acid (TCA)
cycle (i.e. aerobic metabolism). During anaerobic metabolism pyruvate is reduced
to lactate, and ATP is produced only by substrate-level phosphorylation. In general
the total energy production is the sum of the contributions from both aerobic and
anaerobic processes, and the following stoichiometric relationships are generally
accepted
glucose + 6O8 + 38ADP + 38P£ -> 6CO2 + 6H2O + 38ATP
glucose + 2ADP + 2P£ -> 2 lactate + 2ATP.
Provided that other decarboxylation reactions are negligible, the ATP generated
during cultivation can be calculated from the CO2 and lactate produced
ATP formed (moles) = -- CO2 (moles) + lactate (moles).
Determination of maintenance energy
The energy utilized by a microbial cell can be considered to consist of two components: (i) a steady rate required to maintain concentration gradients, internal
organization, repair of degraded molecules and like functions, i.e. maintenance
energy; and (ii) a rate associated with the biosynthesis of new cell material required
for multiplication, i.e. biosynthetic energy; the first will depend on the number
Energetics of mammalian cell growth
647
(or weight) of cells present, while the second will depend upon the rate at which the
cells are growing. It is assumed that the rate of energy generation in terms of ATP
is equivalent to its rate of utilization.
The over-all rate of energy utilization can be expressed by the equation
dE
Adx
- = mx + A^,
(1)
where dEjdt = the total rate of energy expenditure (moles ATP/litre of culture/day),
m = specific maintenance energy rate (moles ATP/cell/day), x = cell concentration
(no. of cells/litre of culture, provided that the average weight per cell is not changing),
A = specific biosynthetic energy rate (moles ATP/cell).
This expression forms the basis of the techniques used by Marr, Nilson & Clark
(1963) and by Pirt (1965) to estimate the maintenance energy of bacteria. These
workers formulated the equation in terms of energy-producing substrate consumed
rather than ATP generated.
During the exponential phase of cell growth
Jt=»X,
(2)
where /.(, = specific growth rate.
Integrating equation (2),
In* = pt+C,
x = Ce>".
(3)
Applying the boundary conditions, x = x0 at t = o,
x = xoe>».
(4)
Substituting for dx/dt from equation (2) and for x from equation (4) in the energy
rate equation (1),
-jt = mx + Afix = (m + A/i)x,
— = (m + A/i)xoe"1.
(5)
Integrating this expression,
E = (m + A/.*) {xo{fi) e'a + C.
(6)
Applying the boundary conditions E = o at t = o, then
Therefore,
C = -(tn + A/i)(xolfi).
E = (m + Afi)(xolfc)(e'u-1).
(7)
The integrated form of equation (1) expresses the relationship between energy
generation and time during the exponential phase of a batch culture. A plot of E
against (e'''—i) should give a straight line passing through the origin with slope =
(m + A/,t)(xQl/.i), provided that at the arbitrary point chosen for E = o, and t = o,
the culture is in exponential growth.
It is possible by growing cultures at different controlled pO2 levels to alter the
648
D. G. Kilburn, M. D. Lilly and F. C. Webb
exponential growth rate /t (Kilburn, Lilly, Self & Webb, 1968). An analysis of the
rate of ATP generation in several such batch cultures allows the values of m and
A to be estimated.
PROCEDURE
All experiments utilized 3-I. suspension cultures grown at 35 + 0-2 °C in Eagle's
minimal essential medium, supplemented with 2-5 g/1. lactalbumin hydrolysate,
1 g/1. carboxymethyl cellulose and 2% (v/v) horse serum. The glucose concentration
of the medium was increased to 2 g/1. The pH was controlled at 7-4 + 0-1 by the
automatic addition of 0-5 M NaOH. Liquid phase pO2 was measured by an oxygen
electrode and controlled by admitting pulses of oxygen to the gas space of the vessel.
Details of the culture vessel, the control systems for pH and pO2, the measurement
of liquid and gas phase pCO2 and the general culture method have been presented
elsewhere (Kilburn & Webb, 1968). The measured CO2 output was found to agree
well with oxygen uptake (Kilburn et al. 1968), indicating that decarboxylation
reactions other than those associated with energy metabolism were negligible.
RESULTS
ATP yield
In Table 1 the cumulative amount of ATP produced during a batch culture
without pOz control is compared with the dry weight of cells produced (sample dry
weight minus initial dry weight after inoculation). The figures for ATP produced
were calculated from the concentrations of CO2 and lactate.
Table 1. Calculated -values of F A T P during a batch culture without pO^ control
Sample
Net dry wt.
(g/1.)
Cumulative ATP
(mole/1.)
2
O-II
O-OI2
3
4
5
O-22
0-30
040
0-47
O-O242
0-0276
O-O388
00430
6
^ATP
=
g dry wt./
mole ATP
9-2
91
109
103
109
Table 2. Calculated values of YA1:F at the maximum cell count for
batch cultures at controlled pOz
Controlled pO2 (mmHg)
YATP, g dry wt./mole ATP
i-6
8-o
12
9 •6
48
32
11
•9
11
•5
96
14-1
96
11-4
160
10-5
These values of YATP agree well with the average value of 10-5 g/mole ATP
reported for bacteria. The dry weights for the samples were based on the measured
dry weight of sample 6, but since the size of cell decreases slightly during the growth
cycle, the estimated dry weights of the initial samples may be slightly low.
Energetics of mammalian cell growth
649
Table 2 shows YATP for the batch cultures at controlled values of pO2 calculated
as previously, but only at the peak of the growth curve, where the dry weight was
determined. These values for YAT1? of LS cells are similar to those reported for
bacterial cells.
Energy utilization
Equation (7) was derived to express the relationship between energy generated
and time during the exponential growth phase of a batch culture. A distinction was
made between the energy used for biosynthesis and that used for maintenance, or
more precisely between growth-associated and non-growth-associated energy utilization. According to equation (7) a graph of ATP generated (the cumulative value
calculated from the lactate and CO2 production) against e'1' — 1 for cells growing at
different rates should still give a straight line passing through the origin with the
slope = (m + A/i)(xolii). Thus, rearranging
— (slope) = m + /uA.
(8)
0-05 -
Fig. 1. Energy produced in batch cultures at controlled dissolved oxygen partial
pressures plotted against ef'—i: • , pO2 = 16 mmHg, x0 = 2 7 x 1 0 ' cells/1.,
/t = 0-30 day- 1 ; • , pO., = i6ommHg, x0 = 2-8 x i o 8 cells/1., fi = 0-53 day" 1 ;
D, pOt = 96 mmHg, x0 = 2-4 x io 8 cells/1., /i = o-6o day" 1 ; A, pO., = 12 mmHg,
#o = i-6 x io 8 cells/1., /* = 0-65 day" 1 .
41
Cell Sci. 4
650
D. G. Kilburn, M. D. Lilly and F. C. Webb
In each case x0 and /i are known, If the values of the left-hand side of the equation
are calculated and plotted against fi a straight line should be obtained, having a slope
equal to A. The value of m may be obtained by extrapolation to /t = o.
u
Figure 1 shows values of ATP generated plotted against (e' — 1) for cultures
grown at four different dissolved oxygen partial pressures. In this way the term
/t/.v0 (slope) in (8) was obtained for six cultures and plotted against [i (Fig. 2). From
11
this graph as described above, m == 17 x icr moles ATP/cell day and A = 2-3 x
10-11 moles ATP/cell.
0-2
04
0-6
Specific growth rate (/t, day-1)
08
Fig. 2. Plot of specific growth rate, fi, against the term fi/x0 (slope) from equation (8).
The value of the slope is taken from the lines in Fig. i ; x0 is the cell concentration
at the beginning of exponential growth.
An independent estimate of m can be obtained from the rate of ATP production
during the stationary phase of the growth cycle. However the stationary phase,
except at 320 mmHg, was too short for accurate measurement of ATP production.
Thus during the period over which the measurements shown in Table 3 were made
there was usually a decrease in viable cell count. Such estimates cannot be accepted
without reservation, because it is suspected that at this stage in a culture energy
generation may be partially uncoupled from NADH oxidation (Paul, 1965). Neverthe-
Energetics of mammalian cell growth
651
less it can be seen that the value of m obtained by solving the rate equation for the
exponential growth phase is only slightly lower than the values calculated from the
rate of ATP production during the stationary phase. The value of m for the 320 mmHg
pO% culture is a special case, made up of a true m and a biosynthetic energy rate
constant. Cell division was inhibited during the interval selected, but the cell size
increased. It is also possible that the actual maintenance requirement of the cell was
increased by the need to maintain itself in a partially reduced state in a highly oxidizing
atmosphere.
For the subsequent discussion, it will be assumed that
m = 1*7 x io~ u moles ATP/cell/day,
A = 2-3 x 10-11 moles ATP/cell.
Table 3. Estimates of the maintenance energy rate constant (m) from
stationary growth phase energy generation
Culture pOa (mmHg)
Time interval (days)
i o " u moles ATP/cell
i-6
2-0
1-9
12
o-8
2-O
i6o
0-9
2-4
320
no pO% control
2-O
i-o
3°
2-0
DISCUSSION
It has been found that the Y ATr of LS cells closely approximates the values
reported for bacterial cells. This observation indicates that the over-all efficiency of
energy utilization is identical in widely different organisms which would seem to
illustrate similarities underlying biological processes as a whole. However, when the
distribution of energy between biosynthesis and maintenance is considered and
the absolute values are estimated, it can be shown that the correspondence of YATP
values for bacterial and animal cells is probably fortuitous and, rather than illustrating
the unity of metabolic processes, it hides some significant differences.
Energy required for cell syntJiesis
In equation (5) the term fiA is the specific rate of energy utilization for biosynthesis.
The average time for the synthesis of a new cell is the mean generation time which
is numerically equal to In2//t. Thus the mean value for the energy required to synthesize one cell is /iA\r\2J/j. = A In2 = i-6 x io~ u moles of ATP/cell.
Paul (1965) estimated that the minimum ATP requirement for the synthesis of
a single L cell was 0-87 x io~ u moles (including turnover of protein and nucleic
acid, but assuming that messenger RNA is conserved). Paul's value is increased to
1-15 x io~ n moles ATP/cell if his calculation is repeated using the cell dry weight
found in the present work (i.e. 6-6 x io" 10 g/cell rather than 5-0 x io" 10 g/cell).
Hence there is good agreement between the purely theoretical figure and that derived
from the experimental data.
The energy required to synthesize r o g dry weight of cells is the biosynthetic
41-2
652
D. G. Kilburn, M. D. Lilly and F. C. Webb
energy per cell times the number of cells per g, i.e. (i-6 x i o ~ u ) ( i ' 5 x io 9 ) = 0-024
moles ATP. The maximum possible YATP ^ n o energy is used for maintenance is
thus 1/0-024 = 42 g cells/mole ATP.
Maintenance energy
If it is assumed that the weight of a single growing cell increases linearly and that
the maintenance energy is proportional to the cell weight, then during the time in
which a new cell is synthesized maintenance energy must be provided on the average
for 1-5 cells. If the doubling time is 1-15 days, the maintenance expenditure in the
net synthesis of one cell is
( I# S) ( I > I S) ( I - 7 x JO"11) = 2-9 x i o ~ u moles ATP.
On this basis the net synthesis of 1 g dry weight of cells requires 0-044 moles A T P
for maintenance functions.
Over-all cell yield
The total A T P required during the synthesis of 1 g dry weight of cells is the
sum of the maintenance energy and biosynthetic energy consumed during the time
taken for synthesis, i.e. 0-024 + 0-044 = 0-068 moles ATP/g cells. The YATP is
therefore 1/0-068 = 14-7 g cells/mole ATP, which is consistent with the experimental
values (Tables 1, 2).
Table 4. Comparison of maintenance energy requirements
Organism
Aerobacter aerogenes
Pemcillium chrysogenum
Mouse LS cells
moles ATP/g
dry wt./day
0-4
o-n
0-044
Assumed moles
ATP/mole glucose
30
38
38
Reference
Pirt (1965)
Righelato et al. (1968)
Present work
In Table 4 the specific maintenance energy requirement of mouse LS cells is
compared with values given in the literature for Aerobacter aerogenes and Penicillium
chrysogenum. The maintenance energy of the bacterium is about 4 times that of the
mould and about 10 times that of the animal cell. This seems reasonable considering
the higher surface area per g of bacteria which would increase the energy needed to
maintain concentration gradients.
Although the absolute value of the maintenance energy for bacteria is higher than
for animal cells, bacteria use a smaller proportion of their total energy for maintenance.
The proportion of the total energy generated that is expended in maintenance will
depend on the specific growth rate, and will be smallest at the highest /*. From the
values calculated earlier for LS cells growing at /.i = o-6o day" 1 , the maintenance
energy represents
—^t(ioo) = 65% of the total energy expenditure.
Energetics of mammalian cell growth
653
From the information given by Pirt (1965), it can be calculated that at a specific
growth rate of 0-5 h"1 (i.e. near the maximum), the maintenance energy of Aerobacter
cloacae represents 7 % of the total energy consumption.
The reason for this difference in maintenance expenditure between animal cells
and bacteria arises, of course, from the higher growth rate of bacteria. Although
the magnitude of the animal cell maintenance energy is smaller, it must be expended
over a much longer time. If the growth rate of a bacterium could be slowed to that
of an animal cell, its maintenance energy would consume almost 90% of the available
energy.
The biosynthetic energy requirement of bacteria can be calculated from the
YATP (i.e. 10-5 g dry wt/mole ATP). Assuming that 90% of the YATV is biosynthetic
energy, the ATP (biosynthesis) is 0-085 mole ATP/g dry wt.
Righelato, Trinci, Pirt & Peat (1968) determined the biosynthetic component of
Penicillium chrysogenum in terms of oxygen uptake. If a phosphorylation ratio (P/O)
of 3 is assumed, this is equivalent to 0-12 moles ATP per g dry weight or approximately
the same value as calculated for bacteria. For LS cells, the ATP (biosynthesis) is
0-024 mole ATP/g dry wt. Thus bacteria and moulds require about 4 times the
energy used by animal cells to synthesize cell material. In view of this it is surprising
that the F A T P values are almost identical. It appears that the higher maintenance
expenditure of animal cells compensates for their energy advantage in biosynthesis.
The apparent inefficiency of biosynthesis in bacteria and moulds might arise from
a higher turnover rate of constituents such as m-RNA. Messengers in higher organisms
are thought to be quite stable; once the m-RNA ribosome complex is formed,
proteins may be turned out continuously—perhaps for days. The biosynthetic energy
requirement found for LS cells is consistent with m-RNA conservation. In bacteria,
however, m-RNA is probably very unstable with a half-life of at most several minutes
(Mahler & Cordes, 1966). While at first sight this seems to account for the inconsistency between the biosynthetic requirements of lower and higher organisms, the
work of Salser, Janin & Levinthal (1968) indicates that despite their short life
bacterial messengers are read repeatedly (30—60 times) and their resynthesis represents
only a small part of the total energy expended in protein synthesis. One must thus
seek some other explanation for the large biosynthetic energy requirement of bacteria.
It is conceivable that bacteria waste more ATP than animal cells because of some
growth-associated, but unproductive, ATPase system. Alternatively, bacteria may
expend a substantial amount of energy on active transport of monomers which,
because of the favourable concentration gradients and low rate of demand, can
enter animal cells by diffusion without the need of energy expenditure.
REFERENCES
BAUCHOP, T. & ELSDEN, S. R. (i960). The growth of microorganisms in relation to their
energy supply. J. gen. Microbiol. 23, 457-469.
GUNSALUS, I. C. & SHUSTER, C. U. (1961). Energy-yielding metabolism in bacteria. In The
Bacteria, vol. 2 (ed. I. C. Gunsalus & R. Y. Stanier), pp. 1-58. New York: Academic Press.
654
D
-
G
- Kilburn, M. D. Lilly and F. C. Webb
D. G., LILLY, M D. SELF. D. A. & WEBB, F. C. (1968). The effect of dissolved
oxygen partial pressure on the growth and carbohydrate metabolism of mouse LS cells.
J. 'CM Sci. 4, 25-37KILBURN, D. G. & WEBB, F. C. (1968). The cultivation of animal cells at controlled dissolved
oxygen partial pressure. Biotedinol. Bioeng 10, 801-814.
MAHLER, H. R. & CORDES, E. H. (1966). Biological Chemistry, pp. 787-795. New York:
Harper & Row.
MARR, A. G., NILSON, E. H. & CLARK, D. J. (1963). The maintenance requirement of Escherichia coli. Ann. N.Y. Acad. Sci. 102, 536-548.
PAUL, J. (1965). Carbohydrate and energy metabolism. In Cells and Tissues in Culture, vol. 1
(ed. E. N. Willmer), pp. 239-276. New York: Academic Press.
PIRT, S. J. (1965). The maintenance energy of bacteria in growing cultures. Proc. R. Soc.
B 163, 224-231.
RICHELATO, R. C, TRINCI, A. P. J., PIRT, S. J. & PEAT, A. (1968). The influence of maintenance
energy and growth rate on the metabolic activity, morphology and conidiation of Penicillium
KILBURN,
chrysogenum. J. gen. Microbiol. 50, 399-412.
W., JANIN, J. & LEVINTHAL, C. (1968). Measurement of the unstable RNA in exponentially growing cultures of Bacillus subtilis and Escherichia coli. J. vwlec. Biol. 31, 237-266.
SENEZ, J. C. (1962). Some considerations on the energetics of bacterial growth. Bad. Rev.
26, 9S-IO7(Received 10 October 1968)
SALSER,