FEMS Microbiology Letters 5 (1979) 357-364
© Copyright Federation of European Microbiological Societies
Published by Elsevier/North-Holland Biomedical Press
357
G E N E R A T I O N O F A N E L E C T R O C H E M I C A L P R O T O N G R A D I E N T I N B A C T E R I A BY T H E
EXCRETION OF METABOLIC END PRODUCTS
PAUL A.M. MICHELS, JAN P.J. MICHELS *, JOHANNES BOONSTRA and WIL N. KONINGS **
Department o f Microbiology, Biological Centre, University o f Groningen, Kerklaan 30, 9 751 NN Haren, and
* Van der Waals Laboratory, University ofAmsterdam, Valckenierstraat 67, 1018 XE Amsterdam, The Netherlands
Received 3 February 1979
1. Introduction
Chemiosmotic phenomena, as postulated by Mitchell
[ 1], play a key role in the energy metabolism of bacterial cells. The chemiosmotic hypothesis is based
upon the assumption that metabolic energy yielding
processes, e.g. electron transfer, lead to the generation of an electrochemical proton gradient (AffH +)
cytoplasmic membrane, which in turn can be used by
the cell to perform energy-consuming processes, such
as active solute transport, ATP-synthesis and flagellar
motion. The electrochemical proton gradient (A/~H+)
consists of an electrical parameter, the membrane potential (A~, interior negative) and a chemical parameter, the pH-gradient (ApH, interior alkaline).
The generation of A~H+ by electron transfer systems has been described in a variety of bacteria. For
instance, Escherichia coli cells develop a Aft of about
- 1 0 0 mV to - 1 5 0 mV [2-4] and a ApH of about
2 pH units during respiration at relatively acid
external pH.
Under anaerobic conditions many facultatively
aerobic bacteria generate a AffH+ in a similar way as
under aerobic conditons, i.e. via electron transfer in
so-called anaerobic electron transfer systems with
fumarate or nitrate as terminal electron acceptor
[5,6]. Direct evidence for the generation of a AffH+
coupled to anaerobic electron transfer systems was
obtained by studies with membrane vesicles from
E. coli, induced for nitrate respiration or the
fumarate reductase system [7,8]. In phototrophic
** To whom reprint requests should be addressed.
bacteria light-induced cyclic electron transfer results
in the generation of an electrochemical proton
gradient [9].
According to the chemiosmotic hypothesis not
only electron transfer-linked proton translocation but
also ATP hydrolysis via the membrane-bound Ca 2+,
Mg2+-ATPase would lead to the generation of a
AffH+. Evidence in favour of this idea has been obtained in glycolysing cells of Streptococcus faecalis
and S. lactis [10] and of ClostrMium pasteurianum
[11 ]. Furthermore, it has been demonstrated with
a l p nuclear magnetic resonance that E. coli develops
a ApH by ATP hydrolysis [12]. These observations
and results from studies with isolated membrane
preparations, leave no doubt about the proton translocating capacity of ATPase. However, the contribution of ATP-hydrolysis in the generation of a A~'H+,
under physiological conditions, in strictly and facultatively aerobic bacteria seems to be limited since
whole cells and membrane vesicles from E. coli,
grown under strictly anaerobic conditions in the
absence of exogenous electron acceptors, can generate
a AffH + by the fumarate reductase system [8].
In strictly fermentative bacteria the fermentation
of 1 mole of glucose yields only 2 moles of ATP. In
these organisms the generation of an electrochemical
proton gradient by ATP-hydrolysis would consume a
considerable fraction of the ATP produced, with the
consequence that less ATP is available for biosynthetic purposes. These considerations suggest that mechanisms other than ATP-hydrolysis, can contribute to
the generation of a AffH+ in these organisms.
358
Besides the possible role of the anaerobic fumarate
reductase systems in strictly anaerobic bacteria [13]
another likely mechanism, is the excretion of protons
in symport with metabolic end products. The chemiosmotic hypothesis postulates that the action of the
carrier protein is completely reversible and symmetrical. Experimental evidence in support of this postulate
has been presented [14]. The driving force for active
transport is the sum of the forces supplied by the
electrochemical proton gradient (A~H+) and the
solute gradient (Ag A). Usually these forces have an
opposite direction. During active transport the
AffH+ will exceed the A~A and solute will accumulate until a steady state level is reached. However,
under conditions of high internal versus external
solute concentration, the A~ A might exceed the
A~'H+ and solute efflux will occur. When this effiux
is accompanied by the efflux of protons and/or
charge, this process can lead to the generation of an
electrochemical proton gradient.
In this paper we have calculated the generation of
the electrochemical proton gradient, during lactate
efflux, for a model cell. It is assumed that during
translocation the carrier-solute-proton complex is
electroneutral [15] and that the proton : solute
stoichiometrv varies with the dissociation state of the
carrier [16].
The results demonstrate that excretion of fermentation products can generate a considerable electrochemical proton gradient and contributes significantly
to the metabolic energy of cells under fermentative
conditions.
2. Description of the system
Calculations are performed for a culture of bacterial cells with the following properties:
(1) Cell dimensions: Cells are spherical with a
diameter of 1/am.
(2) Cell culture: A culture of cells of 1 1, containing 101 x cells, in a medium buffered with 50 mM
phosphate (pK = 7.21). The cell mass does not change
during the period of investigation.
(3) Fermentation and excretion o f fermentation
products: Cells perform a homolactic fermentation of
glucose. The lactate production of the culture was
taken to be 50 gmole/min, corresponding to 5 • 10 - 1 6
in
out
AC
Z H÷
~ CA
J
zH ÷
A-z J
A-z
C ~-
C
H'J
-
~
C-
Fig. 1. Model for t h e m e c h a n i s m of active transport of a
negatively charged solute (A) in bacteria, according to Rottenberg [15]. These symbols used are: A, solute; C, carrier
protein; z, charge o f solute.
mole/min • cell. The intracellular lactate concentration was taken to be 100 mM. Effiux of lactate was
assumed to occur under the influence of a lactate
gradient, via a carrier protein in symport with a
variable number of protons, according to the model
of Rottenberg [15] (Fig. 1). The functional group of
the carrier which is responsible for the change in proton : lactate stoichiometry was taken to have a pK
of 6.8, similar to the pK found for the functional
group of the proline carrier in E coli [16]. The
model of Rottenberg envisages the stoichiometry of
protons : lactate (n) to be only dependent on the
external pH.
(4) A~'H+: The limits of the proton motive force
were taken to be: -0.250 V ~< A~'H+ ~< 0 V. Furthermore, it was postulated that the internal pH cannot
exceed 8, and does not decrease below the external
pH. The in- and external pH values are not allowed to
decrease below 5.
The internal buffer capacity was taken to be 108
H+/cell • pH-unit. This value, which was obtained
from titration experiments with E. coli (unpublished
results), was found to be nearly constant in the pHrange of 5 to 8. Similar values have been reported
[17,181.
The electrical membrane capacity was taken to be
10 -2 F/m 2 [19].
359
(5) Compensatory fluxes: The p r o t o n m o t i v e
force generated during lactate effiux, was c o n s u m e d
b y fluxes o f charge (i = net i n f l u x o f positive charge +
efflux of negative charge ; excluding p r o t o n fluxes)
and p r o t o n influx (j = net p r o t o n influx).
(6) Starting situation; Aft = 0; pHin = p H o u t = 7 ;
lactate c o n c e n t r a t i o n internally 100 mM, externally
0 mM.
3. Mathematical m o d e l
The following e q u a t i o n s were derived to describe
the relation b e t w e e n lactate e x c r e t i o n and the generation o f the A ~ H + (for the e x p l a n a t i o n o f symbols, see
Table 1).
External lactate c o n c e n t r a t i o n is the total lactate
p r o d u c t i o n per culture:
~I(T)N dr
[L]°ut(t) = d
o
V
(1)
/~
A~(t)
{ ( n ( r ) - 1) t(r) - i(r)} A . L
d
(2)
pH-gradient:
ApH = pHin - pHou t
(3)
The change o f the internal p H is d e p e n d e n t on the
H ÷ p r o d u c t i o n during f e r m e n t a t i o n ( - l ) , t h e net
p r o t o n translocation ( n . l - j ) i a n d .the internal buffering
capacity:
pHin(t ) = 7.0 + _f ( n ( r ) - 1} 10- ) - j ( r ) d r
(4)
A.B
o
Changes in the external p H can be described b y
changes in the c o n c e n t r a t i o n s o f H2PO 4- and H P 0 4 2 - ,
caused b y H*-translocation, by means o f the Hasselbalch-Henderson e q u a t i o n :
pHout (t) =
Y[Pi] - / N { n ( T ) }
The m e m b r a n e p o t e n t i a l is d e t e r m i n e d b y the net
charge translocated, divided b y the electrical c a p a c i t y
o f the cell's m e m b r a n e :
dr
C.s
o
o
7.21 + log
(1
-
l(T)
j(7) d r
V
(5)
Y)[Pi] + / N ( n ( v ) }
o
l(T) - - j ( r )
V
TABLE1
E x p l ~ a t i o n o f t h e s y m b o l s u s e d i n t h e mathematicalmodel
Symbol
Explanation
Value
Dimensions
A
B
C
E
F
i
j
K
l
L
n
N
R
s
t
T
v
V
Y
Z
Avogadro's number
intracellular buffer capacity
electrical membrane capacity
elementary charge
constant of Faraday
net influx of positive charge (excluding protons)
net proton influx
dissociation constant of the carrier
rate of lactate production
lactate concentration
transport stoichiometry IV: lactate
number of cells
gas-constant
cell's surface
time
absolute temperature
cell's volume
volume culture
fraction dissociated phosphate buffer at pH 7
2.3 RT/F
6.02 • 1023
108
10-2
1.6 • 10-19
96 500
10- 6.8
5 • 10-16
1011
8.31
3.14 • 10 -12
298
5.3 • 10-16
1
0.32
0.060
molecules • mo1-1
H÷ • pH-unit -1 • cell-1
Farad • m-2
coulomb • charge-1
coulomb • tool-1
charge - min -1 • cell-1
tV • min -1 - cell -1
M
mol • min -1. cell-1
M
_
J • mo1-1 • K-1
m2
min
K
litre
litre
Volts
dr
360
ABH+ = Aq/ -- ZApH
(6)
The stoichiometry 'n' of the proton/lactate symport is determined by the pHout-dependent dissociation of the carrier. This is calculated to be:
n = 1+
K
+
[H ]out + K
(7)
An equilibrium between solute (A) and protongradient is reached when A~'A+ + n A~'H+ = 0 [15].
For a monovalent negative cation, such as lactate,
transported by a dissociable carrier, this equation can
be written as:
Zlog [ L ] i n - ( 1
ILl nut
n)AO +nZApH
(8)
4. Results
4.1. Initial phase o f proton gradient generation
When lactate excretion starts the A@ and ApH
build up as shown in Fig. 2. For this calculation, the
lactate excretion rate was taken to be constant from
the beginning. The Aq/is generated very rapidly and
A,UH+
200
100
.......
/XpH
J
:I:::
Q_
PHo~t
o:1
0:~
0:3
0:~
0:~
time (rain)
Fig. 2. Time course of membrane potential (A¢), pH-gradient
(ApH), electrochemical proton gradient (A~'H+),and the
internal and external pH during initial phase of lactate-proton
effiux.
reaches within milliseconds a membrane potential of
- 2 5 0 inV. The number of translocated protons
responsible for this A@ is so small that no significant
internal pH changes occur during this short period.
The A@ (inside negative) will stimulate the inward
movement of positive ions (and outward movement
of negative charge), for example uptake of potassium
ions or efflux of chloride ions. Discharging of the
membrane by such ion translocations is required to
allow further lactate excretion. The continued lactate
efflux results in an increase of the internal pH, and
consequently in the formation of a ApH. This can
only occur at the expense of the A@, because of the
limits imposed on the A~'H+.
During the initial period of lactate excretion the
lactate gradient and the proton motive force are far
from a thermodynamical equilibrium. The energy of
the lactate gradients exceeds the maximal energy of
- 2 5 0 mV of the proton gradient. If the internal lactate concentration is maintained at 100 mM, the
increase in external lactate concentration by the
excretion of the solute can result in the establishment
of an equilibrium after 0.56 min.
4.2. Relation between lactate gradient and A~H+
The lactate gradient [L] in/[L] o u t reaches a thermodynamical equilibrium with the A~'H+ of --250 mV
consisting of a A~ o f - 1 9 0 mV and a ApH of - 6 0
inV. Further excretion of lactate would decrease the
lactate gradient, and the lactate gradient would
become smaller than the proton gradient. Consequently the carrier-mediated lactate effiux would
stop. Continuous efflux of lactate is only possible
whenthe A~ and/or ApH are decreased. An equilibrium between A~'H+ and A~"L during a constant lactate
production rate can be maintained by an enhanced
influx of charged ions (i) and/or protons (j) (for
example, achieved by ATP-synthesis or active solute
transport). In Figs. 3A and 3B are shown the time
courses of A~, ApH, pHin , pHou t and A~H+ for the
two most extreme conditions. In Fig. 3A the ApH is
decreased by means of H+-influx (j) in order to allow
A~ to be as large as possible. In Fig. 3B the membrane
potential is decreased as much as necessary, via ion
fluxes i, in order to keep ApH as large as possible.
It should be emphasized that under conditions of
maximal proton fluxes (Fig. 3A) ion fluxes have to
361
A
Ap..
.... A ,v
200
200
>
>
E
E
100
lOO
-
At3..
ApH
~pH
pH ,n
7 ......
"1-
-r
O-
pH ,o
6
100
2O0
100
300
co
50
20
10
200
3O0
time (rain)
time (min)
6
co
i
50
,
20
i
10
i
6
[,],o/[L]oo,
[LI,~/[L]ou t
Fig. 3. Time course of the membrane potential (Lx¢), pH-gradient (~pH), electrochemical proton gradient (A~H+), and the
internal and external pH during lactate-proton efflux. The curves were calculated for equilibrium between ~'I-i + and Lx~L. The
curves of Fig. 3A were obtained by taking A¢ as large as possible by reducing ApH, while the curves of Fig. 3B were obtained for
maximal values of ApH (see text).
occur, while under conditions of maximal ion fluxes
(Fig. 3B) protons have to be taken up (see below).
Under both conditions a proton motive force can be
generated during 370 min. After this time an equilibrium cannot be maintained due to the rapid decrease of
the pH. This figure dearly shows that a much higher
A~H+ can be reached when the Aft is allowed to be
maximal, than when ApH is maintained as large as
possible.
4.3. Ion and proton fluxes
The integrated values of the compensatory fluxes i
and j, which occur during the equilibrium situation of
Figs. 3A and 3B are shown in Figs. 4A and 4B. Under
both conditions the fluxes j are nearly the same but
the fluxes i are clearly different. These figures show
that, except for the initial phase of lactate excretion,
ion fluxes i are negligible in comparison to proton
fluxes j.
4.4. Energy yield
Compensatory fluxes of positive charge and protons can be considered as conversion of A~H÷ into
other forms of energy. This enables us to express the
energy yield from the lactate efflux in ATP-equivalents. Based on the assumption that the synthesis of
one molecule ATP requires the uptake of two protons, the additional ATP yield per molecule glucose
metabolised can be calculated. This is shown in Fig. 5.
In the initial phase, during active lactate extrusion the
yield is approx. 0.6 ATP. This yield decreases to zero
at the end of the simulated process. This decrease has
to be ascribed to the decrease of the external pH,
because this pH determines the number of protons
ejected during lactate efflux.
These results demonstrate that, at neutral pH, under the conditions described, excretion of lactate
produced by homolactic fermentation of glucose, can
increase the theoretical ATP yield by about 30%.
362
T
"7"
,
,
--
,
,
-1
- -
2
o
B
D
g
0
3
~=
u
2
\
-1
40
2; . . . .
time (rain)
t
t
Fig. 4. Fluxes o f protons ( f j(r)dr) and cations ( f i(r)dr).
0
o
through the cell membrane. The curves o f Figs. 4A and 4B
are deducted from the data presented in Figs. 3A and 3B,
respectively.
Ln
coJ
> m
"5 o
~2
I
0.6
O]
--~
o
0.4
E-5
E
o2
\
,
100
i
200
i
300
lime (min)
Fig. 5. Energy yield obtained by lactate-proton efflux. The
energy yield is expressed as the additional ATP-equivalents
which can be obtained per molecule glucose metabolized.
5. Discussion
Our calculations demonstrate that excretion of fermentation products might be an important mechanism for the generation of metabolic energy for a
bacterial cell.
In growing cells a considerable fraction of the
metabolic energy is needed for transport of metabolites and ion fluxes (phosphate, Na ÷, K ÷, etc.). Most
or all of energy requirement for these processes
can be supplied by lactic acid efflux. Consequently
more energy generated by substrate level phosphorylation reactions becomes available for biosynthetic
processes.
A utilization of the energy stored in a fermentatior
product gradient, for the cell's energy requirements,
would have the attractive feature that product excretion is not only a mechanism for disposal of metabolic
end-products, but also a form of energy supply.
It has been stated, on the basis of studies with
fluorescent dansylgalactosides in membrane vesicles
ofE. coli, that the membrane potential (outside positive) may facilitate the movement of the negatively
charged unloaded carrier to the outer surface [20].
Our "energy recycling model" would not be consistent with such mechanism. However, recently
Overath et al. [21] attacked the conclusions drawn
from the dansylgalactoside studies, and offered a
completely different explanation. At this moment,
therefore, the mode of response of the unloaded
carrier protein to the A~'H+ or its components has to
be re-assessed.
We have based our model on the production of
lactic acid since this is one of the most common fermentation products. Moreover, lactic acid translocation has been shown to be carrier mediated in several
bacteria [22].
Several simplifications have been made: the [L]in
and the rate of lactate efflux were taken to be constant. Changes in these parameters, however, will not
change the general picture but only affect the time
course of AffH+,ApH or A~ generation (Fig. 3).
Furthermore, the rate and extent of the proton and
ion fluxes were considered to be independent of the
Affu+ or A~.
The maximum possible AffH+ at a given [L]in/
[L]out, has been calculated for two extreme situations, viz. a condition in which the ApH was kept as
large as possible, and a conditon in which the Aft was
maintained at the highest possible value. The A~H +
obtained under both conditions differs considerably.
Under maximal Aqj conditions, the AffH + always
exceeds - 1 5 0 mV, while under maximum ApH conditions the absolute value of the A~'H+ can be as
363
small as 40 inV. The real situation lies, most likely,
between these two extremes, and will depend on the
fluxes of ions and protons across the membrane.
Whatever conditions prevail, the internal pH follows the external pH. When the A~b is kept at a maximum, the internal pH equals the external pH; when
the ApH is kept at a maximum, the pH difference
internally minus externally lies between 0.7 and
1 pH unit. This latter situation most closely resembles the situation found in fermentatively grown cells
ofE. coli [12] orS. faecalis [10].
Under both conditions, the AffH+ collapses when
the internal pH drops below physiological values.
Therefore, in order to maintain a AgH+ for a prolonged period of time, control of the external pH and
removal of external lactate will be required.
The energy yield by excretion of lactic acid via a
carrier protein is determined by the influx of protons,
required for maintaining the AffH+ at a certain value.
The AffH+ is generated by symport of proton(s) with
lactate. Therefore, the yield will depend on the
charge of the carrier. The yield will be higher when (i)
the pK of the carrier is lower (ii) the pH of the medium is higher (iii) the buffer capacity of the medium is
larger.
It is important to note that, at equilibrium, an
increase of the A~'H+ by ATP-hydrolysis will affect
the [L] in/[L] o u t ratio. During lactic acid production
this would mean that the lactate concentration internaUy would increase to very high levels. Only when
the A~H+ consumption is faster than the AffH+ generation by proton-lactate efflux ATP-hydrolysis can
occur without affecting the internal lactate concentration.
A comparable generation of AffH+ will be obtained
during excretion of any other fermentation product,
when the translocation across the membrane is accompanied by the translocation of positive charges and
protons. This will be achieved when a product A z- is
symported with more than z protons. This could
either be symport via a carrier which dissociates in
the physiological pH range (pH 5 - 8 ) , so that the
number of protons symported with the product varies
between z and z + 1, or a constant symport with
more than z protons via a carrier which does not dissociate in the physiological pH range. When efflux of
a product A z- is accompanied with z protons only,
protons and no charge will be translocated. This will
lead to the generation of a pH gradient only. The
energy yield under these conditions will be much
smaller. Such a situation is most likely during excretion of membrane permeable weak acids. Efflux of
only positive charges can also occur but this process
will lead to the generation of a membrane potential
only.
Many organisms will excrete several fermentation
products, in which case efflux of each of these products can contribute to the electrochemical proton
gradient. When the external pH drops below a certain
critical value many bacteria start to excrete neutral
compounds which will prevent further acidification
of the external medium.
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