Institut National de la Santé et de la Recherche Médicale, Faculté de Pharmacie, Université de Paris XI, 92296 Châtenay-Malabry, France
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ABSTRACT |
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The effect of carbonyl
cyanide-m-chlorophenylhydrazone (CCCP)
on Cl uptake across the
brush-border membrane (BBM) was quantified using
36Cl and BBM vesicles from guinea
pig ileum. CCCP inhibited only partially both the pH gradient-activated
Cl
uptake and
Cl
/Cl
exchange activities present in these vesicles. In contrast, CCCP had no
effect on the initial (2-30 s) decay rate of an imposed proton gradient, as determined using the pH-sensitive fluorophore pyranine. Taken together, these results strongly indicate that the main
action of CCCP does not consist of dissipating any imposed pH gradient
but rather in inhibiting directly the pH gradient-activated Cl
uptake and
Cl
/Cl
exchange activities characterizing the intestinal BBM. Because these
two activities can be explained in terms of a single (homogeneous) random, nonobligatory two-site
Cl
-H+
symporter, in which
Cl
/Cl
exchange occurs by counterflow [F. Alvarado and M. Vasseur.
Am. J. Physiol. 271 (Cell Physiol. 40): C1612-C1628,
1996], we developed a new, more general three-site symport model
that fully explains the Cl
uptake inhibitions caused by CCCP. This new model postulates the
existence of a third, allosteric, inhibitory CCCP-binding site separate
from either of the two substrate-binding sites of the
Cl
-H+
symporter, the Cl
-binding
and the H+-binding sites. Finally,
we show that, to explain the partial inhibitions observed, it is
necessary to postulate that all the substrate-bound carrier complexes,
=C-S, I=C-S, A=C-S, and IA=C-S, where C is carrier, I is inhibitor, S
is substrate, and A is activator, can form and be translocated.
chloride transport; carbonyl cyanide-m-chlorophenylhydrazone; chloride ion; hydrogen ion
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INTRODUCTION |
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CARBONYL cyanide-m-chlorophenylhydrazone (CCCP) has long been classified as an uncoupler. By definition, uncouplers increase the proton permeability of the mitochondrial membrane, thereby preventing formation of the proton gradients postulated to be the energy source for ATP synthesis from ADP and phosphate, according to Mitchell's chemiosmotic coupling hypothesis for oxidative phosphorylation (7, 12). CCCP is a weak organic acid thought to act as a classic proton carrier, interacting with protons according to a monomolecular mechanism whereby CCCP and H+ cross the mitochondrial membrane in the neutral, undissociated acid form, CCCP-H. However true, these facts have been unduly generalized to other membrane systems, and this is why CCCP is presently generally regarded, without further evidence substantiating the generalization, as a pure protonophore capable of rapidly dissipating pH gradients across practically any biological membrane, provided, of course, that the appropriate counterions are present.
However, as first pointed out by Bakker et al. (4), the effectiveness of uncouplers may vary considerably, depending on the nature of the membrane, so that indiscriminate generalization of the CCCP effects on mitochondria to other membrane systems appears to be unwarranted.
The present paper concerns the effect of CCCP on pH gradient-activated
Cl uptake across the ileal
brush-border membrane (BBM). As shown previously, this
Cl
uptake involves a
Cl
-H+
symporter that is strongly inhibited by CCCP (3, 17). The observation
that this inhibition occurs in both the absence and presence of
short-circuiting conditions suggested that CCCP may act not only
indirectly, by facilitating dissipation of an imposed pH gradient, but
also, perhaps mainly, by directly inhibiting the
Cl
-H+
symporter (see Refs. 8 and 17). Up to now, a clear-cut explanation of
the mechanism (or mechanisms) involved in CCCP inhibition has been
lacking. The present work, specifically addressing this question, is
based on the premise that a random, nonobligatory
Cl
-H+
symporter can adequately explain both the pH gradient-dependent Cl
uptake and the
Cl
/Cl
exchange activities that characterize the BBM (see Ref. 3). If the main
action of CCCP is to act directly on the
Cl
-H+
symporter, and not indirectly by dissipating an imposed pH gradient, then it should be expected that, in the absence of a pH gradient, both
Cl
uptake and
Cl
/Cl
exchange will be inhibited by CCCP. This proposal was investigated using BBM vesicles from guinea pig ileum.
Cl
uptake was studied as a
function of the extravesicular pH and the
cis
Cl
and CCCP concentrations,
in both the absence and presence of trans
Cl
. The results upheld the
hypothesis that the main action of CCCP is to inhibit
Cl
uptake directly.
A preliminary account of this work has been given (15).
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METHODS |
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Materials
H36Cl (0.4 mCi/mmol; Amersham, Arlington Heights, IL) was neutralized with tris(hydroxymethyl)aminomethane base before use. CCCP, valinomycin, and Triton X-100 were from Sigma (St. Louis, MO); tetramethylammonium hydroxide pentahydrate (TMA) was from Aldrich (Milwaukee, WI); and pyranine was from Eastman Kodak (Rochester, NY). All other chemicals were also of the highest purity available.Membrane Vesicle Preparation and Transport Assay
After they were stunned, guinea pigs were killed by cervical dislocation, and BBM vesicles were prepared as described (14). Transport was measured using a rapid filtration technique (9), with 36Cl as the substrate. Initial uptake rate measurements (2 s) were performed using a short-time incubation apparatus (Innovativ Labor, Zürich, Switzerland) in a constant-temperature room at 23 ± 2°C, as described (17). Similar to valinomycin (17), CCCP dissolved in ethanol was allowed to evaporate to dryness before it was mixed with the membrane vesicle preparation.Results are expressed (6) as either absolute uptakes (nmol/mg membrane
protein) or absolute velocities
(nmol · s1 · mg
membrane protein
1) and
are presented as means ± SD of either representative experiments or
of the pool of several experiments performed with two or more different
membrane preparations. Uptake data were statistically compared by
applying a global one-way analysis of variance (13). Uncorrected
initial absolute entry rates as a function of the cis
Cl
concentration were
fitted by nonlinear least-squares regression analysis to an equation
containing one saturable Michaelian transport system plus a diffusional
component, as described (3). Details on the statistical evaluation of
the kinetic results are given in Table 1.
To test the fit of our data to equations derived from the general
three-site symport model, we used commercial programs such as Multifit
(Day Computing, Cambridge, UK). All calculations were performed using
an Apple Macintosh microcomputer.
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Spectrofluorometrical Studies
Proton fluxes were measured by monitoring changes in the fluorescence intensity of the pH-sensitive dye pyranine previously trapped within the vesicles (17). ![]() |
RESULTS AND DISCUSSION |
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Mixed-Type Inhibitory Effect of CCCP on the
Kinetics of pH Gradient-Dependent
Cl Uptake
The results (Fig. 1 and Table 1) indicate
that the inhibition caused by CCCP is mixed; it involves both an
inhibitory capacity effect and an inhibitory affinity effect, as
indicated by the 69% drop in maximal velocity
(Vmax) and the
167% increase in the apparent Michaelis constant
(KT),
respectively. If CCCP acted solely by facilitating dissipation of the
pH gradient as, for example, trans
K+ is known to do,
Vmax would have
been the only parameter affected (see Ref. 18). Therefore, the above
findings strongly support the interpretation that the main action of
CCCP does not consist of the dissipation of an imposed pH gradient.
Rather, CCCP would act mainly by inhibiting directly the
Cl-H+
symporter. Nevertheless, as such, these results cannot exclude the
possibility that, on top of having a direct effect, CCCP could also
have an indirect effect consisting of at least a partial diminishing of
the pH gradient that constitutes the driving force for
Cl
uphill transport under
these conditions. Further work was therefore performed
to address this question. The results support the conclusion that the
main action of CCCP is indeed direct.
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Effect of CCCP on Cl Influx Rate
Across BBM Vesicles in Both Presence and Absence of Alkaline
pHin Gradients
Effect of CCCP in absence of a pH gradient.
At equilibrium [outside pH
(pHout) = pHin = 5.5], there was a
weak uptake of Cl that
nearly doubled (86% activation) when both the intra- and the
extravesicular pH were increased by 2 pH units (compare Table 2, bottom set of data,
lines
1 and
2). In the presence of 250 µM
CCCP, both these uptakes were strongly inhibited by either 40% at pH = 5.5 or 66% at pH = 7.5. It should be emphasized that, in both cases,
the total Cl
uptake dropped
exactly to the same level (0.04 ± 0.01 nmol · s
1 · mg
protein
1). Because
diffusion is by definition insensitive to inhibition by "regular"
effectors, this result appears to indicate that these uptakes
correspond roughly to those expected from simple physical diffusion. If
this were the case, CCCP inhibition would be complete and all mediated
uptake would be inhibited by CCCP. Alternatively, however, the
possibility exists and has demanded further study that
the diffusion level lies below the line just defined, meaning that CCCP
inhibition might be only partial. One way or another, at this point,
the conclusion already seems inevitable that CCCP inhibits
Cl
uptake both strongly and
directly because, under the present equilibrated pH conditions, CCCP
cannot possibly be said to act by dissipating a nonexisting pH
gradient.
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Effect of CCCP in presence of an alkaline
pHin gradient.
In agreement with previous observations (17), when a pH gradient was
superimposed, for instance, when
pHout/pHin = 5.0/7.5 (Table 2, bottom set of data, line
3), Cl
uptake was strongly stimulated, respectively, by either 657 or 307%,
depending on whether the reference, equilibrated pH, was either 5.5 or
7.5. Again, 250 µM CCCP was strongly inhibitory under these
conditions, but a qualitatively quite meaningful difference became
apparent. In contrast to the results obtained in the absence of a pH
gradient, CCCP inhibition under pH gradient conditions was clearly
partial. The total Cl
uptake rate observed could be decomposed into 64% of a CCCP-sensitive component and 36% of a noninhibitable component, and this last component was clearly greater than zero (0.19 nmol · s
1 · mg
protein
1 vs. 0.04 nmol · s
1 · mg
protein
1 under equilibrated
pH conditions). There is no obvious explanation for the apparent lack
of accord between these results, namely, why inhibition is either
complete or partial in absence and presence, respectively, of a pH
gradient. But, as we show, a closer analysis of the situation proves
that CCCP inhibition is indeed partial under either condition.
Dose-dependent effects of CCCP on
Cl uptake.
To confirm and extend the above observations, the experiment in Table 2
was repeated at variable CCCP concentrations. In both the presence and
absence of a pH gradient (see Fig. 2), CCCP inhibited Cl
uptake in a
concentration-dependent manner. In both cases, a distinct plateau
greater than zero was attained, indicating the existence of partial
inhibition. Again, however, the plateau attained in the presence of a
pH gradient was about five times higher than that observed under
equilibrated pH conditions. To quantify the fraction of
Cl
uptake that is not
inhibitable by CCCP, the results were linearized according to the Inui
and Christensen (10) transformation. From the reciprocal of the
y-axis intercept of the straight lines
obtained (Fig. 2, inset), it was
deduced that ~31 and 35% of the total Cl
uptake at
pH values
of either 0 or 2.5, respectively (where
pH = pHin
pHout), are insensitive to
inhibition by CCCP. From these results, an apparent kinetic diffusion
constant (Kd; for an operational definition of this parameter, see Ref. 6) was also
calculated equal to 13.3 and 63.0 nl · s
1 · mg
protein
1 at
pH values of
either 0 or 2.5, respectively. These
Kd values are
more than 2 and 10 times higher, respectively, than those estimated
previously using a different approach (for further details, see Fig.
7). From the whole set of these results, we conclude that the apparent
diffusion level, which is not constant, does not reflect the true
Cl
physical permeability,
confirming that the inhibition caused by CCCP is indeed
partial. As shown next, two entirely different interpretations of these results can be given, depending on whether the
transport system under investigation is homogeneous or heterogeneous (see Ref. 1).
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Effect of CCCP on
Cl/Cl
Exchange Activity of BBM Vesicles
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Similar to those observed on
zero-trans
Cl uptake, the CCCP effects
on
Cl
/Cl
exchange were also partial. Finally, Fig. 3 further illustrates that
identical uptakes at equilibrium were obtained; i.e., all four curves
in this figure converged after a 2-h incubation period, indicating that
the apparent vesicular volume (or "functional vesicle yield," see
Ref. 5) is not affected by CCCP.
To complement the preceding observations, the experiment in Fig. 3 was
repeated at variable trans
Cl concentrations. The
relevant results (Table 2, bottom set of data) confirm that the rate of
Cl
uptake increases as the
trans
Cl
concentration increases
(see Ref. 17). They further indicate that CCCP inhibits to the same
extent (~68%) all of the
Cl
/Cl
exchange activities observed. As a consequence,
Cl
uptake in the presence
of 250 µM CCCP increases as the
trans Cl
concentration increases.
By dividing this uptake by the substrate concentration (14 mM),
apparent Kd
values were calculated equal to 13.6, 21.4, and 37.9 nl · s
1 · mg
protein
1 at 0, 75, and 200 mM trans
Cl
, respectively. The fact
that the apparent
Kd is not
constant confirms that CCCP inhibition is partial even when
pH = 0.
Effect of CCCP on Cl Efflux at
Equilibrated pH
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Absence of Effect of CCCP on Initial Decay Rate of Alkaline pHin Gradients Across the BBM: Pyranine Experiments
Vesicles charged with the pH-sensitive fluorophore pyranine were used to assay for H+ fluxes in the presence and absence of CCCP under appropriate conditions (see Ref. 17 for rationale of technique). In a first series of experiments (Fig. 5, curves a-h), vesicles charged with a pH 7.5 buffer supplemented with 200 mM TMA gluconate were used. The extravesicular medium contained the same buffer at pH 6.0, but the TMA gluconate was substituted or not with other salts, as discussed below. The time-dependent drop in pyranine fluorescence (intravesicular acidification) was used to monitor the rate of proton gradient decay. Typically, all decay curves were characterized by a rapid drop from the initial pH 7.5 value to a lower level (pH 6.8 in experiments in Fig. 5), representing the practically instantaneous neutralization of extravesicular pyranine bound to the outer vesicle surface. This rapid initial phase was then followed by the true pH gradient decay, consisting of a slower fluorescence decrease toward the limiting equilibrium value (pHin = pHout) determined at the end of each run by lysing the vesicles with Triton X-100.
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The rate of spontaneous proton gradient decay is given in Fig. 5,
curves c and
d, where the vesicles were
equilibrated with TMA gluconate. This rate strongly increased when the
external gluconate was substituted by
Cl
(curves
g and
h), as expected from the known
existence of
Cl
-H+
symport activity in these membranes. In contrast, when the external TMA
was substituted by K+, the decay
rate slowed down significantly (curves
a and
b), indicating operation of an
already described
K+/H+
antiport activity (17). When the TMA gluconate was substituted by KCl,
an intermediate result was obtained
(curves
e and
f) in accord with the previous
observation that the effects of K+
(intravesicular alkalinization) and
Cl
(acidification) tend to
cancel each other, although the effect of
Cl
is stronger than that of
K+ (17).
A statistical analysis of these results indicates that CCCP does not
significantly modify the rates of proton gradient decay just described,
because for each pair of curves (a vs.
b and so on), the results were
indistinguishable during the first 30 s. It was only at longer times
that significant accelerations caused by CCCP on the proton decay
curves became apparent, namely, after either 30 s (TMA chloride), 60 s
(TMA gluconate and KCl), or 110 s (potassium gluconate). From these
data, we conclude that, although CCCP may behave as a protonophore in
these vesicles, its effects are weak and rather slow in the conditions
of our experiments. On the other hand, the results confirm our earlier
conclusion (17) that the
Cl-H+
symport and
K+/H+
antiport activities characterizing the intestinal BBM are both electroneutral.
One comment appears to be necessary here to explain why, contrary to
widespread belief, CCCP does not behave as a strong protonophore in the
present experiments. In principle, the 72 µM CCCP concentration used
is appropriate because it is well above the level at which the CCCP
inhibitory effect on Cl
uptake reaches its maximum (see Fig. 2). One explanation for this
weakness might be the fact that to collapse a pH gradient, CCCP
requires the presence of a permeable counterion, such as a cation in
the trans side or an anion in the
cis side of the membrane. The ions
used in our experiments are not effective in this regard, probably due
to the low ionic permeability characterizing the BBM (17).
Dwelling further on this question, we performed the following experiment (Fig. 5, curve i). Pyranine-loaded vesicles were prepared in which the intravesicular TMA gluconate had been substituted by potassium gluconate. It was expected that trans K+ would act as a counterion for H+, thereby permitting demonstration of the dissipation of the imposed pH gradient by CCCP. But the experiment proved to be inconclusive, due to the fact that intravesicular K+ causes strong intravesicular acidification via the K+/H+ antiport activity previously demonstrated (18). The proton gradient decay rate taking place under such conditions is so large that no further acceleration could be observed on addition of CCCP.
In summary, independent of the possible effectiveness of CCCP as a
protonophore in isolated intestinal brush-border vesicles, our
experiments indicate that in the short time intervals (2 s) used in the
present study of Cl uptake
kinetics, CCCP does not significantly modify the imposed pH gradient.
Therefore, CCCP does not act indirectly by dissipating any pH gradient
but rather acts as a direct inhibitor of the
Cl
-H+
symport activity of these membranes.
Is Cl Uptake Inhibition by CCCP
Partial or Total?
This new approach was found, as we describe. It consisted in developing
a kinetic model and equations that, by fitting to our data by nonlinear
regression analysis, have allowed for a quantitative distinction
between the physical diffusion level and a CCCP-insensitive
Cl uptake
component. The argument is that, if this level was
found to be higher than that of the diffusion, then the conclusion
would be warranted that CCCP inhibition was indeed partial. This would mean that all of our results are open to rationalization in terms of a
single, coherent theoretical model valid in both the absence and
presence of a pH gradient.
This new kinetic model is schematized in Fig. 6. In the remainder of the RESULTS AND DISCUSSION section, we quantitatively test our experimental data using equations arising from this model, the kinetic implications of which are fully developed in the APPENDIX.
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Definition and Testing of a Three-Site Symport Model That Can Fully
Explain the Partial Inhibitions of
Cl Uptake Caused by CCCP
This model gives rise to a general equation (Eq. A1 in APPENDIX) that, in the absence of any restriction, corresponds to the full, random, nonobligatory model (Table 4, submodel 1), in which all the rate constants involved are assumed to have values greater than zero. In addition to this general model, other submodels can be defined that are also capable of fitting our results, as discussed in the APPENDIX (e.g., Table 4, submodels 3 and 4). But these are special cases, the possible existence of which does not modify the fact that submodel 1 is the simplest imaginable and suffices to fully explain our results. The key point is that of all possible substrate (S)-bound carrier (C) complexes (i.e., all those complexes giving rise to transport), the inhibitor (I)-bound ternary (I=C-S) and quaternary (IA=C-S, where A is activator) complexes must be postulated to both be able to form and be mobile, meaning that the rate constants p and q both need to be greater than zero. As explained in the APPENDIX, the possible formation and translocation of other I-bound complexes have no relevance to the question posed in this article, the mechanism of CCCP inhibition.
To verify the agreement of our results with the preceding
postulates, we performed a nonlinear regression analysis of the data in
Fig. 2 to test the fit of
Eq.
A1 to our CCCP inhibition results. The
procedure used is described in Table 3, in
which the resulting kinetic parameters are listed. To facilitate the iteration procedure, before each run was performed, the apparent Kd was fixed to a
reasonable value, namely, 6 nl · s1 · mg
protein
1, which is the
average value of a series of
Kd control
measurements (see Ref. 3) estimated from the limiting slope of
Cl
saturation curves
performed with different batches but the same type of guinea pig BBM
vesicles used in the present work. With the use of these parameters and
Eq.
A1, the theoretical curves in Fig.
7 were computed. The fits are excellent,
which is both evident to the naked eye and supported by the correlation
coefficient values that are practically equal to one for both pH
gradient conditions studied (Table 3). We conclude that the
three-site model in Fig. 6 (and, in particular,
submodel
1 in Table
4) fully explains our CCCP
results.
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Further comment on the meaning of the theoretical curves in Fig. 7
seems warranted here. The two components of
Eq.
A1 can be regarded as representing two
distinct pathways for
Cl uptake, even when
both involve the same molecular entity, the three-site symport
carrier. We begin by considering the second pathway, represented
by the non-Michaelian, convex term of the equation. Its net rate
is highest in the absence of CCCP but decreases hyperbolically to
approach zero at saturating [CCCP]. Thus CCCP behaves here
as a full inhibitor.
In contrast, as concerns the first pathway, CCCP looks like an
activator here because, in the absence of CCCP, the reaction rate is
zero but increases hyperbolically as [CCCP] increases to
reach a constant, limiting value equal to
V1I,o. For
submodels 1, 3,
and 4 (Table 4), the
V1I,o parameter
is by definition greater than zero (see
Eq.
A2). This is, of course, the reason
why CCCP inhibition is partial. At saturating [CCCP], the
overall Cl transport rate
cannot equal zero.
An identical conclusion is reached by considering the results in terms
of individual carrier-substrate complexes. The quantitative participation of each of the two pathways to the total
Cl influx rate will depend
on the outside inhibitor concentration ([I]o) at each given
value of outside and inside hydrogen ion concentration
([H]o and
[H]i, respectively)
and outside and inside substrate concentration
([S]o and
[S]i, respectively).
Thus, for instance, Cl
uptake via both the =C-S and the A=C-S complexes will predominate in
the absence of [I]o
(see Eqs.
A1 and A3). As
[I]o increases, fluxes
via these two complexes will decrease (Fig. 7,
curve
c2), whereas fluxes via the I=C-S-
and IA=C-S- complexes will increase (curve
c1). It is at high
[I]o that fluxes via
these last two complexes will predominate
(Eqs.
A1 and A2). Again, the quantitative participation of the various fluxes to either pathway, involving either
the simple Michaelian or the non-Michaelian components, will depend on
the relative values of
[H]o and
[S]i. At
pHout = 7.5, fluxes via either the
=C-S (curve
c2) or I=C-S- pathways (curve
c1) will predominate [see
Eq.
A3 as outside activator concentration ([A]o) tends to 0 and Eq.
A6, respectively]. In contrast,
at an acidic pHout of 5.0, fluxes
via either the A=C-S (curve
c2) or the IA=C-S-
(curve
c1) will predominate (see
Eq.
A3 as
[A]o tends to infinity
and Eq.
A7, respectively). Finally, Fig. 7
illustrates how, as
[H]o increases, the
overall reaction rate increases, in agreement with the corresponding
increases experienced by each V1I,o and
V2I,o (see
Table 3).
Concluding Remarks
The results presented here permit the conclusion that the mixed-type inhibition of pH gradient-activated Cl ![]() |
APPENDIX |
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General
Cl-H+
Symport Model
Symport Model With an Additional, Inhibitory CCCP-Binding Site
Symport models have already been developed that explicitly consider inhibition. For instance, Turner and Silverman (16) have defined a random, nonobligatory symport model in which binding of the inhibitor and the substrate are mutually exclusive; i.e., they both compete for the same binding site. Furthermore, both the binary complex (I-C-) and the ternary complex (I-C-A) have been assumed not to be mobile. But such a model (that nevertheless can be assimilated to one of the submodels of our general model, e.g., Table 4, submodel 8) is not useful for our present purposes for two main reasons. As defined by Turner and Silverman, I is a competitive inhibitor, and therefore it can cause full inhibition. In contrast, in our BBM ClTo meet this need, we have developed the more general, three-site symport model illustrated in Fig. 6. The key difference between the two models is that, on top of the S- and A-binding sites, the new model postulates the existence of a third, CCCP-specific site. Nevertheless, the new model is formally identical to the original one of Alvarado and Mahmood (2), in which an allosteric modifier can be imagined to act either as an activator (A in the present model, which we have previously defined to be H+) or an inhibitor (I), which is CCCP.
Seven instead of three specific complexes are therefore possible, namely, three binary complexes, A=C-, I=C-, and =C-S; three ternary complexes, A=C-S, I=C-S, and IA=C-; plus a quaternary complex, IA=C-S. To simplify the model's representation and the writing of equations, the three-site carrier (=C-) is drawn only in one dimension, as shown. In effect, to avoid a three-dimensional representation, at the same time indicating that A and I do not bind to the same site, the symbol "=" (which for simplicity is not illustrated in Fig. 6) is used here to suggest the existence of two independent binding sites for A and I, respectively, on the left side of the symbol C. As was the case with the two-site symport model, we assume that all carrier-bound complexes are mobile, meaning that the three-site model remains, by definition, random and nonobligatory.
Rate Equation as a Function of [I]o
We have applied a series of assumptions, similar to those defined earlier for the two-site symport model (3), to obtain a relatively simple set of kinetic equations describing the general three-site symport model in Fig. 6. The key equation concerns the initial rate of S influx (v) as a function of the cis inhibitor concentration, [I]o
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(A1) |
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(A2) |
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(A3) |
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(A4) |
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In Eq. A1, v represents the sum of two hyperbolas, namely, one that is Michaelian (concave) and involves the parameters V1I,o and KI,o and a second (convex) that involves V2I,o and KI,o. As can be seen, Eq. A1 explains fully why CCCP inhibition is partial. Because as [I]o increases, v will tend to V1I,o and the limiting value of v can never be zero.
Nevertheless, for completeness, a series of possible variants of
Eq.
A1 have been considered and are listed
in Table 4. The most general case is represented by the full,
nonobligatory model (submodel
1), in which the ternary (I=C-S-)
and the quaternary (IA=C-S-) complexes are both mobile
(p and
q both >0). Similar kinetic behavior
will be exhibited by those submodels in which p and/or
q have positive values independent of
the absence or presence of the I=C- and IA=C- complexes and with or
without slippage (l and
m both 0). This is because here the
numerator (N) in V1I,o has a
finite value (Table 4, submodels
3, 4,
and
9 - 14). To the contrary, in models in which the
p and
q constants equal zero, the N
parameter will be zero (and therefore
V1I,o = 0), so
that Eq.
A1 will simplify to a (simple) convex
hyperbola. Thus, for the obligatory model and its four possible
submodels (Table 4, submodels
5 - 8),
the inhibition will be total, because when V1I,o = 0, v will tend to zero as
[I]o tends to
infinity.
It seems evident from the above considerations that partial inhibition
is the necessary consequence of the presence of a
Michaelian component in Eq.
A1 whose limiting value (as
[I]o
) is by definition greater than zero. In effect, if we
assume that [I]o
, it is clear that the function
v = f([I]o)
will tend to
V1I,o, which itself depends on
po and/or
qo, and,
furthermore, appears to be a complex function of each
[A]o,
[A]i,
[I]i, and
[S]i (see
Eqs. A5a-A5c).
However, among those models in which
Eq.
A1 applies, two submodels can be
readily rejected (see Table 4,
submodels
13 and
14) because, in both cases,
V1I,o is
independent of [A]o. This result is incompatible with our data indicating the limiting value
of Cl
uptake at very high
CCCP concentration to increase as the
pHout decreases
from 7.5 to 5.0 in presence of a constant
pHin of 7.5 (Fig. 2).
Another question worthy of consideration here is whether one or both of the rate constants in Eq. A2 have positive values. To answer that question, we derived the limiting values of V1I,o when [A]o and/or [S]i tend to either zero or infinity. One difficulty could arise from the fact that [A]o represents a proton concentration that cannot have values of either zero or infinity. Nevertheless, mathematically speaking, the approximation is warranted that, in the present experiments, zero and infinity [H+] can be thought to correspond in practice to pH values of 7.5 and 5.0, respectively (3). For the general three-site model, the limiting values of V1I,o as [A]o tends to either zero or infinity are given by
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(A6) |
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(A7) |
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(A8) |
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(A9) |
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(A10) |
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ACKNOWLEDGEMENTS |
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We thank Michèle Caüzac and Régine Frangne for excellent technical assistance.
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FOOTNOTES |
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This work was supported in part by the Institut National de la Santé et de la Recherche Médicale, by the Fondation pour la Recherche Médicale, Paris, France, and by the INCO Program of the European Economic Community (grant ERB 3514 PL 950019).
Address for reprint requests: F. Alvarado, INSERM, Faculté de Pharmacie, Université de Paris XI, 5, rue J.-B. Clément, 92296 Châtenay-Malabry, France.
Received 30 June 1997; accepted in final form 3 November 1997.
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