[28]
STOICHIOMETRY OF COUPLED TRANSPORT
479
tial. This also has the advantage of avoiding the use of K + and valinomycin, which may not be suitable when K + transport is being monitored. Vesicles are suspended in varying LiC1 solutions (1- 50 mM) maintained isotonic with Tfis-HCI to a total concentration of 300 raM; 10 #M ionophore, AST01, in 25/zM histidine, pH 7.0, is added and the maximum absorbance change noted. This ionophore cannot be used in the presence of Na + since there is significant carriage of this cation. 23 An interesting application of the rate of dissipation of this dye signal, the measurement of membrane resistance, has been described which can be applied with all the other potential dye probes. The technique used in the case of the Na+,K+-ATPase was to stop pump activity (e.g., with vanadate) and measure the decay of the signal. If the decay can be described by a single exponential, the rate constant, k, can be obtained. The resistance of the membrane ([~-cm2) is calculated as (6)
Rm = (1/k)Cm
where CI is the capacitance of the membrane ( - 1 aF cm-2). 24 23A. Shanser, D. Samuel, and R. Korenstein, J. Am. Chem. Soc. 105, 3815 (1983). 24H.-J. Apell, and B. Bersch, Biochim. Biophys. Acta 903, 480 (1987).
[28] S t o i c h i o m e t r y o f C o u p l e d T r a n s p o r t S y s t e m s in V e s i c l e s By R. JAMESTURNER
Secondary active transport systems enable cells or organelles to drive the flux of a transported substrate, S, against its electrochemical gradient by coupling the flux of S to that of another solute (referred to here as an "activator"), A, which is moving down its electrochemical gradient. The stoichiometry of a such a coupled transport event is of considerable interest since it plays a major role in the determination of both the concentrating capacity of the cell or organelle for S and the energetic cost of the transport process, i In this chapter I describe the methods which are currently used to determine the stoichiometries of co- and countertransport systems in membrane vesicle preparations. Generally speaking these methods are also applicable to intact cell or organelle preparations, the primary advantage of R. J. Turner, Ann. N.Y. Acad. Sci. 456, 10 (1985).
METHODS IN ENZYMOLOGY, VOL. 191
Copyright © 1990 by Academic Pre~, Inc. All fights of reproduction in any form reserved.
480
KIDNEY
[28]
vesicles being that it is easier to control and modify the intravesicular and extravesicular media. In order to fully appreciate the principles and problems involved in the experimental methods decribed here it is important to understand the thermodynamic basis of coupled transport events. This topic is reviewed briefly below. A more detailed discussion is given in a previous publication. 1 Thermodynamics of Coupled Transport
Basic Principles Consider first, for simplicity, a cell or organelle whose outer membrane contains a cotransport system for S and A, where S is an electroneutral molecule and A is an ion with one positive charge (the general case of a charged substrate and multiple activators is treated at the end of this section). Assume also that there are no other primary or secondary active transport systems for S in the membrane. On thermodynamic grounds it can be shown that the ratio of the intracellular to extracellular substrate concentrations, [Sx]/[So], must obey the following inequality, ln([Sd/[So] ) -< nA[ln([Ao]/[Ad) + FAq//RT]
(la)
or equivalently,
[Sl]/[So] ~-~[([Ao]/[ai])exp(FA~u/RT)] n^
(lb)
where F, R, and T have their usual thermodynamic interpretations, AV = ~Uo-~'i is the transmembrane electrical potential, and n A is the A :S coupling stoichiometry (the number of moles of A translocated per mole of
S via the transporter). The biological significance of Eq. (1) can be best appreciated by considering the situation where ln([Ao]/[Ai] ) + RA¥/RT is maintained at some fixed (positive) value by other systems in the cell (e.g., Na +, K+-ATPase), and where the distribution of S across the membrane has reached a steady state. Equation (l) may then be thought of as a thermodynamic constraint on the steady state concentration gradient of S resulting from its coupled transport with A. Thus the equality in Eq. (1) gives the maximum thermodynamically allowed concentrating capacity of the system for S. In this case the substrate and activator electrochemical gradients will be at thermodynamic equilibrium via the coupled transporter and the net carrier-mediated flux of both will be zero. The extent to which any real system approaches this thermodynamic limit depends on the magnitude of its relevant leak pathways. These may be divided into two distinct classes:
[28]
STOICHIOMETRY OF COUPLED TRANSPORT
481
those that occur via the coupled transporter (internal leaks) and those which do not (external leaks). External leaks include passive diffusion and any mediated transport pathways for the substrate across the membrane in question. Internal leaks arise when the flux of activator and substrate via the carrier is not tightly coupled, that is, when activator translocation without substrate or substrate translocation with a variable number of activator ions (possibly zero) can occur via the transporter. The presence of internal leaks adds a significant complication to stoichiometric determinations since in this case the coupling stoichiometry may vary with experimental conditions. There have, in fact, been several reports in the literature of transporters that apparently display this type of variability. 2 In a system with internal or external leak pathways the flux via the coupled transporter will reach a steady state determined by kinetic as well as thermodynamic factors. This kinetic steady state will necessarily result in a value of [Sd/[So] that is less than that predicted by thermodynamic equilibrium, t
Multiple Activators and Charge Stoichiometry The more general form of F_xl. (1) for multiple activators and charged substrates is given by ln([Sd/[So]) -< ~ n^ln([Aol/[Ai]) + qFAg//RT
(2)
A
where the sum is over all activators, that is, over all solutes co- or countertransported with S via the carrier. Here nA is positive if A is cotransported with S and negative if A is countertransported with S. The charge stoichiometry, q (the number of moles of charge translocated per mole of S via the transporter), is given by q = Zs + ~
nAZA
A
where Zs and ZA are the charges on S and A, respectively. Flux Measurements: T h e Rapid Filtration Technique A variety of methods have been used to monitor transport or transportrelated events in vesicle preparations, but the most commonly applied and generally applicable procedure for studying coupled transport systems is to measure the flux of radiolabeled ligands using the "rapid filtration" technique. In this chapter I discuss mainly experiments employing this tech2 A. A. Eddy, Biochem. Soc. Trans. 8, 271 0980).
482
KIDNEY
[9.8]
nique; however, stoichiometric determinations may equally well be carried out using other methods of flux determination. The basic procedure for the rapid filtration technique as carried out in our laboratory is the following. Vesicles (10-50gl, 1-3 mg protein/ml) are combined with an incubation medium (10- 100 #1) containing radioactively labeled fig,ands (10-100 gCi/ml) and other constitutents as required in a 12 × 75 disposable borosilicate glass test tube. After an appropriate incubation time, 1.5 ml of an ice-cold stop solution is added and the resulting mixture is removed with a Pasteur pipet and applied to a Millipore filter (HAWP, 0.45 gin; Bedford, MA) under light suction. The filter is then quickly washed with a further 4.5 ml of stop solution, placed in an appropriate scintillation cocktail, and counted for radioactivity along with samples of the incubation medium and appropriate standards. Eitlux studies can be carried out in the same way using vesicles preloaded with labeled substrate. The actual volumes, protein concentrations, and isotopic activities employed in a given experiment will depend on the transporter under study as well as on tissue availability and the cost of radiolabeled ligands. The apparatus we employ consists of a flitted glass filter holder (MiUipore XX10 025 02) connected via flexible tubing to a collection bottle and then to a vacuum pump. We typically use Eppendorf series 4700 fixed volume pipets to dispense vesicles and incubation media; however, any pipet with comparable accuracy and reproducibility (both < 1%) is acceptable. If incubation times of < 5 sec are desired we use the rapid sampling device described by Turner and Moran) A rapid sampling device is also available commercially from Inovativ Labor AG (Adliswil, Switzerland). We have occasionally carried out flux measurements at incubation times of < 2 sec by hand with the aid of a metronome. Owing to the quantitative nature of stoichiometric determinations considerable care is required in the design and performance of experiments in order to avoid the introduction of artifactual or systematic errors. The importance of choosing an appropriate stop solution to prevent isotope efllux or influx during the stopping and washing procedure and the necessity of measuring initial rates of transport have been stressed earlier? Also, when working with coupled transport processes that are electrogenic, variations in membrane potential with experimental conditions must be avoided) -5 In our vesicle preparations we typically clamp membrane potentials at the diffusion potential of a permeant anion such as nitrate or thiocyanate or at the potassium diffusion potential using the potassium 3 R. J. Turner and A. Moran, Am. J. Physiol. 242, F406 (1982). 4 R. J. Turner, 3. Membr. Biol. 76, 1 (1983). 5 U. Hopfer, Am. J. Physiol. 254, F89 (1978).
[28]
STOICHIOMETRY OF COU ,-LED TRANSPORT
483
ionophore valinomycin (2.5-12.5 #g/mg membrane protein). Further discussion of this problem and methods for testing the effectiveness of the above voltage clamping procedures are given in previous publications. 3,4,6,7 Methods of Measuring Stiochiometry Four methods have been devised for measuring the stoichiometry of coupled transport systems. Some experimentation may be required to determine the range of experimental conditions (if any) under which a given method may be successfully performed on a particular carrier. For this reason it is advisable to have accumulated a good experimental data base on the system under study before attempting stoichiometric measurements. Useful information includes the time course of uptake, the magnitude of specific vs nonspecific uptake, the degree of substrate binding and metabolism by the vesicles, and the dependence of uptake on substrate and activator concentrations (the latter is actually a stoichiometric determination--see Method 2, below). It is also important to ensure that all activator species have been identified; a number of secondary active transporters have recently been shown to be coupled to multiple activators (see, e.g., Refs. 6-8). All four methods of stoichiometric determination are equally applicable to cotransport and countertransport systems. In every case the roles of substrate and activator are interchangeable. The use of each method for the determination of both coupling and charge stoichiometries is discussed at appropriate points below.
Method I (Direct Method) The direct method for determining the A: S coupling stoichiometry of a secondary active transport system consists of simultaneously measuring and comparing substrate and activator fluxes via the transporter. There are two ways in which this might be done: (1) by measuring the total transporter-related substrate and activator fluxes (e.g., by measuring fluxes in the presence and absence of a specific inhibitor of the transporter), or (2) by measuring the activator-dependent substrate flux and the substrate-dependent activator flux. For tightly coupled transporters both procedures should give the same result. In the presence of significant internal leak pathways, however, only the former procedure will give the correct coupling stoichiometry since the latter procedure does not take into account 6 y. Fukuhara and R. J. Turner, Am. J. Physiol. 248, F869 (1985). 7 R. J. Turner, J. N. George, and B. J. Baum, J. Membr. Biol. 94, 143 (1986). s R. J. Turner, J. Biol. Chem. 261, 16060 (1986).
KIDNEY
48 4
10.0
[9.8]
a
£
E ~ 5.0
00
50
100 [Na] mM
150
- 150 x 103
150
-IO0 ,z.
,z.
z.
2
rr
u.
50
10170
0
5,0
5O
10.0
Flux (nmol/min.mg protein)
FIG. 1. Initial rate of sodium-dependent succinate uptake into renal outer cortical brush border membrane vesicles measured as a function of sodium concentration. Vesicles were prepared in THM buffer (10 mM HEPES plus 100 mM mannitol buffered with Tris to pH 7.5) containing 600 mM mannitol and 100 mM KSCN. The (isoosmotic) incubation media were THM buffer containing 100 mM KSCN and sufficient p4C]succinate and NaCl to give final extravesicular concentrations of 0.2 and 0-200 mM, respectively. Chofine replaced sodium isoosmotically to obtain the various sodium concentrations studied. Mere-
[28]
STOICHIOMETRY OF COUPLED TRANSPORT
485
uncoupled fluxes via the transporter. The direct method is conceptually the most straightforward and in some ways the most satisfying method of measuring coupling stoichiometries. An electrophysiological version of the direct method has been used by several authors to measure charge stoichiometry in intact epitheliag, t°; however, no attempts to measure substrate flux and charge translocation directly in cell suspensions or vesicle preparations appear to have been attempted.
Method 2 (ActivationMethod) The activation method for determining the A:S stoichiometry of a transport system consists of measuring substrate flux as a function of activator concentration. As discussed below the interpretation of activation method data is considerably more model dependent than the other methods described here. It should also be noted that the activation method is sensitive both to activators that are actually transported with the substrate (energetic activation) and to activators that simply affect substrate flux without being themselves transported (catalytic activation), for example, by binding at a modifier site on the carrier. Thus, whereas the other methods for determining stoichiometries discussed here are sensitive only to transported activators, the activation method provides a measure of the total (catalytic plus energetic) activator involvement in the transport event. For this reason I refer here to the result of an activation method experiment as the A: S stoichiometry rather than the A: S coupling stoichiometry. Note that only transported (energetic) activators are relevant to the thermodynamics of coupled transport [Eqs. (1) and (2)]. A hyperbolic relationship between activator-dependent substrate flux and activator concentration provides good evidence for a 1:1 activator: substrate stoichiometry since this behavior is expected for a 9 E. Frtmter, PfluegersArch. 393, 179 (1982). 1oD. S. Misfeldt and M. J. Sanders, J. Membr. Biol. 70, 191 (1982).
brahe potentials were clamped at zero by the presence of 100 m M KSCN in all solutions and by the addition of 12.5 #g valinomycin/mg protein to the vesicles. (a) A plot of uptake vs sodium concentration. The line drawn through the data points is a fit to Eq. (3) obtained using the nonlinear regression routine NONLIN (Systat, Inc., Evanston, IL). The fit is given by Jm~ = 10.6 - 1.2 nmol/min/mg protein, Ko.5 ffi 54.2 _ 9.3 raM, and n -----2.1 ± 0.4. (b) Plots of flux/[Na] n vs flux for n •ffi I (A), 2 ((3), and 3 ([~), illustrating the way in which data can be fit to Eq. (3) by trial and error. A more quantitative procedure involving linear regression analysis is described in the text. [Redrawn from Y. Fukuhara and R. J. Turner, Am. J. Physiol. 245, F374 (1983).]
486
KIDNEY
[28]
broad class of 1 : l-type models? ,H In this case a plot of flux/[A] vs flux will be linear. In contrast, a sigmoidal dependence of flux on activator concentration as shown in Fig. l a for sodium-dependent succinate transport in renal outer cortical brush border membrane vesicles indicates the involvement of multiple activator ions per substrate translocation event. The most c o m m o n method for interpreting such data is based on analysis in terms of the Hill equationl2: Js = Jtrm[A]n/(K~.5 + [A] n)
(3)
Here Js is the substrate flux, n is the A : S stoichiometry (the "Hill coefficient"), and J ~ and Ko.5 are constants. It can be shown that a tightly coupled transporter with activator:substrate stoichiometry n and strong cooperativity between activator-binding sites will obey such a flux equation. [Note that for n = 1, Eq. (3) reduces to the hyperbolic relationship expected for a l : l system.] In order to get the most information from the activation method it is important to obtain flux data over the widest possible range of activator concentrations. Fluxes at low activator concentrations are particularly important since these often define the sigmoidal portion of the activation curve which identifies and characterizes the involvement of multiple activator ions. Two procedures for analyzing activation method data, based on the Hill equation, are given below. Procedure 1. In this procedure one simply fits the experimental data to Eq. (3) using a least-squares regression or manual method. The line drawn through the data points in Fig. la is a nonlinear least-squares fit obtained using a commercially available nonlinear regression computer program (see figure caption). In carrying out such a fit the points are typically weighted in proportion to the reciprocals of their variances. In our laboratory we frequently employ an alternative to nonlinear least-squares analysis in fitting activation data to Eq. (3). This method takes advantage of the fact that Eq. (3) predicts that a plot of Js/[A] ~ vs Js will be linear. Thus one can search manually for a value of n which results in such a linear plot, as we have done in Fig. lb, or one can carry out a similar search more quantitatively with the aid of a linear least-squares regression routine. This latter procedure is used routinely in our laboratory. 6 We have modified a linear regression program so that it fits a straight line to a Js/[A]" vs Js plot over a range of values of n. The points are weighted in proportion to the reciprocals of the squares of their relative 11R. J. Turner, Biochim. Biophys. Acta 649, 269 (1981). ~2I. H. Segel, "Enzyme Kinetics." Wiley, New York, 1975.
[28]
487
STOICHIOMETRY OF COUPLED TRANSPORT
experimental errors. The best value of n is taken to be the one that minimizes the sum of the squares of the deviations of the experimental points from the calculated regression line. The statistical errors on Jma, and Ko.s are then given directly from the linear least-squares fit and the statistical error on n can be determined using an F test. This procedure was found to give results virtually identical to nonlinear least-squares analysis while requiring only a simpler, more readily available, linear least-squares regression routine. Owing to the rather restrictive assumptions made in deriving the Hill equation (see above) it is unlikely that any real transporter will obey it well. Thus one should expect nonintegral Hill coefficients from the above fitting procedures and/or systematic deviations from linearity on Js/[A]" vs Js plots. In general, the Hill coefficient derived from fitting activation method data to Eq. (3) should be regarded as a lower limit on the A: S stoichiometry. 1 Procedure 2. This procedure is recommended when Jm~ can be accurately determined from the experimental data, i.e., when Js can be measured at activator concentrations which are sufficiently high that saturation is assured. In this case a Hill plot of log[Js/(Jm~- Js)] vs log[A] can be made. For data fitting Eq. (3) such a plot will be linear with slope n. Hill plots for sodium-dependent sulfate transport in renal brush border membrane vesicles at pH 8.0 and pH 6.0 are illustrated in Fig. 2. The linearity of the Hill plot for pH 8.0 with slope 1.02 provides good evidence for a l : 1 sodium: sulfate stoichiometry at this pH while the break in the Hill plot for pH 6.0 may be interpreted as the result of a shift in the sodium: sulfate
+2.0-
+2.0-
PH i = PH 0 = 6.0
PH i = PH0 - 8.0
O-u')O
.l.O-
? +l.O-
cYg mE
f
0.0o~_ ~o -I.Oo J -2.0
0.0-
-1.0-
slope= 1.02 I
o
I
,.o
-2.0 1
l
2.o
LOG
I
o
~
,o
l
l
2.o
[Nal
FIo. 2. Hill plots of the initial rate of sodium-dependent sulfate uptake (J~oi")into renal brush border membrane vesicles measured as a function of sodium concentration. Measurements were made at pH 8.0 equlh~rium (left) and pH 6.0 equilibrium (fight). Jm~ was estimated by extrapolation of a Js/[Na] vs Js plot. (From Abeam and Murer.'3)
488
KIDNEY
[28]
stoichiometry from approximately 1 : 1 to approximately 2: 1 with increasing sodium concentration under these experimental conditions? 3 Given our present (meager) understanding of the kinetics of coupled transport systems a Hill plot is unquestionably the best method for extracting the maximal amount of information from activation method data. I would, however, give two notes of caution. First, because the assumptions made in deriving Eq. (3) are rather restrictive, and because the Hill transformation itself is rather complex, it is not entirely clear what relationship the slope of the Hill plot will bear to the activator: substrate stoichiometry for more realistic flux equations; thus such plots should be interpreted with some caution. This point is discussed in more detail in an earlier publication. ! Second, considerable care should be taken in the determination of Jinx since a small change in this constant can cause a large shift in the Hill plot, especially at high activator concentrations. Indeed it is advisable to test the effects of experimental uncertainties in J ~ on the shape of the Hill plot to be sure that any conclusions reached are not overly dependent on the choice of this parameter. The complex way in which A¢/enters into the kinetic equations of most coupled transport models makes this method very difficult to apply to the determination of charge stoichiometries. To my knowledge no attempts to carry out determinations of this type have been made.
Method 3 (Steady State Method) The steady state method for determining the coupling and charge stoichiometries of a secondary active transport system consists of measuring the steady state substrate gradient generated by the transporter in the presence of known (measured or applied) activator electrochemical gradients. I f the transporter is operating at or close to thermodynamic equilibrium Eq. (2) becomes (the case of a single activator is treated for simplicity) ln([Sd/[So]) = nAln([Ao]/[Ai]) + qFAc//RT
(4)
Thus, for example, n^ can be calculated from the slope of a plot of ln([Sd/[So]) vs ln([Ao]/[Ai]), at constant A~u,and q can be determined in a similar fashion from a plot ofln([Sd/[So]) vs FAc//RTat constant activator chemical gradient. Alternatively, if [Sd/[So], [Ao]/[AI], and A¢/are measured under two or more independent experimental conditions, n^ and q can be calculated from the simultaneous equations resulting from substitution of these numerical values in Eq. (4). Steady state method calculations are particularly simple if measurements can be carded out in the presence 13G. A. Ahearn and H. Murer, J. Membr. Biol. 78, 177 (1984).
[28]
489
STOICHIOMETRY OF COUPLED TRANSPORT
of an activator gradient alone (A~J--0) or an electrical gradient alone [ln([Ao]/[Ad) = 0]. The steady state method is typically applied to whole cells or cell fragments containing an intact activator gradient or membrane potential gradient-generating system. In this case, the relevant gradient can be maintained at a constant value for sufficient time that a steady state substrate gradient can be established and measured.
5L'
4
2
1 I
J
O
In I'SCN-]in rSCN']ou t
I
(o)
I
i
2
or
[C":5"H3+]+,
In [CH3NH~+]ou~(°)
Flo. 3. Steady state dopamine (D) uptake into chromalfin granule ghosts measured as a function of membrane potential ((3) and pH gradient (El). A~ and pH were varied by adding ATP and different amounts of FCCP to ghosts suspended in sucrose and KCI media, respectively (see text). The steady state gradients of radiolabeled dopamine, SCN- and CH3NH3 + were measured after 60 min of incubation at 25 °. The slopes of the lines drawn through the data points are 1.18 +_0.14 (O) and 2.06 +_0.24 (El). (From Knoth et al.15)
490
mONEY
[28]
An example of the determination of the coupling and charge stoichiometries of the H+/dopamine countertransporter in chromaflin granule ghosts is shown in Fig. 3. In these experiments Knoth et al. 14,15were able to generate stable pH and potential gradients independently of one another using an H+-ATPase which is also present in the granule membrane. Briefly, they found that in the absence of permeant ions the H+-ATPase generated a membrane potential but, owing to the high buffering capacity of the ghosts, no pH gradient. The magnitude of the resulting membrane potential could be varied by the addition of different amounts of the H + ionophore FCCP. On the other hand, when the permeant anion C1- was present in the ghost preparation it could follow the actively pumped protons into the ghosts, dissipating the membrane potential and lowering the internal pH. The magnitude of the resulting pH gradient could likewise be varied by adding the uncoupler FCCP. In these experiments the transmembrane potential and pH gradients were monitored using the distribution ratios of radiolabeled thiocyanate and methylamine, respectively)4 The slopes of the lines in Fig. 3 indicate an H +: dopamine coupling stoichiometry of 2: 1 and a charge stoichiometry of 1 : 1. These results are consistent with the exchange of two H + and one dopamine+ by the transporter. As stressed above the stoichiometry derived from the steady state method will be correct only when the transporter is operating at or near thermodynamic equilibrium since it is only then that the ~ sign in Eq. (2) becomes an equality [Eq. (4)]. In the presence of significant internal or external leaks SI/So may deviate significantly from the value predicted by thermodynamic equilibrium and the steady state method will yield an underestimate of the true stoichiometry. The inability of this method to take into account external leak pathways is a potentially serious shortcoming which has received some attention in the literature. L4,t6The presence of contaminating cells or vesicular material can also lead to errors in measurements of relevant substrate and activator gradients, since this material may behave quite differently from the cells or vesicles containing the system under study. Stoichiometries obtained from applications of the steady state method to preparations that cannot maintain activator or electrical gradients over time must be interpreted with some care, since in such preparations the sustained steady state substrate gradient assumed in Eq. (4) never occurs.
14j. Knoth, M. Zallaldan, and D. Njus, Biochemistry 20, 6625 (1981). is j. Knoth, M. Zallakian, and D. Njus, Fed. Proc., Fed. Am. Soc. Exp. Biol. 41, 2742 (1982). t6 I. R. Booth, W. J. Mitchell, and W. A. Hamilton, Biochem. J. 182, 687 (1979).
[28]
STOICHIOMETRY OF COUPLED TRANSPORT
491
Method 4 (Static Head Method) The static head method ~7-2° of determining coupling and charge stoichiometries provides a means of circumventing some of the practical difficulties and limitations of the steady state method. Like the steady state method the static head method is based on Eq. (4), which gives the condition for thermodynamic equilibrium for a tightly coupled transporter. At thermodynamic equilibrium there is no net flux of substrate or activator via such a transporter because the thermodynamic driving forces of the substrate and activator electrochemical graidents are balanced. The principle of the static head method is similar to the steady state method in that one attempts to determine experimental conditions where Eq. (4) holds. Here, however, this determination is based directly on measurements of transport rates via the carrier rather than on steady state distribution ratios produced by the experimental system as a whole. The method is most easily understood by considering a concrete example. A static head experiment for sodium-dependent D-glucose transport in renal outer medullary brush border membrane vesicles is shown in Fig. 4. In this experiment vesicles were preloaded with known concentrations of sodium and labeled glucose and then diluted 1 : 5 into appropriate glucosefree media, thus establishing an intravesicular-to-extravesicular glucose gradient of 6: 1. The glucose retained in these vesicles was then measured as a function of time at various extracellular sodium concentrations. A control run carried out in the absence of sodium was used to measure efflux via unrelated sodium-independent pathways (leaks and/or contaminants). The static head condition (no net substrate flux via the sodium-dependent transporter) is characterized by that external sodium concentration that causes the test run to superimpose on the control. Because membrane potentials were clamped at zero in this experiment (by KSCN and valinomycin, see Figure 4 caption), Eq. (4) reduces to ln([Sd/[So]) = nAln([Ao]/[Ad)
(5)
The values of n indicated on the figure are the sodium: glucose coupling stoichiometries that would be predicted by Eq. (5) were that extravesicular sodium concentration to result in static head conditions. Figure 4 indicates that n^ - 1.8 for this system. 17 R. J. Turner and A. Moran, J. Membr. Biol. 67, 73 (1982). 18 y. Fukuhara and R. J. Turner, Biochim. Biophys. Acta 770, 73 0984). ~9R. J. Turner and A. Moran, J. Membr. Biol. 70, 37 (1982). 20 j. L. Kinsella and P. S. Aronson, Biochim. Biophys. Acta 689, 161 (1982).
492
[28]
KIDNEY +5n=1.6
0
Control z
(.~
-5
n=2.0
n=2.4 -10
I
I
2
4
TIME (SEC)
F[o. 4. The results of a static head experiment designed to measure the sodium:glucose coupling stoichiometry for sodium dependent D-glucosetransport in renal outer medullary (late proximal tubule) brush border membrane vesicles, Vesicles were prepared in THM buffer containing 100 mM KSCN, 0.25 mM v-[l+C]glueoseand L-[3H]glueose, 12.5/zg valinomycin/mg protein, and 20 mMNaCI plus 50 mM choline chloride. At time zero the vesicles were diluted 1 : 5 into incubation media made up of THM buffer containing 100 mM KSCN, sufficient NaCI to give final extravesicular concentrations of 62 mM (O), 49 mM (D), or 42 mM (A), and sufficient choline chloride to produce a solution isoosmotie with the intravesicular medium. The control run (X) was carded out in the absence of sodium at 70 mM choline chloride equih'brium. The stereospeeifie etflux (or influx) of I>-glucose has been expressed as a percentage of the total (equilibrium) intravesieular glucose at time zero. (From Turner and Moran. 19) A static head charge stoichiometry determination for the outer medullary s o d i u m - d e p e n d e n t D-glucose transporter is shown in Fig. 5. Here m e m b r a n e potentials were generated by a potassium gradient in the presence o f valinomycin. T h u s A~, is given to a good a p p r o x i m a t i o n by the potassium diffusion potential, that is, A ¥ = ( R T / F ) l n ( K I / K o ) . Since no sodium gradients were present in this experiment Eq. (4) reduces to ln(Si/So) = qFA~u/RT = q ln(K~/Ko)
(6)
T h e values o f q indicated on the figure are the charge stoichiometries that
[28]
STOICHIOMETRY OF COUPLED TRANSPORT
493
wouM be predicted by Eq. (6) were that potassium diffusion potential to result in static head conditions. Figure 5 indicates that q = 2 for this system. Since, in contrast to the steady state method, the static head procedure is based directly on the determination of transport rates, activator gradients and potentials need only be maintained by the experimental system over times long enough to measure fluxes. This makes this method ideal for vesicle preparations that often can neither generate electrochemical gradients nor maintain them over long time intervals. Also, difficulties arising from the presence of external leaks and contaminants in the preparation
5
E k=
q
--
=
1.0
0 q = 2.0
E control r" 0 0
"5 X
-5
-10
q:
3.0
-
I
I
2
4 Time (sec)
Fie. 5. The results of a static head experiment designed to measure the charge stoichiometry of sodim-dependent D-glucosetransport in renal outer medullary brush border membrane vesicles. Vesicles were prepared in 120 mM K,SO4, 20 mM Na~SO4, 1 mM labeled glucose and valinomycin (12.5/tg/mg protein), then diluted (1:5) into isoosmotic media such that the final extravesicular concentrations of Na2SO4 and labeled glucose were 20 and 0.25 raM, respectively, and the final extravesicular concentrations of K~SO4were 30 mM (0), 60 mM (I), and 75 mM (A). N-Methyl-D-glucamine sulfate was added to the incubation medium to maintain isoosmolarity with the intravesicular solution. In the control run (X) 20 mM Na2SO4 was replaced by 60 mM mannitol in all media. (From Turner.1)
494
KIDNEY
[29]
can be taken into account explicitly in the static head method by an appropriate control run (see Figs. 4 and 5). As in the steady state method, internal leaks will result in an underestimate of coupling and charge stoichiometries by the static head procedure. Concluding Remarks In conclusion, it is worth rcemphasizing that stoichiometric determinations must be tailored to the coupled transport system under investigation and to the experimental system in which it is found. When characterizing a new transporter in our laboratory we typically carry out an activation method experiment first. This experiment provides us not only with a stoichiometric determination but also with information concerning the activator concentration dependence of the transporter. We then attempt the direct method and the steady state method since these are often technically easier experiments than the static head method. Since most of the vesicle systems we work with are not capable of maintaining electrochemical gradients over time our steady state experiments cannot be interpreted quantitatively~; however, they can provide qualitative evidence for energetic coupling by demonstrating concentrative uptake of substrate due to activator or electrical gradients,s,21 Finally, we attempt the static head method. Although this method is often technically ditficult, it provides a direct thermodynamic demonstration of coupled transport and is free from many of the problems associated with other methods of measuring stoichiometry. 2~ y. Fukuhara and R. J. Turner, Am. J. Physiol. 245, F374 (1983).
[29] P h o s p h a t e T r a n s p o r t in E s t a b l i s h e d R e n a l Epithelial Cell Lines By J. BmER, K. MALMSTR6M, S. R~SHKIN, and H. MURER Introduction Phosphate (P.~ is reabsorbed from the lumenal fluid of the renal proximal tubule via a secondary active transport mechanism involving sodium/ phosphate cotransport across the microviUar brush border membrane. Numerous properties of this transport system, such as its kinetic characteristics and functional changes in response to hormones (e.g., parathyroid METHODS IN ENZYMOLOGY, VOL. 191
Copynsht © 1990 by A~lemi~ Press, Inc. All rishts ofreprodu~on in any form reserved.
STOICHIOMETRY OF COUPLED TRANSPORT
479
tial. This also has the advantage of avoiding the use of K + and valinomycin, which may not be suitable when K + transport is being monitored. Vesicles are suspended in varying LiC1 solutions (1- 50 mM) maintained isotonic with Tfis-HCI to a total concentration of 300 raM; 10 #M ionophore, AST01, in 25/zM histidine, pH 7.0, is added and the maximum absorbance change noted. This ionophore cannot be used in the presence of Na + since there is significant carriage of this cation. 23 An interesting application of the rate of dissipation of this dye signal, the measurement of membrane resistance, has been described which can be applied with all the other potential dye probes. The technique used in the case of the Na+,K+-ATPase was to stop pump activity (e.g., with vanadate) and measure the decay of the signal. If the decay can be described by a single exponential, the rate constant, k, can be obtained. The resistance of the membrane ([~-cm2) is calculated as (6)
Rm = (1/k)Cm
where CI is the capacitance of the membrane ( - 1 aF cm-2). 24 23A. Shanser, D. Samuel, and R. Korenstein, J. Am. Chem. Soc. 105, 3815 (1983). 24H.-J. Apell, and B. Bersch, Biochim. Biophys. Acta 903, 480 (1987).
[28] S t o i c h i o m e t r y o f C o u p l e d T r a n s p o r t S y s t e m s in V e s i c l e s By R. JAMESTURNER
Secondary active transport systems enable cells or organelles to drive the flux of a transported substrate, S, against its electrochemical gradient by coupling the flux of S to that of another solute (referred to here as an "activator"), A, which is moving down its electrochemical gradient. The stoichiometry of a such a coupled transport event is of considerable interest since it plays a major role in the determination of both the concentrating capacity of the cell or organelle for S and the energetic cost of the transport process, i In this chapter I describe the methods which are currently used to determine the stoichiometries of co- and countertransport systems in membrane vesicle preparations. Generally speaking these methods are also applicable to intact cell or organelle preparations, the primary advantage of R. J. Turner, Ann. N.Y. Acad. Sci. 456, 10 (1985).
METHODS IN ENZYMOLOGY, VOL. 191
Copyright © 1990 by Academic Pre~, Inc. All fights of reproduction in any form reserved.
480
KIDNEY
[28]
vesicles being that it is easier to control and modify the intravesicular and extravesicular media. In order to fully appreciate the principles and problems involved in the experimental methods decribed here it is important to understand the thermodynamic basis of coupled transport events. This topic is reviewed briefly below. A more detailed discussion is given in a previous publication. 1 Thermodynamics of Coupled Transport
Basic Principles Consider first, for simplicity, a cell or organelle whose outer membrane contains a cotransport system for S and A, where S is an electroneutral molecule and A is an ion with one positive charge (the general case of a charged substrate and multiple activators is treated at the end of this section). Assume also that there are no other primary or secondary active transport systems for S in the membrane. On thermodynamic grounds it can be shown that the ratio of the intracellular to extracellular substrate concentrations, [Sx]/[So], must obey the following inequality, ln([Sd/[So] ) -< nA[ln([Ao]/[Ad) + FAq//RT]
(la)
or equivalently,
[Sl]/[So] ~-~[([Ao]/[ai])exp(FA~u/RT)] n^
(lb)
where F, R, and T have their usual thermodynamic interpretations, AV = ~Uo-~'i is the transmembrane electrical potential, and n A is the A :S coupling stoichiometry (the number of moles of A translocated per mole of
S via the transporter). The biological significance of Eq. (1) can be best appreciated by considering the situation where ln([Ao]/[Ai] ) + RA¥/RT is maintained at some fixed (positive) value by other systems in the cell (e.g., Na +, K+-ATPase), and where the distribution of S across the membrane has reached a steady state. Equation (l) may then be thought of as a thermodynamic constraint on the steady state concentration gradient of S resulting from its coupled transport with A. Thus the equality in Eq. (1) gives the maximum thermodynamically allowed concentrating capacity of the system for S. In this case the substrate and activator electrochemical gradients will be at thermodynamic equilibrium via the coupled transporter and the net carrier-mediated flux of both will be zero. The extent to which any real system approaches this thermodynamic limit depends on the magnitude of its relevant leak pathways. These may be divided into two distinct classes:
[28]
STOICHIOMETRY OF COUPLED TRANSPORT
481
those that occur via the coupled transporter (internal leaks) and those which do not (external leaks). External leaks include passive diffusion and any mediated transport pathways for the substrate across the membrane in question. Internal leaks arise when the flux of activator and substrate via the carrier is not tightly coupled, that is, when activator translocation without substrate or substrate translocation with a variable number of activator ions (possibly zero) can occur via the transporter. The presence of internal leaks adds a significant complication to stoichiometric determinations since in this case the coupling stoichiometry may vary with experimental conditions. There have, in fact, been several reports in the literature of transporters that apparently display this type of variability. 2 In a system with internal or external leak pathways the flux via the coupled transporter will reach a steady state determined by kinetic as well as thermodynamic factors. This kinetic steady state will necessarily result in a value of [Sd/[So] that is less than that predicted by thermodynamic equilibrium, t
Multiple Activators and Charge Stoichiometry The more general form of F_xl. (1) for multiple activators and charged substrates is given by ln([Sd/[So]) -< ~ n^ln([Aol/[Ai]) + qFAg//RT
(2)
A
where the sum is over all activators, that is, over all solutes co- or countertransported with S via the carrier. Here nA is positive if A is cotransported with S and negative if A is countertransported with S. The charge stoichiometry, q (the number of moles of charge translocated per mole of S via the transporter), is given by q = Zs + ~
nAZA
A
where Zs and ZA are the charges on S and A, respectively. Flux Measurements: T h e Rapid Filtration Technique A variety of methods have been used to monitor transport or transportrelated events in vesicle preparations, but the most commonly applied and generally applicable procedure for studying coupled transport systems is to measure the flux of radiolabeled ligands using the "rapid filtration" technique. In this chapter I discuss mainly experiments employing this tech2 A. A. Eddy, Biochem. Soc. Trans. 8, 271 0980).
482
KIDNEY
[9.8]
nique; however, stoichiometric determinations may equally well be carried out using other methods of flux determination. The basic procedure for the rapid filtration technique as carried out in our laboratory is the following. Vesicles (10-50gl, 1-3 mg protein/ml) are combined with an incubation medium (10- 100 #1) containing radioactively labeled fig,ands (10-100 gCi/ml) and other constitutents as required in a 12 × 75 disposable borosilicate glass test tube. After an appropriate incubation time, 1.5 ml of an ice-cold stop solution is added and the resulting mixture is removed with a Pasteur pipet and applied to a Millipore filter (HAWP, 0.45 gin; Bedford, MA) under light suction. The filter is then quickly washed with a further 4.5 ml of stop solution, placed in an appropriate scintillation cocktail, and counted for radioactivity along with samples of the incubation medium and appropriate standards. Eitlux studies can be carried out in the same way using vesicles preloaded with labeled substrate. The actual volumes, protein concentrations, and isotopic activities employed in a given experiment will depend on the transporter under study as well as on tissue availability and the cost of radiolabeled ligands. The apparatus we employ consists of a flitted glass filter holder (MiUipore XX10 025 02) connected via flexible tubing to a collection bottle and then to a vacuum pump. We typically use Eppendorf series 4700 fixed volume pipets to dispense vesicles and incubation media; however, any pipet with comparable accuracy and reproducibility (both < 1%) is acceptable. If incubation times of < 5 sec are desired we use the rapid sampling device described by Turner and Moran) A rapid sampling device is also available commercially from Inovativ Labor AG (Adliswil, Switzerland). We have occasionally carried out flux measurements at incubation times of < 2 sec by hand with the aid of a metronome. Owing to the quantitative nature of stoichiometric determinations considerable care is required in the design and performance of experiments in order to avoid the introduction of artifactual or systematic errors. The importance of choosing an appropriate stop solution to prevent isotope efllux or influx during the stopping and washing procedure and the necessity of measuring initial rates of transport have been stressed earlier? Also, when working with coupled transport processes that are electrogenic, variations in membrane potential with experimental conditions must be avoided) -5 In our vesicle preparations we typically clamp membrane potentials at the diffusion potential of a permeant anion such as nitrate or thiocyanate or at the potassium diffusion potential using the potassium 3 R. J. Turner and A. Moran, Am. J. Physiol. 242, F406 (1982). 4 R. J. Turner, 3. Membr. Biol. 76, 1 (1983). 5 U. Hopfer, Am. J. Physiol. 254, F89 (1978).
[28]
STOICHIOMETRY OF COU ,-LED TRANSPORT
483
ionophore valinomycin (2.5-12.5 #g/mg membrane protein). Further discussion of this problem and methods for testing the effectiveness of the above voltage clamping procedures are given in previous publications. 3,4,6,7 Methods of Measuring Stiochiometry Four methods have been devised for measuring the stoichiometry of coupled transport systems. Some experimentation may be required to determine the range of experimental conditions (if any) under which a given method may be successfully performed on a particular carrier. For this reason it is advisable to have accumulated a good experimental data base on the system under study before attempting stoichiometric measurements. Useful information includes the time course of uptake, the magnitude of specific vs nonspecific uptake, the degree of substrate binding and metabolism by the vesicles, and the dependence of uptake on substrate and activator concentrations (the latter is actually a stoichiometric determination--see Method 2, below). It is also important to ensure that all activator species have been identified; a number of secondary active transporters have recently been shown to be coupled to multiple activators (see, e.g., Refs. 6-8). All four methods of stoichiometric determination are equally applicable to cotransport and countertransport systems. In every case the roles of substrate and activator are interchangeable. The use of each method for the determination of both coupling and charge stoichiometries is discussed at appropriate points below.
Method I (Direct Method) The direct method for determining the A: S coupling stoichiometry of a secondary active transport system consists of simultaneously measuring and comparing substrate and activator fluxes via the transporter. There are two ways in which this might be done: (1) by measuring the total transporter-related substrate and activator fluxes (e.g., by measuring fluxes in the presence and absence of a specific inhibitor of the transporter), or (2) by measuring the activator-dependent substrate flux and the substrate-dependent activator flux. For tightly coupled transporters both procedures should give the same result. In the presence of significant internal leak pathways, however, only the former procedure will give the correct coupling stoichiometry since the latter procedure does not take into account 6 y. Fukuhara and R. J. Turner, Am. J. Physiol. 248, F869 (1985). 7 R. J. Turner, J. N. George, and B. J. Baum, J. Membr. Biol. 94, 143 (1986). s R. J. Turner, J. Biol. Chem. 261, 16060 (1986).
KIDNEY
48 4
10.0
[9.8]
a
£
E ~ 5.0
00
50
100 [Na] mM
150
- 150 x 103
150
-IO0 ,z.
,z.
z.
2
rr
u.
50
10170
0
5,0
5O
10.0
Flux (nmol/min.mg protein)
FIG. 1. Initial rate of sodium-dependent succinate uptake into renal outer cortical brush border membrane vesicles measured as a function of sodium concentration. Vesicles were prepared in THM buffer (10 mM HEPES plus 100 mM mannitol buffered with Tris to pH 7.5) containing 600 mM mannitol and 100 mM KSCN. The (isoosmotic) incubation media were THM buffer containing 100 mM KSCN and sufficient p4C]succinate and NaCl to give final extravesicular concentrations of 0.2 and 0-200 mM, respectively. Chofine replaced sodium isoosmotically to obtain the various sodium concentrations studied. Mere-
[28]
STOICHIOMETRY OF COUPLED TRANSPORT
485
uncoupled fluxes via the transporter. The direct method is conceptually the most straightforward and in some ways the most satisfying method of measuring coupling stoichiometries. An electrophysiological version of the direct method has been used by several authors to measure charge stoichiometry in intact epitheliag, t°; however, no attempts to measure substrate flux and charge translocation directly in cell suspensions or vesicle preparations appear to have been attempted.
Method 2 (ActivationMethod) The activation method for determining the A:S stoichiometry of a transport system consists of measuring substrate flux as a function of activator concentration. As discussed below the interpretation of activation method data is considerably more model dependent than the other methods described here. It should also be noted that the activation method is sensitive both to activators that are actually transported with the substrate (energetic activation) and to activators that simply affect substrate flux without being themselves transported (catalytic activation), for example, by binding at a modifier site on the carrier. Thus, whereas the other methods for determining stoichiometries discussed here are sensitive only to transported activators, the activation method provides a measure of the total (catalytic plus energetic) activator involvement in the transport event. For this reason I refer here to the result of an activation method experiment as the A: S stoichiometry rather than the A: S coupling stoichiometry. Note that only transported (energetic) activators are relevant to the thermodynamics of coupled transport [Eqs. (1) and (2)]. A hyperbolic relationship between activator-dependent substrate flux and activator concentration provides good evidence for a 1:1 activator: substrate stoichiometry since this behavior is expected for a 9 E. Frtmter, PfluegersArch. 393, 179 (1982). 1oD. S. Misfeldt and M. J. Sanders, J. Membr. Biol. 70, 191 (1982).
brahe potentials were clamped at zero by the presence of 100 m M KSCN in all solutions and by the addition of 12.5 #g valinomycin/mg protein to the vesicles. (a) A plot of uptake vs sodium concentration. The line drawn through the data points is a fit to Eq. (3) obtained using the nonlinear regression routine NONLIN (Systat, Inc., Evanston, IL). The fit is given by Jm~ = 10.6 - 1.2 nmol/min/mg protein, Ko.5 ffi 54.2 _ 9.3 raM, and n -----2.1 ± 0.4. (b) Plots of flux/[Na] n vs flux for n •ffi I (A), 2 ((3), and 3 ([~), illustrating the way in which data can be fit to Eq. (3) by trial and error. A more quantitative procedure involving linear regression analysis is described in the text. [Redrawn from Y. Fukuhara and R. J. Turner, Am. J. Physiol. 245, F374 (1983).]
486
KIDNEY
[28]
broad class of 1 : l-type models? ,H In this case a plot of flux/[A] vs flux will be linear. In contrast, a sigmoidal dependence of flux on activator concentration as shown in Fig. l a for sodium-dependent succinate transport in renal outer cortical brush border membrane vesicles indicates the involvement of multiple activator ions per substrate translocation event. The most c o m m o n method for interpreting such data is based on analysis in terms of the Hill equationl2: Js = Jtrm[A]n/(K~.5 + [A] n)
(3)
Here Js is the substrate flux, n is the A : S stoichiometry (the "Hill coefficient"), and J ~ and Ko.5 are constants. It can be shown that a tightly coupled transporter with activator:substrate stoichiometry n and strong cooperativity between activator-binding sites will obey such a flux equation. [Note that for n = 1, Eq. (3) reduces to the hyperbolic relationship expected for a l : l system.] In order to get the most information from the activation method it is important to obtain flux data over the widest possible range of activator concentrations. Fluxes at low activator concentrations are particularly important since these often define the sigmoidal portion of the activation curve which identifies and characterizes the involvement of multiple activator ions. Two procedures for analyzing activation method data, based on the Hill equation, are given below. Procedure 1. In this procedure one simply fits the experimental data to Eq. (3) using a least-squares regression or manual method. The line drawn through the data points in Fig. la is a nonlinear least-squares fit obtained using a commercially available nonlinear regression computer program (see figure caption). In carrying out such a fit the points are typically weighted in proportion to the reciprocals of their variances. In our laboratory we frequently employ an alternative to nonlinear least-squares analysis in fitting activation data to Eq. (3). This method takes advantage of the fact that Eq. (3) predicts that a plot of Js/[A] ~ vs Js will be linear. Thus one can search manually for a value of n which results in such a linear plot, as we have done in Fig. lb, or one can carry out a similar search more quantitatively with the aid of a linear least-squares regression routine. This latter procedure is used routinely in our laboratory. 6 We have modified a linear regression program so that it fits a straight line to a Js/[A]" vs Js plot over a range of values of n. The points are weighted in proportion to the reciprocals of the squares of their relative 11R. J. Turner, Biochim. Biophys. Acta 649, 269 (1981). ~2I. H. Segel, "Enzyme Kinetics." Wiley, New York, 1975.
[28]
487
STOICHIOMETRY OF COUPLED TRANSPORT
experimental errors. The best value of n is taken to be the one that minimizes the sum of the squares of the deviations of the experimental points from the calculated regression line. The statistical errors on Jma, and Ko.s are then given directly from the linear least-squares fit and the statistical error on n can be determined using an F test. This procedure was found to give results virtually identical to nonlinear least-squares analysis while requiring only a simpler, more readily available, linear least-squares regression routine. Owing to the rather restrictive assumptions made in deriving the Hill equation (see above) it is unlikely that any real transporter will obey it well. Thus one should expect nonintegral Hill coefficients from the above fitting procedures and/or systematic deviations from linearity on Js/[A]" vs Js plots. In general, the Hill coefficient derived from fitting activation method data to Eq. (3) should be regarded as a lower limit on the A: S stoichiometry. 1 Procedure 2. This procedure is recommended when Jm~ can be accurately determined from the experimental data, i.e., when Js can be measured at activator concentrations which are sufficiently high that saturation is assured. In this case a Hill plot of log[Js/(Jm~- Js)] vs log[A] can be made. For data fitting Eq. (3) such a plot will be linear with slope n. Hill plots for sodium-dependent sulfate transport in renal brush border membrane vesicles at pH 8.0 and pH 6.0 are illustrated in Fig. 2. The linearity of the Hill plot for pH 8.0 with slope 1.02 provides good evidence for a l : 1 sodium: sulfate stoichiometry at this pH while the break in the Hill plot for pH 6.0 may be interpreted as the result of a shift in the sodium: sulfate
+2.0-
+2.0-
PH i = PH 0 = 6.0
PH i = PH0 - 8.0
O-u')O
.l.O-
? +l.O-
cYg mE
f
0.0o~_ ~o -I.Oo J -2.0
0.0-
-1.0-
slope= 1.02 I
o
I
,.o
-2.0 1
l
2.o
LOG
I
o
~
,o
l
l
2.o
[Nal
FIo. 2. Hill plots of the initial rate of sodium-dependent sulfate uptake (J~oi")into renal brush border membrane vesicles measured as a function of sodium concentration. Measurements were made at pH 8.0 equlh~rium (left) and pH 6.0 equilibrium (fight). Jm~ was estimated by extrapolation of a Js/[Na] vs Js plot. (From Abeam and Murer.'3)
488
KIDNEY
[28]
stoichiometry from approximately 1 : 1 to approximately 2: 1 with increasing sodium concentration under these experimental conditions? 3 Given our present (meager) understanding of the kinetics of coupled transport systems a Hill plot is unquestionably the best method for extracting the maximal amount of information from activation method data. I would, however, give two notes of caution. First, because the assumptions made in deriving Eq. (3) are rather restrictive, and because the Hill transformation itself is rather complex, it is not entirely clear what relationship the slope of the Hill plot will bear to the activator: substrate stoichiometry for more realistic flux equations; thus such plots should be interpreted with some caution. This point is discussed in more detail in an earlier publication. ! Second, considerable care should be taken in the determination of Jinx since a small change in this constant can cause a large shift in the Hill plot, especially at high activator concentrations. Indeed it is advisable to test the effects of experimental uncertainties in J ~ on the shape of the Hill plot to be sure that any conclusions reached are not overly dependent on the choice of this parameter. The complex way in which A¢/enters into the kinetic equations of most coupled transport models makes this method very difficult to apply to the determination of charge stoichiometries. To my knowledge no attempts to carry out determinations of this type have been made.
Method 3 (Steady State Method) The steady state method for determining the coupling and charge stoichiometries of a secondary active transport system consists of measuring the steady state substrate gradient generated by the transporter in the presence of known (measured or applied) activator electrochemical gradients. I f the transporter is operating at or close to thermodynamic equilibrium Eq. (2) becomes (the case of a single activator is treated for simplicity) ln([Sd/[So]) = nAln([Ao]/[Ai]) + qFAc//RT
(4)
Thus, for example, n^ can be calculated from the slope of a plot of ln([Sd/[So]) vs ln([Ao]/[Ai]), at constant A~u,and q can be determined in a similar fashion from a plot ofln([Sd/[So]) vs FAc//RTat constant activator chemical gradient. Alternatively, if [Sd/[So], [Ao]/[AI], and A¢/are measured under two or more independent experimental conditions, n^ and q can be calculated from the simultaneous equations resulting from substitution of these numerical values in Eq. (4). Steady state method calculations are particularly simple if measurements can be carded out in the presence 13G. A. Ahearn and H. Murer, J. Membr. Biol. 78, 177 (1984).
[28]
489
STOICHIOMETRY OF COUPLED TRANSPORT
of an activator gradient alone (A~J--0) or an electrical gradient alone [ln([Ao]/[Ad) = 0]. The steady state method is typically applied to whole cells or cell fragments containing an intact activator gradient or membrane potential gradient-generating system. In this case, the relevant gradient can be maintained at a constant value for sufficient time that a steady state substrate gradient can be established and measured.
5L'
4
2
1 I
J
O
In I'SCN-]in rSCN']ou t
I
(o)
I
i
2
or
[C":5"H3+]+,
In [CH3NH~+]ou~(°)
Flo. 3. Steady state dopamine (D) uptake into chromalfin granule ghosts measured as a function of membrane potential ((3) and pH gradient (El). A~ and pH were varied by adding ATP and different amounts of FCCP to ghosts suspended in sucrose and KCI media, respectively (see text). The steady state gradients of radiolabeled dopamine, SCN- and CH3NH3 + were measured after 60 min of incubation at 25 °. The slopes of the lines drawn through the data points are 1.18 +_0.14 (O) and 2.06 +_0.24 (El). (From Knoth et al.15)
490
mONEY
[28]
An example of the determination of the coupling and charge stoichiometries of the H+/dopamine countertransporter in chromaflin granule ghosts is shown in Fig. 3. In these experiments Knoth et al. 14,15were able to generate stable pH and potential gradients independently of one another using an H+-ATPase which is also present in the granule membrane. Briefly, they found that in the absence of permeant ions the H+-ATPase generated a membrane potential but, owing to the high buffering capacity of the ghosts, no pH gradient. The magnitude of the resulting membrane potential could be varied by the addition of different amounts of the H + ionophore FCCP. On the other hand, when the permeant anion C1- was present in the ghost preparation it could follow the actively pumped protons into the ghosts, dissipating the membrane potential and lowering the internal pH. The magnitude of the resulting pH gradient could likewise be varied by adding the uncoupler FCCP. In these experiments the transmembrane potential and pH gradients were monitored using the distribution ratios of radiolabeled thiocyanate and methylamine, respectively)4 The slopes of the lines in Fig. 3 indicate an H +: dopamine coupling stoichiometry of 2: 1 and a charge stoichiometry of 1 : 1. These results are consistent with the exchange of two H + and one dopamine+ by the transporter. As stressed above the stoichiometry derived from the steady state method will be correct only when the transporter is operating at or near thermodynamic equilibrium since it is only then that the ~ sign in Eq. (2) becomes an equality [Eq. (4)]. In the presence of significant internal or external leaks SI/So may deviate significantly from the value predicted by thermodynamic equilibrium and the steady state method will yield an underestimate of the true stoichiometry. The inability of this method to take into account external leak pathways is a potentially serious shortcoming which has received some attention in the literature. L4,t6The presence of contaminating cells or vesicular material can also lead to errors in measurements of relevant substrate and activator gradients, since this material may behave quite differently from the cells or vesicles containing the system under study. Stoichiometries obtained from applications of the steady state method to preparations that cannot maintain activator or electrical gradients over time must be interpreted with some care, since in such preparations the sustained steady state substrate gradient assumed in Eq. (4) never occurs.
14j. Knoth, M. Zallaldan, and D. Njus, Biochemistry 20, 6625 (1981). is j. Knoth, M. Zallakian, and D. Njus, Fed. Proc., Fed. Am. Soc. Exp. Biol. 41, 2742 (1982). t6 I. R. Booth, W. J. Mitchell, and W. A. Hamilton, Biochem. J. 182, 687 (1979).
[28]
STOICHIOMETRY OF COUPLED TRANSPORT
491
Method 4 (Static Head Method) The static head method ~7-2° of determining coupling and charge stoichiometries provides a means of circumventing some of the practical difficulties and limitations of the steady state method. Like the steady state method the static head method is based on Eq. (4), which gives the condition for thermodynamic equilibrium for a tightly coupled transporter. At thermodynamic equilibrium there is no net flux of substrate or activator via such a transporter because the thermodynamic driving forces of the substrate and activator electrochemical graidents are balanced. The principle of the static head method is similar to the steady state method in that one attempts to determine experimental conditions where Eq. (4) holds. Here, however, this determination is based directly on measurements of transport rates via the carrier rather than on steady state distribution ratios produced by the experimental system as a whole. The method is most easily understood by considering a concrete example. A static head experiment for sodium-dependent D-glucose transport in renal outer medullary brush border membrane vesicles is shown in Fig. 4. In this experiment vesicles were preloaded with known concentrations of sodium and labeled glucose and then diluted 1 : 5 into appropriate glucosefree media, thus establishing an intravesicular-to-extravesicular glucose gradient of 6: 1. The glucose retained in these vesicles was then measured as a function of time at various extracellular sodium concentrations. A control run carried out in the absence of sodium was used to measure efflux via unrelated sodium-independent pathways (leaks and/or contaminants). The static head condition (no net substrate flux via the sodium-dependent transporter) is characterized by that external sodium concentration that causes the test run to superimpose on the control. Because membrane potentials were clamped at zero in this experiment (by KSCN and valinomycin, see Figure 4 caption), Eq. (4) reduces to ln([Sd/[So]) = nAln([Ao]/[Ad)
(5)
The values of n indicated on the figure are the sodium: glucose coupling stoichiometries that would be predicted by Eq. (5) were that extravesicular sodium concentration to result in static head conditions. Figure 4 indicates that n^ - 1.8 for this system. 17 R. J. Turner and A. Moran, J. Membr. Biol. 67, 73 (1982). 18 y. Fukuhara and R. J. Turner, Biochim. Biophys. Acta 770, 73 0984). ~9R. J. Turner and A. Moran, J. Membr. Biol. 70, 37 (1982). 20 j. L. Kinsella and P. S. Aronson, Biochim. Biophys. Acta 689, 161 (1982).
492
[28]
KIDNEY +5n=1.6
0
Control z
(.~
-5
n=2.0
n=2.4 -10
I
I
2
4
TIME (SEC)
F[o. 4. The results of a static head experiment designed to measure the sodium:glucose coupling stoichiometry for sodium dependent D-glucosetransport in renal outer medullary (late proximal tubule) brush border membrane vesicles, Vesicles were prepared in THM buffer containing 100 mM KSCN, 0.25 mM v-[l+C]glueoseand L-[3H]glueose, 12.5/zg valinomycin/mg protein, and 20 mMNaCI plus 50 mM choline chloride. At time zero the vesicles were diluted 1 : 5 into incubation media made up of THM buffer containing 100 mM KSCN, sufficient NaCI to give final extravesicular concentrations of 62 mM (O), 49 mM (D), or 42 mM (A), and sufficient choline chloride to produce a solution isoosmotie with the intravesicular medium. The control run (X) was carded out in the absence of sodium at 70 mM choline chloride equih'brium. The stereospeeifie etflux (or influx) of I>-glucose has been expressed as a percentage of the total (equilibrium) intravesieular glucose at time zero. (From Turner and Moran. 19) A static head charge stoichiometry determination for the outer medullary s o d i u m - d e p e n d e n t D-glucose transporter is shown in Fig. 5. Here m e m b r a n e potentials were generated by a potassium gradient in the presence o f valinomycin. T h u s A~, is given to a good a p p r o x i m a t i o n by the potassium diffusion potential, that is, A ¥ = ( R T / F ) l n ( K I / K o ) . Since no sodium gradients were present in this experiment Eq. (4) reduces to ln(Si/So) = qFA~u/RT = q ln(K~/Ko)
(6)
T h e values o f q indicated on the figure are the charge stoichiometries that
[28]
STOICHIOMETRY OF COUPLED TRANSPORT
493
wouM be predicted by Eq. (6) were that potassium diffusion potential to result in static head conditions. Figure 5 indicates that q = 2 for this system. Since, in contrast to the steady state method, the static head procedure is based directly on the determination of transport rates, activator gradients and potentials need only be maintained by the experimental system over times long enough to measure fluxes. This makes this method ideal for vesicle preparations that often can neither generate electrochemical gradients nor maintain them over long time intervals. Also, difficulties arising from the presence of external leaks and contaminants in the preparation
5
E k=
q
--
=
1.0
0 q = 2.0
E control r" 0 0
"5 X
-5
-10
q:
3.0
-
I
I
2
4 Time (sec)
Fie. 5. The results of a static head experiment designed to measure the charge stoichiometry of sodim-dependent D-glucosetransport in renal outer medullary brush border membrane vesicles. Vesicles were prepared in 120 mM K,SO4, 20 mM Na~SO4, 1 mM labeled glucose and valinomycin (12.5/tg/mg protein), then diluted (1:5) into isoosmotic media such that the final extravesicular concentrations of Na2SO4 and labeled glucose were 20 and 0.25 raM, respectively, and the final extravesicular concentrations of K~SO4were 30 mM (0), 60 mM (I), and 75 mM (A). N-Methyl-D-glucamine sulfate was added to the incubation medium to maintain isoosmolarity with the intravesicular solution. In the control run (X) 20 mM Na2SO4 was replaced by 60 mM mannitol in all media. (From Turner.1)
494
KIDNEY
[29]
can be taken into account explicitly in the static head method by an appropriate control run (see Figs. 4 and 5). As in the steady state method, internal leaks will result in an underestimate of coupling and charge stoichiometries by the static head procedure. Concluding Remarks In conclusion, it is worth rcemphasizing that stoichiometric determinations must be tailored to the coupled transport system under investigation and to the experimental system in which it is found. When characterizing a new transporter in our laboratory we typically carry out an activation method experiment first. This experiment provides us not only with a stoichiometric determination but also with information concerning the activator concentration dependence of the transporter. We then attempt the direct method and the steady state method since these are often technically easier experiments than the static head method. Since most of the vesicle systems we work with are not capable of maintaining electrochemical gradients over time our steady state experiments cannot be interpreted quantitatively~; however, they can provide qualitative evidence for energetic coupling by demonstrating concentrative uptake of substrate due to activator or electrical gradients,s,21 Finally, we attempt the static head method. Although this method is often technically ditficult, it provides a direct thermodynamic demonstration of coupled transport and is free from many of the problems associated with other methods of measuring stoichiometry. 2~ y. Fukuhara and R. J. Turner, Am. J. Physiol. 245, F374 (1983).
[29] P h o s p h a t e T r a n s p o r t in E s t a b l i s h e d R e n a l Epithelial Cell Lines By J. BmER, K. MALMSTR6M, S. R~SHKIN, and H. MURER Introduction Phosphate (P.~ is reabsorbed from the lumenal fluid of the renal proximal tubule via a secondary active transport mechanism involving sodium/ phosphate cotransport across the microviUar brush border membrane. Numerous properties of this transport system, such as its kinetic characteristics and functional changes in response to hormones (e.g., parathyroid METHODS IN ENZYMOLOGY, VOL. 191
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