Correspondence to: Donald W. Hilgemann, Department of Physiology, University of Texas Southwestern Medical Center at Dallas, 5323 Harry Hines Boulevard, Dallas, TX 75325-9040. Fax:Fax: 214-648-8879; E-mail:chinchih{at}iname.com or hilgeman@utsw.swmed.edu.
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Abstract |
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We have developed an alternating access transport model that accounts well for GAT1 (GABA:Na+:Cl-) cotransport function in Xenopus oocyte membranes. To do so, many alternative models were fitted to a database on GAT1 function, and discrepancies were analyzed. The model assumes that GAT1 exists predominantly in two states, Ein and Eout. In the Ein state, one chloride and two sodium ions can bind sequentially from the cytoplasmic side. In the Eout state, one sodium ion is occluded within the transporter, and one chloride, one sodium, and one -aminobutyric acid (GABA) molecule can bind from the extracellular side. When Ein sites are empty, a transition to the Eout state opens binding sites to the outside and occludes one extracellular sodium ion. This conformational change is the major electrogenic GAT1 reaction, and it rate-limits forward transport (i.e., GABA uptake) at 0 mV. From the Eout state, one GABA can be translocated with one sodium ion to the cytoplasmic side, thereby forming the *Ein state. Thereafter, an extracellular chloride ion can be translocated and the occluded sodium ion released to the cytoplasm, which returns the transporter to the Ein state. GABAGABA exchange can occur in the absence of extracellular chloride, but a chloride ion must be transported to complete a forward transport cycle. In the reverse transport cycle, one cytoplasmic chloride ion binds first to the Ein state, followed by two sodium ions. One chloride ion and one sodium ion are occluded together, and thereafter the second sodium ion and GABA are occluded and translocated. The weak voltage dependence of these reactions determines the slopes of outward currentvoltage relations. Experimental results that are simulated accurately include (a) all currentvoltage relations, (b) all substrate dependencies described to date, (c) ciscis and cistrans substrate interactions, (d) charge movements in the absence of transport current, (e) dependencies of charge movement kinetics on substrate concentrations, (f) presteady state current transients in the presence of substrates, (g) substrate-induced capacitance changes, (h) GABAGABA exchange, and (i) the existence of inward transport current and GABAGABA exchange in the nominal absence of extracellular chloride.
Key Words: electrogenic, Markov, neurotransmitter transporter, reaction kinetics, transport model
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Introduction |
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Recent success in determining the structures of several membrane transporters (
The Proposed Alternating Access Model
A cartoon of our model is shown in Figure 1. Transporters exist primarily in two states, designated Ein and Eout, and the transitions between them (reactions 14) take place through transitional states, designated *Eout and *Ein. Within each state, substrate binding is assumed to be at equilibrium. In the Ein state, binding sites are open to the cytoplasmic side, and they bind sequentially one Cl- (Kd, 3.7 mM) and two Na+ (Kds, 442 and 11.5 mM). When the Ein binding sites are empty, a low affinity Na+ binding site (Kd, 0.92 M) can open to the extracellular side (1a; 200 s-1), thereby forming the *Eout state that cannot bind any substrate from the cytoplasmic side. When a Na+ is bound to the *Eout state, it can be occluded into the transporter (1b), thereby forming the stable Eout state. This overall reaction (1; i.e., 1a + 1b) moves +1.1 equivalent charges through the membrane field from outside to inside. In the Eout state, one Cl- (Kd, 8.2 mM) and one Na+ (Kd, 10.1 mM) together with 1 -aminobutyric acid (GABA)1 (Kd, 41 µM) can be bound from the extracellular side. The backward transition to the Ein state (2; i.e., 2a + 2b; 2,000 s-1), which releases one Na+ to the outside, occurs only when the Eout binding sites are empty.
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When the Eout binding sites for Na+ and GABA are occupied, these two substrates can be translocated to the cytoplasmic side (Figure 1, Figure 3a; 40 s-1), regardless of whether extracellular Cl- is bound, thereby forming the transitional state, *Ein. The GABA translocation reaction (3a) has a slight voltage dependence that opposes the overall forward transport process at negative potentials (-0.07 equivalent charges). In the transitional *Ein state, GABA and Na+ can dissociate to the cytoplasmic side. For the transition to the stable Ein state (3b), an extracellular Cl- must be bound, and GABA must have dissociated to the cytoplasmic side. The bound extracellular Cl- is then translocated simultaneously with the release of the occluded Na+ ion to the cytoplasmic side. The reverse reaction (4) to the Eout state at first translocates one cytoplasmic Cl- and occludes one cytoplasmic Na+ (4a; 42 s-1); thereafter, one cytoplasmic Na+ and GABA are translocated (4b). The occlusion of Cl- and Na+ (i.e., 4a) has a weak voltage dependence (+0.17 equivalent charges) that promotes the reverse transport cycle at positive potentials. In the Ein state, charged residues of the binding sites can flex somewhat in the membrane field (-0.18 equivalent charges), which imparts weak voltage dependence on cytoplasmic Cl- binding.
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The Modeling Process
The model just described is the simplest Markovian transport model we have found to account for all significant features of GAT1 transport function in Xenopus oocyte membrane. To develop the model, we first constructed a database of all steady state and kinetic data that we judged to be reliable. Then, with the perspectives of the previous articles (
For brevity, we omit discussion of "dilemmas" encountered during model development. Examples pointed out previously ( Eout transition (Figure 1, Figure 1;
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Materials and Methods |
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Model-Fitting and Integration Method
Our fitting method was described previously (
The model to be presented is a "pseudotwo-state model" because it has only two stable states. Other models that we explored included many different substrate binding schemes and the kinetic simulation of substrate binding reactions. Also, we carefully tested our treatment of transitional states by developing models in which the transitional states were simulated as stable states with rapid exit transitions. Results with the complex and simplified models were identical for the purposes of this article.
For kinetic simulations of two- and three-state models, we used analytical solutions to integrate state transitions over time. For the more complex models, we usually used a stable implicit method to integrate the differential equations (dyi/dt) for the individual states (y1...n) over time with the integration interval, h:
where yih is the state value at the forward time point, yi0 is the state value at the backward time point, and k is the sum of rate constants leading into and away from the given state. The simulation programs were written in Pascal and C++ and compiled with Borland TurboPascal and Borland C++ Builder, respectively (Inprise).
Variability of Experimental Results
Variability in results from different groups of experiments and experimental methods is an important problem in our simulations. The two major cases are the cytoplasmic Cl- dependence of reverse GAT1 current and the voltage dependence of charge movements. Half-maximal Cl-i concentrations vary by a factor of about four, and the midpoint voltage of charge movements varies by at least 25 mV in experiments with different oocyte batches. A similar variability of charge movements was observed in whole-oocyte recordings (Dr. Sela Mager, personal communication). To demonstrate the kinetic behavior predicted by our model, we have simulated one experiment (see Figure 10) with 70 mM extracellular NaCl, rather than the 40 mM used in the experiment.
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Model Assumptions
We describe here the rationale for two implicit model assumptions. For some simulations, we carried out a kinetic simulation of all substrate reactions, similar to a cotransport model proposed by
The second assumption is related to the application of Eyring rate models () moves the electrical field across the site. No "driving force" for binding site closure (ß) is provided by the electrical field because the charge is outside of the field when the site is open. Thus, the reaction will be voltage dependent only in the opening direction, although the amount of charge that moves through electrical field is the same in both directions. A still more extreme asymmetry, which we allow in simulations, is that the valences of forward and reverse reactions can be of opposite sign. This is justified if the overall reaction simulated is thought of as two reactions through a transitional state; the different valences then correspond to two different reactions that can be simulated separately with identical results.
We illustrate our simulation of electrogenic reactions for the case shown in Figure 2, assuming that one equivalent charge is moved. The opening rate coefficient (k) is multiplied by eq
·
,where qß = 0. Total charge moved in the reaction (i.e., one elementary charge) is the sum of the forward and reverse reaction coefficients (q
+ qß).
A major charge-moving reaction of Na+,glucose transporters can be simulated as a very slow, electrogenic Na+ binding reaction (, respectively. The binding site opening rates,
and
, are assumed to be voltage dependent, whereby reaction
moves a fixed negative charge out of membrane field and the Na+ occlusion reaction (
) moves the positively charged Na+ into the electrical field.
Assuming that the *E state never accumulates significantly, this scheme predicts simple monoexponential charge movements with rate constants determined by the rates, and
. Although the opening of empty binding sites (
) is a major source of charge movement, this reaction cannot be isolated in the absence of extracellular Na+. Modifications of this scheme to allow significant accumulation of the *E state predict slow charge movements in the absence of Na+, as predicted (
Designating the fractional occupancy of the binding site by Na+ in Figure 2 as fno, and the extracellular Na+ concentration as No,
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(1) |
From rate theory, the state flux from E1 to E2 (12) will be
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(2) |
and the state flux from E2 to E1 (N21) is
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(3) |
These same expressions were derived by Dr. Vladislav Markin (University of Texas Southwestern Medical Center at Dallas) from the analytical solution of the corresponding three-state model. Since variation of the rates, and ß, simply changes the apparent Na+o affinity, these rates can be eliminated from the model. Thus,
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(4) |
and
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(5) |
whereby the rate coefficients, and
, will be voltage dependent.
We point out one interesting feature of this scheme, which could be relevant to the kinetic function of other transporters. Because Na+ binding in the transitional state inhibits the overall reaction that releases Na+ to the outside, the "off" rate of the charge movement is accelerated by reducing extracellular Na+. This would not be the case for a simple ion binding/dissociation reaction.
Description of the Model
The mathematical description of our model contains 18 parameters. One of these is eliminated to enforce microscopic reversibility of rates and one to enforce charge conservation (i.e., movement of one total charge per transport cycle). We fixed the intrinsic rates of 1a and 2a to 200 and 2,000 s-1, respectively (Figure 1), because the effects of varying these rates by two- to threefold could be fully compensated by changes of substrate binding affinities. Another parameter that is not varied is designated fx. This parameter determines the ratio of extracellular Cl- dissociation constants in the Eout and the *Ein states; it affects only the simulations shown in Figure 7 and Figure 9. Thus, 13 parameters were adjusted by the fitting routine for the results presented.
Designations of the rate coefficients (k1, k2, k3, and k4) correspond to the reaction numbers in Figure 1. Na+ ions are designated N, Cl- ions are designated Cl, and GABA molecules are designated G. Cytoplasmic and extracellular Na+ concentrations are designated ni and no, respectively; Cl- concentrations are designated ci and co, and GABA concentrations are designated gi and go. Dissociation constants for the extracellular side are designated Kno1 and Kno2 for the first and second Na+ ion to bind, respectively, during forward transport. Kgabo and Kclo are the extracellular GABA and Cl- dissociation constants. For the cytoplasmic side, our designations are Kni1 and Kni2 for the first and second Na+ ions to bind, respectively, during reverse transport. Kgabi and Kcli are the cytoplasmic GABA and Cl- dissociation constants. Each of the reactions simulated has an apparent valence, designated q1, q2, q3, and q4, according to the corresponding rate coefficients. Finally, we assume that the cytoplasmic Cl- binding site, while empty, undergoes a weakly voltage-dependent reaction that allows and disallows Cl-i binding. Its valence is designated q5.
The parameter values for the results presented were as follows: k1 = 200 s-1, k2 = 2,000 s-1, k3 = 39.8 s-1, k4 = 42.0 s-1, Kno1 = 917 mM, Kno2 = 10.1 mM, Kgabo = 41.0 µM, Kclo = 8.16 mM, Kni1 = 442 mM, Kni2 = 11.5 mM, Kgabi = 1.77 mM, Kcli = 3.66 mM, q1 = 0.684, q2 = 0.387, q3 = -0.071, q4 = 0.167, and q5 = -0.167.
Microscopic reversibility was enforced at each fitting cycle by forcing a correction factor on one parameter, such that
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(6) |
The factors, h1h5, modify the rates of voltage-dependent reactions. Those reactions that move positive charge in the outward direction are multiplied by their respective factor, and those moving positive charge in the inward direction are divided by their respective factor:
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(7) |
The sum of apparent valences, q(1...5), is 1, corresponding to one net charge moved per transport cycle,
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(8) |
Using d1d5, r1r4, and Kgat as temporary variables, the two-state model is simulated as follows. f0cn is the fraction of Ein transporters whose Cl-/Na+ binding sites are empty and are not available to bind Cl-i (i.e., closed by the fast voltage-dependent reaction related to q5). fcn is the fraction of Ein transporters whose cytoplasmic Cl-/Na+ binding sites are occupied by one Cl-i and the first Na+i to bind in the reverse transport cycle with the Kni1 dissociation constant. Although two Na+ ions can bind in the Ein state, only the first site must be occupied for the transition to the *Ein state:
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(9) |
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(10) |
and
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(11) |
Na+i and GABAi bind sequentially in the *Ein transitional state, although these binding reactions can be treated as parallel reactions with no important changes. f0g is the fraction of transporters in the transitional state whose GABAi binding sites are empty; fnag is the fraction of transitional transporters whose Na+i/GABAi sites are occupied by both Na+i and GABAi:
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(12) |
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(13) |
and
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(14) |
f1no is the fraction of *Eout transporters with a Na+ bound, and f0no is the fraction without Na+ bound:
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(15) |
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(16) |
and
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(17) |
ffullo is the fraction of Eout transporters occupied by Na+o and GABAo, whereby extracellular Na+ (no) and GABA (go) bind sequentially. Again, these binding reactions can be treated as parallel reactions without important changes. f0o is the fraction of Eout transporters with empty Na+/GABA binding sites:
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(18) |
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(19) |
and
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(20) |
fclo is the fraction of extracellularly-oriented Cl- binding sites which is occupied by Cl-:
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(21) |
The rate coefficients, k1 to k4, are multiplied by the appropriate factors to calculate the rates of the Ein Eout (r1 and r4) and the Eout
Ein (r2 and r3) transitions:
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(22) |
and
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Calculation of the reaction rates, r3 and r4, is more complex because more substrates interact with the *Ein state than the *Eout state. These rates are modified by a denominator, h6, derived analogously to that in Equation 2 and Equation 3. The denominator is the sum of the factors that modify exit rates from the *E2 state (Figure 1, Figure 3b and Figure 4b). The dissociation constant for Cl- in the Eout state is multiplied by a factor, fx, to give the dissociation constant in the *Ein state. Microscopic reversibility is maintained by modifying the Eout *Ein transition rate in the absence of Cl-o by the same factor. The extracellular Cl- dependence of the overall reaction, r3, is then
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(24) |
which simplifies to fclo. fx was assigned a value of 0.2 for the simulations presented, and its variation from 0.1 to 0.3 is without significant consequence.
The r3 and r4 rates are calculated as follows:
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(25) |
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(26) |
and
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(27) |
The fractional occupancy of the Ein and Eout states, and the steady state transporter turnover rate (Rgat) are calculated as follows:
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(28) |
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(29) |
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(30) |
and
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(31) |
As required by thermodynamics for a tightly coupled transport process, the complete equation system obeys the relationship,
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(32) |
For nonsteady state (kinetic) simulations, the Ein state at time t, Ein(t), is calculated from its value at time zero, Ein(0), and steady state value, Ein():
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(33) |
The charge moved per second by a single transporter is calculated as follows:
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(34) |
This equation takes into account the model assumption that Ein transporters undergo a fast (instantaneous) charge-moving reaction that enables Cl-i binding. Thus, for each transition that alters the Ein occupancy, it is calculated how much charge is moved simultaneously by a shift of the Ein distribution between the states with and without available Cl-i sites. We note that simulation results were nearly identical when the charge-moving reaction within the Ein state was simulated kinetically, using a three-state model, with forward and backward rate constants of 77,000 s-1, roughly as measured experimentally for Qfast.
Charge signals are presented only for the case that GABA is absent on both membrane sides, so that the r3 and r4 rates are zero. With this limitation, the total transporter-associated charge (Qgat), which has moved through the membrane electrical field, relative to the Eout state (i.e., with one occluded Na+o and no substrates bound), can be calculated:
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(35) |
Calculation of GABA Efflux Rates
Finally, the unidirectional GABA extrusion rate is calculated to relate model function to GABA radioisotope flux studies. The flux has two components: first, an outward GABA flux that occurs via the overall reaction 4 (Figure 1), and second, an exchange component that occurs when the Eout sites undergo conformational changes to the *Ein transitional state, and then return to the Eout state without reaching the Ein state. Thus,
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(36) |
Results were nearly identical when the transitional state was simulated as a stable state with high exit rates, and GABA efflux was calculated as occupancy of that state times the transition rate to the Eout state.
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Results |
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Fully Activated GAT1 CurrentVoltage Relations and Model Overview
Figure 3 shows fully activated currentvoltage relations predicted by the model, together with corresponding data from experiments. Here, and in subsequent figures with steady state model predictions, we plot the calculated transporter turnover rates (y axis), rather than membrane current magnitudes from experiments. The membrane currents (data points) are proportional to the simulated turnover rate (lines), and the current magnitudes are available for all data simulated from the relevant figures in the previous articles (
These simulations allow us to summarize concisely major features of the model's function: outward GAT1 current, in the absence of extracellular Na+, has weak voltage dependence that corresponds to the voltage dependence of substrate occlusion from the cytoplasmic side (k4). This step is rate limiting for reverse current because the deocclusion of Na+ to the extracellular side (k2) is very fast in the absence of extracellular Na+. For the same reason, the ratio of Ein to Eout occupancy does not change when voltage changes or cytoplasmic substrate concentrations are changed over a substantial range (not shown). The maximum turnover rate for outward transport at 0 mV, simulated for results at 32°C, is ~40 s-1.
The relative slope of the fully activated inward current is larger than that of the outward current. This slope is determined mostly by the valence of reaction 1a (Figure 1). The relatively slow rate of this process, even with 120 mM extracellular Na+, determines the 4.5-fold smaller magnitude of fully activated inward current, compared with outward current, at 0 mV. The inward current saturates with increasing hyperpolarization because the GABA translocation step (reaction 3a, Figure 1) becomes rate limiting. This saturation behavior is enhanced by our assumption that this step moves a small amount of negative charge from outside to inside (i.e., in opposite direction from Na+ occlusion). In fact, the model predicts that negative slopes of the currentvoltage relations should be found at more negative potentials. Also, the weak voltage dependence of the GABA translocation reaction (reaction 3a, Figure 1) contributes to a small voltage dependence of current activation by extracellular GABA (see Figure 7 C). The maximum forward transport rate at 0 mV is ~8 s-1. As indicated with bar graphs in Figure 3, changes of membrane voltage in the inward current condition result in large changes in the fractional distribution of the Ein and Eout states. In contrast, voltage changes result in very little shift from the Ein configuration in the outward current condition.
CisTrans Substrate Interactions for Reverse GAT1 Current
As described previously (
Figure 4 B shows the simulation result obtained for ciscis substrate interaction, when reverse current is limited by the "return" step of the alternating access model (i.e., with NaCl in the pipette). In this case, reduction of the cytoplasmic cosubstrate concentration, [Cl-]i, from 120 to 3 mM increases the half-maximal concentration of cytoplasmic GABA. The predicted effect is smaller than the experimental effect. As described at the end of RESULTS, this discrepancy is completely alleviated when the *Ein state is simulated as a stable state that can accumulate significantly.
GABAGABA Exchange
Isotope flux studies of GABAGABA exchange provide another important test of our model. In outside-out synaptic membrane vesicles, extracellular GABA promotes GABA efflux both in the presence and in the nominal absence of extracellular Cl- (
Figure 5 A shows the relevant measurements of GABA efflux by
Cytoplasmic Substrate Interactions in the Activation of Reverse GAT1 Current
The model predictions for cytoplasmic substrate interactions in the activation of reverse GAT1 current were presented together with the relevant data (Lu and Hilgemann, 1999; see Figure 9). Here, we summarize the major features. (a) The GABAi dependence of the fully activated current shows almost no change when either cytoplasmic Na+ or Cl- is reduced. This is because a time-dependent transition takes place between the binding of Cl-i and the first Na+i ion, and the binding of GABAi. Also, the second Na+i ion binds with such a high affinity that reduction of Na+ to a few millimolar has no effect on the apparent GABA affinity. (b) There is almost no change of the apparent Cl-i affinity with reduction of cosubstrate concentrations. This is because the second Na+i and GABAi bind in a state that is temporally separated from that in which Cl-i binds. Also, it is important that one Na+i binds immediately after binding of Cl-i. This arrangement explains why Na+i does not inhibit the inward GAT1 current in the absence of Cl-i (see Figure 8). (c) With [Cl-]i reduction, there is a shift of the half-maximal Na+i concentration to higher values. This is accounted for by the assumed sequential Cl- Na+
Na+ binding order; the inhibitory effect of reducing the Cl-i concentration can be overcome by higher Na+i concentrations.
Voltage Dependencies of Outward GAT1 Current
Figure 6 shows experimental and predicted currentvoltage relations for the outward GAT1 current (20 mM Cl-o and no other extracellular substrates). Figure 6 A shows the effect of adding 120 mM extracellular Na+ via pipette perfusion. Inhibition is ~75% at -120 mV, but only ~10% at +90 mV. The strongly voltage-dependent deocclusion reaction becomes rate limiting for the reverse transport cycle at negative potentials in the presence of Na+o. Positive membrane potential relieves the inhibition because transporters are driven to accumulate in the E1 state. Discrepancies between the experimental and predicted results are in the range of our experimental error.
Figure 6BD, shows results in the absence of extracellular Na+. Figure 6 B shows the effect of lowering the cytoplasmic Na+ concentration from 120 to 20 mM on the outward currentvoltage relation. The model predicts no significant change of the shape of the currentvoltage relation; the measured currentvoltage relation in low [Na+]i is somewhat steeper than predicted. This could reflect a small voltage dependence of Na+i binding (not simulated), whose influence becomes more pronounced when Na+i concentrations are not saturating.
Figure 6 C shows the effect of lowering cytoplasmic GABA from 20 to 0.5 mM. In this case, the simulated currentvoltage relation at the low GABAi concentration is somewhat steeper than experimental results. One possible explanation is that GABAi interaction (binding and/or occlusion) from the cytoplasmic side becomes rate limiting at low GABAi concentrations; the three-state simulation described at the end of RESULTS gives a more accurate account of this result. Figure 6 D shows the effect of reducing cytoplasmic Cl- from 120 to 5 mM on the currentvoltage relation. The discrepancy between predicted and observed results reflects an experimental variability of the apparent Cl-i affinity, as noted in MATERIALS AND METHODS. The shapes of currentvoltage relations are predicted with reasonable accuracy.
Voltage Dependence of Apparent Extracellular Substrate Affinity
Figure 7 shows the substrate dependence of the inward GAT1 current in whole-oocytes at different membrane potentials. These data points have been replotted from *Ein
Ein transition becomes rate limiting.
Figure 7 B shows the Cl-o dependence of the inward current at -140 and -40 mV. The Cl-o dependence is biphasic. Approximately 50% of the current activates with very high affinity, and ~50% with low affinity (Kd = 8 mM). The high-affinity component comes about because the overall Eout Ein transition becomes very fast when [GABA]i is low. This, in turn, depends on our assumption that GABAi can be translocated from the extracellular side in the absence of Cl-o. The apparent affinity will be determined by the ratio of rates 3b to 4a (Figure 1), which in our simplified model is infinity. The effect of membrane potential and the overall Cl-o dependence are predicted accurately.
Figure 7 C shows the GABAo dependence of the inward current. When maximum current is strongly reduced by depolarization, there is a modest increase in the apparent GABAo affinity at less negative potentials. In currentvoltage relations (see Figure 9), this effect results in a more pronounced saturation of current with hyperpolarization when the GABAo concentration is low.
Inhibition of Inward and Outward GAT1 Currents by Substrates from the Trans Side
Figure 8 shows the inhibition of inward GAT1 current in giant patches by cytoplasmic substrates (0 mV; 120 mM extracellular NaCl and 0.2 mM extracellular GABA). Results in Figure 8AC, are for the individual substrates, Cl-i, Na+i, and GABAi, respectively. Cytoplasmic Cl- monotonically inhibits the inward current with half-inhibition at ~15 mM (Figure 8 A). Cytoplasmic Na+ and GABA, when applied individually, have almost no effect (B and C). The lack of effect of Na+i and GABAi relies on the assumption that the *Ein state does not accumulate significantly during inward current. The complete lack of effect of GABAi, in the absence of Cl-i and Na+i, derives from the assumption that Na+i binding precedes GABAi binding in the *Ein state. However, the results are only marginally different when binding of cytoplasmic Na+ and GABA is simulated as parallel reactions (not shown). In the presence of 120 mM Na+i and the absence of Cl-i, GABAi inhibits the inward current with low affinity (Figure 8 D); the predicted inhibition is ~75% with 20 mM GABAi, while the inhibition obtained experimentally is ~60%.
Outward GAT1 current. For brevity, we do not show model results on the inhibition of outward GAT1 current by substrates applied to the extracellular side. The inhibitory effect of extracellular Na+ on outward current was described in Figure 6 A. In the absence of extracellular Na+, outward current is inhibited by only ~10% when [Cl-]o is increased from 0 to 120 mM in the model, and this is in close agreement with our experimental experience. The Cl-o inhibition is small because the Eout state does not accumulate significantly in this condition. Extracellular GABA is without effect in the absence of extracellular Na+ because GABAo binds after Na+o in the model.
Voltage Dependence of the Inward GAT1 Current
Figure 9 shows the predicted and measured currentvoltage relations of the inward GAT1 current in patches (A) and whole oocytes (BD). Figure 9 A shows the effect of Cl-i (0, 30, and 120 mM) on inward current in an oocyte patch. With high [Cl-]i, inward currents lose their tendency to saturate at negative potentials.
Figure 9BD, shows simulation results for whole-oocyte experiments, whereby we have assumed cytoplasmic Na+ and Cl- to be 12 and 50 mM, respectively. Figure 9 B shows the effect of reducing [Na+]o from 96 to 29 mM. In the absence of Cl-i, the currentvoltage relation would be shifted by ~30 mV to more positive potentials. For the most part, the effect of reducing [Na+]o is to shift the currentvoltage relation to more negative potentials, and this is well predicted.
Figure 9 C shows the experimental effect of removing extracellular Cl-. We assume for this simulation that nominally Cl- -free solutions will still contain 1 µM Cl-. With this assumption, the simulated currentvoltage (IV) relations describe the experimental data accurately without violating a fixed transport stoichiometry. Removal of Cl- scales down the IV relation and somewhat enhances the saturation with hyperpolarization. Figure 9 D shows the effect of reducing extracellular GABA from 100 to 10 µM; saturation of IV relations at negative potentials becomes more pronounced at low extracellular GABA.
GAT1 Kinetics
Figure 10 Figure 11 Figure 12 Figure 13 Figure 14 Figure 15 describe model predictions for GAT1 kinetic function. Figure 10 shows the charge movements predicted by the two-state model. These results are shifted by ~25 mV from results shown subsequently under identical conditions. We suspect that this variability, already pointed out in MATERIALS AND METHODS, reflects a variable regulatory process in the oocytes that influences GAT1 function. To demonstrate the kinetic behavior of the model in relation this data, therefore, we have used 70 instead of 40 mM NaClo to simulate this single data set. The results are calibrated as charge moved (e) per single transporter. In agreement with experimental results, the simulated charge signals contain immediate charge jumps on changing potential from positive values to -40 mV. These jumps arise from the charge-moving reaction of the empty Cl-i binding sites (q5), which moves a total of -0.08 equivalent charges per transporter. Clearly, the kinetics of slow charge movements are simulated accurately by the model.
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Figure 11A and Figure B, shows the predicted and measured rate and chargevoltage relations from another experiment with 40 and 60 mM extracellular Na+ and Cl-, respectively. The shapes and positions of both the rate and chargevoltage relations are predicted accurately. Figure 11 C shows the predicted and measured effect of 120 mM cytoplasmic Cl- on chargevoltage relations in the presence of 90 mM extracellular NaCl. Qualitatively, the simulations are in good agreement with the experimental data.
Since the results described next were performed at room temperature with intact oocytes, we describe here the effect of temperature on GAT1 currents. Figure 12 shows the temperature dependence of both the inward and outward transport currents in oocyte patches. Increasing temperature from room temperature (23°C) to 32°C at 0 mV causes a 2.2-fold increase in both currents. Although we have not characterized the temperature dependence of charge movements in detail, we have observed rate changes for individual voltage pulses in this general range. To fit the charge movement rates determined in oocytes, it was essential to divide the predicted model rates by a somewhat larger factor of 3.6. This larger factor might reflect the loss of some inhibitory influence on GAT1 transport upon patch excision.
Figure 13 and Figure 14 show results from whole-oocyte experiments. Figure 13 shows the rates of slow charge movements with 96 mM Cl-o at different extracellular Na+ concentrations (96, 58, 12, and 3 mM). These results are replotted from *Eout transition (i.e., opening of binding sites from the loaded state) is strongly inhibited by Na+o binding at the second extracellular site. There is an additional acceleration at low [Na+]o because the overall Eout
Ein transition is inhibited by Na+o binding to the transitional *Eout state.
Figure 14 shows the voltage and Na+o dependencies of the slow charge movement in intact oocytes and in the model. Figure 14 A presents the voltage dependence of charge moved at different extracellular Na+ concentrations (12, 24, 48, 77, and 96 mM). Again, the results are replotted from
Current Transients
Figure 15 shows simulations of GAT1-mediated currents under the different conditions studied with voltage pulse protocols. The corresponding experimental results ( *Ein transition; the Na+ deocclusion reaction (Eout
*Eout) takes place 10x faster. A predicted experimental result, which we have not tested, is that significant current transients should occur after pulsing to large negative potentials. Figure 15 B shows simulated results for outward current in the presence of 120 mM extracellular NaCl. In this case, current transients at positive potentials are substantial. They come about because in this condition the relatively slow deocclusion of Na+o from the Eout state allows transporters to accumulate in the Na+o-occluded Eout state, which is subsequently released by voltage pulses to positive potentials.
Figure 15 C simulates the inward current condition (i.e., with all substrates on the extracellular side and none on the cytoplasmic side). Upon hyperpolarization to -120 mV, the inward current relaxes by ~75%, and on returning to positive potentials, the "off" transients are smaller (i.e., they would integrate to a smaller total amount of charge moved). The model behaviors are in reasonable agreement with experimental results (see Figure 7 and Figure 8;
Figure 15 E shows simulation results for the "reversal" condition (6 mM Cl-, 120 mM Na+, and 2 mM GABA on the cytoplasmic side; 120 mM Na+, 40 mM Cl-, and 2 mM GABA on the extracellular side). Small steady state currents are generated, but there are essentially no presteady state transients. The major reason is that the transport reactions involving fully loaded transporters are nearly electroneutral.
GAT1-mediated Capacitance Signals: Limited Occupancy of the *Ein State Is Probable
The simulation equations assume that empty transporters undergo a voltage-dependent reaction (q5). This reaction gives rise to a capacitance that decreases when cytoplasmic Cl- binds from the cytoplasmic side, but other details of the Qfast reactions are not represented. In particular, we know that charge-moving reactions still occur in the Cl-i-bound state. To simulate roughly results on capacitance, we assume that the entire Eout state is a null state that contributes no capacitance. We assigned the fractions of the Ein state with no substrates bound a relative capacitance of unity, and we assigned a relative capacitance of 0.93 to the fractions of the Ein state that have at least one bound substrate. From our experimental data (
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Improved Simulations with a Three-State Model: The *Ein State Can Accumulate
The following discrepancies between the two-state model predictions and corresponding experimental data cannot be explained by experimental variability and therefore appear fundamental. (a) In the simulation of ciscis substrate interactions with extracellular Na+ (Figure 4 B), reduction of cytoplasmic Cl- does not shift the GABAi dependence of outward current strongly enough to higher GABAi concentrations. (b) The measured currentvoltage relations for outward current become relatively more shallow with reduction of GABAi (Figure 6 C). (c) The extracellular Na+ dependence of inward current does not saturate strongly enough with increasing [Na+]o at negative potentials (Figure 7 A). (d) In the simulations of capacitance results (Figure 16), the relative capacitance of the substrate-bound Ein fractions must be assumed to be larger than measured experimentally. Also, the presence of Na+i shifts the Cl-i dependence of capacitance to lower Cl-i concentrations.
All of these discrepancies were reduced significantly, or eliminated, in simulations that included kinetic simulation of the *Ein state. The rate coefficients of reactions 3b and 4b (Figure 1) were selected by the fitting routine such that the *Ein state accumulated substantially during reverse GAT1 operation, while its occupancy remained negligible during forward GAT1 operation. Reaction 4b was assigned the voltage dependence of q4, and for simplicity the reactions 4a and 3b were left voltage independent. With these assignments, all other simulation results remained at least as accurate as those presented for the two-state model. The fitted parameters were as follows: k1 = 53.7 s-1, k2 = 1,642 s-1, k3 = 61.7 s-1, k4 = 365.8 s-1, Kno1 = 237 mM, Kno2 = 7.4 mM, Kgabo = 68.3 µM, Kclo = 54.0 mM, Kni1 = 1,283 mM, Kni2 = 8.0 mM, Kgabi = 0.66 mM, Kcli = 5.18 mM, q1 = 0.652, q2 = 0.419, q3 = -0.059, q4 = 0.215, q5 = -0.22, and fx = 0.3. The additional rate constants for reactions 3b and 4b were 1,767 and 52.2 s-1, respectively.
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Discussion |
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Our ability to simulate GAT1 function in oocyte membrane by a model with only two stable states lends confidence to our conclusion that GAT1 works by a simple alternating access mechanism. The model described, while simple, incorporates many detailed assumptions about substrate binding and the dependencies of state transitions thereon. It accounts for many aspects of GAT1 function that we could not explain before undertaking a comprehensive simulation effort. We recognize that our specific assumptions are ad hoc in nature. However, our central assumption is the fundamental principle of enzyme kinetics that substrate binding can either enable or disable individual enzymatic reactions. Also, we recognize that experimental variability limits confidence in the model parameters determined. Nevertheless, the biological variability of GAT1 function, which may reflect the influence of important regulatory processes, does not compromise the simulations presented in any obvious way. We have discussed our simulations for the most part with their presentation.
Cl-o-independent GABA Flux and Transport Current
Our simulations give us no new insight into the significance of uncoupled GAT1 currents, as reported for GAT1 expressed in HEK cells (
An important related issue, which has received less attention in recent years, is the coupling of GABA transport with Cl- movements. Our model assumes tight 1:1 Cl-:GABA coupling during transport, and for the reverse GAT1 transport mode, 20 mM cytoplasmic GABA activates no current in the absence of cytoplasmic Cl-. Our model predicts that GABAo-induced inward currents can be significant at negative potentials with micromolar (or even submicromolar) concentrations of extracellular Cl- (
We stress that experimental evidence for this explanation is still lacking, and three other possibilities must be considered. (a) Extracellular Cl- contamination might be greater than we expect, both in the clefts of oocyte surface and in the pipette tip during our pipette perfusion experiments. (b) The Cl- substitutes employed in experiments might be transported at a slow rate in place of Cl-. (c) Genuine Na+/GABA cotransport may occur under Cl-o-free conditions via transporter reactions that do not occur in the presence of Cl-. This last possibility was suggested from recent isotope flux studies in Xenopus oocytes (Loo, D.D.F., S. Eskandari, and E.M. Wright, personal communication). These authors found that GABA uptake is well coupled with Cl-o uptake in the presence of Cl-o, but that Na+-dependent GABA uptake remains substantial at negative potentials in the absence of extracellular Cl-. Since the current-to-uptake ratio is not much changed in Cl-o-free solution, a 1 Na+/1 GABA uptake mode would explain the results.
Perspectives and Possible Relevance to Other Cotransporters
Finally, it is interesting to compare our model of GAT1 function with relevant models of other transporters. First, we predict that only one Na+ is occluded in an energetically stable state in the GAT1 transporter. This is different from the Na+/K pump in which stable occluded states are formed with three bound Na+ as well as two bound K+ (e.g., Karlish, 1998). Second, we are impressed that transitional states seem important to account for GAT1 function. This is how Na+ occlusion from the outside can be tightly coupled with the empty carrier conformational change that alternates binding site access. Third, our general modeling scheme for the Na+o -dependent charge movements and their kinetics in GAT1 can probably be applied to Na+/glucose transporters, although there is no obvious sequence similarity between these transporters.
In conclusion, our analysis of GAT1 function does not exclude cotransport coupling mechanisms other than the alternating access mechanism. Nevertheless, our analysis of GAT1 function clearly favors conservative interpretations. We have verified rigorously the alternating access model, established probable cytoplasmic and extracellular substrate binding schemes, identified probable sources of electrogenicity, and refined the kinetic analysis of others. Our model of GAT1 function should be useful in understanding GAT1 mutants that exhibit altered kinetics and charge movements (
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Acknowledgements |
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We express our gratitude to Dr. Vladislov Markin for many helpful discussions and mathematical aid. For other acknowledgments, see
Note Added in Proof. We have examined the sensitivity of GAT to several interventions that are relevant to the described variability of GAT1 charge movements and cytoplasmic Cl- dependence. Protein phosphorylation might be important because an alkaline phosphatase (P1030; Sigma Chemical Co.) can strongly inhibit outward GAT1 current (>80%). Cytoskeletal interactions also might be important because microfillament disrupters, cytochalasin D (10 µM) and latrunculin B (25 µm), inhibited the outward current. Phosphatidylinositol-bisphosphate and phosphatidic acid were without effect.
Submitted: August 10, 1998; Revised: July 1, 1999; Accepted: July 2, 1999.
1used in this paper: GABA, -aminobutyric acid
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References |
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