Abstract
At nicotinic and glutamatergic synapses, the duration of the postsynaptic response depends on the affinity of the receptor for transmitter (Colquhoun et al., 1977; Pan et al., 1993). Affinity is often thought to be determined by the ligand unbinding rate, whereas the binding rate is assumed to be diffusion-limited. In this view, the receptor selects for those ligands that form a stable complex on binding, but binding is uniformly fast and does not itself affect selectivity. We tested these assumptions for the GABAAreceptor by dissecting the contributions of microscopic binding and unbinding kinetics for agonists of equal efficacy but of widely differing affinities. Agonist pulses applied to outside-out patches of cultured rat hippocampal neurons revealed that agonist unbinding rates could not account for affinity if diffusion-limited binding was assumed. However, direct measurement of the instantaneous competition between agonists and a competitive antagonist revealed that binding rates were orders of magnitude slower than expected for free diffusion, being more steeply correlated with affinity than were the unbinding rates. The deviation from diffusion-limited binding indicates that a ligand-specific energy barrier between the unbound and bound states determines GABAA receptor selectivity. This barrier and our kinetic observations can be quantitatively modeled by requiring the participation of movable elements within a flexible GABA binding site.
Interactions between neurotransmitters and receptors are often assessed by analyzing the equilibrium concentration–response relationship (Segel, 1976;Pallotta, 1991). However, the applicability of equilibrium conditions is problematic for fast chemical synapses in which the concentration of neurotransmitter rises and falls rapidly (Magleby and Stevens, 1972;Katz and Miledi, 1973; Lester et al., 1990; Clements et al., 1992). Transmitter binding primarily occurs early in the synaptic response when the free transmitter concentration is high, whereas unbinding primarily occurs as transmitter is decaying or after it has been cleared. Furthermore, the EC50 does not reflect any individual transition but is instead an indicator of the total time spent in all channel states (for review, see Jones and Westbrook, 1996). The binding steps probably determine the fraction of receptors activated and the likelihood of intersynaptic communication (Barbour and Häusser, 1997), whereas the gating and unbinding steps determine the response duration. A quantitative understanding of the contributions of binding, gating, and unbinding in shaping synaptic transmission is greatly facilitated by a nonequilibrium approach.
Binding and unbinding kinetics also provide functional (and possibly structural) information about the binding site, which is especially important given the scarcity of crystallographic information for ligand-gated channels. For example, the binding of ACh to nicotinic ACh receptors is almost as fast as that predicted if the rate-limiting step is the diffusion of ligand into the binding site (Colquhoun and Sakmann, 1985; Colquhoun and Ogden, 1988; Papke et al., 1988; Jackson, 1989; Auerbach, 1993; Franke et al., 1993; Sine et al., 1995; Akk and Auerbach, 1996). Such efficient binding suggests that there are few significant barriers to binding and that there is an almost perfect “fit” between agonist and the activated receptor (Jackson, 1989). Binding at AMPA, NMDA, and GABAA receptors appears to be somewhat slower than that for nicotinic ACh (nACh) receptors (Clements and Westbrook, 1991; Jonas et al., 1993; Celentano and Wong, 1994; Jones and Westbrook, 1995; Raman and Trussell, 1995;Häusser and Roth, 1997), although the structural and functional significance of slower binding at these receptors remains unknown.
One approach to understanding the nature of affinity and selectivity is to compare binding and unbinding between different ligands at the same receptor. For nACh and NMDA receptors, affinity was found to be inversely related to the unbinding rate (Colquhoun et al., 1977;Colquhoun and Sakmann, 1985; Papke et al., 1988; Benveniste et al., 1990a,b; Benveniste and Mayer, 1991; Lester and Jahr, 1992; Pan et al., 1993; Akk and Auerbach, 1996). However, there is also evidence that differences in affinity between agonists at nACh and GABAAreceptors are more strongly determined by the binding rate (Sine and Steinbach, 1986; Jones and Westbrook, 1995; Zhang et al., 1995; Akk and Auerbach, 1996). Here, we investigated the binding and unbinding of GABAA receptor ligands with affinities spanning several orders of magnitude, using fast solution exchange methods in outside-out patches. Unbinding rates could not account for affinity if diffusion-limited binding was assumed. In contrast, affinity could be predicted from the binding rates that were much slower than the diffusion limit. These data indicate that an energy-requiring event, such as a conformational change of the GABA binding site, precedes or accompanies binding.
MATERIALS AND METHODS
Cell culture and recording. Cell culture methods were identical to those described previously (Jones and Westbrook, 1995). Outside-out patches were excised from neonatal rat hippocampal neurons maintained in culture from 1 to 4 weeks. Recordings were made under voltage-clamp (Vhold = −60 mV; 25°C). Internal pipette solutions contained (in mm): 144 KCl, 1 CaCl2, 3.45 BAPTA, 10 HEPES, and 5 Mg2ATP, at pH 7.2 and 315 mOsm. The standard external solution contained (in mm): 140 NaCl, 2.8 KCl, 1 MgCl2, 1.5 CaCl2, 10 HEPES, 10d-glucose, 0.01 CNQX, and 0.001 strychnine, at pH 7.4 and 325 mOsm. When β-alanine (100 mm) or 4,5,6,7-tetrahydroisoxazolo[5,4-c]pyridin-3-ol HCl (THIP; 50 mm) were used, the NaCl concentration was adjusted to 110 or 60 mm (plus sucrose) to maintain a constant osmolarity. GABAA receptor agonists and antagonists were added to the external solution and applied to whole cells or patches using multibarreled flow pipes (Vitro Dynamics, Rockaway, NJ) mounted on a piezoelectrical bimorph (Vernitron, Bedford, OH). Two computer-controlled voltage sources in series with the bimorph were used to control solution exchanges. Whole-cell solution exchange required ∼100 msec, whereas the 10–90% rise and fall times of liquid junction currents at the open pipette tip after each patch experiment were <1 msec. Currents were filtered at 1–5 kHz using a four-pole Bessel filter and were acquired at greater than or equal to twice the filter frequency (AxoBASIC; Axon Instruments, Foster City, CA). Muscimol, THIP, and 2-(3-carboxypropyl)-3-amino-6-(4-methoxyphenyl)pyridazinium bromide (SR-95531) were obtained from Research Biochemicals (Natick, MA). GABA, β-alanine, and all other chemicals were from Sigma (St. Louis, MO).
Estimation of unbinding rates. We used a modification of a previously established Markov model of GABAA receptor kinetics (Jones and Westbrook, 1995, 1997) to estimate agonist unbinding rates. Responses from several experiments were averaged together before performing least-squares fitting of the data. Fitting and calculation of confidence limits were performed using SCoP (Simulation Resources, Berrien Springs, MI). The addition of transitions between desensitized states that entail a net counterclockwise movement at steady state allows more accurate fitting of slow components (Jones and Westbrook, 1995) and does not qualitatively alter our conclusions. Data are reported as mean ± SEM unless otherwise noted. Kinetic differences were determined by two-tailed t tests or by one-way ANOVA followed bypost hoc tests when several groups were compared.
A general model of binding and unbinding kinetics. Because rate constants derived from predefined Markov models may depend strongly on the structure of the model chosen, we also used a more general format for describing ligand–receptor interactions. This approach is based on the assumptions common to mass action treatments of binding and enzyme kinetics and requires no a priori knowledge of rate constants or the number and cooperativity of ligand binding sites. We assume that channels are independent and that each channel containsN binding sites. By analogy with Hodgkin–Huxley formalism (Hille, 1992), binding to each site (n) can be described by the reaction: Equation 1so that ωn = [A]konn and υn =koffn, wherePn is the probability of being bound (occupancy), [A] is the ligand concentration, andkon and koff are the rate constants for binding and unbinding. When the ligand concentration is changed, the occupancy will relax over time to a new value according to: Equation 2where the occupancy is Pn0initially (at t = 0) andPn∞ at steady state (ast → ∞): Equation 3The microscopic affinity constantKn can be defined by solving Equation 3for the concentration at half-occupancy, yielding: Equation 4The probability of receptor saturation (Psat) is the product of the individual occupancies: Equation 5and if all sites are equal and independent (i.e., ω1 = ω2 … ωn and υ 1 = υ2 … υn), then: Equation 6As with Equation 4, solving Equation 6 for the concentration of half-saturation defines the macroscopic affinity constantKN , which is a function of both the microscopic affinity and the number of sites N: Equation 7Finally, the equilibration time constant τn at each site is given by: Equation 8whereas the macroscopic equilibration will have Ncomponents. The version of Equation 8 on the right is particularly useful because 1/τn is a linear function of concentration, the slope and intercept of which are the microscopic rate constants.
Additional allowances are required to model agonist-activated currents. For example, agonist efficacy could be described using proportionality constants relating occupancy to open probability, and desensitization could be described by Hodgkin–Huxley-style inactivation parameters. Here, however, we will use the relations as given above and focus our attention on the binding and unbinding of the competitive antagonist SR-95531 that is not expected to cause channel gating or desensitization (Hamann et al., 1988; Jones and Westbrook, 1997; but see Ueno et al., 1997). We first consider a mechanism in which antagonist binding to any one of the binding sites is sufficient to prevent channel opening. For equal and independent sites, the probability that a channel will be available for activation (i.e., all sites remain free of antagonist) is thus: Equation 9For unequal sites, Equation 9 would be expanded to include the individual parameters (compare Eq. 5). This treatment can easily be extended to the case in which all sites must be occupied by antagonist to block the channel, but such a model did not accurately describe our data.
Measuring agonist binding rates. When an agonist and competitive antagonist are rapidly and simultaneously applied to a patch, the resulting peak current is smaller than that produced by agonist alone because some channels initially bind antagonist and become blocked. We refer to such instantaneous competition as a “race” experiment (e.g., Clements et al., 1992; Diamond and Jahr, 1997). For a single site per receptor at which the two ligands compete (see Results): Equation 10and: Equation 11where R is the fraction of receptors bound with either agonist or antagonist, ω is the binding rate (i.e., the concentration times a rate constant), and Iraceis the ratio of peak current produced during the race to that produced by agonist alone. Dividing both the numerator and denominator of Equation 11 by Rag, substituting from Equation 10, and rearranging yield: Equation 12where kon(ag) andkon(ant) are the binding rate constants and [ag] and [ant] are the concentrations of agonist and antagonist. Therefore, if the antagonist binding rate is known and unbinding is slow relative to the current rise time, then Equation 12 can be used to measure the agonist binding rate by performing a race experiment.
Diffusion and energetics. If every encounter between diffusing ligand molecules and the binding site results in ligand attachment, the binding reaction is said to be diffusion-limited. We estimated the theoretical rate constant for such a process by assuming (1) that the radius of the encounter (r) is approximately the same as the size of a GABA molecule (∼4 Å), (2) that the binding site can be approached from any direction, and (3) that the ligand diffusion coefficient (D) is 3 × 10−6 cm2sec−1 (Busch and Sakmann, 1990). The rate constant (kdiff) for a diffusion-limited binding reaction would then be (Freifelder, 1982; Hille, 1992): Equation 13where NA is Avogadro’s number. Other equally plausible assumptions could give values forkdiff greater or smaller than that of Equation13. However, we will show in the Results that such variation is negligible in comparison with the measured differences in agonist binding rates.
When ligand binding is not diffusion-limited, only encounters possessing sufficient energy result in productive binding. The Arrhenius equation (Freifelder, 1982) relates this activation energy (Ea ) to the ratio of observed and diffusion-limited binding rates: Equation 14where R is the gas constant and T is the absolute temperature.
Physical modeling of the agonist binding reaction. We used rudimentary molecular modeling to simulate the experimentally determined energetics of the binding/unbinding reaction. Both the agonists and the binding site were assumed to consist of “particles” that undergo purely van der Waals-like interactions with each other. Each agonist was modeled as two particles representing the agonist endpoints, separated by a fixed length [estimated from minimum energy conformations in vacuo using ChemOffice (CambridgeSoft, Cambridge, MA)]. The binding site was modeled either as being rigid (i.e., two particles a fixed distance apart) or as being flexible (two rigid anchor particles separated by a distanceLsite, associated with two movable arm particles). For the rigid model, unbound agonists were assumed to be associated with additional movable particles representing waters of hydration. The changing energy of the system as ligand binding progressed stepwise was calculated using the Lennard–Jones potential equation (Freifelder, 1982; Morris et al., 1996): Equation 15where r is the distance between any two particle centers (in angstroms). The empirical coefficientsC12 and C6 are related to the repulsive and attractive intermolecular forces, respectively, and are defined in terms of the equilibrium distance between particle centers (reqm) and the depth of the energy well (ε) occurring at that distance (Morris et al., 1996): Equation 16The total energy of the system at each step was the sum of all pairwise particle interaction energies. For simplicity, all particles and movements were coplanar for a rigid site and collinear for a flexible site. Model parameters were optimized for all agonists simultaneously using a simplex algorithm (Nelder and Mead, 1965) to minimize the sum of squared errors in energy. Simulation programs were written in MATLAB (The Math Works, Natick, MA) and run on Macintosh computers.
RESULTS
Deactivation depends on agonist affinity whereas gating does not
The decay of the IPSC represents the relaxation of GABAA receptors from ligand-bound to unbound states. Although oscillations between open and desensitized states are important in shaping this deactivation, the rate of ligand unbinding must also contribute (Jones and Westbrook, 1995, 1996, 1997). To assess this contribution, we examined currents activated by saturating pulses of a series of GABAA receptor agonists (GABA, muscimol, THIP, and β-alanine) to outside-out patches from rat hippocampal neurons. Figure 1Ashows that the duration of deactivation after brief (5 msec) agonist pulses depends strongly on the agonist. The time constants (τfast and τslow) and the relative contribution of the fast decay component (%fast) were 15 ± 2 and 372 ± 39 msec (50 ± 6%), respectively, for muscimol (n = 4); 14 ± 2 and 233 ± 17 msec (64 ± 3%) for GABA (n = 18); and 12 ± 2 and 109 ± 32 msec (87 ± 4%) for THIP (n = 4). In four of six patches, β-alanine currents were best fit by a single exponential of 9 ± 2 msec. In contrast to the agonist-dependent deactivation, current amplitudes and kinetics were indistinguishable during long (505 msec) pulses that maintained the receptor in the fully bound state (Fig.1B). Desensitization was fitted with two exponential components for all agonists [e.g., for GABA, 20 ± 4 msec, 786 ± 40 msec, and 40 ± 3% (n = 18)]. Deactivation at the end of long agonist pulses was agonist-dependent and followed the same rank order as that for brief pulses (Fig.1B). Because the agonists produced indistinguishable currents under saturating conditions (i.e., they appear to have identical efficacy), any kinetic differences were presumably caused by binding or unbinding. Thus, agonist-dependent deactivation results from agonist-specific unbinding.
The role of unbinding kinetics in deactivation and receptor affinity
Affinity describes the probability of finding a ligand molecule bound to the receptor for a given ligand concentration, whereas selectivity refers to differences in affinity between ligands. Both measures depend on the time that each ligand spends in the binding site but also on the likelihood that the ligand becomes bound in the first place. To understand the factors governing the entry and exit of ligands at the binding site, we began by measuring the apparent affinities of muscimol, GABA, and β-alanine from peak whole-cell concentration–response plots using the Hill equation (Fig.2A,B). For muscimol, KH was 10.9 μmN, and N was 0.96; for GABA, KH was 15.4 μmN, and N was 0.93; and for β-alanine, KH was 5.9 mmN, and N was 1.0. Caution is necessary in interpreting such data because the overlapping time courses of desensitization and whole-cell solution exchange may distort the peak current. We therefore estimated the EC50values of muscimol, GABA, THIP, and β-alanine in outside-out patches in which solution exchange is much faster. Figure 2C shows ensemble average currents activated by maximal and half-maximal (i.e., peak current between 45 and 55%) agonist concentrations. The patch EC50 values spanned several orders of magnitude with the rank order being muscimol < GABA < THIP < β-alanine, identical to the rank order for the rate of patch current deactivation.
We estimated the microscopic unbinding rate (koff) by fitting currents activated by pulses of the four agonists to a kinetic model of the GABAAreceptor (Jones and Westbrook, 1995, 1996, 1997). The model (Fig.3A) was first optimized to fit the responses to 5 and 505 msec pulses of GABA (10 mm). Thereafter, only koff was allowed to vary as a free parameter in fitting currents activated by the other agonists. The optimum values of koff were (in sec−1) 40 for muscimol, 131 for GABA, 1125 for THIP, and 4500 for β-alanine (Fig. 3B). Both the overall patch current deactivation rates [i.e., 1/(the weighted average of fast and slow components); Fig. 3C] and the EC50 values (Fig. 3D) were strongly correlated with koff, suggesting that agonist unbinding kinetics are important in shaping the current as well as in determining the agonist selectivity. However, if diffusion-limited binding is assumed (Eq. 13), the expected microscopic affinity constants (Eq. 4) obtained using these unbinding rates were 4.3 nm for muscimol, 14 nm for GABA, 124 nm for THIP, and 490 nm for β-alanine, values more than a thousand times lower than the EC50 values observed experimentally (Fig. 2). These results imply that large differences in binding rate (kon) between agonists contribute to agonist selectivity.
Comparison of GABA and β-alanine binding
As a direct test for differences in agonist binding rates, we set up a race for the binding site between agonists and a competitive antagonist. When an agonist and a competitive antagonist are rapidly and simultaneously applied to a patch, some channels will bind agonist and open, whereas others bind antagonist and become blocked. The resulting current (Irace = current with both ligands/current with agonist alone) depends on which ligand binds faster on average. We first used the antagonist SR-95531 (Hamann et al., 1988; Jones and Westbrook, 1997; Ueno et al., 1997) to determine whether or not GABA and β-alanine have similar binding rates. SR-95531 [KN of 160 nm(Hamann et al., 1988)] meets the classical criteria for competitive antagonism in that it causes parallel right-shifts in the GABA concentration–response curve but evokes no response on its own. Its action is also modified by mutations in the putative GABA binding site (Ueno et al., 1997), suggesting that it interacts with the same regions occupied by GABA and other agonists. Coapplication of 1 mmSR-95531 and 1 mm GABA blocked 89 ± 2% (n = 11) of the peak current evoked by 1 mmGABA alone (Fig. 4A). Because no current at all was observed when 1 mm SR-95531 was coapplied with 1 mm β-alanine, the concentration ratio was adjusted to favor β-alanine binding by a factor of 1000. Coapplication of 100 μm SR-95531 with 100 mmβ-alanine blocked 66 ± 5% (n = 3) of the current evoked by 100 mm β-alanine alone (Fig.4B). This result suggests that GABA and β-alanine have widely different binding rates and argues against diffusion-limited binding.
Binding and unbinding kinetics of the competitive antagonist SR-95531
The notion that agonist binding is not diffusion-limited is interesting because it implies that the mere physical proximity of ligand and receptor is not sufficient to produce binding but rather that some additional event must occur. The quantification of binding rates using race experiments might disclose the nature of such an event but requires knowledge of the antagonist kinetics. We therefore measured binding and unbinding rates for SR-95531. Figure5 shows the method used to study equilibration of SR-95531 with the GABAA receptor. A saturating GABA pulse was applied as an assay of the maximum channel availability. The patch was then exposed to antagonist for a variable time interval, immediately after which the availability was measured again with a second GABA pulse (Fig.5A,B). A plot of availability (i.e., the fraction of channels not blocked by antagonist) versus the duration of SR-95531 exposure confirms that both the rate and extent of block by SR-95531 depend on the antagonist concentration (Fig.5C; four to six patches per concentration). After 400 msec, the availability had essentially reached steady state (see Eq. 3) and provides an estimate of the equilibrium block by SR-95531 in the absence of GABA. Therefore, a plot of the availability at 400 msec versus SR-95531 concentration (Fig.6A) contains much the same information as that revealed by traditional dose–ratio methods (e.g., Schild analysis) but has the advantage that only a single agonist concentration is required. The data were described by a modified Hill equation (see Fig. 6 legend), in which N was constrained to be an integer. The best fit occurred withN ≅ 1, yielding KN =Kn = 216 nm, near the IC50 for block in Figure 6A and near to previously published values (Hamann et al., 1988; Ueno et al., 1997). These results confirm that the method is equivalent to the dose–ratio analysis used by Hamann et al. (1988) and suggest that there may be only a single functional antagonist binding site (see below), although there are more complicated interpretations.
The macroscopic affinity constant KN is a function of the microscopic binding and unbinding rates as well as the number of binding sites (Eqs. 4-7). These same factors determine the time course of the blocking relaxation (see Fig. 5C) and can therefore be extracted from it using Equation 8. A microscopic equilibration time constant τn was first derived by fitting the data of Figure 5C to an exponential relaxation equation (see Eqs. 2, 9). Plotting 1/τn versus the concentration of SR-95531 yields a different straight line for each value of N, the slopes of which are kon and which cross they-axis at koff (Fig.6B). To determine further which combination ofN, kon, andkoff is most accurate, we directly and independently measured the SR-95531 unbinding time course (Fig.7) (Jones and Westbrook, 1997). Patches were pretreated with a saturating concentration (10 μm) of SR-95531, and the fraction of available channels was tested with a saturating GABA pulse at increasing intervals after removal of the antagonist. As the unbinding interval was increased, larger currents could be evoked by the GABA pulse (Fig. 7A). This unbinding time course was fit to an exponential relaxation equation (see Eqs. 2,9), yielding microscopic unbinding time constants (τn) of 110, 61, and 47 msec forN = 1, 2, and 3 (Fig. 7B). If there is more than one antagonist binding site and occupancy of any one site is sufficient to block the receptor, then the unbinding time course should be sigmoidal as shown by the fits for N = 2 and 3. However, the best fit to the data was obtained withN = 1, yielding a microscopic unbinding rate (koff = 1/τn) of 9.1 sec−1. The calculated microscopic affinity constant (Kn = KN =koff/kon, where kon = 4.28 × 107m−1 sec−1 forN = 1 from Fig. 6B) was thus 213 nm, indistinguishable from the value obtained in Figure6A. These results demonstrate that our estimates of kinetic parameters and the number of binding sites derived from separate analyses of the onset, steady-state, and offset kinetics of SR-95531 are in excellent agreement.
Binding rates are agonist-specific and are not limited by diffusion
Having established the antagonist binding rate, we used race experiments to measure the agonist binding rates (Eq. 12). Race experiments between SR-95531 and muscimol, GABA, THIP, and β-alanine are illustrated in Figure8A. Coapplication of the antagonist always produced smaller currents than did the agonist alone. For muscimol and GABA, equal concentrations (1 mm) of agonist and antagonist were used. For the other two agonists, the ligand concentration ratios (agonist/SR-95531) were adjusted to favor the agonist (THIP, 30 mm/200 μm; β-alanine, 100 mm/100 μm) because currents were difficult to detect when concentrations were equal. The agonist binding rates calculated from the measured values ofIrace, the known ligand concentrations, and the binding rate of SR-95531 measured in the previous section are shown in Figure 8B. Also shown is the predicted binding rate constant for a diffusion-limited process (kdiff; Eq. 13). The binding rates were (in m−1 sec−1) 9.1 (× 109) for diffusion, 4.28 ± 0.8 (× 107) for SR-95531 (n = 4–6), 5.38 ± 0.8 (× 106) for GABA (n = 11), 4.74 ± 0.6 (× 106) for muscimol (n = 4), 4.57 ± 0.2 (× 105) for THIP (n = 3), and 2.25 ± 0.2 (× 104) for β-alanine (n = 3). Therefore the binding rates were two to five orders of magnitude slower than was that of a diffusion-limited process. To ensure that using unequal agonist and antagonist concentrations did not yield artificially slow binding rates, we also raced 1 mm THIP against 1 mm SR-95531 and 10 mm β-alanine against 100 μm SR-95531. In these experiments, the calculated binding rates were (in m−1sec−1) 9.55 ± 0.6 (× 105) for THIP (n = 2) and 3.22 ± 0.9 (× 104) for β-alanine (n = 3), demonstrating that changing the (agonist/antagonist) concentration ratio by a factor of 150 altered the binding rate estimate only by a factor of two, a negligible difference in comparison with the wide range of binding rates.
Binding energetics critically determine the affinity of the GABAA receptor
The two major theories of chemical reaction kinetics, collision theory and Eyring’s transition state theory, both use the concept of activation energy (Ea) to account for the rate constant of a reaction (Wentworth and Ladner, 1972; Freifelder, 1982). The reactants (e.g., unbound ligand and receptor) and the products (e.g., the bound receptor) are viewed as being separated by an energy barrier. Only that fraction of encounters between ligand and receptor possessing sufficient energy will result in binding. If the height of the barrier is zero, then all encounters will lead to binding, and the rate will be limited by the rate of diffusion of ligand into the binding site. We therefore used the deviation from diffusion-limited binding to calculate the activation energy of ligand binding from the Arrhenius equation (Fig. 8C; Eq. 14). The activation energies were (in kcal m−1) 3.2 ± 0.6 for SR-95531, 4.4 ± 0.6 for GABA, 4.5 ± 0.6 for muscimol, 5.8 ± 0.3 for THIP, and 7.6 ± 0.7 for β-alanine.
Figure 9A illustrates the correlation between the microscopic rateskdiff, kon, and koff and the macroscopic EC50values for the ligands tested. The unbinding rate increased with increasing EC50 as shown in Figure 3D, whereas the binding rate decreased with increasing EC50 and departed entirely from the rate expected for diffusion. The correlation between kon and EC50 was steeper than that for koff, demonstrating that binding kinetics contribute more than unbinding to determining selectivity.
The close correspondence between binding kinetics and affinity can be attributed primarily to the height of the activation energy barrier. Figure 9B shows that two separately derived estimates of affinity, the directly measured macroscopic EC50 values (triangles) and the ratio of microscopic rate constantskoff/kon(circles) estimated kinetically, were correlated with activation energy and were similar to each other. As expected, the macroscopic measurements deviate somewhat from the microscopic values for low-affinity agonists because, as the unbinding rates increase, the gating steps become rate limiting in determining the apparent affinity. Neither the microscopic nor macroscopic affinities were compatible with those predicted for diffusion-limited binding (squares ony-axis). These results have two important implications. First, the similarity between macroscopic measurements and microscopic estimates shown in Figure 9B suggests that the simplifying assumptions we made (see Materials and Methods) were reasonable approximations. Second, the fitted line through the microscopic affinities in Figure 9B intersects the y-axis at 15 pm, which would therefore be the microscopic affinity constant for a hypothetical ligand with diffusion-limited binding (i.e., requiring zero activation energy). This value is a theoretical maximum limit for any agonist at the GABAA receptor, assuming that binding occurs via the same reversible mechanism as that studied here. All known ligands have much lower affinities, suggesting that none bind in a diffusion-limited manner.
The energetics of binding, unbinding, and affinity are summarized in Figure 9C. Each thick dark line can be viewed as the energy barrier diagram for one ligand (cf. Wentworth and Ladner, 1972; Freifelder, 1982). The reaction coordinate axis is an as yet unspecified measure of progress from unbound to bound (see Discussion). The hypothetical diffusion-limited ligand faces no energy barrier as binding progresses (from I to II) and binds rapidly. However, this ligand must climb out of a deep energy well to unbind and thus unbinds slowly. Such a ligand would have maximal affinity. As ligand affinity decreases (from I to III), the height of the barrier increases (from II to IV), and the energy depth of the bound state decreases, reducing the deactivation energy (Ed). This energy surface therefore accounts for the correlation between binding and unbinding rates and provides an empirical explanation for the ligand selectivity of the receptor. The deactivation energies were (in kcalm−1) 13.8 for diffusion, 12.3 for SR-95531, 10.7 for GABA, 11.4 for muscimol, 9.4 for THIP, and 8.6 for β-alanine. Finally, for each ligand the total energy difference between the unbound and bound states defines the equilibrium affinity constant by the relation: Etot =Ea − Ed =RTln(koff/kon). The total energy differences were (in kcalm−1) 13.8 for diffusion, 9.1 for SR-95531, 6.3 for GABA, 6.9 for muscimol, 3.6 for THIP, and 1.0 for β-alanine.
DISCUSSION
We examined the contributions of the microscopic binding and unbinding transitions to the affinity of ligands at the GABAA receptor. Unbinding is a major determinant of the deactivation time course after brief GABA pulses such as are likely to occur at the synapse. However, binding was much slower than expected for a diffusion-limited process, suggesting that a significant energy barrier limits the fraction of encounters between the ligand and receptor that result in channel activation. The height of this barrier is ligand-specific and can thus account for ligand selectivity.
Validity of the initial assumptions
Our findings contrast with the widespread view that ligand binding is diffusion-limited and that affinity is primarily determined by the unbinding rate. However, the few studies that have directly compared microscopic binding rates between different ligands at nACh (Sine and Steinbach, 1986; Papke et al., 1988; Zhang et al., 1995; Akk and Auerbach, 1996) or glutamate receptors (Benveniste et al., 1990b;Benveniste and Mayer, 1991) have found these rates to be at least slightly ligand-dependent. In particular, Zhang et al. (1995) concluded that affinities for several nACh receptor ligands were primarily determined by nondiffusion-limited binding. We used ligands spanning a large range of affinities, which allowed a systematic treatment of correlations between ligand kinetics, selectivity, and structure.
We interpreted the kinetics of SR-95531 blocking and unblocking in microscopic terms under the assumption that this antagonist prevents gating. However, SR-95531 and bicuculline noncompetitively inhibit currents activated by general anesthetics (Ueno et al., 1997), suggesting that channel gating occurs with antagonist bound under certain conditions. If the channel can desensitize with antagonist bound, then our estimates of SR-95531 kinetics actually reflect macroscopic processes. This scenario is unlikely, however, because some treatments that increase macroscopic desensitization [e.g., inhibition of calcineurin (Jones and Westbrook, 1997)] also speed the unblocking of SR-95531, opposite to what is expected if the unblocking time course involves desensitized states.
Our kinetic estimates also depend on the number and cooperativity of binding sites. Interestingly, the best fits occurred with only one SR-95531 site despite the presence of at least two agonist sites (Constanti, 1977a,b; Macdonald et al., 1989; Twyman et al., 1990), suggesting that only one of these sites can bind antagonist. This idea is consistent with Hill coefficients close to unity observed by others for SR-95531 and bicuculline (Ueno et al., 1997; Jonas et al., 1998) and with reports of nonequivalent agonist binding sites on many receptors (Dionne et al., 1978; Sine and Steinbach, 1986; Colquhoun and Ogden, 1988; Jackson, 1989; Raman and Trussell, 1995; Sine et al., 1995; Akk et al., 1996; Lavoie and Twyman, 1996; Lavoie et al., 1997;Clements et al., 1998). The possibility remains that we could not detect multiple antagonist sites because of limited time resolution or because the sites are so unequal that only one is rate limiting. However, the estimated binding rate of SR-95531 changed less than twofold whether assuming one or three sites. Therefore, errors in SR-95531 measurements would cause proportional errors in agonist binding rate estimates but would not qualitatively alter our conclusions.
Physical properties governing selectivity
Despite remarkable biochemical and molecular advances in understanding receptor structure, there is still insufficient information for a detailed structural picture of binding or gating. A complementary approach is to generate highly simplified structural models of the binding site with dynamics that reproduce the kinetics of ligand selectivity. For the GABAA receptor, these kinetics can be summarized by the energy surface in Figure 9C, which is a function of two nonstructural parameters: affinity and a reaction coordinate. What structural correlates might be assigned to these parameters to yield a plausible binding-site model?
Ligand chemistry, conformational flexibility, and orientation may all affect interactions with the receptor. None of these, however, can account for the kinetics we observed. For example, GABA and β-alanine have similar chemistry and flexibility (Fig.10A) but are near opposite ends of the kinetic spectrum. Furthermore, the speed of reorientation is inversely related to size (Lauffer, 1989), yet the smallest ligand, β-alanine, binds most slowly. In contrast, the excellent correlation between affinity and the “length” of the GABA-like region of each ligand (Fig. 10B) strongly suggests a length-based selectivity mechanism (Chambon et al., 1985).
The reaction coordinate is a common, often qualitative, metric of the progress of a reaction. Formally, it is the steepest path along an energy hypersurface connecting the reactants and products that passes through the transition state (Eyring, 1935; Marcus, 1964). For length-based selection, an appropriate reaction coordinate is the physical distance between the ligand and the groups comprising the binding site.
Finally, an energy barrier implies an uncomfortable region between the unbound and bound states. Such a region might exist, for example, if the ligand must lose waters of hydration or the binding site must change shape before binding can occur. Similar hypotheses have been considered for the nACh receptor (Zhang et al., 1995). We simulated our observations using both scenarios. Here, we present only the latter because it provides a natural link between binding and channel gating.
A flexible binding-site model
We treated the agonist as a pair of particles separated by a fixed length and the binding site as another set of particles. The energy of interaction between any two particles varies nonlinearly with distance (see Materials and Methods). The energy profile for each agonist is thus the changing energy of the system as the agonist and the binding site are brought together. The binding site behaves as a pair of mobile “arms” attached to fixed “anchor” sites by spring-like tethers (Fig.11A). The anchors are separated by a length (Lsite), and the arms rest in the energy wells created by the anchors (Fig.11B). Binding occurs when the agonist falls into the secondary energy wells created by the arms. Binding is diffusion-limited only if the agonist is long enough to span the distance between these wells. Shorter agonists bind more slowly because the arms must move to accommodate them, which requires activation energy. In addition, because the arms are displaced from rest, the energy of the bound state is higher and unbinding is faster than for long agonists. The kinetics and selectivity resulting from this model closely match those observed experimentally (Fig. 11C).
We interpret the well depths and radii of the model as the average local environment experienced by the ligand and not as descriptions of specific amino acid residues, although the latter is also possible. The model predicts that both binding and unbinding depend on receptor structure rather than on diffusion, involving energies on the scale of a few van der Waals or hydrogen bonds (Morris et al., 1996). The model also explicitly requires the ligand to perform thermodynamic work (approximately the activation energy) on the receptor by moving the arms away from rest, and this movement could be coupled to gating. The receptor expends compensatory work (approximately the deactivation energy) to stabilize the ligand. Our data suggest that the binding of two GABA molecules can perform enough work (∼12 kcalm−1) to drive a coupled gating reaction from 0.01 to 99.99% completion (Freifelder, 1982). We cannot yet say how much of this work is actually used to drive gating, whether it is conserved, or how it is distributed among enthalpic and entropic components (Maksay, 1994). Nonetheless, such a mechanism implies that only nondiffusion-limited ligands can be agonists because otherwise they cause no movement of the receptor.
Because ligand chemistry was ignored, it is unsurprising that the model fails to predict the fast binding and slow unbinding of the antagonist SR-95531. Many GABAA receptor antagonists contain aromatic rings (Chambon et al., 1985; Hamann et al., 1988; Huang and Johnston, 1990) that may tether the ligand near the binding site. Such tethering could simultaneously enhance the probability of binding, slow unbinding, and interfere with movements involved in the coupling of binding to gating. Finally, muscimol is slightly shorter than GABA but unbinds more slowly. Perhaps GABA can twist and shorten while in the binding site, leading to premature unbinding, whereas muscimol cannot because of its conformational restriction.
Multiple protein domains affect the apparent affinity of many receptors (Stern-Bach et al., 1994; Smith and Olsen, 1995). For example, in GABAA, glycine, and nACh receptors, discontinuous segments including aromatic residues appear to come together to form a binding pocket (Dennis et al., 1988; Schmieden et al., 1992, 1993;Vandenberg et al., 1992; Amin and Weiss, 1993). Furthermore, mutations that alter these regions by as little as a single hydroxyl group dramatically alter the EC50 (Amin and Weiss, 1993;Schmieden et al., 1993). Our model is compatible with these findings in that (1) successful binding involves the coordinated motion of separate parts of the receptor and (2) variations of a fraction of an angstrom or a single hydrogen bond cause quite large changes in affinity. Such small structural effects may arise physiologically via subunit differences or movements propagated through the protein because of interactions with the cytoskeleton or phosphorylation (e.g., Jones and Westbrook, 1997).
Implications for synaptic transmission
We studied responses evoked by different agonists at the same receptor. However, at GABAergic synapses the agonist is always the same, whereas the receptor subtypes may differ. Because deactivation is strongly influenced by the rate of agonist unbinding, some of the observed variation in IPSC duration probably results from differences in unbinding between receptor subtypes because of differing subunit compositions or regulation (Puia et al., 1994; Verdoorn, 1994; Tia et al., 1996; Auger and Marty, 1997; Jones and Westbrook, 1997). If binding rates depend on receptor structure, as in the flexible site model, then the correlations between binding, unbinding, and affinity suggest that receptors mediating rapidly decaying IPSCs may be less efficient at binding GABA than are those mediating long-lasting IPSCs. Binding efficiency is critical at low GABA concentrations, such as may occur during “spillover” (Isaacson et al., 1993; Nusser et al., 1997) or “cross talk” (Barbour and Häusser, 1997). Thus, neurons with fast IPSCs may be less sensitive to these modes of inhibition. Even in situations in which the concentration is high, different binding rates will result in different degrees of occupancy if the GABA transient is brief (Clements et al., 1992; Frerking and Wilson, 1996; Auger and Marty, 1997; Diamond and Jahr, 1997; Galarreta and Hestrin, 1997; Perrais and Ropert, 1997). Receptors underlying fast IPSCs may thus have a lower occupancy than those underlying slow IPSCs.
Footnotes
M.V.J. was sponsored in part by the American Epilepsy Society with support from the Milken Family Medical Foundation. Y.S. was supported by a grant from the Japanese Ministry of Education, Science, and Culture. This work was supported by National Institutes of Health Grants F32 NS09716 (M.V.J.) and NS26494 (G.L.W.). We thank Drs. Jeff Diamond, Craig Jahr, and Tom Otis for helpful discussions and Jeff Volk for culture of hippocampal neurons. Special thanks to Dr. Gary Yellen for an invaluable conversation.
Correspondence should be addressed to Dr. Mathew V. Jones, The Vollum Institute, Oregon Health Sciences University, L474, 3181 Southwest Sam Jackson Park Road, Portland, OR 97201.