INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

The kinetics of GABAergic inhibitory postsynaptic currents (IPSCs) plays a key role in the integration of signals at CNS synapses (Cherubini and Conti 2001). The time course of synaptic currents depends on agonist transient and on the gating of the postsynaptic receptors. Transmitter released from nerve terminals decays quickly (predominant _clearance of approximately 100 µs; Clements 1996; Mozrzymas et al. 1999). The estimated peak values of synaptic GABA concentrations range from hundreds of micromoles to several millimoles (Jones and Westbrook 1995; Maconochie et al. 1994; Mozrzymas et al.1999; Nusser et al. 2001; Perrais and Ropert 1999), and it is still not clear whether synaptic GABA reaches saturating concentrations (Frerking and Wilson 1996; Frerking et al. 1995; Hajos et al. 2000; Mody et al. 1994; Nusser et al. 2001Perrais and Ropert 1999). Synaptic transmission is thus a dynamic, nonequilibrium process that depends on changes in synaptic agonist concentration, which in turn affects the time course and pharmacology of IPSCs (Barberis et al. 2000; Mozrzymas et al. 1999; Nusser et al. 2001). For a comprehensive description of IPSC mechanisms, it is necessary to mimic the dynamics of the synaptic agonist transient. This becomes possible by using piezoelectric-driven perfusion systems (Franke et al. 1987; Jonas 1995), which are capable of applying the agonist in the time scale comparable to that of synaptic neurotransmitter transient. However, large differences in the rise times of responses to saturating [GABA] (Barberis et al. 2000; Jones and Westbrook 1995; Mozrzymas et al. 1999; Perrais and Ropert 1999) raise the possibility that the application speed may significantly affect the measured currents.

Accurate determination of the key rate constants for transitions between several channel conformations is a requirement for analyzing gating mechanisms. One approach has been to apply simplified models to selected phases of current traces. Alternatively, the characteristics of current responses (e.g., amplitude concentration dependence) have been attributed to selected kinetic properties (e.g., to agonist binding). Such approaches, however, may potentially lead to several misinterpretations. An example of complex kinetic behavior has been recently discussed by Colquhoun (Colquhoun 1998; see also Colquhoun and Farrant 1993). He has shown that the occupancy of bound states for receptors with low affinity and high efficacy is higher than that inferred solely from their affinity. This is due to the fact that "if binding affects activation (transduction, gating) then activation must affect binding." Another example of coupling between channel states is the involvement of unbinding and desensitization in shaping the deactivation kinetics of GABA-evoked currents (Jones and Westbrook 1995). In general, such interactions are expected to occur between all channel states. The standard approach based on Markovian schemes of interconnected states inherently includes the assumption that the time evolution of the occupancy of any conformation depends on all the rate constants and occupancies of all other states. However, since channel gating involves several conformations, the interaction between all these states is extremely complex. It is therefore interesting to assess the impact of conformation coupling in dynamic conditions similar to those that take place in the synapse. For this purpose, we have examined the effects of different GABA_A receptor conformations on the basic characteristics (such as rise time, deactivation, or desensitization) of current responses evoked by ultra-fast GABA applications. In particular, we show that current rising phase and amplitude concentration dependence strongly depend on both singly and doubly bound desensitized states. Opening/closing transitions are involved in shaping the current decay induced by long, saturating GABA pulses. The occupancy of bound receptors depends not only on binding rates, but also on opening/closing and desensitization rates. Interaction between channel states is found to be especially large in conditions of high nonequilibrium that presumably take place during synaptic transmission. In addition, the concentration dependence of current rising phase indicates a positive cooperativity between agonist binding sites. We also provide evidence that the presence of low GABA concentrations, which by themselves activate very small or negligible currents, may strongly reduce GABAergic currents due to receptor trapping into a singly bound desensitized state.

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Cell culture

The primary cell culture was prepared as described in detail by Andjus et al. (1997). Briefly, P2- to P4-day-old Wistar rats were decapitated after being anesthetized with an intraperitoneal injection of urethane (2 g kg¹). This procedure is in accordance with the regulation of the Polish Animal Welfare Act and was officially approved by the Local Ethical Committee for Animal Research. Hippocampi were dissected from 2- to 4-day-old rats, sliced, treated with trypsin, mechanically dissociated and centrifuged twice at 40g, plated in petri dishes, and cultured. Experiments were performed on cells that remained between 10 and 15 days in culture.

Electrophysiological recordings

Currents were recorded in outside-out patch-clamp configuration using an EPC-7 amplifier (List Medical, Darmstadt, Germany). GABA-elicited currents in the excised patch configuration were recorded at a holding potential (V_h) of 70 mV. The pipette solution contained (in mM) 137 CsCl, 1 CaCl₂, 2 MgCl₂, 11 1,2-bis(2-aminophenoxy)ethane-N,N,N',N'-tetra acetic acid (BAPTA), 2 ATP, and 10 HEPES (pH 7.2 with CsOH). The composition of the external solution was (in mM) 137 NaCl, 5 KCl, 2 CaCl₂, 1 MgCl₂, 20 glucose, and 10 HEPES (pH 7.4 with NaOH). All experiments were performed at room temperature (22-24°C).

The current signals were low-pass filtered at 10 kHz with a Butterworth filter and sampled at 50-100 kHz using a CED micro1401 A/D converter (Cambridge, UK) and stored on a computer hard disk. The acquisition and analysis software were kindly given by Dr. J. Dempster (Strathclyde University, Glasgow, UK).

GABA or -alanine were applied to excised patches using an ultra-fast perfusion system with piezoelectric-driven theta-glass application (Jonas et al. 1995). The piezoelectric translator was from Physik Instrumente (Waldbronn, Germany) and the theta-glass tubing from Hilgenberg (Malsfeld, Germany). Open tip recordings of the liquid junction potentials revealed that a complete exchange of solution occurred within 40-60 µs. The speed of this solution exchange was also estimated around the excised patch by the 10-90% onset of membrane depolarization induced by the application of concentrated (25 mM) potassium saline. In this case, the value of rise time was 50-90 µs, i.e., close to that found for the open tip recordings. The time of solution removal around the open tip was slightly faster (10-90% removal within 35-50 µs) than the application. The speed of solution exchange was checked before each series of experiments. Since agonist exchange is considerably faster than any characteristics of the measured currents, it seems that the agonist application speed is sufficient to reliably resolve the gating parameters of the studied receptors. In the case of high GABA concentration (10 mM), osmolarity was adjusted by reducing glucose. In the solution containing 100 mM of -alanine, glucose was omitted and NaCl was reduced from 137 to 100 mM. This chloride concentration was still saturating for single channel conductance of GABA_A receptor channels.

Analysis

Decaying current phase was fitted with a function in the form

(1)

where, A_i is the fraction of the respective component, A_s is the steady-state current, and _i is the time constant. For normalized currents, A_i + A_s = 1. The deactivation time course was well fitted with a sum of two exponentials (n = 2) and A_s = 0. The desensitization onset was fitted with either one or two exponentials and A_s > 0.

Kinetic modeling was performed with Bioq software kindly provided by Dr. H. Parnas from the Hebrew University, Jerusalem. Bioq software converted the kinetic model (Figs. 4-8) into a set of differential equations and solved them numerically assuming as the initial condition that for t = 0 no bound or open receptors were present. Various experimental protocols were simulated by setting up the agonist concentration time course in the form of square-like pulses (ultra-fast perfusion experiments). The solution of such equations yielded the time courses of occupancies of all the states assumed in the model. The fit to experimental data were performed by optimizing the rate constants of a given experimental protocol to reproduce its current time course.

For the considered model, fit quality was assessed by the ² statistics

(2)

where: n is the number of data points, y_i is the average experimentally measured value, m_i is the model prediction, and SD_i is the SD.

Data are expressed as a mean ± SE.

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Current responses to saturating GABA concentrations

The minimum requirement model for GABA_A receptor gating must include binding as well as open, closed, and desensitization transitions. It is known that a good fit to experimental data are obtained when opening and desensitizing transitions are allowed directly from the bound closed states (see e.g., Barberis et al. 2000; Jones and Westbrook 1995, 1997; Li and Pearce 2000; McClellan and Twyman 1999; Mozrzymas et al. 1999).

Despite the complexity of the binding reaction (e.g., the number of binding sites and cooperativity), it is to be expected that at sufficiently high (saturating) [GABA], the binding step becomes much faster (effective rate of binding = k_on·[GABA]) than the conformational transitions (see scheme in Fig. 1A). When k'_on·[GABA]/k'_off approaches , the ratio [A_n1R]/[A_nR] tends to 0, meaning that at saturating [GABA], all receptors tend to be fully bound and distributed among the A_nR, A_nR*, and A_nD states (k'_on and k'_off are the binding and unbinding rates for the last, nth agonist molecule, respectively). Thus during exposure to a saturating concentration of GABA, the kinetic behavior of the receptors is determined by the concentration-independent rate constants for transitions between fully bound states (for our model , , d, r). Assuming that the saturating free agonist is removed instantaneously, the deactivation phase will be additionally shaped by unbinding kinetics. Therefore analyzing current responses to saturating [GABA] may give an insight into conformational state kinetics without a precise knowledge about the binding reaction itself, except for the unbinding rate.

View larger version (21K): [in this window] [in a new window]   Fig. 1. Current responses to saturating concentrations of GABA and -alanine reveal the transition rates between fully bound states. Since, at saturating agonist concentrations, the occupancy of singly bound receptors is low, the scheme was simplified assuming that the receptor may reach the open (AnR*) or desensitized (AnD) conformation only from a fully bound state (AnR, A). GABA (10 mM, B-F) or -alanine (100 mM, G-J) were applied in the form of different protocols. Short GABA pulse (2 ms, B) revealed the maximum onset rate; long pulse (300 ms, C) induced the desensitization. Deactivation time course was measured following a short (1-2 ms) GABA pulse (D). Short (2 ms) double pulse protocol for GABA (E and F) and for -alanine (G). Desensitization onset induced by -alanine (H) and double pulse protocol (long conditioning and short test pulse) intended to describe the recovery from desensitization kinetics (I and J). The values of the rate constants (K) determined basing on the analysis of current responses elicited using different protocols (B-J) of saturating agonist applications. As explained in RESULTS, the rate constant k'off describes the unbinding rate for the first molecule dissociated from a fully bound receptor. Insets: application of agonist.

We have used several experimental protocols (Fig. 1, B-F) to measure currents evoked by saturating concentrations of GABA and found they were (Fig. 1, B-F) not significantly affected when [GABA] varied above 4-6 mM. This implies that 4-6 mM GABA may be considered saturating and confirms the prediction that at saturating [GABA], receptor behavior is determined by the rate constants, which do not depend on GABA concentration.

To estimate the rate constants for conformational transitions between fully bound states, current responses to 10 mM GABA applied for different time intervals (1-300 ms) were recorded (Fig. 1, B and C). Short GABA pulses revealed the maximum onset rate of GABA-evoked currents (10-90% rise time = 0.21 ± 0.01 ms, n = 21, Fig. 1B), while long pulses induced the desensitization onset (Fig. 1C). For GABA pulses of 300 ms, the desensitization onset was clearly biphasic (_fast of 4.1 ± 0.6 and _slow of 138 ± 14.9 ms, A₁ = 0.42 ± 0.09, A₂ = 0.23 ± 0.03, A_s = 0.3 ± 0.14, n = 12). However, the slower component is unlikely to significantly influence synaptic current time course, thus analysis was limited to the fast component that was predominant for a 50-ms pulse (_fast of 4.2 ± 0.7 ms, A₁ = 0.61 ± 0.09, A_s = 0.39 ± 0.14, n = 12). Since the rise time and desensitization onset time course provided too little information to estimate the four rate constants (, , d, r), additional experimental protocols were used. The deactivation phase of the current responses (Fig. 1D) was clearly biphasic (_fast = 4.3 ± 0.5 ms, A_fast = 0.49 ± 0.04, _slow = 96.7 ± 8.2 ms, A_slow = 0.51 ± 0.05, n = 15). It has been demonstrated that deactivation kinetics critically depend on the relation between the unbinding rate and desensitization (Jones and Westbrook 1995, 1997). When unbinding is sufficiently slow, the receptors may visit the desensitized state and reopen, giving rise to prolonged deactivation. The analysis of deactivation kinetics therefore provided a tool for estimating the ratios of unbinding (k'_off), desensitization (d), and opening () rates. An expected consequence of slow unbinding is the reduced amplitude of the response to the second short pulse in the paired pulse experiments (Fig. 1, E and F). Thus after the first short agonist pulse, a slow unbinding favors entrances into the desensitized state, while a slow desensitization rate (r) gives rise to an accumulation of receptors in this conformation (Barberis et al. 2000; Jones and Westbrook 1995). Further evidence for such a mechanism is provided by experiments with -alanine, which has a much faster unbinding rate than GABA (Jones et al. 1998). As shown in Fig. 1G, no additional desensitization occurred when responses to double short pulses of -alanine were recorded (n = 5). These data (Fig. 1, E-G) show that when using GABA, the observed recovery of the second response in the short double pulses experiments does not represent solely recovery from desensitization, but rather a complex process that is a result of functional coupling between unbinding, opening/closing, and desensitization. Long (50 ms) application of -alanine revealed a similar desensitization onset ( = 5.7 ± 1.4 ms, A₁ = 0.43 ± 0.05, A_s = 0.57 ± 0.06, n = 14; Fig. 1H) as in the case of GABA (Fig. 1C), showing that -alanine is not a "nondesensitizing" agonist. Such reduced interaction between unbinding and desensitization in the case of -alanine precludes multiple sojourns and accumulation in the desensitized state (Fig. 1G). For this reason, experiments with -alanine provide a better estimate of the kinetics of recovery from desensitization than those with GABA. A protocol consisting of a long (50 ms) conditioning pulse (to induce desensitization) followed by a short -alanine test pulse (Fig. 1I) was used. These experiments were performed for intervals between pulses ranging between 2 and 1,000 ms (Fig. 1J). Data obtained using the protocols shown in the Fig. 1, B-J, were used to estimate the rate constants , , d, and k'_off. The unbinding rate k'_off, estimated using such procedures, describes the rate of unbinding from a fully bound receptor of the first agonist molecule. Thus if there were n agonists bound to n equivalent binding sites, then the unbinding rate for the first molecule is k'_off = n · k_off, where k_off is the unbinding rate from a single binding site. For the reasons explained above, the parameter r was estimated basing on experiments with -alanine, and it was assumed that this parameter is equal to that of GABA (see also Barberis et al. 2000; Jones and Westbrook 1995). Although, as explained above, it is difficult to directly compare the parameter r for -alanine and GABA, the fact that the kinetics of GABA-evoked responses could be properly reproduced using parameter r estimated for -alanine indicates that this difference is minor. Moreover, the time course of current rising phase and desensitization onset are similar for -alanine and GABA, suggesting that the main difference between -alanine and GABA is in affinity to the GABA_A receptor, while transitions between bound states show similar kinetics for both agonists (Barberis et al. 2000; Jones and Westbrook 1995).

Optimization of the rate constants , , d, r, and k'_off was performed using model simulations. The entire set of rate constants was considered optimal for a given model when it gave the best prediction for all protocols (Fig. 1, B-J). The values of these rate constants (Fig. 1K) were then included in the model (Fig. 1A) and used in subsequent analysis. Some details regarding the experimental conditions and protocols employed in determining the conformational transitions rate constants are described also in Barberis et al. (2000).

Suppression of current responses by low tonic [GABA] indicates the involvement of singly bound desensitized states

Although there is agreement that at saturating [GABA], partially bound receptors play at best a minor role, such partially bound conformations can contribute to the current time course at low GABA concentrations (Jones and Westbrook 1995; Macdonald et al. 1989; Mozrzymas et al. 1999; Twyman et al. 1990). In particular, there is evidence based on single channel analysis that singly bound open states give rise to short-living openings (Macdonald et al. 1989; Twyman et al. 1990). Evidence for partially liganded desensitized states has been deduced from the formal fitting of models to current traces (Jones and Westbrook 1995, 1997; Jones et al. 1998). Recently, it has been shown that preequilibration at low [GABA] favors the entrance into a slow desensitized state that is likely to be singly bound (Overstreet et al. 2000). However, the nature and kinetics of this state have not been determined. For this purpose, we employed the experimental protocol used by Overstreet et al. (2000) and examined the current responses to saturating [GABA] after a preequilibration in the presence of low GABA concentrations that by themselves activate small or negligible currents. In our experiments, the application of 1 µM GABA elicited the current that corresponded to only 0.94 ± 0.2% of the response evoked by 10 mM GABA in the same patch, while 0.3 µM GABA induced an increase in the baseline noise (<0.3%). Thus it is expected that at these GABA concentrations most of receptors do not reach fully bound states and a considerable proportion of bound receptors remains in a partially liganded conformation. Thus if there exists a slowly absorbing, partially bound and desensitized state, treatment with such low GABA concentrations would favor the accumulation of receptors in this conformation. In contrast, as already explained, very fast successive binding would preclude entrance into the singly bound desensitized state at high (saturating) [GABA]. It is thus expected that the current response to saturating [GABA] following preequilibration in low [GABA] will be reduced by a factor corresponding to the proportion of receptors that accumulated in the singly bound desensitized state. This hypothesis is based on the assumptions that exiting from the partially bound desensitized state is slower than activation kinetics and that preequilibration is performed at [GABA] sufficiently low to impede a considerable occupancy of the fully bound desensitized conformation. As shown in Fig. 2, the preequilibration with 0.3 and 1 µM GABA resulted in reductions of 93.2 ± 3.2% and 78.6 ± 4.1% in the current evoked by saturating (10 mM) GABA, respectively. Thus the relative decrease in currents is more than one order of magnitude larger than the currents evoked by these GABA concentrations, clearly indicating that pretreatment with low [GABA] caused an accumulation of receptors in the desensitized states. As shown in the next paragraph, analysis provides evidence for a predominant role of the singly bound desensitized state in this effect. The time course (rise time and deactivation kinetics) of control currents and those elicited after pretreatment with 1 µM GABA did not show any significant difference (both currents were evoked by 10 mM GABA applied for 2 ms).

View larger version (14K): [in this window] [in a new window]   Fig. 2. Preequilibration of receptors at low GABA concentrations suppresses the current responses evoked by saturating [GABA]. A: first, the current responses were evoked by 2-ms application of 10 mM GABA (insets) after pretreatment for 1 min with normal saline (wash, left), and then the current was elicited after preequilibration at 1 µM GABA (1 µM, middle) and again after pretreatment with normal saline (wash, right). Recordings have been performed from the same patch. B: analogous experiment as in A, but the current trace in the middle panel was recorded from excised-patch preequilibrated at 0.3 µM GABA. C: averaged data obtained from experiments presented in A and B.

Rising phase kinetics indicates the cooperativity of binding sites

The dose dependence of the current rising phase provides a tool for exploring the kinetics of binding reactions. For this purpose, current responses were recorded for GABA concentrations ranging from 10 µM to 10 mM (Fig. 3), and the values of 10-90% rise times were measured (Fig. 4A). For a quantitative description, the model frame in Fig. 1A was used with different schemes for binding reactions. For models assuming two binding sites, additionally singly bound states were considered (Fig. 4, E and G). The values of the rate constants (, , d, r, k'_off) were taken from the analysis of current responses to saturating [GABA] (Fig. 1) and kept unchanged for all considered models (note that the parameters , , d, r, k'_off correspond to , , d, r, k_off in Fig. 1, B and C, and to ₂, ₂, d₂, r₂, 2k_off in D-G). The values of binding rates were optimized for a chosen binding reaction to obtain the best reproduction of the experimental data (Fig. 4A). For the simplest model, assuming only one binding site, good reproduction of rise times was obtained only at high [GABA] (Fig. 4B). Moreover, the model predicted that the application of 0.3 and 1 µM GABA evokes approximately 7.3% and 12.3% of the response elicited by saturating [GABA], respectively. This is not the result that was observed experimentally (<0.3% and 0.94%, Fig. 2). An attempt was made with the reaction postulating one binding site that binds two GABA molecules (2A + R  A₂R), but the predictions of this model (data not shown) diverged even more from experimental data than those of the model presented in the Fig. 4B and other figures studied here (Figs. 4, C-G). To explore the validity of this type of binding scheme, the stoichiometric coefficient h was formally considered as a free noninteger fitting parameter. Such operations are often performed when Hill's ("logistic") equation (that basically describes this type of reaction) is fitted to the experimental data. The value of h = 1.25 was found optimal, but only a moderate improvement with respect to the model in Fig. 4B was achieved (Fig. 4, C and H). The application of 0.3 and 1 µM GABA yielded 0.83% and 3.5% of peak maximum response (to 10 mM GABA). These values are closer to experimental data than those for the model in Fig. 4B. However, the prediction of this model for the preequilibration protocol (Fig. 2) reduced the current to 98.6% and 95.2% for 0.3 and 1 µM GABA, respectively, which is smaller than that observed experimentally (Fig. 2). Moreover, the meaning of such noninteger stoichiometry for binding is obscure. This result was interpreted as an indication that the binding reaction is more complex than the binding of a single molecule (Fig. 4B).

View larger version (11K): [in this window] [in a new window]   Fig. 3. Typical family of current responses evoked by GABA concentrations ranging from 10 µM to 10 mM (indicated above the traces in A and B). The duration of agonist application was sufficiently long for the response to reach its peak or steady-state value. C: concentration dependence of averaged current response amplitudes.

View larger version (39K): [in this window] [in a new window]   Fig. 4. The rise time analysis reveals GABA binding reaction. Averages of experimentally determined 10-90% rise times (A) for GABA concentrations indicated above the bars. Each mean value was calculated for at least 10 patches. B-G: predictions of 10-90% rise times for the models indicated on the left. The solid horizontal bars represent the averaged experimental values for respective GABA concentrations. In the models B-G, the values of the rate constants , , d, r, and koff were taken from the analysis of responses to saturating GABA concentrations (Fig. 1). Note that in models D-G, these values refer to 2, 2, d2, and r2. For the models assuming two binding sites (D-G), the unbinding rate koff fulfills the relationship 2 · koff = k'off and k'off = 0.26 (Fig. 1I). The values of the 2 statistics for models B-G optimized to best reproduce experiment A are shown in H. *Model with which the fit reached statistical significance (P < 0.05). For model F, the fit was at the borderline of statistical significance (P = 0.097). The binding rates were optimized for each model (B-G) as explained in RESULTS: B, kon = 4 ms1mM1; C, kon = 7 ms1mM1, h = 1.25; D, kon = 6 ms1mM1; E, kon = 5.5 ms1mM1, 1 = 0.15 ms1, 1 = 1.5 ms1, d1 = 0.045 ms1, r1 = 0.014 ms1; F, kon1 = 4 ms1mM1, kon2 = 8 ms1mM1; G, kon1 = 2.5 ms1mM1, kon2 = 20 ms1mM1, 1 = 0.15 ms1, 1 = 1.5 ms1, d1 = 0.14 ms1, r1 = 0.02 ms1.

The next scheme was the sequential binding to two identical and independent binding sites. As seen in the Fig. 4, D and H, this model gave a significant improvement in the reproduction of experimental data with respect to those previously analyzed (Fig. 4, B and C). However, it failed to properly reproduce the rise times at low GABA concentrations (10 and 20 µM GABA), suggesting that it is still oversimplified. This model properly reproduced the amplitude of response at very low agonist concentrations (0.3 and 1 µM GABA produced 0.15% and 1.3% of the maximum current, respectively) but failed to mimic current suppression after preequilibration at these low [GABA] (at 1 µM GABA pretreatment reduction to 98% of control, compare with Fig. 2). The next step was to include the singly bound open and desensitized states in the scheme postulating two identical and independent binding sites. An estimation of the rate constants (₁, ₁) for partially liganded open states was based on the evidence from single channel analysis (Macdonald et al. 1989; Twyman et al. 1990), as well as on assessments made in similar models (e.g., Jones and Westbrook 1995; Maric et al. 1999). In all these studies, the rate constant of entrance into the singly bound state (₁) has been found to be much slower than that leading into the fully bound state (₂), and the rate of return into the closed state (₁) was fast. This reproduces the low frequency and short duration of openings of singly bound channels. In our model simulations, these rate constants were assigned the values ₁ = 0.15 ms¹ and ₁ = 1.5 ms¹, which is in agreement with estimations made in works mentioned above and allowed an optimal fit of our experimental data. The ratio r₁/d₁ is the equilibrium constant that defines the steady-state distribution between singly bound closed and desensitized states. As expected, the suppression of currents evoked after preequilibration in low [GABA] (Fig. 2) could be well reproduced when r₁/d₁ was set sufficiently high. Thus after having determined this ratio, the optimization of the rate constants simplified to only one degree of freedom. For the considered model (Fig. 4E), the optimization procedure was run for parameters k_on and r₁ (or d₁). When the desensitization rate was set slower than 0.01 ms¹ and k_on was in the range 4-8 mM¹ms¹, the response evoked by 10-20 µM GABA had a faster rise time than for the model in Fig. 4C. During prolonged exposure to GABA, the currents, after having reached a peak, showed a fading phase (data not shown). This prediction is contrary to what was observed in experimentsthe currents reached steady-state values without any fading (not shown) for 500-ms applications of 10 and 20 µM GABA. Optimization procedures were run for r₁ > 0.01 ms¹, but for these values, no improvement with respect to the model in Fig. 4C was obtained (Fig. 4, E and H).

A better fit to experimental data were achieved when the values of two binding rates, k_on1 and k_on2, were assumed to be free fitting parameters and no singly bound states were considered (Fig. 4F). For this scheme, the best reproduction of experimental data were obtained when the second binding rate k_on2 was twice as large as k_on1, indicating a positive cooperativity between the binding sites (Fig. 4, E and F). However, the dose dependence of rise times was still unsatisfactory, especially al low concentrations of GABA (Fig. 4, F and H). An attempt has been made to consider additionally the singly bound states (Fig. 4G). The optimization procedure was run similarly as in the case of the model in Fig. 4E with an additional degree of freedom resulting from considering the two binding rates k_on1 and k_on2 as free fitting parameters. As shown in Fig. 4, G and H, the inclusion of both singly bound conformations and binding site cooperativity yielded a pronounced improvement in reproducing the concentration dependence of the rise time kinetics. Fitting with the model in Fig. 4G, it reached statistical significance (P < 0.05), as assessed by ² statistics. Interestingly, the best fitting model (Fig. 4G) postulates a much stronger cooperativity between the binding sites (k_on2/k_on1 = 8), with respect to the model in which the singly bound states were omitted (Fig. 4F).

Although the present data provide evidence that the doubly bound, fast desensitized state (A₂D) is not responsible for the current suppression following preequilibration at low [GABA] (Fig. 2), it cannot be ruled out that a slowly absorbing fully liganded desensitized conformation could be involved in this process. Since at very low [GABA], the occupancy of the doubly bound closed state (A₂R) is low, such an absorbing desensitized state should be characterized by a high entrance (d) to desensitization (r) ratio. We made an attempt to reproduce the effect of preequilibration with 1 µM GABA by using a model that omitted the singly bound desensitized state and included an additional, doubly liganded, slowly absorbing one. However, for a wide range of d and r parameters, such a state would strongly affect the deactivation phase of responses elicited by a saturating [GABA] (data not shown), which is contrary to our data and to that observed by Overstreet et al. (2000).

Concentration dependence of current amplitudes critically depends on desensitization

An important source of information on receptor gating is the concentration dependence of current amplitudes (Fig. 3C). Since the occupancy time course of any conformation depends on all the rate constants and occupancies of all the other states, the transitions to any conformation may potentially affect the peak current (occupancy of the open states). However, the amplitude dose-response characteristics are commonly ascribed to the affinity and efficacy of channels and the potential impact of desensitization on GABAergic current amplitudes remains obscure. To assess the contribution of desensitization in shaping the amplitude concentration dependence, dose-response relationships were simulated for the models considered in Fig. 4. First, the models with only the fully bound desensitized state were investigated (Fig. 4, B-D and F). As shown in Fig. 5, within the considered range of [GABA] (10 µM-10 mM), predictions of concentration dependencies for these schemes are similar and all of them were close to the experimental data. To illustrate the impact of the desensitized state on the amplitude dose-response relationship, two models (Fig. 6, A and B) were investigated (since the concentration dependencies of amplitudes were similar for the models with rate constants optimized to reproduce the experimental data, the simplest schemes were chosen). The simulated dose-responses are presented in Fig. 6C. Interestingly, the inclusion of the desensitized state caused a marked shift in the dose-response relationship, despite of the fact that these models postulate exactly the same affinity (K = k_off/k_on, k_on = 4 mM¹ms¹, k_off = 0.26) and efficacy (E = /,  = 8 ms¹,  = 1 ms¹). The inspection of simulated current responses to different concentrations of GABA and of the occupancies of the desensitized state provide (Fig. 6, D-G) an explanation of the observed skew in the dose-response relationship (Fig. 6C). For a high [GABA] (10 mM), rise time is fast and the percentage of desensitized receptors at peak is low (Fig. 6, D and G). However, at lower GABA concentrations (100, 20 µM), the current onset is slower and more receptors enter the desensitized state before the response reaches its maximum (Fig. 6, E-G). Thus the observed shift in the dose-response relationship (Fig. 6C) is related to the concentration dependence of balance between the occupancy of open and desensitized states (Fig. 6G), rather than to a change in binding kinetics. It is worth noting that in the general case, the fact that the peak current response to prolonged application of low [GABA] is not followed by decay should not be interpreted as a "nondesensitizing response." As shown in Fig. 6F, at low [GABA] no decay is present but the occupancy of the desensitized state is larger than that of the open one.

View larger version (15K): [in this window] [in a new window]   Fig. 5. Normalized dose-response ([GABA] in millimolar) of averaged current amplitudes (). To compare the experimentally observed concentration dependence of current amplitude to those predicted by models, for each GABA concentration, the maximum () and minimum () values were selected among the amplitudes predicted by the considered models (shown in Fig. 4, B-D and F).

View larger version (26K): [in this window] [in a new window]   Fig. 6. Desensitization affects the concentration dependence of current amplitudes. The simulated dose-responses for models shown in A and B are presented in C ([GABA] in millimolar). For both models, the rate constants kon = 4 mM1ms1, koff = 0.26 ms1,  = 8 ms1,  = 1 ms1 are assumed to be identical and therefore the modification of the dose-response relationships are due to the desensitization process. D-F: time courses of occupancies of the open state (AR*, thick line) and the desensitized state (AD, thin line) for responses elicited by applications of different GABA concentrations (indicated above the traces). G: occupancies of the open state (solid bars) and desensitized state (open bars) at peak of responses evoked by GABA concentrations indicated above the bars.

The inclusion of singly bound desensitized states in the models of Fig. 4, E and G, did not dramatically change dose-response relationships for current amplitudes. Only at low GABA concentrations (10-50 µM) was a decrease in amplitude found, due to trapping into the singly bound desensitized states. For responses evoked by 10, 20, and 50 µM, the occupancies of open states were 0.262, 0.322, and 0.394 for the model in Fig. 4D and 0.179, 0.250, and 0.356 for Fig. 4E, respectively. Amplitudes of currents evoked by 10, 20, and 50 µM GABA were 0.267, 0.327, and 0.398 for Fig. 4F and 0.230, 0.292, and 0.367 for Fig. 4G, respectively. Thus singly bound states appear to have a moderate impact on the amplitude dose-response while the role of the fully bound desensitized state appears to be crucial.

It is worth noting that the application of a commonly used procedure based on the fit of a "logistic equation" 1/[1+(EC₅₀/[GABA])^h] could lead to misinterpretations. First, such shift in dose-responses, as presented in Fig. 6C, suggest a modification in receptor affinity. Second, a formal fit of the "logistic equation" to the experimentally obtained dose-response for amplitudes (Fig. 5) would yield the Hill's coefficient to be around 0.6, suggesting a "negative cooperativity." However, both these conclusions are false, because the amplitude dose-response relationship depends not only on receptor affinity and efficacy, but also on desensitization kinetics, which is neglected in the "logistic equation." Moreover, the "logistic equation" is derived with the assumption that the system is in equilibrium, which is obviously not the case when the current response is reaching its maximum value.

Desensitization shapes current rise time kinetics

The current response onset kinetics is often ascribed only to binding and transitions between closed and open bound conformations. However, the current rising phase could also be influenced by desensitization. The involvement of several conformations in receptor gating makes it difficult to construct experimental protocols that allow the direct assessment of the impact of a chosen (e.g., desensitized) state on onset kinetics. On the other hand, the optimal reproduction of responses obtained using several experimental protocols (Figs. 1-3) provides us with estimated rate constants for the models. Thus the strategy to assess the impact of desensitization on the current rise time was based on the analysis of simulated responses for the models in which this conformation is either present or absent while all other rate constants are assumed equal for both models. First, to indicate the qualitative trends, simulations for the simplest schemes assuming only one fully bound desensitized state (Fig. 7, A and B) were run. Later, models including the partially liganded desensitized state were investigated. The concentration dependence of 10-90% rise times for the models in Fig. 7, A and B, are presented in Fig. 7, C and D. Interestingly, the rise time kinetics for these two models show considerable differences for the entire range of considered GABA concentrations. In particular, for 50-300 µM GABA, the rise time for the model without desensitization is markedly slower (Fig. 7, C and D). The reason for this prediction is illustrated in Fig. 7E. At these GABA concentrations, the effective rate of binding (k_on·[GABA]) is comparable to the desensitization rate d. Therefore it is not surprising that desensitization participates in the shaping of current onset. Moreover, as shown in Fig. 7E, the progress in receptor accumulation in the desensitized state produces a peak before the nondesensitizing response does (i.e., for model B in Fig. 7). Even more surprising is the prediction that desensitization affects rise time also at saturating GABA concentrations (10 mM). However, this is a natural property of bifurcating reactions. For instance, in the case of a simplified reaction (since d r and   , this scheme is expected to give a good approximation for the initial phase of current onset for saturating [GABA]), both the onset of current response (occupancy of AR*) and entry into the desensitized state (AD) proceeds with the time constant  = 1/( + d), i.e., faster than entry into the open state (1/) in the absence of the desensitized state (the model in Fig. 7A)

(3)

View larger version (28K): [in this window] [in a new window]   Fig. 7. Desensitization affects the kinetics of current rising phase. The concentration dependence of the 10-90% rise time for the models with (A) or without the desensitized conformation (B) is presented in C and D (solid and open bars correspond to the model A and B, respectively) and GABA concentrations are indicated above. The values of the rate constants: kon = 4 mM1ms1, koff = 0.26 ms1,  = 1 ms1,  = 8 ms1 are equal for models A and B. In model A, d =1.5 ms1 and r = 0.12 ms1. E: time course of occupancies of the open state (AR*) in the models A and B and of the desensitized state (AD) for model A for response to 100 µM GABA. Note that for responses to 100 µM GABA, the rise time is faster for the model including desensitization. The responses to 1 µM GABA were simulated for model including binding only (F), binding and opening (G), and binding, opening, and desensitization (H). For models F-H, binding kinetics is assumed to be the same (kon= 4 mM1ms1, koff = 0.26 ms1) and E = / = 8 and B = d/r = 12.5. Time course of normalized (I) and absolute values (J) of occupancies of the states AR (for model F) and AR* (for models G and H).

Effect of desensitization is present also at low GABA concentrations

We investigated mechanisms underlying the rising phase of responses evoked by very low concentrations of GABA (e.g., 1 µM; Fig. 7C). These responses were simulated for the models including only binding (Fig. 7F), binding and opening (Fig. 7G), and binding, opening, and desensitization (Fig. 7H). In all these models (Fig. 7, F-H) the binding kinetics (k_on and k_off) are assumed to be the same. At GABA concentrations as low as 1 µM, binding is sufficiently slow to assume that opening/closing and desensitization are in equilibrium (Fig. 7, G and H, E = / and B = d/r). As shown in Fig. 7I, the presence of the open (AR*) and desensitized state (AD) strongly slowed down the rate of onset. The reason for this difference is that at low [GABA] there is a strong coupling between binding, opening/closing, and desensitization. Thus in the case of binding alone (Fig. 7F), the onset rate is equal to k_on·[GABA] + k_off while for models that include opening/closing (Fig. 7G), k_on·[GABA] + k_off 1/(1 + E) and for the scheme including both opening/closing and desensitization (Fig. 7H), k_on [GABA] + k_off · 1/(1 + E + B). This explains the relations between onsets at low [GABA] (Fig. 7D). The respective time constants  ( = 1/onset rate) of current rising phase have the values of 3.79, 30.4, and 62.1 ms for models in Fig. 7, F, G, and H, respectively. Since the relation between the 10-90% rise time (RT_10-90%) and  is RT_10-90% 2.2 · , the expected 10-90% rise times would be 8.34, 66.9, and 136.6 ms, which closely matches the 10-90% rise times of simulated responses for the models in Fig. 7, F ,G, and H: 8, 68.2, and 140 ms, respectively (Fig. 7I). Large differences in the occupancies of bound and open states (Fig. 7J) indicate that at low [GABA] the occupancy of bound and open receptors depends not only on affinity, but also on efficacy and desensitization kinetics. This prediction may be particularly useful when interpreting the results of both binding and electrophysiological experiments.

As shown in Fig. 4, E and G, the singly liganded desensitized state plays an important role in shaping the rising phase kinetics, although its role is limited to the low GABA concentrations. A possible mechanism whereby this state affects the current onset is presented in Fig. 8. After the application of 10 µM GABA, the occupancy of the singly bound closed state (AR) reaches its maximum and then decays. Such transient accumulation in this state favors entrance into a singly bound desensitized conformation (AD). Delay in the onset of AD state with respect to AR is due to a slow rate constant that leads to this state. When the occupancy of AR decreases, a proportion of receptors exits the AD state. Since the desensitization rate constant r₁ is very small, the decay in occupancy of the AD state is slow. Part of the receptors leave the AD conformation, bind a second GABA molecule, and open, increasing the occupancy of the open states (A₂R*).

View larger version (15K): [in this window] [in a new window]   Fig. 8. Occupancies of AR, AD, and A2R* states for model in Fig. 4G for the rate constants best fitting the experimental dose-response for current rise times (Fig. 4), after application of 10 µM GABA for 400 ms. Note that the decay of singly desensitized state AD coincides with a slowing rising phase of the fully bound open state A2R*.

An attempt has been made to include the connections between singly and doubly open and desensitized bound states in the model, but no significant improvement in reproduction of experimental data were achieved.

Apparent desensitization onset depends on opening/closing kinetics

Current decay during a prolonged exposure to a saturating concentration of agonist (see e.g., Fig. 1B) is usually ascribed to receptor desensitization. In these conditions, as mentioned, the singly bound states are believed to play a negligible role and therefore only the impact of the fully bound desensitized state will be discussed. The fast component of the desensitization onset was described by the time constant _fast = 4.2 ms. However, an attempt to estimate this time constant as 1/(d + r) would yield   0.6 ms. The reason for this discrepancy is that the desensitized state is coupled with the closed and open bound states. Assuming that [GABA] is saturating and that opening is fast enough to be in equilibrium, the rate of desensitization is r + d × 1/(1 + E), and the resulting time constant is   3.5 ms, which is much closer to the value observed during experiment. This implies that the apparent desensitization onset critically depends not only on the desensitization rate constants (d, r) but also on opening/closing transitions (, ). The assumption that during desensitization onset opening/closing transitions are in equilibrium may be an oversimplification for rapidly desensitizing GABA_ARs, although there is general agreement that desensitization is considerably slower than opening/closing both in native and recombinant receptors (see e.g., Barberis et al. 2000; Bianchi et al. 2001; Haas and Macdonald 1999; Mozrzymas et al. 1999; Jones and Westbrook,1995; Puia et al. 1994; Tia et al. 1996).

	DISCUSSION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

The present work addresses a fundamental problem of the relationship between the kinetics of specific GABA_AR conformational transitions and the time course of macroscopic current responses. Since, as in any Markovian system, all channel states are coupled, any kinetic feature of the measured responses reflects a complex process that is shaped by all the conformations present. Our approach presented new aspects of specific GABA_AR conformations (especially desensitization) and allowed the assessment of their impact on the time course of measured currents. Functional coupling between the channel states appears particularly important in conditions of extreme nonequilibrium that result from rapid application and clearance of the agonist. For example, the effect of desensitization on rise time (Fig. 7) and on the concentration dependence of current amplitude (Fig. 6) is clearly manifested only within the initial part of the response, and therefore would be obscured in steady-state conditions or if agonist application was slow.

Responses to saturating [GABA] reflect transitions between fully bound receptors, allowing conformational state kinetics to be studied independently from binding reactions. This is of considerable advantage, because binding schemes are usually complex and add several degrees of freedom to the optimization procedures. We used the following strategy for studying GABA_AR gating: 1) assessment of the saturating concentration by finding the [GABA], at which the responses become concentration independent; 2) recording of current responses to saturating [GABA] using various protocols (e.g., as in Fig. 1) and optimization of the entire set of the rate constants; and 3) measurement of the current responses for a wide range of [GABA] and fitting them to a chosen binding reaction model. In this study, this procedure was employed for relatively simple models (Fig. 4). In particular, fully bound slow desensitized states were not considered. However, for very slowly absorbing fully bound desensitizing states, the model simulations suggest that their role is minor. Another possibility are the connections between singly and doubly bound open and desensitized states as (Jones et al. 1998; Twyman et al. 1990; see also classical model for AChR: Cachelin and Colquhoun 1989; Katz and Thesleff 1957). In our analysis, these additional connections did not give any significant improvement. In previous papers, which considered connections between singly and doubly bound desensitized states, the respective rate constants for this link were orders of magnitude smaller than those connecting closed states (Jones et al. 1998). It therefore seems that the structure of GABA_AR model gating qualitatively differs from the classical cyclic AChR model. While GABA_ARs binding and dissociation occurs predominantly from the closed conformation, in the case of AChR these processes may additionally occur in the open or desensitized states, conferring the cyclic shape of the gating model.

Determination of rate constants requires the explicit consideration of interaction between the channel states

A proper association between current response time course and rate constants is of crucial importance in studies with mutagenesis (see e.g., Bianchi et al. 2001; Wagner and Czajkowski 2001) or pharmacology (see e.g., Barberis et al. 2000; Jones and Westbrook 1997; Li and Pearce 2000; Mozrzymas et al. 1999; Shen et al. 2000). Certain misinterpretations arise from the failure to consider coupling between receptor conformations.

The onset rate of current responses evoked by saturating [GABA] is commonly ascribed to the transition rate from the bound closed to bound open state (). However, the present study provides evidence that the rise time of response evoked by saturating [GABA] depends also on the desensitization process and that the rate of rise may be approximated as  + d [ = 1/( + d)]. When the channel loses the desensitized state (d = 0), rise time is expected to become slower ( = 1/). A plausible (and perhaps more intuitive) interpretation could be a decrease in the transition rate from closed to open state (), but such a conclusion requires knowledge about the fate of the desensitization rate (d). The fact that desensitization kinetics may affect rising phase kinetics has been reported for AMPA receptors (Clements et al. 1998).

Response decay during a long application of saturating [GABA] (Fig. 1C) is often ascribed solely to the desensitization process, but as mentioned in RESULTS, it also strongly depends on open/close transition [1/  r + d · /( + )]. Thus when efficacy (E = /) increases, the rate of apparent "desensitization onset" will decrease tending to the desensitization rate r for receptors with high efficacy E [/( + ) 1].

Most difficult is the determination of the desensitization rate r. In several studies, the standard short double pulse protocol is used as the only tool to estimate this parameter. In the present work we show that such an approach is insufficient, as the recovery process observed in these experiments depends not only on desensitization (r) but also on the unbinding (k_off), opening/closing (, ), and desensitization rate (d). It needs to be additionally emphasized that in the case of short double pulses (Fig. 1, E and F), a decrease in amplitude of in the second peak is more indicative for a large affinity rather than for a slow "recovery from desensitization."

Rising phase kinetics provides key information on binding scheme

We found that the most commonly used scheme, which postulates two identical and independent binding sites (Barberis et al. 2000; Gingrich et al. 1995; Jones and Westbrook 1995 1997; Jones et al. 1998; Mozrzymas et al. 1999; Li and Pearce 2000; Twyman et al. 1990;), fails to reproduce the dose dependence of rising phase kinetics for a wide range of GABA concentrations (Fig. 4D). Our data suggest that the main source of this discrepancy is the fact that the binding sites are cooperative. This cooperativity is a property of several systems such as hemoglobin, AMPA receptors (Clements et al. 1998), or nicotinic acetylcholine receptors. For the latter, Jackson (1989) proposed that one binding site has larger affinity and provides little energy for opening, while the second has lower affinity and contributes more energy to channel opening. For GABA_A receptors, a cooperativity of binding sites was reported for some recombinant and for native GABA_ARs in mouse cortical neurons (Lavoie et al. 1997; McClellan and Twyman 1999). Although the inclusion of binding site cooperativity and partially liganded states greatly improved the reproduction of experimental data, the values of ² statistics for these models indicate that the gating scheme may be still more complex (only the model in Fig. 4G reached statistical significance and the P value for this model was close to 0.05). For instance, it cannot be excluded that the number of binding sites is larger than two. However, the verification of this hypothesis would require the estimation of several additional rate constants and more data would be needed.

Although current responses to rapid GABA applications properly reproduce the basic kinetic properties of IPSCs, the conditions of GABA_AR activation are not exactly the same in the two situations. The recorded current responses most likely result from the activation of a mixture of synaptic and extrasynaptic receptors present in the excised patches. Moreover, intracellular soluble modulators are lost on patch excision, which possibly gives rise to modifications in receptor properties. For instance, the deactivation phase of IPSCs is faster than that of current responses, probably due to differences in receptor subtypes and in the environment (Banks and Pearce 2000; Jones and Westbrook 1995; Mozrzymas et al. 1999). Nevertheless, the model of "surrogate IPSCs" based on current responses to ultra-fast agonist applications presents the most reliable kinetic description of receptor gating in the time scale of synaptic events. Thus even if there are quantitative differences between the kinetics of synaptic GABA_ARs and those present in excised patches, general gating properties, such as interaction between receptor conformations, the role of desensitization on deactivation and rise time, are expected to be qualitatively the same in both cases.