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The Journal of Neuroscience, September 15, 2001, 21(18):7026-7036
Dominant Gating Governing Transient GABAA Receptor Activity: A First Latency and Po/o Analysis
Paul M. Burkat1, Jay Yang1, 2, and Kevin J. Gingrich1, 2 Departments of 1 Pharmacology and Physiology and 2 Anesthesiology, University of Rochester School of Medicine and Dentistry, Rochester, New York 14642
ABSTRACT
TOP
ABSTRACT
INTRODUCTION
Steady-state, single-channel gating of GABAA receptors (GABARs ) is complex. Simpler gating may dominate when triggered by rapid GABA transients present during fast inhibitory synaptic transmission and is critical to understanding the time course of fast IPSCs. We studied the single-channel activity of expressed
1
1
2 GABARs in outside-out patches from human embryonic kidney 293 cells triggered by rapidly applied GABA (10-2000 µM) pulses (2-300 msec). Activation was analyzed with the time to first channel opening after GABA presentation, or first latency (FL). FL distributions are monoexponential at low GABA concentrations and biexponential above 30 µM GABA. The fast rate increases supralinearly to a plateau of ~1100 sec
1, the apparent activation rate. The slow rate and amplitude are insensitive to GABA concentration. The results argue that doubly liganded receptors can rapidly desensitize before opening. Gating after the first opening was quantified with analysis of open probability conditioned on the first opening (Po/o). Po/o functions are biexponential, dominated by a fast component, and insensitive to GABA concentration. This suggests that open channels convert primarily to fast but also to slow desensitized states. Furthermore, dual modes of fast desensitization may influence IPSC amplitude and thereby synaptic efficacy. The findings provided for the construction of a mathematical gating model that accounts for FL and Po/o functions. In addition, the model predicts the time course of macroscopic current responses thought to mimic IPSCs. The results provide new insights into dominant gating that is likely operational during fast GABAergic synaptic transmission.
Key words: recombinant GABAA receptors; transient; single-channel; gating; first latency; conditional open probability; modeling
INTRODUCTION
GABA is the primary inhibitory neurotransmitter in the mammalian CNS. After release from a presynaptic terminal, GABA binds to postsynaptic GABAA receptors (GABARs) and induces conformational changes culminating with the opening of an integral, anion-selective pore. Extensive studies on single GABARs under equilibrium conditions have advanced our understanding of microscopic channel properties and revealed that channel gating is complex, with multiple open and closed states (Hamill et al., 1983
; Bormann and Kettenmann, 1988
In this study, we identify dominant states governing transient GABAR activity through the analysis of single-channel behavior. Single-channel analysis using first latency (FL) (Aldrich et al., 1983
Here, outside-out membrane patches containing expressed
MATERIALS AND METHODS
Cell culture and transient transfection. Transformed HEK-293 cells, purchased from American Type Culture Collection (Bethesda, MD), were plated on 18 × 18 mm glass coverslips in 60 × 15 mm Falcon dishes (Becton Dickinson, Lincoln Park, NJ) and cultured in minimum essential medium (MEM) supplemented with 10% fetal bovine serum (FBS) and 1% each of penicillin, streptomycin, and glutamine (all from Life Technologies, Grand Island, NY). After incubation in 37°C, 5% CO2 for 48 hr, cells were transiently transfected using a lipofection technique described previously (Gingrich et al., 1995
Electrophysiological recordings. Coverslips with transfected cells were transferred to the lid of a culture dish mounted on the stage of an Olympus IMT-2 (Olympus, Lake Success, NY) inverted microscope with Hoffman modulated optics. The cells were immersed in a modified Tyrode's solution containing (mM) 132 NaCl, 4.8 KCl, 1.2 MgCl2, 1 CaCl2, 10 HEPES, 5 dextrose, pH 7.3. Glass pipettes were prepared from borosilicate glass (Corning Pyrex, Corning, NY) with a multistage puller (Flaming Brown model P-97, Sutter Instrument Company, Novato, CA), fire polished (MF-9 Microforge, Narishige, Greenvale, NY), and coated with Sylgard (Dow Corning Company, Midland, MI). Recording pipettes were filled with (in mM): 140 CsCl, 1 MgCl2, 5 MgATP, 10 HEPES, and 10 EGTA. Open tip resistances were typically 5-10 M
under these ionic conditions. Currents were recorded with the outside-out configuration of the patch-clamp technique (Hamill et al., 1981
3 dB, four-pole Bessel) and sampled at 12.5 kHz. Single-channel currents were filtered at 2 kHz (
Rapid solution changes. GABA (Sigma, St. Louis, MO), stored in aliquots of 10 mM and diluted to the desired concentrations, both in Tyrode's solution, was transiently applied to patches via an electromechanical solution changer. Control and test solutions were gravity-fed separately into the lumens of dual-barreled pipettes constructed from pulled borosilicate theta tubing (Sutter Instrument Company). Test solutions containing GABA were applied by delivering a filtered (model LPF-100B, four-pole Bessel, 200 Hz; Warner Instrument Corporation, Hamden, CT) voltage pulse to a high-voltage amplifier (model P-275.10, Physik Instruments, Waldbronn, Germany) that drove the macro-block translator such that a dual-barreled pipette tip moved a short distance. In this way, control and test streams bathing the membrane patch could be interchanged rapidly. GABA pulses were applied every 15 sec (GABA in micromolar, duration in milliseconds): 10, 300; 30, 200; 100-2000, 100. Macropatch current responses to brief (2 msec), high-concentration GABA (2000 µM) pulses replicated IPSCs (Jones and Westbrook, 1995
Data analysis. Single-channel events were detected by half-height criterion (Sachs et al., 1982
). The number of active channels in a patch (n) was determined by the stacking of unitary events, which is a good estimator, especially for n < 4 (Horn, 1991
First latency distributions were created using standard histogram techniques (Aldrich et al., 1983
Precise determination of n from multichannel patches is necessary to construct single-channel first latency functions. We therefore investigated the accuracy of the channel estimator using single-channel simulations of the model that accounts for many features of GABAR gating (see Fig. 6A). A single-channel simulator (implemented in Matlab v5.1; Mathworks, Natick, MA) was used to determine the probability of n and n
Po/o functions were constructed as described by Yue et al. (1990)
where Po(t + tj) is the unconditional probability that a channel is open at time (t + tj). The convolution (Eq. 2) of the first latency probability density function [f(t)] and Po/o(t) specifies the time-dependent channel open probability [P(t)], which is a scaled version of the macroscopic current [I(t); n = channel number;
(1) V = electrochemical driving force]) (Eq. 3):
(2)
Up to a two-exponential function [A1exp(
(3) 1) + A2exp(
Model simulation and parameter estimation. The seven-state dominant gating model was implemented in Matlab v5.1 (Mathworks, Natick, MA) by solving the matrix equation:
where X(t) is a 7 × 1 state variable vector indicating the occupation of the states (i.e., R, CG, CG2, D1, O, D2, D3) at time t, X(0) = [1 0 0 0 0 0 0]T initial state vector at time 0 assuming all channels in the resting R state, and Q(t) = the 7 × 7 state transition matrix of rate constants governing the transition rates between all connected states. The single open state is O, the singly and doubly liganded receptors are CG and CG2, respectively, and the three desensitized states are D1, D2, and D3 (see Fig. 6A). The simulation period was divided into GABA wash-in and wash-out, and changes in concentrations were assumed to be instantaneous. Parameter optimization used a least squares technique that simultaneously used mean empirical FL* and Po/o values at 10, 100, and 2000 µM GABA as performance targets.
RESULTS
GABA induces single-channel activity in rapidly perfused, outside-out membrane patches from cells expressing
We focused initially on dominant features of GABAR activation by exploring first latencies. Figure 1A shows consecutive single-channel traces evoked by rapidly applied, periodic GABA pulses delivered to an outside-out membrane patch that contained a single, active
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Figure 1. Single-channel activity from a rapidly perfused, outside-out membrane patch from a cell expressing
Markov models have been used widely to describe ion channel gating where the random nature of transitions between conformational states can be described by a Poisson process. A key feature of such a process is the stationary increment assumption (Ross, 1997
Figure 1C shows the corresponding FL function in a complement of the distribution form, which conveys the probability that the first opening will occur at a time after that specified on the abscissa. This function concisely conveys FL information for all 186 sweeps from this patch and shows that most first openings occurred within 40 msec. The plateau (~0.5) reports the probability that a channel will fail to open during a given GABA application. Indeed, inspection of individual sweep records reveals sweeps without activity (nulls). These can be explained by either a resting, closed channel converting to a desensitized state during the present GABA pulse before opening or a long-lived, desensitized state persisting from the previous pulse. Null sweeps appeared to cluster, thus arguing for the latter possibility. Single-channel analysis assumes that the receptor is in the same resting conformation before each GABA application. Therefore, to further investigate for a persistent, slow desensitized state, single-channel protocols were applied in macropatch current experiments.
GABARs enter a long-lived, desensitized state
Figure 2A shows macropatch current responses to GABA pulses (100 msec, 2000 µM) delivered every 15 sec. Current time course initially shows a rapid downward increase representing channel activation that is followed by decay reflecting fast desensitization. The peak amplitude of subsequent responses progressively declines until an apparent plateau is reached around the eighth pulse. Preparation stability was ensured by the return to control amplitude of a response evoked 180 sec after the pulse train. The results support GABA-induced entry into a desensitized state sufficiently long-lived to accumulate from pulse to pulse. For accumulation to occur, the recovery time constant must be on the order of the interstimulus interval (15 sec). This finding was confirmed in grouped data (Fig. 2B) in which peak amplitudes declined in a monoexponential manner to a plateau of ~0.5. A plateau is consistent with a pseudo-equilibrium condition established between pulse-induced entry into and interstimulus recovery from a long-lived, desensitized state. According to this reasoning, approximately half the channels are unavailable for activation at the end of the pulse train. Once the mean probability of this state is determined for a given experimental protocol, null sweeps and FL values can be corrected. Therefore, macropatch current experiments were performed for all protocols, mean responses were calculated, and monoexponential fitting were performed. Derived plateau values were plotted for each protocol and designated by GABA concentration (Fig. 2C). This slow desensitized state accords with reports from heterologous expression systems (Haas and Macdonald, 1999
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Figure 2. Peak amplitude of macropatch currents decreases during trains of GABA pulses. A, Macropatch currents triggered by GABA (2000 µM) pulses (100 msec) every 15 sec (series of short horizontal bars). Single long bar on left marks baseline. Deactivation time course has been truncated for clarity. B, Peak current amplitudes (I) from A normalized to the amplitude of the first pulse (Imax) and plotted versus time of pulse (means ± SEM; n = 3). A monoexponential function fit is shown (smooth solid line) with a plateau of 0.52 (see Materials and Methods). C, Bar graph of plateau values derived from monoexponential fitting to macroscopic peak amplitude decrement for single-channel GABA pulse protocols (10 µM, 300 msec; 30 µM, 200 msec; and 100-2000 µM, 100 msec) with a period of 15 sec.
Increasing GABA concentration shortens first latencies and reveals a slow component of activation
Figure 3B shows first latency functions corrected for nulls (FL*) associated with a slow desensitized state. The function at 10 µM GABA exhibits a brief delay followed by a slow decline, which is well fit by a delayed monoexponential function without a constant (see Materials and Methods). The FL* at 30 µM GABA is also monoexponential but is accelerated relative to 10 µM GABA, consistent with enhancement of forward rate constant(s). Increasing GABA concentration to 100 µM continues to accelerate the fast component and introduces a second slow monoexponential component. Higher GABA concentrations (>100 µM) caused little additional acceleration of the fast component without changing the slow.
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Figure 3. First latency analysis of activation. A, Representative, nonconsecutive single-channel traces evoked by GABA pulses (solid lines) at indicated concentrations (in micromolar) from individual single-channel patches. Downward current deflections denote channel opening. Ensemble average currents (below, irregular lines) are similar to the time course of representative macropatch currents at these concentrations (heavy lines). Open circle marks a subconductance opening excluded from single-channel analysis. At the higher concentration (500 µM), delayed first openings, occurring after the ensemble current peak, are indicated (asterisks). B, Single-channel First Latency* functions (corrected for a slow desensitized state; see Materials and Methods) at indicated GABA concentrations, in micromolar (means ± SEM; n = 3-5). Superimposed relationships (smooth lines) are delayed monoexponential (10 and 30 µM) and biexponential (100-2000 µM) function fits to the data (see Materials and Methods). The fit to the 100 µM response is difficult to visualize because it nearly overlies the empirical response at all time points. C, Concentration-response relationships for rates (fast and slow) and slow fraction derived from parameters from multiexponential function fits in B. The fast rate (open circles) is well fit (smooth line) by a logistical function [Rate = Ratemax × (1 + (EC50/[GABA])slope)
We explored gating reflected in FL* values by examining the dependence of exponential parameters on GABA concentration (Fig. 3C). The fast rate increases supralinearly (slope factor related to the Hill coefficient of 1.47) from 20 sec
Open probability conditioned on the first opening (Po/o) is biphasic and GABA insensitive
We next considered channel gating subsequent to the first opening. Figure 4A shows representative single-channel traces aligned at the first opening by eye for comparison. Gating after the first opening is qualitatively similar at both concentrations and is characterized by openings that occur singly and in bursts separated by long closed intervals. We quantitatively analyzed this gating using conditional open probability analysis (Sigworth, 1981
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Figure 4. Open probability conditioned on the first opening (Po/o). A, Nonconsecutive, single-channel records evoked by 30 and 500 µM GABA from patches in Figure 3A, with first openings aligned at the dotted vertical lines by eye for comparison. Sweeps with similar gating across concentrations were paired for comparison. B, Mean Po/o functions for indicated GABA concentrations (micromolar) that nearly superimpose. For clarity, error bars are shown only for the 2000 µM decay (means ± SEM; n = 3-5). Inset, Biexponential fit (dashed line) to the 2000 µM response with indicated parameters. C, A simple gating scheme consistent with Po/o findings in which open channels (O) convert to adjacent fast and slow desensitized states (D2 and D3, respectively). Dotted line represents states that may contribute to Po/o but are not shown (see Results and Discussion).
Convolution of FL probability density and Po/o reproduces the macroscopic current time course
Single-channel open probability [P(t)] is a scaled version of the macroscopic current time course and can be calculated by convolving (see Materials and Methods) the first latency probability density function (f) with the Po/o function (Fig. 5, A and B, respectively). If our analytical techniques are correct, then the computed P(t) will duplicate gating manifest in ensemble current averages derived from the same single-channel data. Figure 5C shows that computed P(t) accurately reproduces the time course of the mean ensemble current average, thereby confirming the validity of our approach.
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Figure 5. Single-channel open probability derived from convolution of first latency and Po/o reproduces the time course of macroscopic current. Calculation of single-channel open probability [P(t)] induced by a long 100 µM GABA pulse. A, First latency probability density function (f, vertical lines) composed of first latencies collected from all patches at this concentration (n = 3). Mean complement of the distribution (smooth line) replotted from Figure 3B for reference. B, Mean Po/o function replotted from Figure 4B (±SEM). C, Plot of single-channel open probability [P(t), solid line)] constructed by convolving f with Po/o (see Materials and Methods) and ensemble average current (dotted line; mean ± SEM; n = 3). Horizontal bar marks GABA pulse. Responses were normalized and peaks aligned in time to facilitate comparison of time courses.
A parsimonious gating model accounts for FL* and Po/o values and predicts the properties of microscopic and macroscopic gating
As a first attempt to construct a parsimonious model of dominant GABAR gating, we simply combined the gating subschemes separately proposed for FL* and Po/o findings at the single open state (Fig. 6A). We then estimated model parameters using empirical FL* and Po/o values as performance targets (see Materials and Methods) to determine all final values except those (d3, d
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Figure 6. Mathematical model of dominant GABAR gating during transient GABA. A, Left, Gating model formed by combining subschemes separately proposed for first latency and Po/o functions. Brackets encompass states and gating that primarily contribute to each function. A resting channel (R) sequentially binds two molecules of GABA (G) to either open (O) (fast component in FL* functions) or rapidly desensitize (D1). Channel emerges from D1, to subsequently open, giving rise to the slow component in the FL*. Open channels rapidly desensitize to D2 or convert transiently to CG2 before finally desensitizing to D1. D3 likely accounts for apparent null sweep grouping and macropatch amplitude decrement. Right, Parameter values of model (see Results). B, C, Model reproduces empirical responses used in its construction. Response of peak amplitudes of macropatch currents during pulse trains (Ba), Po/o (Bb), and FL* (Ca-c) for the indicated conditions (GABA in micromolar). Model simulations are superimposed (connected filled circles in Ba; smooth solid lines in Bb, Ca-c). Experimental results replotted from Figures 2B, 3B, and 4B.
Previous studies have identified up to three distinct open states for GABARs (Twyman et al., 1990
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Figure 7. Model predicts mean open time and macroscopic GABAR gating. A, Log-binned open time histograms at 10 and 2000 µM GABA. Maximum likelihood fits of transformed biexponential functions (thin line) and individual components (dashed lines). Thick lines represent model open time histograms. B, Macropatch current (irregular line; mean ± SEM; n = 3) evoked by the indicated GABA pulse (bar). The model response [simulated P(t), smooth line] normalized for peak amplitude accurately predicts the empirical time course. C, Macropatch current response (irregular line; mean ± SEM; n = 4) to a brief (2 msec) high concentration GABA (2000 µM) pulse marked by filled square, which replicates an IPSC. Long horizontal bar at left indicates baseline. Normalized model response (smooth line) reproduces the empirical time course. Inset, The same responses on an expanded timescale. Calibration: 10 msec.
The main focus of this study is to understand the dominant gating underlying the time course of IPSCs. If the model predicted the time course of IPSCs then it could provide new insight into the underlying gating. Therefore, we first considered whether the model predicts the time course of empirical macroscopic currents triggered by long GABA pulses. Figure 7B shows that the model predicts the mean macropatch current response triggered by a 100 µM GABA pulse lasting 100 msec. We next considered IPSCs. The IPSC time course in cultured neurons is mimicked by macropatch current responses induced by brief (<5 msec) pulses of saturating GABA concentrations (>1 mM) (Maconochie et al., 1994
Model parameter sensitivity analysis and dual modes of fast desensitization influence model peak open probability and synaptic efficacy
The role of model states and gating transitions in performance is investigated by examining model sensitivity to changes in associated parameters (parameter sensitivity analysis). Charge transfer mediated by receptor activity is a primary determinant of synaptic efficacy. We used the integral of model open probability [P(t)] induced by brief, high concentration GABA pulses as an index (
P) of charge transfer because they are proportional. We examined changes in
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Figure 8. Model parameter sensitivity analysis. A, Percentage change in simulated integral of single-channel open probability (
Increasing d1 depressed peak open probability (Pmax) by more than twofold and enhanced the amplitude of the fast component of decay (Fig. 8Ba, left). d1 promotes entry into D1 and thereby reduces the fast component of the FL* (Fig. 8Bc, left). The slow activation component is markedly enhanced, which primarily affects P(t) after the peak, thereby underscoring the utility of first latency analysis. This change enhanced the amplitude of the fast component, accelerated the slow component, and depressed the apparent plateau of the Po/o (Fig. 8Bb, left). This indicates that D1, in addition to D2, contributes importantly to gating after the first opening and thus Po/o. Examination of related rate constants (Fig. 6A) support this conclusion. Overall, the simple subscheme proposed earlier (Fig. 4C) must be extended to include these states, which is reflected in the identification of subgroups of states and transitions underlying Po/o (Fig. 6A). Decreasing d1 had the expected converse effects on P(t), FL*, and Po/o.
Increasing d2 suppressed Pmax, accelerated the fast component, and decelerated the rate and increased the amplitude of the slow component. d2 promotes entry into D2 and thereby markedly accelerates Po/o decay and depresses the apparent plateau (Fig. 8Bb, right), whereas it has no effect on FL* (Fig. 8Bc, right). The marked depression of Pmax arises from increased transitions from O to D2, which blunts the probability of O. Decreasing d2 caused converse effects on P(t), FL*, and Po/o. The results identify key model states and support the involvement of fast desensitization in shaping the IPSC time course (Jones and Westbrook, 1995
Dominant gating underlying replicated IPSCs
The central goal of this study was to identify the dominant gating underlying the time course of IPSCs. The GABAR response to brief, high concentration GABA pulses "mimics" or replicates IPSCs (Jones and Westbrook, 1995
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Figure 9. Model gating underlying primary phases of replicated IPSCs. Top, Probability of resting (R) (dashed line), open (O), and desensitized states (D1 and D2) (solid lines) during replicated IPSC (bottom) triggered by a brief (2 msec) high concentration (2000 µM) GABA pulse (middle trace). See Results. Bottom, Replicated model IPSC to the same GABA pulse is coarsely divided into four phases: early activation, activation to peak current, fast decay, and slow decay. Early activation, rapid downward current deflection, results from fast transition from R to CG2. This reduces the R probability to zero during the pulse. The number of channels directly converting to O is reduced by those entering D1. Peak amplitude is determined in part by early activation, but also by rapid conversion of O to D2 that depresses the peak. Fast decay phase is the rapid current decay after the peak, which is attributable to continued transitions to D1 and D2. Finally, slow decay is primarily governed by slow ligand unbinding that is impeded by a relatively fast pseudo-equilibrium among CG2, O, D1, and D2.
DISCUSSION
We investigated dominant gating governing GABAR activity triggered by transient GABA application with a unique combination of experimental and analytical techniques. The findings provide new insight into the dominant states and connectivity operative during transient GABAR activity. The primary results are as follows: doubly liganded closed channels can visit an adjacent fast desensitized state before opening; open channels rapidly convert to a second distinct fast desensitized state; a doubly liganded state(s) undergoes a conformational change to a slow desensitized state; and dual fast desensitized states may affect synaptic efficacy by influencing IPSC amplitude. Finally, a mathematical gating model predicts the time course of replicated IPSCs and thus provides new insight into the underlying GABAR gating.
Comparison of the dominant-gating model with previous models
Work by Weiss and Magleby (1989)
Maconochie et al. (1994)
A limitation of our study, as well as that of Maconochie et al. (1994)
The critical role of desensitized states in IPSC relaxation was proposed by Jones and Westbrook (1995)
Slow GABAR desensitization has been reported previously (Celentano and Wong, 1994
Haas and Macdonald (1999)
GABARs, two open states connected to two nonconducting states and a separate slow desensitized state were required. For
Dual fast desensitized states
Our modeling efforts indicated an important role of dual fast desensitized states in determining peak open probability and consequently synaptic efficacy (Fig. 8). However, our simulated Pmax of ~0.3 is less than previous reports for GABARs, with values of ~0.6 (Newland et al., 1991
Jones and Westbrook (1995)
This work demonstrates the powerful utility of first latency and conditional open probability analysis in identifying dominant states and connectivity that underlie the kinetics of GABAR opening and closing. We add this approach to those already applied to probe GABAR gating (Weiss and Magleby, 1989
FOOTNOTES Received Feb. 12, 2001; revised July 9, 2001; accepted July 11, 2001.
This work was supported by Medical Scientist Training Program Grant T32-GM07356 to P.M.B., National Institutes of Health (NIH) Grant GM52325 to J.Y., and Whitaker Foundation and NIH GM56958 grants to K.J.G. We thank P. G. Patil and D. T. Yue, Departments of Biomedical Engineering and Neuroscience, Johns Hopkins University, for analysis software.
Correspondence should be addressed to Kevin Gingrich, Merck Research Laboratories, Clinical Pharmacology, 10 Sentry Parkway, BL 1-2, Blue Bell, PA 14922. E-mail: kgingric{at}together.net.
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