Experimentally monitored calcium dynamics at synaptic active zones during neurotransmitter release in neuron–muscle cell cultures

Ca2+‐dependent K+ (BK) channels at varicosities in Xenopus nerve–muscle cell cultures were used to quantify experimentally the instantaneous active zone [Ca2+]AZ resulting from different rates and durations of Ca2+ entry in the absence of extrinsic buffers and correlate this with neurotransmitter release. Ca2+ tail currents produce mean peak [Ca2+]AZ ~ 30 μM; with continued influx, [Ca2+]AZ reaches ~45–60 μM at different rates depending on Ca2+ driving force and duration of influx. Both IBK and release are dependent on Ca2+ microdomains composed of both N‐ and L‐type Ca channels. Domains collapse with a time constant of ~0.6 ms. We have constructed an active zone (AZ) model that approximately fits this data, and depends on incorporation of the high‐capacity, low‐affinity fixed buffer represented by phospholipid charges in the plasma membrane. Our observations suggest that in this preparation, (1) some BK channels, but few if any of the Ca2+ sensors that trigger release, are located within Ca2+ nanodomains while a large fraction of both are located far enough from Ca channels to be blockable by EGTA, (2) the IBK is more sensitive than the excitatory postsynaptic current (EPSC) to [Ca2+]AZ (K1/2–26 μM vs. ~36 μM [Ca2+]AZ); (3) with increasing [Ca2+]AZ, the IBK grows with a Hill coefficient of 2.5, the EPSC with a coefficient of 3.9; (4) release is dependent on the highest [Ca2+] achieved, independent of the time to reach it; (5) the varicosity synapses differ from mature frog nmjs in significant ways; and (6) BK channels are useful reporters of local [Ca2+]AZ.

K E Y W O R D S BK channels, Ca 2+ domains, Ca 2+ dynamics, neuromuscular junction, neurotransmitter release

| INTRODUCTION
Neurotransmitter release is triggered by transient [Ca 2+ ]-AZ domains at synaptic active zones (AZs).These may be nanodomains, where vesicular release depends on the localized cloud of Ca 2+ generated by the opening of one or a very few nearby Ca channels, often functionally defined by total or partial resistance to block by BAPTA, or microdomains, where release is triggered by summed Ca 2+ from multiple open Ca channels and release sensors are sufficiently far from individual Ca channels for BAPTA to block effectively.If far enough from Ca channels, EGTA too can block effectively (Eggermann et al., 2012;Kasai, 1993;Oheim et al., 2006;Stanley, 2015Stanley, , 2016)).Using these criteria, synapses of both types have been described (reviewed by Eggermann et al., 2012).Specific parameters of both types of Ca 2+ domains have been modelled extensively (Bennett et al., 2000;Chad & Eckert, 1984;Dittman & Ryan, 2020;Fogelson & Zucker, 1985;Laghaei et al., 2018;Luo et al., 2015;Nakamura et al., 2015Nakamura et al., , 2018;;Naraghi & Neher, 1997;Oheim et al., 2006;Roberts, 1994;Shahrezaei & Delaney, 2005;Simon & Llin as, 1985;Stanley, 2016;Wang & Augustine, 2015;Yamada & Zucker, 1992;Zucker, 1993), but there is little experimental evidence to refine and verify these models.The magnitude and time course of a Ca 2+ microdomain will depend not only on the distribution of open Ca 2+- channels, the duration of Ca 2+ channel opening and the properties of endogenous mobile and fixed buffers, but also on the degree to which diffusion of Ca 2+ away from the channel mouths is obstructed.For all of these reasons, rigorous modelling is difficult.It is desirable to have experimental evidence for the effective [Ca 2+ ] experienced by the Ca 2+ sensors and the relationship between release and the magnitude and time course of changes in [Ca 2+ ] AZ .
Low-affinity Ca 2+ -sensitive dyes have shown localized presynaptic Ca 2+ influx opposed to postsynaptic receptor aggregates in the squid giant synapse (Llinas et al., 1992;Sugimori et al., 1994), vertebrate hair cells (Issa & Hudspeth, 1996;Tucker & Fettiplace, 1995) and Xenopus neuromuscular synapses-the synapses used in the present report (DiGregorio et al., 1999;DiGregorio & Vergara, 1997)-and the calyx of Held (Nakamura et al., 2015).Similarly, total internal reflection fluorescence microscopy has revealed sharply localized 'hot spots' of Ca 2+ entry at the membrane surface in bipolar neurons, inner hair cells (Beaumont et al., 2005;Zenisek et al., 2003) and Xenopus oocytes (Demuro & Parker, 2003).However, estimates of the time course of build-up and decay and the absolute values of Ca 2+ concentration achieved within these domains, as well as the dimensions of the domains, are limited by the buffering properties of the introduced dyes (McMahon & Jackson, 2018;Nakamura et al., 2015Nakamura et al., , 2018)), the presynaptic volume being monitored and the resolving power of light optics (Schneggenburger & Neher, 2005;Thorn, 2012).
Experiments on coupling photorelease of caged Ca 2+ and Ca 2+ imaging with presynaptic capacitance measurements or deconvolution of postsynaptic responses have yielded measurements of the Ca 2+ sensitivity of release and of the Ca 2+ buffering capacity which differ widely for different terminals (Babai et al., 2014;Beutner et al., 2001;Bollmann et al., 2000;Heidelberger et al., 1994;Hsu et al., 1996;Millar et al., 2005;Schneggenburger & Neher, 2000;Sun et al., 2007;Thoreson et al., 2004;Thorn, 2012;Wadel et al., 2007;Wang et al., 2008).However, such experiments do not emulate the normal geometry of the Ca 2+ domain, the dynamics imposed by Ca 2+ influx through Ca channels, the steep gradients in [Ca 2+ ] as a function of distance from open Ca channels and Ca 2+ binding to intrinsic buffers.Moreover, normal release is triggered by Ca 2+ transients so brief that Ca 2+ -binding kinetics may be more important than binding affinity (Shahrezaei & Delaney, 2005).Bollmann and Sakmann (2005) have generated brief Ca 2+ transients at the calyx of Held by photorelease from caged Ca 2+ in the presence of exogenous buffers, but these transients were not localized to AZs and eliminated the role of endogenous mobile buffers.Nevertheless, the release was sensitive to the time course as well as the magnitude of the transient, reinforcing the importance of binding kinetics.In short, most available techniques have not been able to experimentally quantify the normal relationship between [Ca 2+ ] AZ and release.
A powerful alternative method of characterizing Ca 2+ domains is to take advantage of high conductance Ca 2+dependent K + (BK) channels, which co-localize with Ca channels at AZs, and can be used as reporters of local [Ca 2+ ] AZ .BK channels are present at many synapses, where they associate with P/Q-, N-or L-type Ca channels and contribute to repolarization of action potentials and truncation of release (Crest & Gola, 1993;Issa & Hudspeth, 1994;Prakriya & Lingle, 2000;Roberts et al., 1990;Robitaille et al., 1993).Indeed, BK channels form tight macromolecular complexes with Ca channels when purified from rat brain or co-expressed in cultured cells or Xenopus oocytes (Berkefeld et al., 2006;Gandini & Zamponi, 2021;Loane et al., 2007;Vivas et al., 2017).We have previously reported that BK channels are prominent in the presynaptic varicosity synapses formed by Xenopus motoneurons on muscle cells in nervemuscle co-cultures where they are ideally located to report the local [Ca 2+ ] in the few nanometres of space immediately inside the presynaptic membrane at the AZ, close to where the Ca 2+ -sensors for release are also located (Pattillo et al., 2001;Sun et al., 2004;Yazejian et al., 1997Yazejian et al., , 2000)).Moreover, the use of BK channels as reporters avoids the necessity for the introduction of extrinsic Ca 2+ -sensitive dyes/buffers or washout of endogenous cytoplasmic buffers and other contents as well.The magnitude of the I BK that can be elicited by step depolarizations at various times during a Ca 2+ tail current or action potential tracks Ca 2+ influx closely (Yazejian et al., 2000), indicating that the kinetics and Ca 2+ sensitivity of the BK channels in this preparation are in the range needed to make them potentially ideal reporters of local [Ca 2+ ].
These potential advantages have led investigators to use the degree of BK channel activation to quantify [Ca 2+ ] in frog and turtle hair cells (Art et al., 1995;Roberts et al., 1990;Sy et al., 2010), bipolar cell terminals (Sakaba et al., 1997), and rat chromaffin cells (Prakriya et al., 1996;Prakriya & Lingle, 1999).BK channels are dependent both on the level of depolarization and ambient [Ca 2+ ].At large depolarizations, the magnitude of the I BK tends to saturate at moderate levels of [Ca 2+ ], but the rate of I BK activation continues to increase as [Ca 2+ ] increases.We have shown that the activation time constant of the I BK is proportional to instantaneous [Ca 2+ ] when a depolarizing pulse is applied and can be used to track dynamic changes in [Ca 2+ ] AZ (Sun et al., 2004), a conclusion reinforced by the findings of Berkefeld et al. (2006) in membrane patches co-expressing Ca 2+ and BK channels.The usefulness of BK channels as reporters of [Ca 2+ ] AZ depends on their close coupling to Ca channels.Perhaps the most compelling evidence for such coupling is the fact that the activation time constant of the I BK during Ca 2+ tail currents, action potentials or other depolarizing waveforms, when calibrated by the behaviour of single BK channels exposed to known [Ca 2+ ], indicate that peak [Ca 2+ ] AZ can reach levels of over 100 μM, which would only be achieved within a few tens of nm from open Ca channels (Yazejian et al., 2000;Sun et al., 2004; and see below).Moreover, the amplitude of the I BK evocable by a step depolarization imposed at various times during a Ca 2+ tail current tracks the time course of the rising phase of the tail current with a delay of no more than 50 μs, reaches peak magnitude within 50-100 μs of the peak of the tail current and declines as the I Ca declines (Yazejian et al., 2000).
In the present paper, we extend the use of BK currents at AZs to correlate the changes in [Ca 2+ ] AZ with the magnitude and dynamics of release and discuss the implications of these findings for the distribution of BK and Ca channels, the properties of the Ca 2+ sensors that trigger release, the effects of intrinsic Ca 2+ buffers and the effect of duration of exposure to [Ca 2+ ] AZ on release.

| Animal care and use
Experimental protocols were approved by the UCLA Animal Committee and were performed in accordance with the National Research Council's Guide for the Care and Use of Laboratory Animals (2011) frog protocol.

| The preparation
Motoneuron-muscle cell co-cultures were prepared from stage 18-22 Xenopus laevis embryos as described previously (Sun et al., 2004).Within 24-48 h of culturing, neurites have formed varicosity synapses on muscle cells, some of which are large enough (4-10 μm diameter) to patch, allowing electrophysiological characterization of presynaptic ionic currents for correlation with simultaneous patch electrode recording of excitatory postsynaptic current (EPSCs) (Sun et al., 2004;Yazejian et al., 1997).Most recordings were made in cultures 3 days after culturing, when varicosities tend to be less fragile than in younger cultures, and show more robust release.The varicosity synapses develop at approximately the same rate they would in vivo (Kullberg et al., 1977) and exhibit presynaptic and postsynaptic anatomical specializations and release properties characteristic of other vertebrate neuromuscular junctions (Cohen & Weldon, 1980;Evers et al., 1989;Kidokoro et al., 1980;Weldon & Cohen, 1979;Yazejian et al., 1997).

| Electrophysiological recording
Paired perforated whole cell voltage clamp recordings were made on presynaptic and postsynaptic membranes as previously described (Sun et al., 2004;Yazejian et al., 2000).Voltage clamp experiments were done with Axopatch 200B (Axon Instruments, Union City, CA, USA) patch clamp amplifiers at room temperature (22 C-25 C).Patch electrodes were fabricated from borosilicate glass (1.5-mm outer diameter) with a Flaming-Brown horizontal puller (P-87, Sutter Instruments Co., Novato, CA, USA).Electrodes were fire polished and coated with beeswax to reduce pipette capacitance.After filling, electrodes (with our solutions) had a final resistance of 2-5 MΩ.Amphotericin B (Sigma, St. Louis, MO, USA) was freshly dissolved in dimethyl sulfoxide (60 mg ml À1 ) and further diluted with internal solution containing (mM): 52 K 2 SO 4 , 38 KCl, 1 EGTA and 5 HEPES, pH 7.3, to yield a final amphotericin B concentration of 240 μg ml À1 .A series resistance of <15 MΩ was reached within 10 min after the formation of a gigaohm seal (seal resistance, >2 GΩ) and remained stable for up to .5-1h.Series resistance compensation was optimized.All current recordings were corrected for linear leakage resistance and capacitance by using a P/-N procedure.The average varicosity membrane capacitance (C m ) was 4.6 ± .2pF.The bath solution was normal frog Ringer, NFR (116-mM NaCl, 2-mM KCl, 1.8-mM CaCl 2 , 1-mM MgCl 2 , 1-mM NaHCO 3 , pH 7.3), containing in addition 1-mM 3,4-dihydropyridine (DAP) and 300-nM TTX (pH 7.3).Pulse generation, data acquisition and analysis were done with a PC equipped with a Digidata 1200 or 1322A analog-to-digital (A/D) interface in conjunction with Clampex 6.0-9.0 programmes (Axon Instruments).Currents were filtered with a 4-pole Bessel filter at 10 kHz.Unless otherwise specified, the holding potentials were À70 mV (varicosity) and À80 mV (muscle cell).

| Ca 2+ imaging and photolysis of caged Ca 2+
Co-cultured muscle and motor neuron preparations were loaded with 1-μM Fluo-4FF AM and o-nitrophenyl EGTA AM for 30-60 min in high calcium (5 mM) NFR.Fluorescent Ca 2+ images were taken by a Cascade 650 CCD camera (Cascade Photometrics, USA) mounted in a Zeiss Axo 35 inverted microscope under illumination of high power blue LED light source.A series of images was built with sampling rate of 10-25 ms/frame, depending on the imaging area.To uncage Ca 2+ , brief UV-light flashes generated by a flash lamp (Rapp OptoElectric, Germany), guided through an optical fibre located 50-100 μm from the muscle-varicosity complex, were applied during Ca 2+ imaging and electrophysiological recording.Therefore, Ca 2+ imaging data and presynaptic and postsynaptic currents were obtained simultaneously.Time series images were analysed off-line using ImageJ software.

| Data analysis and statistics
The values of peak amplitude of I BK and EPSC were obtained by direct measurement of current traces using pCLAMP software.The calcium concentrations were calculated by an empirical equation established previously (Sun et al., 2004) by fitting the rising phase of ensemble I BK single-channel currents recorded in inside-out patches with a series of [Ca 2+ ].All data are presented as mean ± standard error unless otherwise mentioned.Smooth curves were generated by fitting data points to a Hill function that is included in analytic software, Origin 7.0.Two-sample Student's t test was used for evaluating statistical significance.

| Experimental evidence for close coupling of BK and Ca channels
In situ evidence for close functional coupling of BK and Ca channels comes from single-channel recordings from varicosities made in the cell-attached configuration.In on-cell recordings without TTX in the bath, we occasionally observed large current deflections associated with spontaneous action potentials (Figure 1a).In three of six patches showing these, a single-channel current frequently followed the peak of the large deflections.These BK channel openings can be seen clearly in expanded traces (Figure 1b, A-D).The large current associated with each action potential is subject to a combination of the effects of membrane capacitance, membrane conductance and leak current (Fenwick et al., 1982;McLarnon et al., 1995).Because of the potential for significant phase shifting due to membrane capacitance, it is difficult to determine precisely the point in the action potential when this current deflection peaks, but it probably approximates the time of fastest depolarization of the terminal.The openings of the single BK channel in the preparation shown in Figure 1 appear to have started as early as during the initial phase of I Ca (see also Yazejian et al., 1997, Figure 6).
From the experiment showing the most instances of coupling between spontaneous action potentials and BK channel openings, we used a first-latency analysis method to quantify the mean activation time constant.The cumulative distribution of latencies between the peak of action potential-associated current deflection and initial openings of the single BK channel could be fitted by a single exponential function with a time constant of .38 ms (Figure 1c).The earliest opening of the channel occurred at <.1 ms after the peak of the AP-associated current, and the cumulative curve reached a plateau after $1.0 ms.Although the transmembrane voltage at the time of these BK channel openings was not known, they are likely to have occurred during the early falling phase of the action potentials, when the inward I Ca occurs, so an estimate of +20 to 0 mV is reasonable (although openings occurring at greater delay would have decreasing driving force for K + , making them harder to detect).Based on calibrations of single-channel activation time at +20 mV (Sun et al., 2004) the time constant of .38 ms for the cumulative latency distribution would correspond to a [Ca 2+ ] of >250 μM, a concentration that would put this BK channel well within a nanodomain.This finding is consistent with the conclusion that some BK channels can experience a mean [Ca 2+ ] > 100 μM during opening of Ca channels during an action potential (Yazejian et al., 2000;Sun et al., 2004).
To ensure that the single channel was a BK channel, single-channel currents activated by depolarizing pulses were examined in the same patch.By linearly fitting the I-V curve for this channel, the slope conductance was found to be 87.5 pS (Figure 1d), which is close to the mean value for BK channels in asymmetrical solution (78.3 ± 6.2 pS, n = 35, see Sun et al., 2004).influx or evoked release (normally +130 mV), then stepped for varying lengths of time to different intermediate potentials (IPs) to allow Ca 2+ influx at different rates, dependent upon the Ca 2+ driving force at these IPs (Figure 2a) (Sun et al., 2004;Yazejian et al., 2000).In these experiments, the initial depolarization elicits a slowly rising outward current that is not decreased by Ca 2+ or BK channel blockers (data not shown).However, during the subsequent period at an IP where Ca 2+ can enter the terminal (0 mV in the case of Figure 2b), a Ca 2+ -dependent outward current (I BK ) develops that is superimposed on the Ca 2+ -independent current at that potential.The I BK builds up at different rates at different IPs, depending on the [Ca 2+ ] AZ that results from each rate of Ca 2+ influx and the IP (see Figure 3a).At IPs of À20, À40 and À70 mV, because of increasingly rapid Ca 2+ channel closure, the I Ca is a transient tail current.At more positive IPs, the Ca channels remain open throughout the IP (+20 and +40 mV), or close with a time course of several ms (0 mV).The EPSCs recorded simultaneously (Figure 2e) quantify the release in response to the Ca 2+ that has entered during the different durations at this IP (and also to the tail current at the conclusion of the test pulse from most IPs).Ca 2+ entry is then terminated by a re-depolarization to +130 mV (the 'test pulse'), which opens additional BK channels that had not opened at the IP and imposes a larger driving force for current through already open BK channels.The I BK component of the outward current during these waveforms (Figure 2f) can be obtained by subtracting responses to the same set of waveforms after blocking BK channels with 2-μM paxilline (Sanchez & McManus, 1996) (2B minus 2C).Further block of Ca channels with Cd 2+ (Figure 2 D) and subsequent subtraction yields the I Ca (Figure 2g).

| Time course of [Ca
Figure 3 summarizes the I BK data from 28 experiments in which I BK and EPSC data were obtained at the full range of durations and IPs.When the IP was À70 or À40 mV, the I BK reached peak magnitudes when the +130-mV test pulse came $200-300 μs after the step to the IP, only slightly after the presumed peak of the I Ca tail current.As the I Ca decayed beyond 200-300 μs, the I BK evocable by the test pulse also declined.Thus, the I BK indicates the magnitude of the [Ca 2+ ] near BK channels at the time the test pulse was imposed.Significantly, at progressively more positive IPs (0, +20 and +40 mV), where Ca channels remain open, but Ca 2+ influx rates are progressively smaller, increasing the duration of the IP led to a gradual increase in the I BK response to the +130-mV test pulse until it reached peak values almost twice those elicited by the Ca 2+ that was present near the AZs during tail currents at À70 or À40 mV.The peak I BK magnitude evocable by the test pulse typically occurred after approximately 1 ms at an IP of 0 mV, 1.8 ms at an IP of +20 mV and 2.5 ms or longer at an IP of +40 mV.At an IP of +40 mV the [Ca 2+ ] builds up too irregularly for the I BK rise time to be fitted by a single exponential function.At an IP of +60 mV the rate of Ca 2+ influx was so slow that even after influx for 3 ms, the [Ca 2+ ] AZ was only sufficient for the test pulse to open about half the number of BK channels opened at 0 to +40 mV.The EPSC (Figure 3b) parallels the I BK except that once release was evoked, it did not decrease in magnitude as the IP duration was increased whereas the I BK fell as Ca channels closed (at 0, À20, À40 and À70 mV).
That the peak I BK that could be elicited by a +130-mV test pulse was essentially the same after different durations of Ca 2+ entry at IPs of 0, +20 and even +40 mV indicates that the number of open BK channels was the same after these different lengths of time at the different IPs.This peak I BK amplitude apparently represents a saturation value where all nearby openable BK channels had been opened, leaving no additional channels that could be opened by continued influx of Ca 2+ .Direct evidence that this is the case is shown by the results of an experiment in which the [Ca 2+ ] ext was varied from the normal 1.8 mM to .5 or 3 mM.Both the peak I BK magnitudes and the peak EPSCs were essentially the same at the 1.8-and 3-mM concentrations (Figure 4).The displacement in the IP voltage of peak I BK and EPSC with change in [Ca 2+ ] ext is a reflection of the change in equilibrium potential for Ca 2+ .
Figure 3c shows the mean [Ca 2+ ] AZ values derived from measurements of the activation time constants of the I BK in response to test pulses during Ca 2+ entry at different IPs, based upon calibrations of the activation time constant of single BK channels in inside-out patches exposed to known [Ca 2+ ] (Sun et al., 2004).The mean maximal [Ca 2+ ] AZ achieved during influx at À70 to À20 mV was 20-30 μM.At more positive IPs (+20 and +40 mV), although the driving force for Ca 2+ entry is much reduced, most or all Ca channels remain open, and Ca 2+ influx remains essentially constant.At these potentials, the [Ca 2+ ] AZ reached a mean maximum of 45-60 μM, depending on the IP, nearly twice the peak during a tail current.There was a great deal of variability in this value between preparations, however, with a range of about 22-134 μM in peak values.] generated during different IPs, calibrated with single BK channels in insideout membrane patches exposed to known Ca 2+ concentrations (Sun et al., 2004).Data averaged from 13 to 28 varicosities yielding full sets of data.channels are responding to Ca 2+ that has entered through multiple Ca channels.If they were responding only to Ca 2+ entry through the single closest Ca 2+ channel, the I BK amplitude would decrease as the Ca channels dropped out, but the I BK rise time (reflecting the [Ca 2+ ]-AZ ) would stay relatively constant.This observation does not preclude the possibility that some fractions of the BK channels are opened by one or two open Ca channels.
F I G U R E 4 Effect of extracellular Ca 2+ on BK currents and EPSCs.(a) Presynaptic currents evoked in response to a voltage waveform similar to that described for Figure 2 with an IP of +30 mV in three different external Ca 2+ concentrations: .5 mM (black), 1.8 mM Ca 2+ (red) and 3.0 mM Ca 2+ (green).In brief, the presynaptic voltage was held at À70 mV, stepped to +130 mV for 20 ms followed by a step to the IP of +30 mV for 5 ms, before a test step was made to +130 mV for an additional 10 ms.Neurotransmitter release was quantified by measuring both the peak EPSC magnitude and the integral of the EPSC resulting from a given duration of Ca 2+ entry at each IP.Because the durations of Ca 2+ entry were short and release was quasi-synchronous, measurements of peak EPSC amplitude provide a good measure of relative rates of release at different potentials.Figure 3b shows the mean EPSC peak magnitudes resulting from different durations of Ca 2+ entry at different IPs, based on the same set of experiments that generated the mean I BK values shown in Figure 3a and the mean [Ca 2+ ] AZ values of Figure 3c.Like the I BK , the EPSC appeared most quickly and increased in amplitude most rapidly at negative IPs where the driving force for Ca 2+ was greatest; and like the I BK , the EPSC response to tail currents at À70 and À40 mV reached only 40%-50% of the magnitude achieved by longer periods of Ca 2+ influx at more positive IPs.EPSCs also reached a maximum at about the same [Ca 2+ ] AZ values as the I BK , that is, around 50-55 μM.This was achieved after $1 ms of Ca 2+ entry at an IP of 0 mV, after about 2 ms at an IP of +20 mV.At an IP of +40 mV, with a much reduced Ca 2+ influx rate, release levels climbed slowly to achieve maximal levels in 4-5 ms.As in the case of the I BK , the saturation level of release is probably the point at which all immediately releasable vesicles have been released because increasing the [Ca 2+ ] ext level to 3 mM did not increase release (Figure 4).
Both the I BK magnitude in response to the +130 mV test depolarization and the EPSC are proportional to [Ca 2+ ] AZ , independent of the IP and rate of Ca 2+ influx, that is, how rapidly that [Ca 2+ ] AZ is achieved.However, their quantitative relationship to [Ca 2+ ] AZ differs.To quantify the relationship more accurately between [Ca 2+ ]-AZ and the I BK and EPSC, simultaneous presynaptic and postsynaptic recordings were made from 10 varicositymyoball pairs as [Ca 2+ ] AZ increased at an IP of +20 mV (Figure 6).The I BK appears at a [Ca 2+ ] AZ of 2-3 μM and builds up rapidly to $60 μM, beyond which the response begins to saturate.The EPSC, in contrast, only begins to be significant at [Ca 2+ ] AZ of about 20 μM and increases sigmoidally to reach a peak at approximately the same [Ca 2+ ] AZ as the I BK .The concentration-response relationship showed K ½ values of 26.3 and 36.9 for the I BK and EPSC, respectively.The Hill coefficients for the I BK and EPSC as a function of [Ca 2+ ] were 2.5 and 3.9.
BK channels, like release sensors, are coupled to both N-and L-type Ca channels.In contrast to mature amphibian motor nerve terminal AZs, which are thought to contain only N-type Ca channels, the presynaptic AZs at Xenopus varicosities contain both N-type and L-type Ca channels, as judged by the effect of dihydropyridines (nifedipine and nimodipine) and ω-CgTX in blocking different components of the I Ca (Sand et al., 2001;Thaler et al., 2001).Nifedipine-resistant (N-type) channels appear to be prevalent, but this is difficult to determine rigorously because of Ca 2+ -dependent inactivation of nifedipine-sensitive (L-type) channels.On the average, release is coupled to both types with approximately equal effectiveness, that is, in proportion to its fraction of the I Ca .However, the nifedipine-sensitive component exhibits faster kinetics, with an activation time constant of .46 ± .08 ms, compared with a time constant of 1.42 ± .12 for the nifedipine-insensitive component (Sand et al., 2001).Because of these differences in activation kinetics, a disproportionate fraction of the release in response to an action potential waveform in the varicosity synapses is due to Ca 2+ entry through L-type channels.
Figure 7a shows a representative example, employing the usual waveform, in which the I BK developing at an IP of +20 mV was treated sequentially with 10-μM NIF, to block the L-type I Ca component, and then 1-μM ω-CgTX was used to block N-type Ca channels.As Figure 7b shows, in this preparation, the I BK components attributable to Ca 2+ entering through the L-type channels, obtained by subtraction of the I BK after nifedipine block from the total I BK , was approximately the same magnitude as the I BK component blocked by subsequent application of ω-CgTX.The apparently faster kinetics of the nifedipine-blocked component was not due to the ] of half maximal activation (K1/2) for I BK and EPSC were 26.3 ± 2.4.1 and 35.9 ± 2.7 μM, respectively, and the Hill coefficients were 2.5 ± .5 and 3.9 ± .8,respectively.differences in the kinetics of the Ca channels because both were opened fully by the +130 mV prepulse.Instead, this suggests functional spatial overlap of L-and N-type Ca channels near a large fraction of the BK channels, leading them to see a higher [Ca 2+ ] AZ when both Land N-type channels are open compared with when either type is blocked.The decline in the L-typedependent I BK might be explained by some degree of Ca 2+ -dependent inactivation of L-type channels after some Ca 2+ had entered the varicosity.When varicosities were exposed to 10-μM NIF or 1-μM ω-CgTX, I BK was blocked by 59.3% ± 13.6% (n = 7) or 58.9% ± 15.2% (n = 8), and at the same time, [Ca 2+ ] was reduced from 33.1 ± 13.3 to 13.5 ± 7.2 μM and from 44.8 ± 19.3 to 12.3 ± 4.9 μM, expressed as mean ± standard deviations, respectively (Figure 7c,d).This indicates that the I BK is substantially dependent on summed Ca 2+ entering through both types of channels, which overlap in their distribution.

| Response to photorelease of Ca 2+
To further test the relationship between Ca 2+ dynamics and activation of I BK and release, we adopted a Ca 2+- channel-independent method of elevating [Ca 2+ ] AZ : by photorelease of caged Ca 2+ .The varicosity-muscle cell preparation was loaded with the ÀAM form of both onitrophenyl EGTA and the calcium indicator Fluo-4FF so Ca 2+ fluorescence intensity, I BK and transmitter release could be monitored simultaneously.EPSCs on postsynaptic myoballs were detected immediately following four different UV-flashes at an interval of $5 min.and I BK values in varicosities were obtained at different times following each flash (Figure 8).[Ca 2+ ] values were calculated by fitting the rising phase of the I BK to determine the time constant of activation and plotted against time after the flash.Although [Ca 2+ ] immediately after the flash could not be measured due to contamination by the UV light flash, it declined from 18.2 μM at 10 ms to 4.2 μM at 100 ms after the flash, and remained almost constant for 250 ms.A [Ca 2+ ] of 18.2 μM is consistent with [Ca 2+ ] AZ values attained 1.5 ms after cessation of loading varicosities by Ca 2+ influx through synaptic Ca channels for 2 ms at +20 mV (see Figure 10).The slow decay in bulk [Ca 2+ ] is consistent with Ca 2+ fluorescence imaging data (DiGregorio et al., 1999).

| Effects of extrinsic Ca 2+ buffers on I BK and release
The measurements outlined above were made with perforated patch presynaptic electrodes, so responses were affected only by intrinsic Ca 2+ buffers.Differential blocking effects of the two extrinsic chelators, BAPTA and EGTA, are widely used to provide insight into the distance Ca 2+ must travel to reach its targets (Adler et al., 1991;Borst & Sakmann, 1996;Naraghi & Neher, 1997;Oheim et al., 2006;Wang & Augustine, 2015;Stanley, 2016; but see Nakamura, 2019).Conventional whole cell patch clamp was not feasible in these experiments because of the rapid wash-out of release in this configuration.Hence, we exposed other preparations to 10-20 μM BAPTA-AM or 10-40 μM EGTA-AM, which have comparable affinities for Ca 2+ (K ½ $192 nM for BAPTA, $170 nM for EGTA) but very different binding rates (k on = 4 Â 10 8 M À1 s À1 for BAPTA, k on = 2.5 Â 10 6 M À1 s À1 for EGTA; Naraghi & Neher, 1997).
EGTA-AM had essentially no effect on release or on the I BK generated during waveforms like those described in Figure 2a in which the IP was À70 to À20 mV and the Ca 2+ driving force was large (data not shown).During [Ca 2+ ] build-up at an IP of +20 mV, however, high concentrations of EGTA-AM (e.g., Figure 9a) decreased both the I BK and release by 20%-50%, indicating that that fraction of BK channels and release sensors were sufficiently far from open Ca channels for EGTA to buffer [Ca 2+ ] AZ below threshold.The distance at which EGTA becomes an effective buffer is model dependent, with estimates ranging from 100 nm (Augustine et al., 2003), down to 20 or 30 nm (Nakamura et al., 2018) or even less (Nakamura, 2019).Nevertheless, most of the I BK and the EPSC were resistant to EGTA-AM block.BAPTA-AM (10 μM), a much faster Ca 2+ buffer, blocked both the I BK and release almost totally, although usually 10%-20% of the I BK persisted (e.g., Figure 9b).The blocking effect of both buffers could be partially reversed by increasing the [Ca 2+ ] ext to 5 mM (not shown).

| Rate of decline of [Ca 2+ ] AZ after varying degrees of Ca 2+ loading
The [Ca 2+ ] levels described above are restricted to the region of the AZ and are much higher than the bulk [Ca 2+ ] resulting from short periods of Ca 2+ entry (DiGregorio et al., 1999).To determine how rapidly [Ca 2+ ] AZ declines and free Ca 2+ disperses from the region of the AZ, we employed a waveform in which Ca channels were first opened by a +100-mV prepulse, followed by a step back to an IP of +20 mV to allow Ca 2+ entry for various lengths of time.After different periods of Ca 2+ entry, the potential was stepped abruptly from the IP back to +100 mV to determine the maximal I BK after each period of Ca 2+ entry, or down to À70 mV to close Ca channels (which also generates a brief Ca 2+ tail current).The potential was then held at À70 mV for various lengths of time before another test pulse to +100 mV was used to measure the [Ca 2+ ] AZ based on the rise time of the I BK obtained by subtraction of the response to the +100-mV prepulse from the test +100-mV depolarization (Sun et al., 2004).Figure 10b-A  results of 6 experiments with IP durations of .4-.5, 1, 2, 4 and 8-10 ms at +20 mV.
Data points in Figure 10b-A are means with standard error from six experiments.The longer the duration of Ca 2+ entry at +20 mV, the higher the [Ca 2+ ] AZ measured with a test pulse at the end of the IP.For relatively short periods of Ca 2+ entry (.4-2 ms), with concentrations approaching 30-100 μM at the end of the IP, the [Ca 2+ ] AZ collapsed to <1 μM with virtually identical time constants: $.59 ± .05ms at .4-.5 ms IP duration, .66± .04 ms at 1 ms duration and .60 ± .02ms for the 2 ms IP duration.After 4 and 8-10 ms of Ca 2+ entry at +20 mV, the collapse was slower, and good fits required two exponentials.For 4 ms, these were time constants of .26± .01 and 1.6 ± .33 ms; for durations of 8-10 ms, the time constants were .38 ± .1 and 2.69 ± .32 ms.
In addition to the exponential fits described above, to better understand the roles of intrinsic buffers in governing levels of free [Ca 2+ ], we have developed an AZ model, which is described in Appendix A. The curves in Figure 10b-A,B are predictions of this model for concentrations of Ca 2+ and of Ca 2+ bound to buffers, respectively, at a point adjacent to the membrane, 30 nm from the closest Ca channel.The model uses a published model (Bischofberger et al., 2002) for predicting the I Ca input from an array of 25 Ca channels, together with a reaction-diffusion model for predicting Ca 2+ movement within and extrusion from a terminal containing three intrinsic Ca 2+ buffers: Buffer A, a low-affinity, highcapacity fixed buffer (the phospholipid and phosphate groups lining the inside of the plasma membrane) (Bers et al., 1985;Bers & Peskoff, 1991;Post & Langer, 1992); Buffer B, a moderate-affinity, lower-capacity fixed buffer corresponding to Ca-binding sites on internal structures in and around the AZ; and Buffer C, a mobile buffer with the properties of calbindin D 28 (Müller et al., 2005) (see full description of the model in Appendix A).The model yielded predictions for the time course of decay in free [Ca 2+ ] as a function of distance from the Cachannel array after differing amounts of Ca 2+ influx, shown by the curves in Figure 10b-A for 90 nm from the centre of the array (30 nm from the closest Ca channel) for .4,1, 2, 4 and 8 ms at the +20-mV IP.The model also generated the predictions shown in Figure 10b-B, which shows the concentrations of Ca 2+ bound to each of the three buffers 30 nm outside the array as a function of time during and after Ca 2+ influx for the case of 4 ms at the +20-mV IP, along with the free Ca 2+ curve (black), which is a repeat of the 4-ms curve in Figure 10b-A.The model is by necessity oversimplified, but has the virtue of relating the data to physical parameters that characterize the system and allows us to draw useful conclusions about the intrinsic Ca 2+ buffering inside the presynaptic varicosity.
As Figure 10b-B shows, although all three buffers contribute importantly to setting the [Ca 2+ ] AZ , the degree to which the shape of the curve for free [Ca 2+ ] mirrors that of the fixed Buffer A suggests that the phospholipid Ca 2+ -binding sites in the plasma membrane play a The present experiments were aimed at extending our descriptions of presynaptic Ca 2+ domains, as reported by BK channels, and answering questions about the relationship between the domains and neurotransmitter release, for example, what [Ca 2+ ] occurs at the sites of the calcium sensors for release, and how rapidly does it build up and decay?

| Validity of the technique
Our technique allows us to estimate the average [Ca 2+ ] AZ at any given instant, as reported by the BK channels.For this to answer questions about the [Ca 2+ ] experienced by the calcium sensors that trigger synaptic vesicle release requires that the BK channels that respond to Ca 2+ influx be located near those sensors, within the Ca 2+ domains that trigger release.Evidence suggests that this is the case.Based upon the low-affinity Ca 2+ dye characterization of action potential-induced presynaptic calcium domains in this same preparation (DiGregorio et al., 1999), calcium channels are concentrated at sites of muscle cell innervation.Moreover, the 1.6-μm average half-width of the sharply localized Ca 2+ 'hot spots' that these authors described (range .5-3μm) is consistent with the ultrastructural dimension of localized clusters of vesicles and presynaptic and postsynaptic membrane specializations in spontaneously formed varicosity-muscle synapses in the same type of preparations we used F I G U R E 1 0 Effects of Ca 2+ -loading duration on the decay of [Ca 2+ ] AZ .(a) Sample waveforms (a-A) and current traces (a-B) in which the varicosity was first depolarized to +100 mV for 10 ms, then stepped down to +20 mV to allow Ca2+ entry for 4 m, and then either stepped up to +100 mV to determine the maximal I BK or stepped back to À70 mV for various lengths of time before another +100 mV test pulse was imposed to generate I BK .(b-A) Mean [Ca 2+ ] AZ after .4-.5, 1, 2, 4 and 8-10 ms of Ca 2+ entry during +20 mV were plotted against time at À70 mV.Data were averaged over six experiments.The curves in (b-A) were generated by an AZ model described in Appendix A. The parameters of the model were adjusted to optimize the fit to the data points.The model used a published model (Bischofberger et al., 2002) to generate the Ca 2+ current entering via 25 Ca channels at the centre of one face of a 1 Â 1 Â 1 μm cube (Figure A1) containing Ca 2+ and three buffers: (bufa) the charged phospholipid head groups located on the intracellular membranes, and (bufb) a fixed buffer and (bufc) a mobile buffer distributed uniformly over the volume.(b-B) shows the concentration profiles for free Ca 2+ and Ca 2+ bound to the three buffers, for the case of 4 ms at the IP of +20 mV.The left axis indicates concentration for free Ca 2+ and for Ca 2+ bound to buffers b and c.For buffer a only, the right axis indicates the surface density (Ca 2+ ions/[15 nm] 2 ) of Ca 2+ bound to the phospholipids; the left axis indicates the concentration of buffer a after conversion from ions/surface area to μM, obtained by assuming the surfacebound Ca 2+ is spread over a 7.5-nm thick layer adjacent to the membrane.The small blips near the beginning of each curve are the result of a small amount of Ca 2+ entry during the onset of the 10-ms initial depolarization from À70 to +100 mV.At t = À4 ms, the voltage was stepped to +20 mV, imposing a driving force for Ca 2+ entry, and at t = 0 ms, the voltage was stepped to À70 mV, generating a brief tail current that caused a transient increase in [Ca 2+ ], followed by the decay of [Ca 2+ ]. (Buchanan et al., 1989).As noted in Section 1, BK channels tend to cluster with Ca channels, even forming tight macromolecular complexes in some cases.A study of single BK channels in detached membrane patches from neurons in cultures of the same preparation we used in the present study showed no BK channels in the motoneuron cell somas, low density in isolated varicosities (not in contact with a muscle cell), but five or more BK channels/patch in membrane from the synaptic surface of varicosities (Sun et al., 2004).Thus, BK channels are present throughout the varicosity membrane, but are concentrated at synapses, probably in close association with multiple Ca channels as appears to be the case at more mature synapses (Harlow et al., 2001;Roberts et al., 1990).Extrasynaptic BK channels, activated by Ca 2+ from more distant or non-synaptic Ca channels, would not be expected to report the high [Ca 2+ ] values that BK channels do in our preparations, or be closely correlated with neurotransmitter release.Nor would they report the rapid collapse of [Ca 2+ ] domains that we see, from as much as 100 μM to less than 1 μM in under 1 ms (Figure 10).We conclude, therefore, that the BK channels are largely reporting [Ca 2+ ] AZ .
The calculation of [Ca 2+ ] AZ values by measurement of the time constant of activation of the I BK is subject to a few caveats: (1) they represent averages of [Ca 2+ ] seen by different BK channels that are located at different distances from one or more open Ca channels.Although we have no definitive information about the calcium channel distribution or the location of BK channels or the Ca 2+ sensors that trigger release within the AZ, the fact that BK channels and release sensors show similar resistance to exogenous Ca 2+ buffers (Figure 9) suggests that they are similarly distributed relative to Ca channels; (2) the [Ca 2+ ] AZ values are based on calibrations using single BK channels in patches exposed to known [Ca 2+ ] (Sun et al., 2004); and (3) they assume that the BK channels are responding to instantaneous [Ca 2+ ] AZ .In practice, the latter two uncertainties probably introduce minimal errors, and the first-the distribution of BK channels and release sensors with respect to Ca channels-is an unknown that our data are intended to help resolve.
In addition, however, it is important to emphasize that the pattern of behaviour of [Ca 2+ ] AZ with Ca 2+ driving force and duration of Ca 2+ entry is more important than absolute values of [Ca 2+ ] AZ .For example, the absolute values obtained in the experiments plotted in Figure 3 were obtained by successive measurement with different IPs and durations of Ca 2+ entry, followed by block of the I BK with paxilline, and subtraction to obtain the isolated I BK on the basis of which [Ca 2+ ] AZ was determined.Although the 28 experiments used to obtain that average data were selected for stability during the experiment, there was usually some significant run-down of the preparation over the 15-20 min needed to make all the measurements, that is, repeats of measurement under the same conditions close to the beginning and end of the experiments often showed some decline in the I BK amplitude and rise time.The peak value of 50-60 μM for the [Ca 2+ ] AZ is thus probably an underestimate.This is also implied by the higher values obtained for peak [Ca 2+ ] AZ in the experiments of Figure 10, where measurements were made over a much shorter period of time for each of the six junctions studied, and the I BK was obtained by subtraction of the response to the initial +100 mV depolarization, without Ca 2+ entry, from the response to the same test pulse after Ca 2+ entry.Probably for the same reasons, early experiments using action potential waveforms to drive Ca 2+ entry yielded [Ca 2+ ] AZ values of up to 175 μM (Yazejian et al., 2000).In all experiments, however, the relative value of [Ca 2+ ] AZ as a function of Ca 2+ driving force and duration of Ca 2+ entry, and the relative levels of release (which depletes with repeated stimulation), showed the same behaviour.
On balance, the I BK offers a means of tracking dynamic changes in [Ca 2+ ] AZ in the immediate submembrane region of the terminal where the Ca 2+ sensors for release are located.These dynamic changes in [Ca 2+ ] AZ can then be correlated with neurotransmitter release on a nanoscale in a way not afforded by any other known technique.Moreover, it does this in intact terminals, with no introduced Ca 2+ buffers and minimal disruption of normal cytoplasmic contents and buffering.

| The I BK is triggered predominantly by microdomain [Ca 2+ ] in this preparation
Most BK channel openings depend on the summed Ca 2+ influx through multiple open Ca channels (Ca 2+ microdomains) rather than on Ca 2+ influx through a single nearby Ca 2+ channel (nanodomains).Blocking Ca channels result in a progressively slower rise time for the I BK (Figure 5).If the BK channels mainly reflected the [Ca 2+ ] in nanodomains near open channels, the reported [Ca 2+ ] AZ would not have decreased smoothly to sub-μM level.Indeed, the fact that the BK channels report a [Ca 2+ ] AZ that continues to rise for 2-3 ms at positive IPs means that they are not reporting nanodomains, but are instead responding mostly to microdomains.Finally, the finding that the rise time of the I BK decreases sharply when either L-or N-type Ca channels are blocked (Figure 7) is evidence that most BK channels in these immature junctions are summing Ca 2+ influx through both types of Ca channels, that is, microdomain [Ca 2+ ].BK channels within nanodomains formed by single open Ca channels of either type would be unaffected as other Ca channels are blocked.The I BK would decrease in amplitude, but not in activation time.That is not what we observe.This does not preclude the possibility that some BK channels are activated by Ca 2+ nanodomains, but if so, they represent a small fraction of the population.
These observations are not inconsistent with the evidence that some BK channels are close enough to individual Ca channels to be activated by nanodomain [Ca 2+ ], as indicated by Figure 1 and the fraction of the I BK resistant even to BAPTA block (see Figure 8).However, that EGTA-AM can reduce [Ca 2+ ] below threshold for 20%-50% of BK channels and release sensors responding to build-up of [Ca 2+ ] AZ at +20-mV IP is evidence that a substantial fraction of both is located far enough from the nearest open Ca channels to be dependent on [Ca 2+ ] summed from multiple Ca channels (microdomains).
Release is also dependent on summed Ca 2+ influx through multiple calcium channels.At IPs of +20 mV and more positive values, where all Ca channels have been opened by the preceding +130-mV depolarization and remain open, release continues to grow with IP duration, just as the I BK does.The nanodomain [Ca 2+ ] would not change significantly under these conditions, but the microdomain concentration measured by BK channels clearly does.The peak [Ca 2+ ] AZ , which continued to rise slightly even after the I BK and EPSC had reached their maxima (Figure 3c), represents the balance between rate and duration of Ca 2+ influx, the rate of diffusion into the bulk volume of the varicosity, and the gradual reduction of local Ca 2+ buffering due to saturation of intrinsic buffers (Nakamura et al., 2018).The increase in EPSC magnitude with increasing IP duration at positive potentials occurs without a significant change in its waveform (Figure 2e).Some fraction of release might be driven by nanodomains, but a major fraction tracks the gradual increase in [Ca 2+ ] AZ .This is particularly clear when Ca 2+ enters relatively slowly, at +40or +60-mV IP (Figures 3 and 6).

| Relationship between I BK , [Ca 2+ ] AZ , and neurotransmitter release (EPSC)
The I BK and release show similar dependence on the IP duration, which determines what fraction of the calcium channels opened by the preliminary +130-mV depolarization remain open and for how long, as well as on the driving force for Ca 2+ influx through those channels.At negative IPs, calcium channels close during the IP (most rapidly at À70 mV, less so at À40 and À20 mV), resulting in transient calcium tail currents and [Ca 2+ ] AZ values that peak well below values achieved when calcium channels stay open but with much lower Ca 2+ driving force.The EPSC and the I BK in response to a test pulse show correspondingly submaximal peak values for negative IPs (Figure 3).
The I BK and release grow at rates dependent on the Ca 2+ driving force and duration of Ca 2+ entry.The larger the Ca 2+ driving force for maintained influx, the faster the I BK and release reach their peak levels.The [Ca 2+ ] AZ values calculated from the I BK rise time increase rapidly at an IP of 0 mV to reach a mean maximum of about 45 μM at 1-ms duration, and then level off and begin to decline (Figure 3c), reflecting the fact that some Ca channels close at 0 mV.More prolonged influx at an IP of +20 mV, where most or all Ca channels remain open, produces a [Ca 2+ ] AZ that levels off at 55-60 μM, despite continued Ca 2+ influx.The observation that neither the I BK nor release increased in the experiment in which [Ca 2+ ] ext was raised from 1.8 to 3 mM (Figure 4) supports the conclusion that in many if not all experiments the [Ca 2+ ] AZ level reached with 1.8 mM [Ca 2+ ] ext is sufficient to activate all of the BK channels and vesicle release sensors present in the AZs.Additional Ca 2+ influx, for example by prolonging the IP at +20 mV, can increase [Ca 2+ ] AZ but has little or no effect on I BK amplitude and increases release only slightly by prolonging the falling phase of the EPSC.

| Differences in [Ca 2+ ] AZ dependence of I BK and release
Although the I BK and EPSC behaved very similarly in our experiments, there was an important difference in their dependence on [Ca 2+ ] AZ .The I BK is more sensitive to low levels of [Ca 2+ ] AZ , and above $5 μM increases almost linearly with increasing [Ca 2+ ] AZ .In contrast, there was little release until the [Ca 2+ ] AZ reached $15 μM, after which it rose rapidly to peak at approximately the same [Ca 2+ ] AZ as the I BK (Figure 6).The rapid increase in EPSC above this threshold presumably is a reflection of the well-established cooperativity of Ca 2+ in triggering release (Dodge & Rahamimoff, 1967).It is noteworthy that both I BK and release are determined by the highest [Ca 2+ ] AZ achieved, largely independent of the Ca 2+ driving force or duration of Ca 2+ influx generating that [Ca 2+ ] AZ (Figure 6).As can be seen in Figures 3 and 6, at IPs of À70 and À40 mV, where the rate of Ca 2+ influx is the fastest, the amplitude of the EPSC rises more quickly than at IPs with slower Ca 2+ influx.
In addition to showing little response to levels of [Ca 2+ ] AZ lower than 15-20 μM, the cooperativity of Ca 2+ action on release results in a strong dependence on the time of exposure during early stages of Ca 2+ influx.For example, during the Ca 2+ tail current generated by stepping from +130 to À70 mV, a maximal [Ca 2+ ] AZ of $22 μM, as reported by BK channels (Figure 3a,c), had built up after 200 μs.Truncating Ca 2+ entry by stepping back to +130 mV at that point evoked a little less than 20% of the maximal EPSC while, on average, another 100 μs at approximately the same [Ca 2+ ] AZ elicited more than twice as large a mean EPSC (Figure 3b,c).Similarly, the maximum [Ca 2+ ] AZ was reached after about .5 ms during a tail current at an IP of À20 mV.If Ca 2+ influx was terminated at that time, release was about 45% maximal.When Ca 2+ influx was allowed to continue for another .5 ms (at a decreasing rate), the [Ca 2+ ] AZ actually fell significantly, but release increased to about 70% of maximal release.This time dependence can help explain the strong dependence of release on action potential duration or rate of repolarization (Sabatini & Regehr, 1997).

| Differences between developing varicosity synapses and mature frog neuromuscular junctions
Several properties of the varicosity synapses differ from the AZs in mature neuromuscular junctions (nmjs).Although only N-type calcium channels trigger release at mature frog neuromuscular synapses, both L-and N-type Ca channels contribute to generation of an I BK and release in the varicosity synapses (Figure 7, see also Sand et al., 2001, Thaler et al., 2001).This is also reported to be the case for release in developing frog neuromuscular junctions (Gray et al., 1992;Sugiura & Ko, 1997).
Also, there is compelling evidence that, in mature frog nmjs, Ca 2+ channel opening is a low-probability event, and release of a vesicle is triggered-still with a low probability-by opening of one or two adjacent Ca channels, possibly coupled to that docked vesicle, that is, a Ca 2+ nanodomain (Luo et al., 2011(Luo et al., , 2015;;Markus et al., 2013;Shahrezaei et al., 2006).Our conclusion that release in the varicosity synapses depends largely on Ca 2+ microdomains suggests that during development vesicles become more tightly associated with Ca channels.This has been shown to occur during development in another synapse, the calyx of Held (Fedchyshyn & Wang, 2005;Wang et al., 2008;Wang & Augustine, 2015).
Our results also suggest that the probability of Ca 2+ channel opening on terminal depolarization decreases with the development in frog nmjs.I Ca values as large as 200-400 pA at an IP of +20 mV can be measured in the varicosities.Measurements of I Ca during single-action potentials also yielded peak values of 100-360 pA (Yazejian et al., 2000).The current through a single Ca 2+ channel averages about .2pA at À20 mV (Church & Stanley, 1996;Weber et al., 2010).Given the much smaller driving force at +20 mV, the single Ca 2+ channel current at that IP is probably about half as large as at À20 mV, so an I Ca of 200-400 pA would correspond to the opening of 1000-2000 channels.What fraction of these is at the AZ is unknown, but this seems a surprisingly high value.The I Ca has not been measured in mature frog motor terminals, which are much larger than varicosity synapses and likely incorporate many more Ca channels.However, current evidence (Dittrich et al., 2018;Luo et al., 2011Luo et al., , 2015) ) suggests that each mature AZ contains approximately 20-40 Ca channels, many fewer than the number of intramembranous particles, and the probability of a Ca 2+ channel opening during an action potential is only about .2, that is, on average about six to seven channels open during an action potential at any given AZ.The probability of release of a vesicle/open Ca 2+ channel is about .05,and the probability of release is <1 quantum/AZ (Dittrich et al., 2018;Luo et al., 2015).If seven channels/AZ open to an action potential and there are 500 AZs in a synapse, that would be $3500 channels, comparable with the number that open in the much smaller varicosity synapses.The varicosity synapses, which are roughly the equivalent of one mature AZ in size (Buchanan et al., 1989;DiGregorio et al., 1999), can release as many as 100 quanta of transmitter (up to 5 nA) to an action potential or Ca 2+ tail current.We conclude that in the varicosity synapses, not only does vesicle release depend on the opening of multiple Ca channels, but the probability of Ca 2+ channel opening on depolarization is much higher than in mature frog AZs.This would have adaptive value, because to have successful synaptic transmission with so little AZ structure, the probability of release has to be much higher than in a mature junction with hundreds of AZs.Interestingly, regenerating and developing frog nmjs also show much higher probability of release per AZ than mature terminals (Ding, 1982a(Ding, , 1982b)).As was noted above, the I BK in the varicosity synapses reaches a value of up to $4 nA at +130 mV in some cases, corresponding to the opening of up to 200 BK channels (Sun et al., 2004), so they are only a little more common than releasable vesicles.

| The distribution of BK channels and release sensors with respect to Ca channels
Several observations provide information about the distribution of BK channels and release sensors with respect to Ca channels.The I BK and release parallel each other in their relationships to [Ca 2+ ] AZ , including reaching maximal mean values of 56.5 ± 10.6 μM [Ca 2+ ] AZ after 2.8 ms of Ca 2+ entry at +20-mV IP (Figure 3).This suggests that they are similarly distributed.On the other hand, a small fraction (10%-20%) of the I BK resists block by BAPTA (10-15 min application of 10-20 μM BAPTA-AM), while release is normally totally blocked by similar application of BAPTA-AM.Although we do not know accurately the intra-terminal concentration of BAPTA under these conditions, these results suggest that a small but significant population of BK channels are very close to Ca channels, if not within nanodomains, while few if any release sensors are that close.At the other end of the distribution, both the I BK and release in response to Ca 2+ influx at +20 mV are reduced 20%-50% by application of 20-40 μM EGTA-AM for 10-15 min in different preparations, indicating that a substantial fraction of both BK channels and release sensors are far enough from Ca channels (perhaps 40-50 nm or more) for EGTA to be effective in blocking.On the other hand, BK channels are, on average, activated at lower [Ca 2+ ] AZ than is release (Figure 6).Hence, for the I BK and release both to saturate at the same [Ca 2+ ] AZ , the most distant Ca 2+ sensors for release to be activated must be somewhat closer to the open Ca 2+ -channel array than the most distant BK channels to be activated.In either case, the distribution is apparently different than in mature nmj AZs, where release sensors appear mainly to be in Ca 2+ nanodomains (Luo et al., 2015).A source of variability among our preparations may be the degree of maturation of the synapses.

| Intrinsic buffering and the collapse of the Ca 2+ domain
Models of Ca 2+ diffusion predict a rapid drop off in [Ca 2+ ] away from open Ca channels or arrays of channels into a large volume (Nakamura et al., 2018;Naraghi & Neher, 1997;Roberts, 1994).Fixed Ca 2+ buffering sites tend to saturate quickly with sustained Ca 2+ entry but play an important role in buffering Ca 2+ transients.After an initial transient period, the balance between Ca 2+ influx and mobile Ca 2+ buffers maintains an elevated [Ca 2+ ] AZ dependent on the binding and unbinding kinetics of the buffer(s), their mobilities, the volume of the terminal and the effectiveness of Ca 2+ uptake and extruding mechanisms.For varicosity measurements on the scale of a few millisecond, Ca 2+ uptake into internal compartments and extrusion are minor factors (Naraghi & Neher, 1997).In their optical study of Ca 2+ domains in this same Xenopus varicosity preparation, DiGregorio et al. (1999) found that the fluorescent Ca 2+ hot spots generated by action potentials decayed with an initial time constant of $1.7 ± 1 ms, which was not affected by even high concentrations of EGTA.There were second and sometimes third time constants, however, of $15 and $75 ms that were significantly shortened by EGTA >.5 mM.The second time constant was shortened to 9 ± 7 ms in the presence of 2-mM EGTA.
Our experiments (see Figure 10), involving only intrinsic buffers and measuring the dynamics of the Ca 2+ domain by the method of using BK channels as reporters of [Ca 2+ ] AZ , showed time constants of collapse of approximately .6-.7 ms after durations of Ca 2+ entry at +20 mV of up to 2 ms, from peak [Ca 2+ ] AZ of 30-100 μM.These values are probably equivalent to or exceed the amounts of Ca 2+ entry and [Ca 2+ ] AZ occurring during normal action potentials (Yazejian et al., 2000).The collapse of the domains we see is faster than that measured by low-affinity Ca 2+ dyes (DiGregorio et al. (1999).It is somewhat faster than the average $800-μs decay of light emission by aequorin after action potentials at squid giant synapses (Sugimori et al., 1994).The domain collapse is too rapid to be significantly driven by Ca 2+ pumps or the Na + -Ca 2+ exchanger.In the absence of Ca 2+ buffers, our model shows that the drop in free [Ca 2+ ] AZ would be much faster than .6 ms.Internal buffers must therefore be slowing the collapse.
As Figure 10b-A shows, the reaction-diffusion model fit to the data is only approximate.It does pick up the general overall feature of the data that going from .4 to 8 ms, the family of curves exhibit increasing value and slower decline.The fits for .4-2ms Ca 2+ entry are close, with initial time constants of decay around .6 ms.There are significant deviations from a close fit at early times after the termination of Ca 2+ entry for 4 and 8-10 ms, that is, at high levels of [Ca 2+ ].This is not surprising.The model is a greatly simplified version of reality, which does not take into account (mostly unknown) details of actual morphology.There are doubtless varieties of fixed localized Ca 2+ -binding sites inside the terminal, which we have collapsed into one (Buffer B), distributed uniformly over the interior volume, and there may be multiple mobile Ca 2+ buffers, none of which may have the specific properties of calbindin-D 28 .Nevertheless, the approximations we have adopted allow us to recognize the relative contributions of fixed and mobile buffers and draw the conclusion that the principal determinant of the rate of fall of free [Ca 2+ ] AZ is the unbinding kinetics of the low-affinity, high-capacity Ca 2+ -binding sites on the inner surface of the plasma membrane, which both slow the decay of [Ca 2+ ] AZ and govern its rate of decay.The model suggests that Buffers B and C play important roles in later stages of decay.
Xenopus embryonic nerve-muscle varicosity synapses permit a quantitative assessment of the functional relationship between the [Ca 2+ ] AZ (determined by the rate of BK channel activation) and the amount and timing of neurotransmitter release.This correlation is done using intrinsic molecules as reporters of [Ca 2+ ] AZ , without the introduction of extrinsic buffers or dyes.Making comparable measurements is not possible by other known methods and has not been done in other preparations.The results, in terms of the [Ca 2+ ] needed for release and for activation of BK channels, are useful in that they provide experimental measurements that are consistent with mathematical modelling.Our experiments show that both BK channels and release sensors are responding predominantly to microdomains of [Ca 2+ ], as opposed to nanodomains.This is probably an immature property, with further development leading to the mostly nanodomain-triggered release characteristic of mature amphibian neuromuscular junctions.Both the release and the rate of activation of the I BK are determined by the highest [Ca 2+ ] AZ achieved, largely independent of the rate and duration of Ca 2+ influx.Both I BK and release increase gradually in magnitude with continued Ca 2+ entry at constant driving force to reach levels nearly twice those that can be elicited by a short duration I Ca with high driving force, as would occur during an action potential.[Ca 2+ ] AZ domains that build up during short periods of Ca 2+ entry collapse with a time constant of less than 1 ms, dependent primarily on the unbinding kinetics of the phospholipid binding sites in the inner plasma membrane.
phospholipid binding sites are known to exist in all cell membranes.Their effect has been calculated on the exterior surface of the membrane (Bers & Peskoff, 1991).
Here we consider the effect of the intracellular membrane phospholipids on intracellular calcium buffering.
Centred on the z = 0 face of the cube is a 5 Â 5 square array of 25 Ca channels with 30-nm spacing between channels.On this face and the other three membrane faces, there is a uniform distribution of Ca 2+ pump and exchanger sites and a small amount of inward leakage.On the z = 0 face, it is assumed that there is no flow of Ca 2+ ions or mobile buffer across the boundary except for the Ca 2+ influx through the Ca channels and the efflux via the Ca 2+ pumps and exchangers, and some leakage that balances the pumps and exchangers at [Ca 2+ ] ≤ 100 nM, and on the other three membrane surfaces (y = ±.5 μm and z = +1 μm), it is assumed that there is no flow of Ca 2+ ions or mobile buffer across the boundaries, again, except for the efflux via the Ca pumps and exchangers and leakage.On the faces at x = ±.5 μm, it is assumed that there is an equal, offsetting amount of flow from the opposite sides of virtual boundary faces from the two adjacent cubes.This is one of several idealizations of the problem that makes the computation more tractable.In a further idealization, it is assumed that every channel has the identical Ca 2+ flux.Then, by symmetry, the [Ca 2+ ] is identical in each quarter of the cube, and there is no net Ca 2+ flux across the two virtual faces (parallel striped surfaces in Figure A1b) separating the front right quarter of the cube from the other three quarters of the cube.Therefore, the normal derivative of [Ca 2+ ] vanishes on these two virtual faces.It also vanishes on the open face at x = +.5 μm, and on the three membrane surfaces of the quarter cube.Thus, we have boundary conditions on all six faces of the quarter cube, and we can do the computation in just one quarter of the cube.This reduces the computations by 75%.
The system of four coupled partial differential equations for determining the free calcium concentration and the concentrations of calcium bound to each of the three buffers is is the concentration of free Ca 2+ ; and B i,1 and B i,2 are the free and bound concentrations, respectively, of the buffer i, i ¼ a, b,or c ð Þ , at position x, y and z and time t; B i,tot is the total concentration of the buffer i; and k þ i and k À i are the forward and backward rate constants of the buffer i. D Ca ¼ :22 μm 2 ms À1 (Naraghi & Neher, 1997) and D c are the diffusion coefficients of Ca 2+ and the mobile buffer, respectively, and the latter is assumed to be the same for mobile buffer with or without Ca 2+ bound and its value to be determined by fitting the model to data.
is the Laplacian operator in Cartesian coordinates.Buffers b and c are distributed throughout the interior of the cube; Buffer a is nonzero only on the four membrane surfaces.The numerical solution of Equation ( 1) is set up on a 66 Â 66 Â 66 three-dimensional rectangular grid with grid spacing Δx ¼ Δy ¼ Δz ¼ 15 nm:C, B b,1 ,B b,2 , B c,1 and B c,2 are represented by discrete values at each grid point, which in the interior region are the averages of the concentrations over the 15 Â 15 Â 15 nm cubic volume element with the grid point at its centre, and at the surface are the averages of the concentrations in the 15 Â 15 Â 7.5 nm half-cube extending from the surface half-way to the first interior layer of grid points.B a,1 and B a,2 are zero at all interior grid points.On the membrane surface, they are represented by their values at each surface grid point, which are the averages over the 15 Â 15 nm square centred on the surface grid point.The surface density (sites m À2 ) is converted to an equivalent volumetric concentration (sites m À3 ) by dividing by half the distance between surface grid points and the first inner layer of grid points, ½Δz ¼ ½Δy ¼ 7:5 Â 10 À9 m, and then converting from sites m À3 to moles m À3 (mM) by dividing by Avogadro's number, which then yields the concentration B a,2 (mM) that appears in Equation (1).
Calcium channel current source ∂C=∂t ð Þ I Ca is the Ca 2+ source term.It is the rate of change of [Ca 2+ ] that results from the calcium current influx at each of the 25 individual calcium channels.The Ca 2+ current entering via the channels resulting from our voltage protocol is modelled using a five-state model for the channel open probability with four voltage-dependent transitions between four closed states and one open state, and a modified Goldman-Hodgkin-Katz (GHK) equation for the current through an open channel (Bischofberger et al., 2002).The five-state sequential model we used is unchanged from Bischofberger et al., 2002, α The parameters for the voltage-dependent forward, α n = α n,0 exp(V/V n ), and backward, β n = β n,0 exp(ÀV/ V n ), rate constants, where n = 1, 2, 3, 4, were α 1,0 = 4.04 ms À1 , β 1,0 = 2.88 ms À1 , V 1 = 49.14 mV, α 2,0 = 6.7 ms À1 , β 2,0 = 6.3 ms À1 , V 2 = 42.08 mV, α 3,0 = 4.39 ms À1 , β 3,0 = 8.16 ms À1 , V 3 = 55.31 mV, α 4,0 = 17.33 ms À1 , β 4,0 = 1.84 ms À1 , and V 4 = 26.55mV.We used these published parameters without change, but different parameters were used in the modified GHK equation.The Ca 2+ current through an open channel is (Hille, 1984) where E Ca is the calcium reversal potential and V m is the membrane potential.We set the magnitude of the constant A so that when V m = À20 mV in Equation (3), the current is i Ca = 2 Â 10 À13 amperes (Weber et al., 2010).
In the classic GHK equation, A/2F is the permeability of the channel where F is the Faraday, the total electric charge in a mole of electrons.The GHK equation for a +2 valence ion would have V 0 ¼ RT=2F = 12.6 mV.This was replaced with V 0 = 80.036 mV by Bischofberger et al., 2002 to fit their data; we set V 0 = 30 mV for a fit to our data.Such a modification could be interpreted as the result of a partial screening of the +2e charge on the calcium ion as it passes through the channel.We set the calcium reversal potential to E Ca = 100 mV, corresponding to our experiment.In Bischofberger et al. (2002), the reversal potential was 80 mV; in the GHK equation it would be about 128 mV for a resting intra-terminal calcium concentration C 0 = 100 nM and external calcium concentration of 2 mM.
The current at each open channel in the 25 Ca 2+ channel array is given by Equation (3).The Bischofberger et al., 2002 3) by the open probability O, and by the number of channels.We have made the simplification that instead of each channel opening and closing randomly, each channel conducts the same current as every other channel: i Ca O. Without this simplification and the symmetry of the Ca 2+ channel array, the computation would be much more complex.With this simplification, the total current I Ca from the 25 channels, from Equations ( 2) and ( 3) is where Δx ¼ Δy ¼ 15 nm, and δ x À 2iΔx ð Þδ y À 2jΔy ð Þδ z ð Þ is the three-dimensional Dirac delta function for a point source at each of the 25 surface grid points, spaced 30 nm apart, where a calcium channel is located.
The single-channel current i Ca in Equations ( 3) and (4) at a surface point causes a rate of increase of the free calcium concentration in the surface volume element corresponding to that point.Dividing i Ca by 2F to convert from amperes (coulombs s À1 ) to moles s À1 and dividing by the volume of the surface element ΔxÁΔyÁ½Δz, the contribution to the rate of increase of [Ca 2+ ] in the z = 0 surface element, from a single channel located at each of the channel locations is where O t ð Þ is the open probability in the five-state model in Equation (2).∂C=∂t ð Þ I Ca in Equation ( 1) is then the sum of Equation 5 evaluated at the 25 channel locations defined by the arguments of the delta functions in Equation (4), that is, at x ¼ 2iΔx, y ¼ 2jΔy, z ¼ 0, for i and j ¼ À2, À 1, 0, 1 and 2. In the numerical computation, at each time step, C is incremented by the amount given by Equation (5), at the 25 channel grid points.
In the model of the calcium current source, some of the parameters of the model have been adjusted to obtain a fit to the Figure 10b-A data; others are the (Bischofberger et al. 2002) values that have been used without change.This is what we do in the rest of this Appendix, using published values where possible and adjusting values when necessary to improve the fit.We have found a set of parameters that yields a reasonable fit to the data in Figure 10b-A, but adding additional buffers might yield an equally good or better fit.

Calcium extrusion
The À ∂C=∂t ð Þ extrusion term accounts for the net efflux through the membrane from a calcium pump, a sodium-calcium exchanger, and inward Ca 2+ leakage.This term serves to return the intracellular free [Ca 2+ ] to the resting value of C 0 ¼ 100 nM after the calcium current source has been turned off.We adopt the simple relationship (Bennett et al., 2000), where V p is the maximum extrusion rate and K p þ C 0 is the value of C at the half-maximum extrusion rate.The value of V p used in Equation ( 6) adjusted for the fit to the Figure 10b Widely differing values for V p (mol m À2 ms À1 ) have been used: 3:2 Â 10 À12 (Bennett et al., 2000), 2:0 Â 10 À13 (Sala & Hernandez-Cruz., 1990) and 3:2 Â 10 À14 (Kargacin & Fay, 1991).Our value falls between the Bennett et al. and the Sala and Hernandez-Cruz values.We have set the K p value to K p ¼ C 0 in Equation ( 6).

Fixed phospholipid Buffer a
The density of binding sites on the membrane (Buffer a) is adjusted to .36 sites nm À2 , or 6 Â 10 À11 mol cm À2 to fit the data in Figure 10b-A.This is one-third of the 2 Â 10 À10 mol cm À2 value measured in cardiac cells (Peskoff et al., 1992;Post & Langer, 1992).The surface density (.36 Â 10 18 sites m À2 ) is converted to an equivalent volumetric concentration (sites m À3 ) in the surface volume element by dividing by half the distance between grid points, ½Δz ¼ 7:5 Â 10 À9 m, and then converting from sites m À3 to moles m À3 (mM) by dividing by Avogadro's number, which then yields the concentration B a,tot = 80 mM that appears in Equations (1).
The forward and backward rate constants were set at k þ a = 20 mM À1 ms À1 and k À a = 22 ms À1 , respectively, to get the measured K d = 1.1 mM (Peskoff et al., 1992;Post & Langer, 1992).The rate constants themselves were not measured but are physiologically reasonable values and have a ratio that yields the measured K d .Also, the fit was insensitive to changes in the forward and backward rate constants, though not to changes in K d .

Mobile Buffer c
The parameters used for the mobile buffer are those of .04 mM calbindin-D 28 , with four sites per molecule for an effective concentration of .16mM of binding sites, with forward and backward rate constants k þ c = 27 mM À1 ms À1 and k À c = .019ms À1 , respectively (K d = k À c /k þ c = .7 μM), both as measured by Müller et al., 2005, and diffusion coefficient D c = .01μm 2 ms À1 , which is half Müller's of D c = .02μm 2 ms À1 .

Boundary conditions
By limiting consideration to only Ca 2+ source arrays symmetric about the x-and y-axes, the computation needs to be done only over one quarter of the cube (the volume shown in Figure A1b), on a 33 Â 33 Â 66-point grid rather than the 66 Â 66 Â 66-point grid.The boundary condition on each of the two newly created surfaces of the quarter-cube: the x-z surface at y = 0 and the y-z surface at x = 0, is that the normal derivatives are zero (Neumann boundary condition) by virtue of the symmetry.

Initial conditions
In the computation to model the data in Figure 10c, it is assumed that at the initial time the system is at equilibrium at a membrane potential of À70 mV, with the free Ca 2+ concentration at 100 nM and with the three buffers at equilibrium with the free Ca 2 , all the calcium channels are closed, and there is no current flow.The potential is then stepped from À70 to +100 mV, held there for 10 ms and then stepped down to +20 mV, causing Ca 2+ current influx, and held there for various durations: t duration = .4,1.0, 2.0, 4.0 or 8.0 ms, after which it is stepped to À70 mV, resulting in a brief Ca 2+ tail current followed by closing of the Ca channels.
The computation start times for the five curves in Figure 10c are at t = t 0 = À10 À t duration = À10.4,À11.0, À12.0, À14.0, and À18.0 ms.The initial condition for the free calcium concentration at t = t 0 everywhere in the cube is The three buffers are in equilibrium with the Ca 2+ , so that for buffer a, which in the quarter cube in Figure A1b, is present only at the three membrane faces at z = 0 μm, z = 1 μm, and y = .5μm, and for buffers b and c everywhere inside the quarter-cube volume (including its six faces): where i = a, b or c.At t = t 0 the Ca channels are totally closed with the five-state Ca 2+ model, Equation (3), in the lowest closed state C1, C2, C3, C4, O ð Þ ¼1, 0, 0, 0, 0 ð Þ ð 9Þ At t = t 0 the voltage is stepped from +100 to +20 mV; at t = 0 ms, the voltage is stepped from +20 to À70 mV.The steps are not instantaneous but follow an exponential time dependence with time constant equal to .12 ms.

Numerical computation
The numerical problem is set up on a three-dimensional 33 Â 33 Â 66-point rectangular grid with grid spacing of Δx = Δy = Δz = 15 nm.The physical dimension of the computation region is 495 Â 495 Â 990 nm.The threedimensional reaction-diffusion equations, Equation (1), are solved in Cartesian coordinates using the explicit (Euler) finite-difference method in which the concentrations at each time step are computed in terms of the concentrations at that grid point and at the surrounding six grid points at the previous time step.We used a time step of Δt ¼ :1 μs that satisfies the stability condition that Δt < ⅙ Δx 2 /D Ca = .17μs, where D Ca = .22μm 2 ms À1 is the diffusion coefficient of Ca 2+ ions.A Fortran programme has been written to solve the numerical problem (PGI Visual Fortran, The Portland Group, Portland, Oregon) and run on a Dell XPS 8900 PC, Intel Core CPU @ 4.00 GHz.The run time for computing each curve in Figure 10b-A is about 5 min.
Table A1 summarizes the parameters used in the model.

F
I G U R E 1 Single BK channel activated by spontaneous action potentials in a varicosity.A cell-attached patch was formed on a varicosity with sub-giga Ohm seal resistance.NFR was in the pipette and bath solutions.(a) Superimposed traces showing large current deflections, which are mainly capacitive currents induced by spontaneous action potentials, followed in many cases by single-channel-like currents.(b) (A-D) four representative expanded traces (thick lines) from a (labelled with the same number) were superimposed on a blank current trace i.e. without single-channel openings (thin lines).(c) First latency distribution of single-channel openings.The times between the peak of the large current deflection and initiation of single-channel opening in each trace were counted and plotted as a cumulative distribution.The smooth line represents a single exponential fit to the data.Bin width, .1 ms, n = 14.(d) Cell-attached single-channel current (left) and current-voltage relation curve (right) obtained from the same varicosity as in subparts (a,b) at different voltages.Linear regression showed the slope conductance was 87.5 pS.The resting membrane potential was estimated to be À60 mV.

F
I G U R E 2 Representative paired recordings from a presynaptic varicosity and postsynaptic myoball.(a) Waveform applied to varicosity.The membrane was held at Vh = À70 mV, stepped up to +130 mV for 10 ms, then stepped back to an intermediate potential (IP) of 0 mV for different lengths of time, then stepped back to +130 mV again to test BK current.(b) Presynaptic current recorded in NFR.(c) In the presence of 2 μM of paxilline, blocking the I BK .(d) After further addition 10-μM Cd 2+ to block I Ca .(e) EPSCs recorded in NFR.(f) BK current (I BK ) obtained by B-C.(g) Ca 2+ current (I Ca ) by C-D.

3. 3 |
Individual BK channels respond to Ca 2+ from more than one Ca 2+ channel When the I BK was progressively blocked by paxilline, the time constant of the I BK remained essentially unchanged, indicating no change in the [Ca 2+ ] AZ reported by BK channels that remained open.In contrast, the gradual block of I Ca with ω-CgTX and NIF caused a progressive slowing in the rise time of the I BK , reflecting the decrease in [Ca 2+ ] AZ .Figure 5 shows representative data from one experiment of each type.The [Ca 2+ ] AZ , indicated by the time constant of activation of the I BK as BK channels were gradually blocked, was in the range of 50 ± 20 μM as the magnitude decreased, consistent with the averages from Figure 3b.The gradual slowing in I BK rise time as Ca channels were progressively blocked shows that BK F I G U R E 3 Relationship of normalized presynaptic BK current (I BK ), EPSCs and estimated [Ca 2+ ] as a function of duration of various intermediate potentials (IP).(a) Plots of normalized I BK versus IP at À70 mV (black), À40 mV (red), À20 mV (green), 0 mV (blue), +20 mV (cyan), +40 mV (magenta) and +60 mV (olive).(b) Normalized EPSCs evoked by the voltage waveform against duration at different IPs.(c) Plots of estimated [Ca 2+ (b) EPSCs recorded in response to the waveform described in a. (c) Plots of peak presynaptic currents recorded during the test step to +130 mV as a function of IPs between À60 mV and +130 mV for the three different extracellular Ca 2+ concentrations tested.(d) Peak EPSCs recorded during the +130 mV test steps as above.(a,b) Taken from IP of +30 mV (arrows).

F
I G U R E 5 Differential effects of Ca 2+ blockers and paxilline on BK current.(a) Sample traces of I BK activated by a pulse waveform (upper) before and after application of Ca 2+ blockers (middle) or the BK channel blocker paxilline (below).The rising rate of the I BK was progressively reduced at both +20 and +130 mV after application of Ca 2+ blockers, but showed no major changes after paxilline, though I BK declined in both cases.(b) The whole-cell BK currents elicited by +130 mV test pulses during IPs of +20 mV were reduced either by bath application of paxilline (2 μM), which selectively blocks BK channels or by ω-CgTX (1 μM) and nifedipine (5 μM), which blocks Ca 2+ channels.[Ca 2+ ] calculated by obtaining the time constants of activation of BK currents.Data points from different varicosities are shown for paxilline (solid symbols) and for ω-CgTX (open symbols) treatment, respectively.The line was obtained by fitting the data after ω-CgTX and NIF application to a Hill function.

F
I G U R E 6 Quantitative dependence of I BK and EPSC on [Ca 2+ ].Plots for I BK and EPSC against [Ca 2+ ] at an intermediate potential of +20 mV from 10 experiments with paired data.I BK and EPSC are plotted against [Ca 2+ ] determined by activation time constant of I BK and fitted to the Hill function.The [Ca 2+

F
I G U R E 7 I BK is equivalently dependent on both L-and N-type Ca 2+ channels.(a) I BK elucidated by the usual waveform (top) in absence (Ctl, black) and presence of 10 μM nifedipine (NIF, red) to block L-type Ca 2+ channels and after further adding 1 μM ωCTX to block N-type channels (blue).Blockers were applied in alternative order.(b) Enlarged I BK blockable by Ca 2+ channel blockers (thin line) and the nifedipine (grey line) or ω-CgTX blocked (thick black line) components at an ±intermediate potential of +20 mV, derived by subtraction of current traces shown in (a).(c) Average I BK component blocked by NIF (n = 7) or ωCTX (n = 8).Blocked components were derived by subtraction of the I BK after applying the blocker from the initial current.(d) Reduction of [Ca 2+ ] after NIF or ω-CgTX.Mean values are test was shown as horizontal lines.Two-sample Student's t test used for comparison of means.*p < .01,**p < .001.
shows the averaged F I G U R E 8 Presynaptic BK current, EPSC and fluorescent Ca 2+ imaging in response to uncaging Ca 2+ .(a) Light micrograph showing presynaptic varicosity and patch clamped postsynaptic myoball (left).Fluorescent images taken before UV-uncaging (middle) and after UVflash (right).(b-A), fluorescent intensity changes of the varicosity after uncaging.(b-B) I BK traces evoked by depolarizing membrane to 100 mV at 10, 50, 100 and 250 ms after UV-flash.(b-C) EPSCs recorded from myoball after flashes.(c-A), expanded and aligned I BK traces b, with their exponential fits (dash lines).(c-B) [Ca 2+ ] calculated by exponential fitting I BK .

F
I G U R E 9 Effects of EGTA-AM (a) and BAPTA-AM (b) on I BK and EPSCs.Both the varicosity and the myoball were voltage clamped.The varicosity membrane potential was held at À70 mV and first depolarized to +130 mV (prepulse), then stepped back to an IP of +20 mV for Ca 2+ entry.A test pulse of +130 mV was then applied to measure the I BK .(a) At the top, the ratios of I BK evoked by test pulse over that by prepulses; at the bottom, amplitudes of EPSCs were plotted before and after 40 μM EGTA AM was applied by superfusion, as indicated by the horizontal bar.Sample current traces below the curve were taken during the superfusion of chelator at times near the beginning and end of each trial.(b) A similar experiment in which 10 μM BAPTA-AM was applied by superfusion as indicated by the horizontal bar during recording.dominant role in determining the instantaneous free [Ca 2+ ] AZ level, which in turn governs release.
To test the effects of rate and duration of Ca 2+ influx on the time course of build-up of [Ca 2+ ] AZ near BK channels and release sites, terminals were first depolarized from the holding potential of À70 mV to a potential close to or above E Ca for 5-10 ms to open Ca channels without Ca 2+ five-state model yields the open probability O of a single channel, and it yields the actual time course of the macroscopic current by multiplying i Ca in Equation ( T A B L E A 1 Parameters used in the model.
aValue determined by best fit to data.