Calcium Sensitivity of Neurotransmitter Release Differs at Phasic and Tonic Synapses

Introduction

Transmitter release evoked by a nerve impulse (“synaptic strength”) differs enormously among synaptic connections (Atwood and Karunanithi, 2002). Likewise, short-term plasticity is very diverse, ranging from severe depression to dramatic facilitation. This diversity is linked to functional requirements of the neural circuits in which the connections occur. Many variables contribute to differences in presynaptic performance: ion channel number, properties, and location; synaptic vesicle availability; properties of presynaptic proteins regulating Ca²⁺ dynamics and vesicle exocytosis; and synaptic morphology. For any specific connection, all of these factors must be considered in searching for an explanation of release properties.

Crustacean phasic and tonic glutamatergic motor neurons provide one of the best available examples of synaptic specialization (Kennedy and Takeda, 1965a,b). At synapses of the paired phasic and tonic motor neurons of limb muscles, quantal release from a phasic synapse in response to a single action potential is typically 100- to 1000-fold greater than for a tonic synapse sharing the same postsynaptic muscle cell (Msghina et al., 1998). Moreover, phasic synapses depress rapidly to repeated activation, whereas tonic synapses display facilitation as great as 100,000% to a 100 Hz train.

Ultrastructural comparisons of individual synaptic boutons revealed that bouton size, synaptic contact area of individual synapses, and number of synapses per bouton are greater for tonic nerve terminals, contrary to the expectation that these features might be positively correlated with initial release probability (King et al., 1996; Msghina et al., 1998). Estimated Ca²⁺ entry per synapse is similar for both types of nerve terminals, and no other differences were found that could account for a 1000-fold difference in probability of quantal release (Msghina et al., 1999) and dramatically different forms of plasticity.

In mammalian cultured neurons, the initial probability of transmitter release is proportional to the size of the readily releasable pool (RRP) (Dobrunz and Stevens, 1997; Schikorski and Stevens, 1997). At crayfish terminals, however, the size of the RRP for tonic synaptic boutons is larger than at phasic synapses, whereas the fractional release per impulse of the RRP is 1500-fold smaller (Millar et al., 2002). One mechanism that might explain the differences between tonic and phasic synapses is the Ca²⁺ dependence of the release process. In this study, we compared release rates during changes in presynaptic intracellular [Ca²⁺] ([Ca²⁺]_i) produced by flash photolysis of caged Ca²⁺, which elevates [Ca²⁺]_i rapidly and uniformly throughout terminal boutons. For a given [Ca²⁺]_i, release rates at phasic synapses were at least one order of magnitude higher than for tonic synapses. Among several models explored, one in which the secretory trigger binds three Ca²⁺ ions at one site and two Ca²⁺ ions at another site, with explicit priming of vesicles in the RRP, was best able to account for characteristics of responses to [Ca²⁺]_i steps, single action potentials, and a train of spikes. In this model, tonic and phasic synapses have identical Ca²⁺ sensitivities of the secretory trigger but have very different states of Ca²⁺-dependent priming.

Materials and Methods

Animals and preparation. Freshwater crayfish (Procambarus clarkii; 2-5 cm body length) were obtained from Atchafalaya Biological Supply (Raceland, LA) and maintained under standard laboratory conditions as outlined by Bradacs et al. (1997). We used the carpopodite extensor muscle preparation, which is innervated by two excitatory motor axons: one tonic and one phasic. This preparation has been described in detail previously (Bradacs et al., 1997; Msghina et al., 1998).

Solutions. The preparation was dissected and bathed in a modified Van Harreveld's crayfish solution containing the following (in mm): 205.3 NaCl, 5.3 KCl, 13.5 CaCl₂, 2.5 MgCl₂, and 10 HEPES buffer, pH 7.4. In some experiments, we further modified the crayfish solution to contain differing concentrations of Ca²⁺. Solutions contained the following (percentage of normal Ca²⁺, [CaCl₂], in mm): 0%, 0; 10%, 1.35; 25%, 3.38; 50%, 6.75; 75%, 10.13; 100%, 13.5; 200%, 27; and 800%, 108. Experiments were performed at room temperature (20 ± 1°C).

For “caged calcium” experiments, nerve terminal axons were pressure-injected with a solution containing the following (in mm): 50 dimethoxynitrophenyl-EGTA-4 (DMNPE-4), 37.5 CaCl₂, 50 K-HEPES, 13.2 or 6.6 brilliant sulfaflavine (BS), 1.32 or 0.66 Oregon green 488 BAPTA 6F (OG), and 55 KCl (551-567 mOsm).

UV photolysis. [Ca²⁺]_i was controlled using the recently developed caged Ca²⁺ chelator DMNPE-4 (Ellis-Davies, 2003). Caged Ca²⁺ was photolyzed with a flash lamp (T.I.L.L. Photonics, Grafelfing, Germany) or a xenon arc lamp (Optikon, Guelph, Ontario, Canada) controlled with a Uniblitz electronic shutter (Vincent Associates, Rochester, NY). Both devices were coupled to an Optiphot 2 upright microscope (Nikon Canada, Mississauga, Ontario, Canada) via a fused silica light guide and a T.I.L.L. Photonics two-port condenser with 400 nm dichroic and 400 nm short-pass filters. The light from the condenser was passed through the microscope to a 40× UV water-dipping objective (Olympus Optical, Tokyo, Japan). This produced a 20 × 20 μm square of light in the focal plane of the objective. The remaining port on the condenser was coupled through another light guide to a T.I.L.L. Photonics Polychrome IV monochrometer.

When using the flash lamp, we controlled the light intensity by changing the insertion depth of the light guide in the lamp housing. This altered the amount of light entering the light guide by moving the aperture out of the focal plane of the light beam. Gradations were marked on the light guide adapter corresponding to the intensity of light at the output of the objective, which was measured using a fast photodiode in the focal plane of the objective. To monitor flash duration and intensity during experiments, we placed a photodiode at a small opening in the two-port condenser; its output was digitized concurrently with imaging and electrophysiological data.

[Ca²⁺]_i measurement. We estimated [Ca²⁺]_i in boutons using the two-dye, dual-excitation wavelength technique of Oheim et al. (1998). This technique measures the ratio of the fluorescence of a single-wavelength, Ca²⁺-sensitive dye to that of a Ca²⁺-insensitive dye to correct for dye concentrations and path length. We used OG as the Ca²⁺-sensitive dye and BS as the Ca²⁺-insensitive dye. Both dyes were pressure-injected into presynaptic terminals along with caged Ca²⁺. Injected materials were allowed to diffuse to terminal boutons for 30 min. Fluorescence was measured by alternately exciting OG and BS at wave-lengths of 480 and 420 nm, respectively, using the T.I.L.L. Photonics monochrometer. Fluorescence emission (535 ± 20 nm) was measured by the T.I.L.L. Photonics photodiode system, and the output was digitized at 10 kHz using a PowerLab data acquisition system (AD Instruments, Colorado Springs, CO). Fluorescence intensities were corrected for tissue fluorescence by subtracting backgrounds measured from a muscle region adjacent to the filled nerve.

[Ca²⁺]_i calibrations. Fluorescence measurements were converted to [Ca²⁺]_i by standard methods (Grynkiewicz et al., 1985) using the ratio of OG fluorescence intensity to excitation at 480 nm divided by BS fluorescence intensity to excitation at 420 nm for three calibration solutions containing no Ca²⁺ (R_min), 5 mm Ca²⁺ (R_max), and 4.5 μm Ca²⁺ (_Rmid). Solution fluorescence was measured from a microcuvette chamber (20 μm path length; VitroCom, Mountain Lakes, NJ) placed in the focal plane of the microscope objective, with background subtraction of the cuvette fluorescence filled with water.

R_min was measured for a solution containing the following (in mm): 10 K₂H₂-DMNPE-4, 1.32 BS, 0.132 OG, 15 HCl, 50 K-HEPES, 10 K₂-EGTA, and 175 KCl, pH 7.4. The HCl was added to neutralize the DMNPE-4, which was provided in highly basic tetrapotassium form; this produced 15 mm KCl, and the K₄-DMNPE-4 stock solution contained another 5 mm KCl (calculated from its degree of protonation estimated from the pH of a diluted solution). R_max was measured in a solution of (in mm): 10 CaK₂-DMNPE-4, 1.32 BS, 0.132 OG, 50 K-HEPES, 5 CaCl₂, and 185 KCl plus 20 mm KCl from the K₄-DMNPE-4, pH 7.4. The ionic strength of these solutions was 280 mm, the same as for crayfish Ringer's solution. R_mid was measured in a solution containing the Ca²⁺ buffer 1,3-diaminopropane-2-ol-N,N′-tetraacetic acid (DPTA; Sigma, St. Louis, MO) to control the [Ca²⁺] at an intermediate concentration near the K_D of OG. The solution contained the following (in mm): 10 CaK₂-DMNPE-4, 1.32 BS, 0.132 OG, 20 CaK₂-DPTA, 30 K₃H-DPTA, 50 K-Trizma, pH 8.0, and 20 KCl produced by neutralization, with a slightly hypertonic ionic strength of 316 mm. At this pH and ionic strength, DPTA has an effective Kd for Ca²⁺ of 6.9 μm (interpolated from Grimes et al., 1963; Neher and Zucker, 1993; Ohnuma et al., 2001), and the free [Ca²⁺] of the solution should be 4.5 μm (confirmed by measurement with Ca²⁺ ion-selective electrodes; Microelectrodes, Londonderry, NH). If CaK₂-DMNPE-4 is made stoichiometrically, it will affect neither pH nor the free [Ca²⁺]; therefore, it was produced by titrating DMNPE-4 with Ca²⁺ using Ca²⁺-sensitive electrodes. The pCa of a stock solution containing everything except the DMNPE-4 and the dyes was also checked and confirmed with ion-sensitive electrodes.

Averaging several calibrations, R_max/R_min was 5.32, whereas without DMNPE-4, R_max/R_min was ∼10, so DMNPE-4 appears to partially quench OG fluorescence, particularly when bound to Ca²⁺ (cf. Zucker, 1992), and to reduce its sensitivity to Ca²⁺. Typical parameter values of R_max, R_min, and R_mid were 4.84, 0.91, and 2.9, respectively, corresponding to a K_D of 4.4 μm. This is substantially higher than the nominal OG K_D of 3 μm. From the effect of ionic strength on similar indicators (cf. Grynkiewicz et al., 1985; Zhong et al., 2001), a K_D of 4.5 μm would be expected, and we used this value for converting fluorescence ratios to [Ca²⁺].

The calibration solutions contained DMNPE-4, OG, and BS in the same ratios (but one-tenth of the concentrations) as the solutions in injection pipettes. Two-dye [Ca²⁺]_i measurements require that the concentration ratio of the dyes remain constant and equal to that used for calibrations. However, OG and BS diffuse at different rates (Oheim et al., 1998); therefore, their ratio is likely to be variable in different boutons and at different times and not equal to that of calibration solutions. This problem, along with variations in the light source spectrum, results in different values of R_min in each experiment. However, R_max/R_min is un-affected by the concentration ratio. The free [Ca²⁺] in our injection solution equals the resting [Ca²⁺]_i in axons (100 nm), which is 2% of the K_D of OG, so the initial fluorescence ratio should be within 2% of the range from R_min to R_max. We thus used the initial resting fluorescence ratio as R_min for converting R to [Ca²⁺]_i in each experiment.

We tested for effects of bleaching by photolysis flashes using the Ca-free or Ca-loaded solutions for determining R_min and R_max. A full-intensity flash caused a little less than 5% bleaching, which would not introduce much error into estimates of [Ca²⁺]_i, because this flash brought [Ca²⁺]_i into the middle of the Ca sensitivity range of OG in which bleaching effects are least consequential.

Predicting Ca(t) during the flash artifact and the effect of our flashes.To analyze how putative reaction schemes for transmitter release would respond to the time course of [Ca²⁺]_i, Ca(t), we had to replace the artifact in the Ca(t) recording with an estimated time course of Ca(t). This was especially important because, for large [Ca²⁺]_i increases, most transmitter release occurred during the first 50 ms after the flash, when the artifact obscured the Ca(t) measurement. The Ca(t) measurement missed the expected “spike” in Ca(t) that occurs during the flash (Zucker, 1994; Ellis-Davies, 2003) because of saturation of the detector during the flash. The time course of the saturation artifact over the 50 ms after the beginning of the flash was similar in boutons that contained just the indicators (data not shown) and in boutons that contained indicators and DMNPE-4 except for the elevated baseline after the flash in DMNPE-4-containing boutons.

To calculate the temporal profile of Ca(t) during and immediately after the flash, we used a simplified reaction scheme for DMNPE-4 similar to that outlined by Ellis-Davies et al. (1996). It included a one-step photolysis process and no Mg²⁺ binding (which is negligible for DMNPE-4) or binding of Ca²⁺ to photoproducts (which has negligible effects in the presence of endogenous Ca²⁺ buffers). The evolution of photolysis of DMNPE-4 was estimated by convolution of the measured time course of the photolysis flash (recorded from reflected light with a photodiode) with the photolysis rate of DMNPE-4. The photolysis efficiency of the flash for DM-nitrophen was estimated using small droplets under oil of a mixture of DM-nitrophen and fluo-3, as described by Zucker (1994), and converted to an efficiency for DMNPE-4 by accounting for the relative UV absorbances and quantum efficiencies of the two caging compounds.

This temporal reduction in [DMNPE-4] was used to drive a series of differential equations representing the binding of DMNPE-4 to Ca²⁺ and an endogenous cytoplasmic Ca²⁺ buffer and removal of free Ca²⁺ by a first-order pump. The equations were solved using a BASIC program and first-order Euler methods. The affinity of DMNPE-4 for Ca²⁺ depends on pH and ionic strength; we used a value of 48 nm, the affinity at pH 7.2 in mammalian ionic strength and approximately appropriate for the higher ionic strength (∼280 mm) of crayfish cytoplasm, and a pH of ∼7.3 (Ellis-Davies et al., 1996), which have opposite effects on affinity. We assumed an on rate of 1.7 × 10⁷ m/s, the value for the chemically similar compound nitrophenyl-EGTA (Ellis-Davies et al., 1996). Measurement of the fluorescence intensity of indicators coinjected with the DMNPE-4 in boutons set the initial unphotolyzed DMNPE-4 concentration at 2-4 mm. Ca loading of the injection solution was 75%, resulting in a free [Ca²⁺] of 106 nm. This is close to the resting [Ca²⁺]_i in motor nerve terminals (Delaney et al., 1991), so it was assumed that pumping did not alter the DMNPE-4 Ca²⁺ loading before photolysis.

Endogenous Ca²⁺ buffering has a buffer ratio of 600 in crayfish opener motor neuron terminals (Tank et al., 1995). Because the endogenous buffer is not saturated by several micromolar [Ca²⁺]_i, implying a high capacity, we represented it as 10 mm Ca²⁺-binding buffer sites with 16 μm Ca²⁺ affinity, although less buffer of higher affinity remains possible. We assumed an on rate of 5 × 10⁷ m/s, one-half that of the endogenous Ca²⁺ buffer in mammalian chromaffin cells (Xu et al., 1997), to account for higher crayfish ionic strength. Simulations included the effects of Ca²⁺ binding to OG, with affinity of 4.5 μm and on rate of 1 × 10 ⁸ m/s (typical for BAPTA derivatives, but reduced for crayfish) (Kao and Tsien, 1988; Ellis-Davies et al., 1996). Its concentration was set to 2.6% that of DMNPE-4, as in the injection mixture, or 52-104 μm, as determined by the range of fluorescence intensities of filled boutons compared with the fluorescence of a known concentration in microcuvettes containing cytoplasm-like fluid and correcting for the relative thickness of the cuvettes and boutons.

Ca²⁺ was removed to a steady-state level of 100 nm by a nonsaturating pump at a rate of 0.12/ms, which pumps Ca²⁺ off the native buffer with a time constant of 5 s, as observed experimentally (Tank et al., 1995).

Simulations of the effects of a bright flash on Ca(t) were compared with Ca(t) measurements to a full flash in a typical experiment (see Fig. 5A) and found to match closely for an assumed bouton DMNPE-4 concentration of 2.75 mm and Ca indicator concentration of 72 μm, after subsidence of the flash artifact. This is 5% of the concentration of material in the injection pipette, which is typical of the level of filling achievable in boutons within a few hundred micrometers of the injection site; moreover, the dye concentration needed for simulations to match measurements is right in the middle of our estimate of dye concentration from fluorescence intensity (52-104 μm). The correspondence between simulations and measurements provides an independent check of our calibration of the Ca²⁺ sensitivity of OG, as well as a check of our estimate of the photolysis efficiency of our flash apparatus. These concentrations of DMNPE-4 and OG were therefore selected for simulations of a series of eight light flashes at between 15 and 100% of the full intensity flash, which covered the full range of Ca(t) measurements in our experiments. The Ca(t) waveforms generated by these simulations (see Fig. 5A) were used to predict the responses of reaction schemes used to represent various molecular schemes for transmission at phasic and tonic synapses.

The highest [Ca²⁺]_i level achieved by photolysis in our experiments was ∼3.2 μm. This value seems low but actually matches our predictions, as outlined below. A 3 mm concentration is far less than the levels exceeding 100 μm typically achieved in cells perfused with DM-nitrophen. For example, when mammalian cells are perfused with an Mg²⁺-free solution, the effective Ca²⁺ affinity for DM-nitrophen remains at 5 nm, and the DM-nitrophen can be almost fully loaded with Ca²⁺ and still leave [Ca²⁺]_i at 100 nm. Then whatever amount of DM-nitrophen is photolyzed (e.g., 80% of 10 mm = 8 mm), the same amount of free [Ca²⁺] is released onto a native buffer with a typical buffer ratio of 50 (for most cells), resulting in a [Ca²⁺]_i increase to 160 μm (Neher and Zucker, 1993). When injecting nerve terminals, the Mg²⁺ cannot easily be removed from boutons 100-300 nm away, and this Mg ²⁺ would displace Ca²⁺ from DM-nitrophen, leading to a “loading transient” that itself would activate secretion and might exhaust the RRP before flash experiments begin (Neher and Zucker, 1993). Therefore, we used Mg²⁺-tolerant DMNPE-4, but its affinity for Ca²⁺ is one-tenth that of DM-nitrophen, and it can only be 75% loaded with Ca²⁺; otherwise, resting [Ca²⁺]_i is increased too much. The quantum efficiency and absorbance of DMNPE-4 are similar to those of DM-nitrophen, so a flash would photolyze a similar fraction of DMNPE-4 to release approximately three-fourths as much Ca²⁺. However, we can only fill boutons by injection with one-fourth the chelator concentration often used when perfusing whole cells. Moreover, crayfish cytoplasm has 12 times the buffer capacity of typical mammalian cells. These considerations lead to the expectation that we should be able to elevate [Ca²⁺]_i to ∼2.5 μm.

Predicting Ca(t) during an action potential. Vesicle release is triggered by the local increase in [Ca²⁺]_i in “microdomains” because of the entry of Ca²⁺ ions through clusters of Ca²⁺ channels with individual “nanodomains” that overlap (Zucker et al., 1999; Augustine et al., 2003). In this situation, the local Ca(t) will follow closely the time course of the summed Ca²⁺ fluxes through the individual channels in the cluster, which corresponds to the macroscopic Ca²⁺ current (Roberts, 1994). Transmitter release at crayfish motor nerve terminals is governed by Ca²⁺ entry through P-type Ca²⁺ channels (Araque et al., 1994; Blundon et al., 1995), the kinetics of which closely resemble those that have been studied exhaustively at the squid giant synapses (Wright et al., 1996). We therefore used a kinetic model of the squid presynaptic Ca²⁺ current (Llinás et al., 1981) as modified by Llinás et al. (1982), with the temperature set to 19°C, typical of the present experiments. The kinetic equations were driven with an action potential waveform recorded from motor nerve axons at 19°C. (No difference was observed between phasic and tonic axons.) The resulting Ca(t) was almost exactly described by a Gaussian curve, so a closely fitting Gaussian curve (σ = 250 μs) was used to represent Ca(t). The peak [Ca²⁺]_i amplitude reached during an action potential depends critically on the Ca²⁺ flux per channel, the number of Ca²⁺ channels opening near a docked vesicle, their exact distances from the secretory trigger, and the binding kinetics and mobilities of endogenous buffers (Tang et al., 2000; Matveev et al., 2002, 2004). Because none of these is known with sufficient precision, the peak [Ca²⁺]_i amplitude produced by an action potential at the secretory trigger remained a free parameter (cf. Bollmann et al., 2000; Schneggenburger and Neher, 2000).

Electrophysiology. Conjointly with measuring [Ca²⁺]_i, neurotransmitter release was assayed by focal extracellular recording at visualized phasic and tonic nerve terminal boutons, using procedures described by Msghina et al. (1998). Loose macropatch recordings (Dudel, 1981; Wojtowicz et al., 1994; Cooper et al., 1995) of the presynaptic nerve terminal action potentials and excitatory junction currents (EJCs) were obtained in current-clamp mode from single visualized tonic and phasic terminal boutons. In this mode, the extracellular voltage provides a measure of local postsynaptic current density. As first demonstrated by Ravin et al. (1997), a crayfish bouton can be effectively illuminated and visualized to measure [Ca²⁺]_i while a macro-patch electrode is in place to measure transmitter release from the same bouton.

Release rate determination. To estimate rates of neurotransmitter release in phasic and tonic boutons, we applied a procedure based on Fourier transforms of both EJCs and miniature EJCs (mEJCs) recorded from the same bouton (Van der Kloot, 1988). We used the equation F[n(t)] = F[EJC]/F[mEJC], where F[EJC] is the Fourier transform of an evoked response, F[mEJC] is the Fourier transform of the averaged quantal events, and F[n(t)] is the Fourier transform of the quantal release rate at time t. The inverse Fourier transform of F[n(t)] yields n(t). As shown in Figure 1 A, deconvolution of an EJC with averaged mEJCs produced a maximum release rate of 17.5/ms, and cumulative release of 7.8 quanta was estimated, which compares well with the quantal content of 7.5 obtained by dividing the EJC area by the mEJC area. Deconvolution of responses to a flash was also used to estimate release rate versus time after the flash; an example is shown in Figure 1 B.

To evaluate our deconvolution algorithm, we used the procedure proposed by Van der Kloot (1988), in which a predicted evoked response is reconstructed from the calculated release rate and compared with the actual response. We used the equation: F[pred] = F[mEJC] × F[n(t)], where F[pred] is the Fourier transform of the predicted evoked event; the inverse Fourier transform of this function did in fact reproduce the actual evoked event. An additional test of the procedure was conducted by constructing an artificial EJP from a series of mEJPs designated as occurring at predetermined times. Deconvolution analysis reproduced the predetermined rate of release and total number of quantal events. Additional tests were conducted on flash-evoked responses in which quanta could be detected and counted individually. Our procedure produced release rates and total quantal counts that agreed with estimates derived directly from measuring the time of occurrence of each event. Cumulative quantal contents to an action potential or for a defined period after a flash were estimated by integrating the calculated release rates or by counting quanta in responses where they were individually distinguishable.

Data collection and analysis. Electrophysiological and photometric signals were low-pass-filtered at 5 kHz using a 2004-F Signal Conditioner (Intronix Technologies, Toronto, Ontario, Canada) and subsequently digitized at 10 kHz using a PowerLab/4sp data acquisition system (AD Instruments). Data analysis was performed using Excel (Microsoft, Redmond, WA). Mathematica (Wolfram Research, Champaign, IL) was used for the Fourier analysis.

Modeling molecular reaction schemes. First-order Euler approximations of differential equations were implemented in IgorPro 5.01 (Wave-metrics, Lake Oswego, OR), based on algorithms kindly provided by R. Schneggenburger (Max-Planck Institute for Biophysical Chemistry, Göttingen, Germany). Parameters were varied over a wide range, and we present those giving the best fits of multiple response characteristics to data as determined by eye. Some fits are imperfect; for these, it was found that parameter choices improving fits for one characteristic resulted in worse fits for other characteristics. Thus, an (arbitrary) choice was sometimes made as to which characteristics to fit best.

Results

Discussion

Our key finding is a large difference in the Ca²⁺ sensitivity and kinetics of the transmitter release machinery between phasic and tonic synapses in response to step rises in [Ca²⁺]_i. As pointed out in Introduction, no other property has been found differentiating the two synaptic types that could explain the much stronger efficacy of release from phasic boutons to a single action potential. In the second part of our study, we found that three molecular reaction schemes could describe the kinetics and magnitudes of release to a series of [Ca²⁺]_i steps and could account for the responses to single spikes and trains of action potentials at phasic and tonic synapses.

We began by with a scheme of the sequential binding of up to five Ca²⁺ ions to a secretory trigger, followed by a fusion step. This scheme accounted reasonably well for the properties of responses to step rises in [Ca²⁺]_i, to the expected time course of local [Ca²⁺]_i during an action potential, and to trains of five action potentials. The phasic synapses resemble many vertebrate synapses at which depression dominates, and our parameter values are similar to those for this scheme at the calyx of Held (Bollmann et al., 2000; Schneggenburger and Neher, 2000). Applying the first scheme to tonic synapses assumed differences in Ca²⁺-binding properties of the secretory trigger. Initially, we imagined that tonic synapses bind Ca²⁺ with lower affinity than phasic synapses, making them less sensitive to [Ca²⁺]_i. Such a reduced affinity could arise, for example, from faster Ca²⁺ dissociation rates from the secretory trigger. In that case, facilitation would not have arisen from Scheme 1, and we would have attributed it to some independent process. However, we were unable to fit the results of our experiments on [Ca²⁺]_i steps by reducing Ca²⁺-binding affinity, whether by increasing Ca²⁺ dissociation rates or increasing Ca²⁺ association rates; instead, we could only fit the results by reducing both on and off rates for Ca²⁺ binding, i.e., by slowing the kinetics of Ca²⁺ binding. Under these conditions, facilitation to a train of action potentials arose from the slow dissociation of Ca²⁺, contradicting evidence that facilitation is attributable to residual Ca²⁺.

The second scheme attributed the difference between synapse types to different Ca²⁺ sensitivities and resting states of priming, with most vesicles in the RRP unprimed at rest in tonic synapses. This scheme could also account for most aspects of responses to steps in [Ca²⁺]_i, but it predicted too high an increase in asynchronous release at tonic synapses. In this situation, trigger molecules with three or four Ca²⁺ ions bound were too sensitive to residual Ca²⁺ because of the increasing Ca²⁺ affinities of successive binding steps.

The third scheme was a variant of the priming model in which a modified secretory trigger with Ca²⁺ binding independently at two binding sites was used, more in keeping with the Ca²⁺-binding structure of synaptotagmin. This scheme provided the best description of the different responses to Ca²⁺ steps and action potentials, as well as short-term plasticity and asynchronous release, at phasic and tonic synapses. The Ca²⁺ association rate derived by fitting this scheme to our data (1.2 × 10⁸ m/s) is similar to estimates from kinetic studies of Ca²⁺ binding to the C2A domain of synaptotagmin (4 × 10⁷-1 × 10⁸ m/s) (Davis et al., 1999; Millet et al., 2002); moreover, binding of Ca²⁺ to C2A and C2B domains appears to be similar, which was a simplifying assumption in our choice of parameters. In this scheme, facilitation arises from the priming of vesicles by Ca²⁺ (Worden et al., 1997) acting at a site relatively distant from a Ca²⁺ channel and as such is a variant of the two-site model of facilitation (Tang et al., 2000; Matveev et al., 2002). This new scheme may be closer to what is actually happening at synaptic terminals.

A finding of general importance is that Scheme 1 also produces too high an asynchronous release rate when the effects of residual Ca²⁺ are considered. Thus, incorporating residual Ca²⁺ at the release trigger into simulations of Scheme 1 generates a large interspike release similar to those shown in the bottom left plots of Figure 7, C and D (simulation not shown). This might be a problem for any preparation in which Scheme 1 has been applied (Heidelberger et al., 1994; Bollmann et al., 2000; Schneggenburger and Neher, 2000; Beutner et al., 2001; Felmy et al., 2003) but has not been noted because previous applications of Scheme 1 did not specifically treat the effects of residual Ca²⁺ on asynchronous release between action potentials. Scheme 3, which attempted to incorporate Ca²⁺-binding features of synaptotagmin in the way that Ca²⁺ bound to the secretory trigger, may therefore also be valuable in modeling release at other synapses.

Preliminary experimental results support the concept of Ca²⁺-dependent priming at tonic synapses. When maximal release rates are imposed by pretreatment with Cs⁺ and high-frequency stimulation (Millar et al., 2002), quantal release always facilitates for a few impulses before attaining a maximal value and then depressing. This effect may be attributable to a priming process initiated early in the train of stimuli. In contrast, phasic synapses do not show an initial priming phase during production of maximal release in Cs⁺-treated terminals. Steady presynaptic depolarization of tonic nerve endings also potentiates release by action potentials, presumably by increasing steady-state intracellular Ca²⁺ (Wojtowicz and Atwood, 1983, 1984). When tonic nerve endings are injured by pressure from a macropatch electrode, resting [Ca²⁺]_i rises, and action potential-evoked release increases. These observations, although incomplete, suggest a Ca²⁺-dependent priming process, which can increase evoked release at tonic synapses, in support of the priming-dependent reaction schemes presented here

Alternative formulations of priming to those presented here might also be used to model the data. Phasic synapses were modeled as “preprimed” because of a higher Ca²⁺-affinity of the priming step; we could equally well have assumed that, at phasic synapses, the priming process is simply absent. Alternatively, we could imagine that only tonic synapses contain a special brake on priming that is relieved by Ca²⁺. It is also possible that priming acts in parallel or simultaneously with the secretory process (Yamada and Zucker, 1992) rather than anterior to it. Furthermore, our modification of the secretory trigger in Scheme 3 is only the simplest of several we could think of. For example, the two binding sites envisaged in the secretory trigger may have different Ca²⁺-binding kinetics, multiple synaptotagmins may participate in vesicle release (Hua and Scheller, 2001), and vesicles may be heterogeneous in their release probabilities (Trommershäuser et al., 2003). Thus, the exact details of Scheme 3 remain to be substantiated and may be modified in light of additional data. The major point of the modeling is the demonstration that only a difference in the Ca²⁺ dependence of priming can explain all the differences between tonic and phasic synapses.

The present results beg the question of the identity of the priming molecule(s). Popular candidates include munc13, rab3-interacting molecule, rabphillin, synapsin/Ca-calmodulin-dependent kinase, SNAP-25 (synaptosome-associated protein of 25 kDa), and neuronal calcium sensor-1 (Geppert and Südhof, 1998; Hilfiker et al., 1999; Duncan et al., 2000; Lonart, 2002; Martin, 2002; Rettig and Neher, 2002; Zucker, 2003; Heidelberger and Matthews, 2004). Because we are suggesting that the same molecule(s) may be responsible for synaptic facilitation, their identification and characterization become doubly important. A further mystery is how the molecular machinery controlling the differences between phasic and tonic synapses is regulated. A clue is provided by the discovery that different terminals of a single neuron can display widely different degrees of facilitation and initial release probability that appear to be target-dependent (Atwood, 1967; Bittner, 1968; Atwood and Bittner, 1971; Markram et al., 1998; Reyes et al., 1998), suggesting post-transcriptional and perhaps posttranslational presynaptic modifications under postsynaptic regulation. In the case of crayfish junctions from different motor neurons with very different properties projecting onto the same target, postsynaptic regulation would not seem to be the defining mechanism.