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The Journal of Neuroscience, December 15, 2002, 22(24):10593-10602

Timing and Efficacy of Ca²⁺ Channel Activation in Hippocampal Mossy Fiber Boutons

Josef Bischofberger, Jörg R. P. Geiger, and Peter Jonas

Physiologisches Institut, Universität Freiburg, D-79104 Freiburg, Germany

	ABSTRACT

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

The presynaptic Ca²⁺ signal is a key determinant of transmitter release at chemical synapses. In cortical synaptic terminals, however, little is known about the kinetic properties of the presynaptic Ca²⁺ channels. To investigate the timing and magnitude of the presynaptic Ca²⁺ inflow, we performed whole-cell patch-clamp recordings from mossy fiber boutons (MFBs) in rat hippocampus. MFBs showed large high-voltage-activated Ca²⁺ currents, with a maximal amplitude of ~100 pA at a membrane potential of 0 mV. Both activation and deactivation were fast, with time constants in the submillisecond range at a temperature of ~23°C. An MFB action potential (AP) applied as a voltage-clamp command evoked a transient Ca²⁺ current with an average amplitude of ~170 pA and a half-duration of 580 µsec. A prepulse to +40 mV had only minimal effects on the AP-evoked Ca²⁺ current, indicating that presynaptic APs open the voltage-gated Ca²⁺ channels very effectively. On the basis of the experimental data, we developed a kinetic model with four closed states and one open state, linked by voltage-dependent rate constants. Simulations of the Ca²⁺ current could reproduce the experimental data, including the large amplitude and rapid time course of the current evoked by MFB APs. Furthermore, the simulations indicate that the shape of the presynaptic AP and the gating kinetics of the Ca²⁺ channels are tuned to produce a maximal Ca²⁺ influx during a minimal period of time. The precise timing and high efficacy of Ca²⁺ channel activation at this cortical glutamatergic synapse may be important for synchronous transmitter release and temporal information processing.

Key words: mossy fiber boutons; presynaptic Ca²⁺ inflow; presynaptic Ca²⁺ channels; hippocampus; kinetic model; glutamatergic synapse

	INTRODUCTION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

The mossy fiber synapse on CA3 pyramidal neurons is a key synapse that mediates information flow in the trisynaptic circuit of the hippocampus (Jonas et al., 1993; Jung and McNaughton, 1993; Lisman, 1999; Henze et al., 2000). Glutamate release at this synapse is initiated by a complex series of events. These include the invasion of the action potential (AP) into the presynaptic terminal (Geiger and Jonas, 2000), the activation of presynaptic P/Q-, N-, and R-type Ca²⁺ channels (Castillo et al., 1994; Gasparini et al., 2001), and the inflow of Ca²⁺ ions into the presynaptic terminal. The presynaptic Ca²⁺ inflow finally triggers the fusion of synaptic vesicles but also contributes to the regulation of synaptic strength (Salin et al., 1996; Tong et al., 1996; Sabatini and Regehr, 1999).

The spatiotemporal profile of the presynaptic Ca²⁺ transient is of critical importance for the efficacy, timing, and regulation of transmitter release at the mossy fiber synapse. A brief, local transient may trigger fast and highly synchronized glutamate release (Brown and Johnston, 1983; Jonas et al., 1993). In contrast, a more long-lasting, global Ca²⁺ increase is necessary to evoke the release of peptides, e.g., dynorphin (Verhage et al., 1991; Derrick and Martinez, 1996; Williams and Johnston, 1996). Finally, changes in synaptic strength, such as facilitation, post-tetanic potentiation, and long-term potentiation, are thought to be primarily determined by the residual Ca²⁺ (Salin et al., 1996). Short-term plasticity is completely suppressed by the slow exogenous Ca²⁺ buffer EGTA, whereas fast transmitter release is only partly reduced (Salin et al., 1996). This suggests that Ca²⁺ sensors for release and plasticity sense Ca²⁺ signals with different spatiotemporal profiles.

The shape and duration of the presynaptic Ca²⁺ signal is determined by several molecular and structural properties of the presynaptic element, including the duration of the spike, the number of Ca²⁺ channels per release site, the gating properties of the presynaptic channels, and the concentration of endogenous Ca²⁺ buffers (Neher, 1998). The calyx of Held is the only mammalian synapse in which these factors have been determined systematically (Forsythe, 1994; Borst and Sakmann, 1996). In cortical glutamatergic synapses, however, these properties are unknown.

To directly examine the presynaptic Ca²⁺ channels at a cortical glutamatergic synapse, we made patch-clamp recordings from hippocampal mossy fiber boutons (MFBs) in acute brain slices (Geiger and Jonas, 2000; Geiger et al., 2002). We investigated the time course of presynaptic Ca²⁺ inflow and the gating properties of the presynaptic Ca²⁺ channels using whole-cell voltage-clamp recordings. Our approach revealed several fundamental functional parameters of synaptic transmission at the mossy fiber synapse, such as the proportion of Ca²⁺ channels that open during a presynaptic AP and the number of Ca²⁺ ions entering per spike.

Part of the results have been published previously in abstract form (Bischofberger et al., 2001).

	MATERIALS AND METHODS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

Slice preparation. Transverse 300-µm-thick slices were cut from the hippocampus of 20- to 26-d-old Wistar rats with a custom-built (Geiger et al., 2002) or a commercially available Vibratome (DTK-1000, Dosaka, Japan). The animals were killed by decapitation, in accordance with national and institutional guidelines. Slices were kept at 35°C for 30 min after slicing and then at room temperature. For the dissection and storage of slices, we used a saline containing (in mM): 64 NaCl, 25 NaHCO₃, 10 glucose, 120 sucrose, 2.5 KCl, 1.25 NaH₂PO₄, 0.5 CaCl₂, and 7 MgCl₂. For the experiments, the slices were transferred into a recording chamber and superfused with a physiological extracellular solution containing (in mM): 125 NaCl, 25 NaHCO₃, 25 glucose, 2.5 KCl, 1.25 NaH₂PO₄, 2 CaCl₂, and 1 MgCl₂ (equilibrated with 95% O₂/5% CO₂ gas mixture).

Electrophysiology. Mossy fiber boutons in stratum lucidum of the hippocampal CA3 region were visually identified by their size and location (3-4 µm apparent diameter) (see Fig. 1A) (Geiger and Jonas, 2000) using infrared differential interference contrast videomicroscopy (Stuart et al., 1993). Identification was confirmed by the small capacitance (~1 pF whole-cell capacitance readout of the amplifier) and the high input resistance (>1 G). A subset of boutons was filled with biocytin for 30 min in the whole-cell recording configuration. Slices were fixed in 4% paraformaldehyde, stained with Fluorescein Avidin D (Vector Laboratories, Burlingame, CA), and embedded with ProLong Antifade (Molecular Probes, Eugene, OR). Images were taken using a confocal laser scanning microscope (LSM 510, Zeiss, Göttingen, Germany) (see Fig. 1A).

Patch pipettes were pulled from borosilicate glass tubing (2.0 mm outer diameter, 0.7 mm wall thickness; Hilgenberg, Malsfeld, Germany). A modified Axopatch 200A amplifier (Axon Instruments, Foster City, CA) was used for current-clamp (I-Clamp fast) and voltage-clamp recording. The amplifier included a bridge-balance circuit for compensation of series resistance in the current-clamp mode, similar to that available in the Axopatch 200B. Current and voltage signals were filtered at 5 and 10 kHz, respectively, with a four-pole low-pass Bessel filter and stored online using a CED 1401plus interface (Cambridge Electronic Design, Cambridge, UK) connected to a personal computer. The sampling frequency was two to four times the filter frequency. Pulses were generated using commercial (CED) or self-made (P. Jonas) programs; the latter allowed us to apply previously recorded APs as voltage-clamp commands.

For whole-cell current-clamp recordings, we used 7-10 M patch pipettes filled with internal solution containing (in mM): 150 KMeSO₄, 0.2 EGTA, 2 MgCl₂, 2 Na₂ATP, 0.3 NaGTP, and 10 HEPES (the pH was adjusted to 7.3 with KOH). Bridge balance was used to compensate the series resistance. In addition, capacitance compensation was used to decrease the charging time of the pipette to <50 µsec. Resting potentials were between 65 and 80 mV. Membrane potentials were set to 80 mV by applying a small hyperpolarizing holding current if necessary. Stimulation of the mossy fiber tract was made with a patch pipette located in the stratum lucidum in subregion CA3c. A stimulus isolation unit (List, Darmstadt, Germany) was used to generate pulses with a duration of 200 µsec and amplitude of 5 to 10 V.

For whole-cell voltage-clamp recordings, we used 5-7 M pipettes filled with a solution containing (in mM): 135 CsCl, 10 EGTA, 4 MgCl₂, 4 Na₂ATP, 0.3 NaGTP, 10 Na₂-phosphocreatine, and 10 HEPES (the pH was adjusted to 7.3 with CsOH). The bath solution contained (in mM): 105 NaCl, 25 NaHCO₃, 25 glucose, 2.5 KCl, 1.25 NaH₂PO₄, 2 CaCl₂, 1 MgCl₂, 1 µM tetrodotoxin, 20 tetraethylammonium chloride, and 5 4-aminopyridine to block voltage-gated Na⁺ and K⁺ channels, respectively. Leak and capacitive currents were subtracted using two P/4 sequences within each protocol. Current traces shown in the figures represent the averages of two to five sweeps. Series resistance compensation was enabled in all experiments (compensation 80-90%; lag 20-30 µsec).

The series resistance was typically between 20 and 50 M. Assuming a membrane capacitance of ~1 pF (Geiger and Jonas, 2000), this would correspond to a voltage-clamp time constant  = R_s C_m of 20-50 µsec. If the series resistance exceeded a value of 50 M, the recordings were aborted. In some recordings, unclamped tail currents with very slow time course were apparent (these currents may have been generated in neighboring boutons). These recordings were discarded. All chemicals were obtained from Sigma (St. Louis, MO), Merck (Darmstadt, Germany), Riedel-de Haën, or Gerbu. Recordings were made at 23 ± 1°C.

Data analysis. The activation time course of the Ca²⁺ current was fitted with a monoexponential function with delayed onset:

(1)

where I₀ is the amplitude,  is the activation time constant, and  is the delay of Ca²⁺ channel activation. To account for the small delay introduced by the lag of series resistance compensation (20-30 µsec) and by electronic filtering (mostly at 5 kHz), the current trace was shifted in time by 100 µsec; with this shift, the end of the rectangular current pulse corresponded to the time when the tail current rose to ~50% of its peak amplitude. The time course of deactivation was fitted with a monoexponential function starting from 50-100 µsec after the peak of the tail currents to minimize contamination by residual capacitive artifacts. The number of Ca²⁺ ions was calculated from the total charge q as n = q N_A/z F with the Avogadro number N_A = 6.02 10²³/mol, the Faraday constant F = 96,485 C/mol, and z = 2. Time course fitting was performed using programs written in Pascal (P. Jonas) based on a modified Gauss-Newton algorithm.

The steady-state activation curve was fitted with a Boltzmann function of the form f(V) = 1/(1 + exp[(V_half  V)/V_slope]) with V_half = 3.9 mV and V_slope = 7.1 mV as best-fit parameters. The values for V_half and V_slope were then used to fit the I-V relationship with a modified Goldman-Hodgkin-Katz equation of the form:

(2)

with the voltage V, an amplitude factor P, a steepness factor C, and a parameter D determining current rectification and reversal potential (Sala, 1991). The best-fit parameters were P = 3.003 pA/mV, C = 80.36 mV, and D = 0.3933. The voltage dependence of activation time constants was fitted with the function:

(3)

where k₁ are k₂ are coefficients and V₁ and V₂ are steepness factors. The voltage dependence of current amplitudes and time constants was fitted using Prism 3.0 (GraphPad, San Diego, CA).

Amplitude and duration at half-maximal amplitude of APs were measured from baseline potential. Membrane potentials are given without correction for liquid junction potentials. The values indicate mean ± SEM. The error bars also represent SEM. The significance of differences was assessed by a two-tailed Wilcoxon-Mann-Whitney test (Prism 3.0) at the significance level (P) indicated.

Modeling. The simulations were performed with Mathematica 4.0 (Wolfram Research, Champaign, IL). A set of linear differential equations was defined for a kinetic model with four closed and one open state with voltage-dependent microscopic rate constants for the forward [_i(V)] and backward [_i(V)] transitions. The differential equations were defined using the Q-matrix approach of Colquhoun and Hawkes (1977) and numerically solved using Mathematica's NDSolve routine. The analysis of simulated data was identical to that of experimental data; the simulated activation and deactivation time course of the open state were fitted with a monoexponential function with delayed onset and an exponential decay, respectively. The values for activation , delay, deactivation , and steady-state activation were compared with experimental data by calculating the total sum of the squares of the differences. This sum was minimized by using the FindMinimum routine of Mathematica.

The microscopic rate constants were exponentially dependent on voltage as described by the equations:

(4)

with the best-fit parameters _1o = 4.04 msec¹, _1o = 2.88 msec¹, V₁ = 49.14 mV, _2o = 6.70 msec¹, _2o = 6.30 msec¹, V₂ = 42.08 mV, _3o = 4.39 msec¹, _3o = 8.16 msec¹, V₃ = 55.31 mV, _4o = 17.33 msec¹, _4o = 1.84 msec¹, and V₄ = 26.55 mV.

	RESULTS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

Whole-cell recordings were made from MFBs in acute rat hippocampal slices (Fig. 1). MFBs were identified by their small size, their small capacitance (~1 pF), and their high input resistance (>1 G) (Geiger and Jonas, 2000). A subset of the boutons was filled with biocytin and stained with Fluorescein Avidin D. Figure 1A shows a confocal image of a biocytin-filled MFB, which illustrates the staining of the parent axon and an adjacent MFB. The image also shows filopodial extensions originating from the boutons, which are highly characteristic structural properties of mossy fiber terminals (Acsády et al., 1998).

View larger version (44K): [in this window] [in a new window]   Figure 1.   Rapid time course of locally evoked and orthodromically propagated APs in MFBs. A, Confocal image of an MFB filled with biocytin during the recording and stained with fluorescein avidin D after fixation. Note that the axon runs through the stratum lucidum parallel to the CA3 pyramidal cell layer. B, Current-clamp recording from an MFB in whole-cell recording configuration. A small current injection (40 pA, 10 msec) reliably evoked an AP with large amplitude and rapid time course. C, Current-clamp recording of an AP evoked by extracellular stimulation of the mossy fiber tract. D, AP recorded from a granule cell soma.

The presynaptic AP is the primary event that activates presynaptic Ca²⁺ channels and thereby triggers transmitter release. Similar to other presynaptic elements (Borst and Sakmann, 1996; Sabatini and Regehr, 1996; Bischofberger and Jonas, 1997), the MFBs were shown to have APs with very rapid time course (Geiger and Jonas, 2000). Figure 1B shows a current-clamp recording from an MFB. A small current injection of 20-40 pA evoked an AP with an amplitude of 122.9 ± 2.4 mV and a half-duration of 915 ± 44 µsec (range, 540-1140 µsec; n = 13). Similarly, APs could be evoked by extracellular stimulation of the mossy fiber tract (Fig. 1C). The amplitude (122.8 ± 2.7 mV) and half-duration (852 ± 62 µsec; n = 6) of the AP evoked by remote stimulation were not significantly different from those evoked by direct current injection (p > 0.4). In contrast, the half-duration of APs recorded from granule cell somata was much longer, as shown in Figure 1D (2.06 ± 0.09 msec; n = 9; p < 0.01). Thus both locally evoked and orthodromically propagated APs in MFBs showed a fast time course that was significantly faster than APs in granule cell somata.

MFB Ca²⁺ channels have steep voltage dependence and rapid activation kinetics

To determine the proportion of Ca²⁺ channels opened by the fast presynaptic AP waveform, we analyzed the gating properties of the presynaptic Ca²⁺ channels in MFBs (Figs. 2-4). Figure 2A shows whole-cell voltage-clamp recordings of pharmacologically isolated Ca²⁺ currents evoked by 20 msec voltage steps from 70 mV to +60 mV, and Figure 2B illustrates the corresponding current-voltage (I-V) relationship. The Ca²⁺ currents were activated above 40 mV and reached a maximal current amplitude of 98 ± 11 pA at 0 mV (n = 16). At more positive potentials the inward currents decreased, resulting from a reduction in the driving force (Augustine et al., 1985; Borst and Sakmann, 1998).

View larger version (24K): [in this window] [in a new window]   Figure 2.   Presynaptic voltage-gated Ca2+ currents in MFBs. A, Voltage-clamp recording of Ca2+ currents evoked by 20 msec voltage pulses from a holding potential of 80 mV to potentials of 70 to 60 mV in an MFB. B, The maximal current amplitude during the pulses is plotted against pulse potential (n = 16) and fitted with Equation 2 (continuous line; see Materials and Methods). C, To obtain the steady-state activation curve, tail current integrals were plotted against the amplitude of the preceding pulse (5 msec duration). Data were normalized to the maximal value in each experiment, averaged across experiments, and then normalized to the maximal average value (n = 6). The activation curve was fitted with a Boltzmann function (continuous line). norm., Normalized.

To obtain the steady-state activation curve, we plotted the integral of the tail currents against the voltage of the preceding pulse (Fig. 2C). Because the tail currents were measured at the same potential, the integral gives a precise measure of the number of channels open at the end of the preceding pulse. The steady-state activation data were adequately fitted by a Boltzmann function with a slope factor of 7.1 mV and a midpoint potential of 3.9 mV. We then fitted the bell-shaped I-V relation in Figure 2B with the product of a Boltzmann function representing channel activation and a modified Goldman-Hodgkin-Katz equation describing the driving force for ion flow (Sala, 1991). The parameters of the Boltzmann function were constrained to the previously determined values. From the fitted curve, the extrapolated reversal potential was determined to be 75.0 mV (Fig. 2B). In conclusion, presynaptic Ca²⁺ channels in MFBs show a high activation threshold and a steep voltage dependence.

We next examined the activation and deactivation kinetics of presynaptic Ca²⁺ channels. The time course of activation could be well fitted by a monoexponential function with delayed onset relative to the onset of the pulse (Fig. 3A,B). The activation time constant  and the delay are plotted in Figure 3C as a function of voltage. The activation  was fast and voltage dependent, ranging from  = 842 ± 137 µsec at 10 mV to 201 ± 35 µsec at 50 mV (n = 6). The voltage dependence could be fitted by Equation 3 with coefficients k₁ = 1.12 msec¹ and k₂ = 0.14 msec¹ as well as slope factors V₁ = 31.5 mV and V₂ = 8.6 mV. In contrast, the delay was independent of voltage, with a mean value of ~200 µsec. Linear regression revealed that the slope of the fitted line was not significantly different from 0 (p > 0.4).

View larger version (17K): [in this window] [in a new window]   Figure 3.   MFB Ca2+ currents show fast voltage-dependent activation kinetics. A, Ca2+ currents evoked by rectangular voltage pulses from 30 to 50 mV were analyzed. The part indicated by the horizontal bar is shown in B at an expanded time scale. B, The activation of the Ca2+ currents could be well fitted by a monoexponential function with a short delay relative to the onset of the pulse (thick superimposed lines). C, The activation time constant  () and the delay () are plotted against voltage (n = 6). The voltage dependence of the activation  was fitted with Equation 3 (continuous line). The voltage dependence of the delay was fitted by linear regression (dashed line).

Because the amount of Ca²⁺ inflow depends on how long the channels remain open during the presynaptic AP, we further analyzed the deactivation kinetics after a voltage step from 0 mV to negative potentials (10 mV to 60 mV) (Fig. 4A). As shown in Figure 4B, the deactivation could be adequately fitted by a monoexponential function. The deactivation  was fast, ranging from 813 ± 90 µsec at 10 mV to 148 ± 11 µsec at 60 mV (n = 6). The voltage dependence could be described with an exponential function with an e-fold change per 15.0 mV (Fig. 4C). Thus both activation and deactivation time constants were fast and highly voltage dependent.

View larger version (13K): [in this window] [in a new window]   Figure 4.   MFB Ca2+ currents show fast voltage-dependent deactivation kinetics. A, A voltage pulse to 0 mV was used to activate the Ca2+ channels. The deactivation time course was analyzed after the membrane potential was stepped back to different potentials. The part indicated by the horizontal bar is shown in B at an expanded time scale. B, The deactivation time course could be well fitted with a monoexponential function (thick superimposed lines). C, The deactivation time constant  is plotted against voltage (n = 6; same MFBs as in Fig. 3). The voltage dependence of the deactivation  was fitted by a monoexponential function (continuous curve).

Presynaptic Ca²⁺ channels are effectively opened by MFB APs

To study the presynaptic Ca²⁺ inflow during natural stimuli, we used previously recorded AP waveforms as voltage-clamp commands (Scroggs and Fox, 1992) (Fig. 5). A propagated AP evoked a large and brief Ca²⁺ inflow starting at the peak of the AP (Fig. 5A). During the repolarization phase the current rapidly increased, reaching a peak amplitude of 187 ± 36 pA (n = 9). This current was substantially larger (177 ± 17%) than the maximum peak current amplitude during rectangular voltage pulses to 0 mV in the same MFBs (102 ± 16 pA; p < 0.01). The half-duration of the AP-evoked Ca²⁺ current was very short (540 ± 12 µsec; n = 9), most probably because of the fast deactivation of the channels at negative potentials. Similar results were obtained with a locally evoked AP waveform (Fig. 5C, dashed line). The relative peak amplitude and half-duration were 175 ± 10% and 590 ± 19 µsec (n = 18), very similar to the respective values for the propagated AP. If data with both waveforms were pooled, a peak amplitude of 171 ± 20 pA (corresponding to a relative amplitude of 173 ± 9%), a half-duration of 579 ± 15 µsec, and a total charge of 119 ± 13 fC were obtained (n = 24). This corresponds to an inflow of ~370,000 Ca²⁺ ions per single AP.

View larger version (26K): [in this window] [in a new window]   Figure 5.   Rapid and effective activation of Ca2+ currents during AP waveforms. A, An AP waveform applied as a voltage-clamp command (top trace) instead of a rectangular voltage pulse evoked a transient Ca2+ inward current in an MFB (bottom trace). The orthodromically propagated AP was previously recorded from a different MFB. B, For a 5 msec prepulse period the command voltage was digitally set to +40 mV, which evoked a slightly larger Ca2+ peak current (continuous line) as compared with control (dashed line). C, An AP recorded from an MFB (dashed line) and a much slower somatic AP waveform (continuous line) evoked Ca2+ currents with different amplitudes and time courses (bottom traces). Both somatic and MFB AP were evoked by direct current injection. D, The amplitude and half-duration of currents evoked by different AP waveforms are shown. The peak current was normalized to the maximal current amplitude of the I-V relationship (at 0 mV) in the same boutons (corresponding to 100%). The bar graph summarizes data from MFB AP experiments (n = 24), prepulse experiments (2-5 msec; n = 9), and soma AP experiments (n = 5); in all cases the waveforms were applied to MFBs.

To estimate the relative open probability (P_open) of the Ca²⁺ channels during the AP, we added a prepulse to +40 mV to the AP waveform (Fig. 5B,D) (Borst and Sakmann, 1998). According to the steady-state activation curve (Fig. 2C), this pulse should activate the Ca²⁺ channels with a maximal P_open. The peak amplitude of the evoked Ca²⁺ currents, however, was only slightly larger as compared with control (124 ± 3% of control; p < 0.01; n = 9). This indicates that the presynaptic Ca²⁺ channels are opened very effectively by the AP waveform and that the peak P_open with a natural stimulus reaches ~80% of the maximal value.

To further elucidate the relation between AP waveform and Ca²⁺ channel activation, we compared the Ca²⁺ current evoked by a fast MFB AP with that evoked by a slow somatic AP waveform (Fig. 5C,D). The somatic AP evoked a Ca²⁺ current with a half-duration of 1232 ± 51 µsec, significantly larger than that evoked by the brief AP (p < 0.01). However, the peak amplitude was reduced (84.6 ± 1.1% of control; p < 0.01; n = 5). This decrease in peak current amplitude appears to be fundamentally different from the increase in current during AP broadening reported previously for both somatic (Scroggs and Fox, 1992; Wheeler et al., 1996) and presynaptic Ca²⁺ channels (Augustine, 1990; Sabatini and Regehr, 1997). In conclusion, the data suggest that MFB Ca²⁺ channels are effectively opened by the presynaptic APs. To understand the complex dynamic process of activation and deactivation during AP waveforms, we developed a computational model of Ca²⁺ channel gating.

Ca²⁺ channel gating in MFBs can be described by a five-state kinetic model

The pore-forming ₁ subunit of voltage-gated Ca²⁺ channels consists of four domains, each having a positively charged S4 segment, which is believed to be involved in the voltage-dependent gating of the channels (Hille, 2001). Therefore, a model with four voltage-dependent transitions between four closed states and one open state was used (Fig. 6A). The microscopic rate constants _i and _i were assumed to be exponentially dependent on voltage (Eq. 4) (Fig. 6B). For a given parameter set, the occupancy of the open state during rectangular voltage pulses was simulated, and the resulting traces were fitted with exponential functions, similar to the experimental data. The parameters for the rate constants _i and _i were changed until the best approximation of the experimental values for activation , delay, deactivation , and steady-state activation were achieved. Figure 6, C and D, shows a comparison of the experimental data with the predictions of the final model (continuous lines). In the final set of rate constants, the last transition shows the steepest voltage dependence (V_i = 49, 42, 55, and 27 mV), suggesting cooperativity in channel gating (Fig. 6B) (see also Materials and Methods).

View larger version (25K): [in this window] [in a new window]   Figure 6.   A kinetic model of Ca2+ channel gating in MFBs. A, A serial model with four closed states and one open state was developed (top panel). The occupancy of the open state was simulated (bottom panel), and the resulting traces were fitted with a monoexponential function with delayed onset, in the same way as the experimental data. Imax is the current corresponding to an open probability of 1. Pulse from 80 to 0 mV. B, The microscopic rate constants for the transitions i(V) and i(V) as calculated according to Equation 4, using the best-fit parameters given in Materials and Methods. Note the different steepness of the voltage dependence of the rates. C, Comparison of measured activation  (filled circles), deactivation  (open circles), and delay (squares) with the values predicted by the model (continuous lines). D, Comparison of the measured steady-state activation (filled circles) with the steady-state activation curve of the model (continuous line).

We then simulated the Ca²⁺ inflow during APs, using the established model of Ca²⁺ channel gating and the driving force from the I-V relation fitted with Equation 2 (Fig. 7). If the brief MFB AP was applied as a voltage command, the simulated Ca²⁺ current had a peak amplitude of 161 pA and a half-duration of 596 µsec. The peak amplitude corresponded to 176% of the current amplitude during a rectangular voltage pulse to 0 mV, very similar to the experimental data (relative current amplitude 173%; half-duration 579 µsec) (Fig. 5). As shown in Figure 7A, the channels started to open during the rising phase of the AP and reached an open probability of 51% at the peak of the AP. The maximal open probability occurred during the early repolarization phase at a potential of 15 mV (P_open = 90%). The peak Ca²⁺ inward current occurred slightly later, at a potential of 20 mV (P_open = 68%). Subsequently, the channels closed very rapidly and deactivated before complete repolarization to the resting potential. Consistent with the effective opening of the Ca²⁺ channels during the MFB AP, the peak current amplitude was only slightly increased by a 5 msec prepulse to 40 mV (Fig. 7B).

View larger version (28K): [in this window] [in a new window]   Figure 7.   High open probability of the model Ca2+ channels during AP waveforms. A, A propagated MFB AP was used as a voltage command to simulate the activation of the model channels. The calculated open probability (gray line) was multiplied by the driving force for Ca2+ using Equation 2 to simulate the Ca2+ current. B, A 5 msec prepulse leads to a slight increase of the Ca2+ current (continuous line) as compared with control (dashed line). C, Comparison of the MFB AP (dashed line) with a slower somatic AP (continuous line). Note that the peak of the Ca2+ current occurs at different potentials, as indicated. D, Comparison of the relative peak current amplitude and the half-duration during an MFB AP, the prepulse simulation, and the soma AP application (filled bars). For the relative peak current, 100% corresponds to the simulated current amplitude during a rectangular voltage pulse to 0 mV.

To examine the mechanisms underlying the reduction in peak amplitude of the Ca²⁺ current during the slower somatic AP (Fig. 5C), we used simulations to compare Ca²⁺ channel activation by fast and slow APs. Similar to the experimental data, the simulated Ca²⁺ current during a broad somatic AP had a prolonged time course and a reduced amplitude (Fig. 7C). The simulation shows that the reduction in peak amplitude is caused by a reduction in driving force at this point (10 vs20 mV). By contrast, the open probability of the channels at the peak of the Ca²⁺ current was very similar. Figure 7D shows a comparison of the relative peak amplitude and half-duration of simulated Ca²⁺ currents evoked by different waveforms. The simulated values for the MFB AP were in close agreement with experimentally determined values (Fig. 5). The results of experiments and modeling converge toward the conclusion that a brief AP waveform leads to efficient and rapid activation of the Ca²⁺ channels, resulting in a high peak open probability.

Open probability of presynaptic Ca²⁺ channels is highly sensitive to changes in AP waveform

The shape of the presynaptic AP in MFBs is not constant but regulated in an activity-dependent manner (Geiger and Jonas, 2000). Thus we systematically examined the effects of modified AP waveforms, scaled in amplitude and shape in comparison with the original MFB AP (Fig. 8). Figure 8A shows the effect of amplitude scaling on the evoked Ca²⁺ inflow, and Figure 8B illustrates plots of peak amplitude and charge as a function of AP amplitude. The simulations show that the control AP waveform (vertical lines) is a very effective stimulus, producing a presynaptic Ca²⁺ signal with near-maximal peak amplitude and total charge (89 and 98% of the maximal value, respectively). By contrast, a reduction of the AP amplitude by Na⁺-channel inactivation during high-frequency activity or steady-state depolarization, for example by presynaptic kainate receptors, will substantially reduce the presynaptic Ca²⁺ inflow (Kamiya and Ozawa, 2000; Schmitz et al., 2000).

View larger version (36K): [in this window] [in a new window]   Figure 8.   Presynaptic Ca2+ inflow is highly sensitive to changes in AP amplitude and shape. A, The amplitude of the measured MFB AP was scaled from 10 to 120% in 10% steps and used to activate the Ca2+ channel model. B, The resulting peak amplitude and the total charge were plotted against the AP amplitude. The amplitude of the measured AP is indicated by the dashed vertical lines. C, The decay phase of the AP waveform was scaled by digitally shrinking or expanding the timescale of the trace after the peak from 50 to 500% in 50% steps. D, The resulting peak amplitude and the total charge were plotted against the AP half-duration. The half-duration of the measured AP is indicated by the dashed vertical lines. In B the data points were connected by straight lines, and the curves in D are fits with an exponential function plus a constant (top graph) or linear function (bottom graph).

Similarly, we modified the half-duration of the AP waveform by slowing the time course of repolarization in comparison with the MFB AP (Fig. 8C,D). The peak amplitude was exponentially dependent on the half-duration (Fig. 8D, top graph). In contrast, the total charge could be fitted by linear regression (Fig. 8D, bottom graph), yielding a slope of 73 fC/msec. Thus the model predicts a total Ca²⁺ inflow of ~77-121 fC for the experimental half-durations ranging from 540 to 1140 µsec. Furthermore, it explains the previous observation that dynamic AP broadening leads to a decrease in peak amplitude but an increase in total charge of presynaptic Ca²⁺ inflow (Geiger and Jonas, 2000).

In conclusion, the simulations show that the natural AP is a highly effective stimulus for the activation of the presynaptic Ca²⁺ channels. Additionally, the Ca²⁺ signal can be regulated via the half-duration of the presynaptic AP waveform.

Ca²⁺ channel gating is optimal for large Ca²⁺ inflow

Similarly, we examined the effects of alterations in channel gating on the amplitude and charge of Ca²⁺ inflow (Fig. 9). Figure 9A shows the effects of slower gating, generated by multiplication of all rates with constant factors in the range 1-0.1, and Figure 9B shows the effects of acceleration of gating, using factors in the range 1-10. In all simulations, the natural MFB AP waveform was used as a stimulus. Plots of peak amplitude and total charge against the scaling factor indicate that gating kinetics is a critical determinant of the total Ca²⁺ inflow (Fig. 9C,D). Surprisingly, both slowing down and speeding up the rate constants reduced the Ca²⁺ peak current and the integral. The peak amplitude and total charge produced by the native channels (scaling factor of 1) were 99 and 97% of the maximal values, which were reached with factors slightly below 1. Furthermore, both slowing down and speeding up of the rates lead to prolonged time course of Ca²⁺ inflow. In particular, the acceleration of the rates by a factor of >2 leads to a biphasic Ca²⁺ current, increasing the total time interval during which Ca²⁺ inflow occurs (Fig. 9B). In conclusion, these simulations unequivocally show that the gating of presynaptic Ca²⁺ channels in MFBs is optimal for producing a transient Ca²⁺ inflow with maximal amplitude and minimal duration. Whether this conclusion also holds true at physiological temperatures remains to be established. However, because the Q₁₀ values for AP duration (~2.2) (Geiger and Jonas, 2000; this paper) and Ca²⁺ channel activation kinetics are similar (~2.5) (Swandulla and Armstrong, 1988), this appears to be very likely.

View larger version (25K): [in this window] [in a new window]   Figure 9.   Presynaptic Ca2+ inflow is highly sensitive to changes in gating kinetics. A, All rate constants in the kinetic model were multiplied by a constant factor (1-0.1 in steps of 0.1) to selectively slow channel gating without affecting steady-state activation. Simulated Ca2+ currents are shown superimposed. B, The gating was accelerated by multiplying rate constants with a constant factor (1-10 in steps of 1). C, D, Peak amplitude (C) and charge (D) of the simulated current, plotted against the scaling factor on a logarithmic scale. The properties of the original Ca2+ channel are indicated by the vertical dashed lines. Curves in C and D represent cubic spline interpolations.

	DISCUSSION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

The present results provide the first description of Ca²⁺ channel gating in a cortical presynaptic terminal. The major finding was that the fast activation kinetics of the channels leads to a high open probability and a remarkably large Ca²⁺ inflow of ~370,000 Ca²⁺ ions during a single AP. The gating of presynaptic Ca²⁺ channels appears to be precisely tuned to achieve a maximal Ca²⁺ influx during a minimal period of time.

Rapid gating of presynaptic Ca²⁺ channels

The gating of presynaptic Ca²⁺ channels could be adequately described by a serial gating model with four closed states and one open state. In contrast, neither alternative models with two or three closed states nor Hodgkin-Huxley models with an integer number of independent gating particles provided a sufficient description of the data (J. Bischofberger, unpublished data). In the models with two or three closed states, the delay of activation was smaller than that observed experimentally. In Hodgkin-Huxley models, deactivation is faster than activation at the same potential, with a ratio that approaches the number of gating particles (Kay and Wong, 1987; Zidanic and Fuchs, 1995; Mennerick and Matthews, 1998). Thus the functional properties of presynaptic Ca²⁺ channels in MFBs are inconsistent with the assumption of independently moving gating particles.

Our model suggests that the voltage dependence differs among the transition rates. This has to be interpreted as a different movement of the S4 segments, the putative voltage sensors, because the number of positive charges per S4 segment is comparable among domains (approximately five) (Soong et al., 1993). For the first three transitions, the steepness factors range from 42 to 55 mV, which would correspond to an S4 segment movement by 9-12% along the total electric field. In contrast, for the final transition leading to the open state, the steepness factor is 27 mV, which would correspond to an S4 segment movement by 19%. Interdomain differences in voltage-dependent movement of S4 segments were experimentally demonstrated for voltage-dependent Na⁺ channels (Cha et al., 1999). An analogous biophysical approach will reveal whether similar interdomain differences exist in voltage-gated Ca²⁺ channels, as our results would suggest.

Efficiency and timing of Ca²⁺ channel opening during single APs

The activation kinetics of the presynaptic Ca²⁺ channels in MFBs appear to be much faster than the activation of Ca²⁺ channels in invertebrate presynaptic terminals (Llinás et al., 1981; Wright et al., 1996). For the squid giant synapse it was suggested that the relative open probability of Ca²⁺ channels during a single AP was ~10% (Pumplin et al., 1981; Augustine, 1990), markedly less than the value estimated for the MFB (~90%). The gating is also faster than that described for somatodendritic high-voltage-activated Ca²⁺ channels in CA1 pyramidal neurons (Kay and Wong, 1987). This may be correlated to the slower time course of somatodendritic voltage signals, e.g., synaptic potentials or backpropagating APs (Magee and Johnston, 1995; Normann et al., 2000).

The activation kinetics of the Ca²⁺ channels in MFBs, however, is similar to that reported for presynaptic Ca²⁺ channels in giant vertebrate synaptic terminals (Zidanic and Fuchs, 1995; Borst and Sakmann, 1998; Mennerick and Matthews, 1998). In the calyx of Held, single APs evoke a Ca²⁺ current with a relative peak open probability of ~70% and an average half-duration of ~400 µsec (24°C) (Borst and Sakmann, 1998), comparable with the values reported here. Thus, although the two types of synapses differ in morphological properties, subunit composition of postsynaptic receptors, and functional role in the neuronal circuit, the efficacy and timing of presynaptic Ca²⁺ inflow appear to be similar (Von Gersdorff and Borst, 2002).

In the MFB, the Ca²⁺ channels open very early during the rising phase of the AP with a relative P_open of ~50% at the peak of the AP; however, no substantial current can be detected at this point, because of the small driving force. The Ca²⁺ inflow is restricted to the repolarization phase of the AP (Figs. 5A, 7A). In contrast, for parallel fiber synapses in the cerebellum, it was reported that rapid Ca²⁺ channel gating leads to substantial Ca²⁺ current during the upstroke and peak of the presynaptic AP (Sabatini and Regehr, 1996, 1997). This situation appears to be very different from that in the MFB because the experimentally determined I-V relationship for the Ca²⁺ currents in the MFB is obviously inconsistent with a large driving force at the peak of the AP (at ~45 mV) (Fig. 2B). If these discrepancies are not caused by technical difficulties in deriving the voltage and Ca²⁺ current time course from fluorescence signals (Sabatini and Regehr, 1996, 1997), they may suggest a synapse-specific difference in presynaptic ion flow.

How many Ca²⁺ ions are necessary for transmitter release?

The present results provide quantitative estimates of fundamental parameters of the early presynaptic events that are relevant for both efficacy and timing of synaptic transmission. We found that the average peak amplitude of the presynaptic Ca²⁺ current evoked by a natural AP is 170 pA. With a single-channel current of 0.2 pA at physiological external Ca²⁺ concentrations (Gollasch et al., 1992), this corresponds to 850 Ca²⁺ channels open at the peak in a presynaptic terminal. The total Ca²⁺ inflow evoked by a single AP was 120 fC, corresponding to ~370,000 Ca²⁺ ions per bouton.

MFBs have multiple release sites (up to 37 in an incompletely reconstructed large MFB) (Chicurel and Harris, 1992). Thus the measured presynaptic Ca²⁺ current would approximately correspond to 23 Ca²⁺ channels open at the peak at a single release site, producing an inflow of ~10,000 Ca²⁺ ions per site. Although these are only rough estimates, the results are consistent with previous suggestions at boutons of neocortical pyramidal cells (~40 channels per bouton, ~5500 Ca²⁺ ions) (Koester and Sakmann, 2000) and the calyx of Held (~20 channels per site, ~13000 Ca²⁺ ions) (Borst and Sakmann, 1996; Sätzler et al., 2002). Furthermore, they are consistent with the cooperativity between different types of Ca²⁺ channels in triggering transmitter release at the mossy fiber-CA3 synapse (Castillo et al., 1994) and other cortical glutamatergic synapses (Luebke et al., 1993; Wheeler et al., 1994; Dunlap et al., 1995). Although we cannot exclude a subpopulation of release sites endowed with a single Ca²⁺ channel (Stanley, 1997), our results suggest that most of the sites are controlled by multiple channels. This may increase the reliability of excitation-secretion coupling in central glutamatergic synapses.

Functional significance for synaptic transmission at MFB-CA3 pyramidal neuron synapse

The quantitative properties of the presynaptic Ca²⁺ inflow are also critical for the timing of transmitter release. A large Ca²⁺ signal may help to minimize synaptic delay. Transmitter release requires the binding of multiple Ca²⁺ ions to the Ca²⁺ sensor (Augustine, 2001). As shown for the calyx of Held, the sequential binding of multiple Ca²⁺ ions introduces a significant delay between the Ca²⁺ inflow and the transmitter release (Schneggenburger and Neher, 2000). This delay was strongly dependent on the Ca²⁺ concentration. Thus, a large Ca²⁺ signal will provide a rapid onset of neurotransmitter release. Additionally, the fast deactivation of the presynaptic Ca²⁺ channels may be important for the termination of exocytosis. The rapid Ca²⁺ signaling will be a critical determinant of the precise timing of transmitter release at the MFB to CA3-pyramidal cell synapse, where the half-width of the first latency distribution is ~500 µsec (Jonas et al., 1993). Similar rules may apply for synapses formed by the mossy fiber system onto other types of target cells, e.g., at the granule cell to basket cell synapse, formed by mossy fiber collaterals on inhibitory interneurons (Geiger et al., 1997).

The precise timing during single APs may be relevant for the temporal encoding of information in the hippocampus (Lisman, 1999). It was shown that granule cells and pyramidal cells fire APs in a specific temporal relationship to the theta rhythm when the animal passes through the place field of the cell (Jung and McNaughton, 1993; O'Keefe and Recce, 1993). When the animal is in the center of the place field of a given neuron, this neuron fires APs earlier in the theta cycle than neurons with adjacent place fields (Skaggs and McNaughton, 1996; Skaggs et al., 1996). For temporal coding with high fidelity, neurons with the same place field should fire exactly at the same time (Lisman, 1999). Because the mossy fiber tract is the major excitatory pathway that connects the associative network in the dentate gyrus/hilus with that in the CA3 region, the precise timing of presynaptic Ca²⁺ inflow and transmitter release might be important for the correct temporal sequence of place cell firing and, more generally, for the temporal coding of episodic memory.

	FOOTNOTES

Received June 14, 2002; revised Sept. 19, 2002; accepted Sept. 30, 2002.

J.B. was supported by grants from the Deutsche Forschungsgemeinschaft (Bi 642/1-2 and SFB 505/C9). We thank Dr. U. Kraushaar, Dr. S. Hefft, and C. Schmidt-Hieber for critically reading this manuscript, F. Heyde for secretarial help, and A. Blomenkamp and K. Winterhalter for technical assistance.

Correspondence should be addressed to Dr. Josef Bischofberger, Physiologisches Institut, Universität Freiburg, Hermann-Herder-Strasse 7, D-79104 Freiburg, Germany. E-mail: Josef.Bischofberger{at}physiologie.uni-freiburg.de.

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