European Journal of Neuroscience, Vol. 24, pp. 1591–1605, 2006
doi:10.1111/j.1460-9568.2006.05028.x
Ryanodine receptor–transmitter release site coupling increases quantal size in a synapse-specific manner Tyler W. Dunn and Naweed I. Syed Hotchkiss Brain Institute, Department of Cell Biology and Anatomy, Faculty of Medicine, University of Calgary, 3330 Hospital Drive, NW, Calgary, Alberta T2N 4N1, Canada Keywords: Ca2+, Lymnaea, neurotransmitter release
Abstract The mechanisms by which presynaptic neurones differentially regulate synaptic transmission with multiple postsynaptic targets in the brain are not fully understood. Using intracellular sharp electrode and whole-cell voltage-clamp recordings of soma–soma synapses between identified Lymnaea neurones, we provide direct evidence that quantal size is regulated presynaptically through the coupling of multiple release sites. This coupling effectively multiplies quantal size, thereby providing significant influence over parameters of synaptic transmission that are influenced by quantal size, such as the variance in transmitter release at stationary release probabilities. Variation in the degree of coupling is dependent on the identity of the postsynaptic cell, even though the variation in quantal size is of presynaptic origin. We have therefore demonstrated the presence of a novel mechanism by which presynaptic neurones may differentially regulate quantal size at select synaptic connections, in turn providing them with a means of regulating synaptic transmission with multiple postsynaptic cells.
Introduction Ryanodine receptors (RyRs) are Ca2+ channels to intracellular Ca2+ stores of the sarco(endo)plasmic reticulum and have long been known to participate in excitation–contraction coupling in muscle fibres (Fill & Copello, 2002). Ca2+ activation of the RyR leads to Ca2+-induced Ca2+ release from intracellular stores, which effectively amplifies the Ca2+ signal via positive feedback through these same receptors. Recent evidence suggests that similar RyR-dependent Ca2+ signals participate in transmitter release at some synapses (see Collin et al., 2005 for review). According to the quantal hypothesis, the spontaneous miniature postsynaptic current (mPSC) represents the release of a single vesicle of transmitter, many of which are released when synchronized by Ca2+ influx associated with the presynaptic action potential (Del Castillo & Katz, 1954). At some synapses, largeamplitude mPSCs (many times larger than the expected amplitude of a single vesicle of transmitter) appear to be multivesicular events, synchronized by an internal Ca2+ signal involving RyRs (Llano et al., 2000; Sharma & Vijayaraghavan, 2003; Gordon & Bains, 2005). Such multiple release site synchronization outside the action potential begs the question of whether these Ca2+-sensitive RyRs interact with the Ca2+ signal generated with an action potential. Investigation of the effects of RyR inhibition with micromolar ryanodine suggests presynaptic involvement of RyRs in long-term depression in neonatal rat hippocampus (Caillard et al., 2000) and cultured CA3 hippocampal synapses (Unni et al., 2004) that argue for the involvement of RyRs in evoked transmitter release. The apparent involvement of RyRs in mossy fibre N-methyl-d-aspartate receptorindependent long-term potentiation adds further complexity to the possible contribution of RyRs to transmitter release (Lauri et al.,
Correspondence: Dr Naweed I. Syed, as above. E-mail:
[email protected] Received 7 April 2006, revised 15 June 2006, accepted 20 June 2006
2003). Indeed, the potential significance of RyR-dependent signalling in transmitter release is made evident by the observation of a 70% reduction in transmitter release in the presence of ryanodine at cerebellar basket cell terminals (Galante & Marty, 2003). Although the purpose of such complexity in the Ca2+ signal involved in transmitter release has yet to be proposed, this recent evidence suggests that Ca2+ sources other than the extracellular space participate in evoked release at some synaptic connections. In this study, synapses between functionally well-defined neurones from the mollusc Lymnaea stagnalis were reconstructed in cell culture in a soma–soma configuration. We have previously demonstrated that the soma–soma synapses between Lymnaea neurones are both morphologically and electrophysiologically similar to those seen in vivo (Feng et al., 1997, 2000; Hamakawa et al., 1999; Smit et al., 2001; Woodin et al., 2002; Munno et al., 2003) and are also similar to those that form between the neurites of cultured neurones (Syed et al., 1990; Spencer et al., 1999). Specifically, the identified respiratory central pattern-generating neurone, visceral dorsal 4 (VD4), makes cholinergic excitatory or inhibitory synapses with a variety of its postsynaptic targets (Munno et al., 2003). In addition to their somata, the synaptic sites of both the pre- and postsynaptic neurones are also readily amenable to electrophysiological and pharmacological manipulations, providing improved access to synaptic sites and eliminating several confounding factors, such as large electrotonic differences between release sites. The soma–soma synapses enabled us to measure both action potential-evoked postsynaptic currents (PSCs) and mPSCs that were recorded at various release probabilities. Using intracellular sharp electrode and whole-cell voltage-clamp recordings, we provided direct evidence that multiple presynaptic release sites can share a single release probability so that the release unit is a multiple of the univesicular current. Through the buffering of presynaptic Ca2+ with EGTA and blocking RyRs with ryanodine, we demonstrated that some
ª The Authors (2006). Journal Compilation ª Federation of European Neuroscience Societies and Blackwell Publishing Ltd
1592 T. W. Dunn and N. I. Syed synaptic connections have complex quanta that are multivesicular and require Ca2+ travel over relatively long intracellular distances. As such, our data were consistent with results obtained at other synapses and collectively suggested that the large-amplitude mPSCs are indeed multivesicular release (MVR) events (Llano et al., 2000; Sharma & Vijayaraghavan, 2003; Gordon & Bains, 2005). The effect of our interventions on quantal size also translated into an observed effect on the evoked synaptic event; ryanodine-sensitive MVR increased PSC variation, greatly affecting synaptic transmission. By recording from four serially paired neurones, we have shown that, although the variation in quantal size is presynaptic in nature, the extent of release site coupling at any given synaptic connection is probably determined by the identity of the postsynaptic target. Such selective, postsynapticcell-specific control of transmitter release efficacy provides a unique mechanism by which synapses could selectively and differentially modulate the statistical properties of transmitter release at multiple postsynaptic targets.
Materials and methods Animals and cell culture Experiments were conducted on neurones isolated from the central ring ganglia of the fresh-water snail L. stagnalis (Syed et al., 1990). Specifically, snails 10–15 mm in length (2–4 months old) were used in all experiments. The central ring ganglia were isolated from the intact animals and prepared for cell culture. The neurones VD4 (presynaptic) and a medial, left pedal A or E cluster (LPeA) (postsynaptic) were isolated as described previously (Syed et al., 1999) and cultured in a soma–soma configuration (Feng et al., 1997) in the presence of brain conditioned medium (Hamakawa et al., 1999; Syed et al., 1999; Munno et al., 2003). Simultaneous intracellular and whole-cell recordings were made with the paired cells after 14–24 h of pairing. In most instances, the paired cells established strong, inhibitory, cholinergic synaptic connections that exhibited a d-tubocurarine-sensitive chloride current, as observed in other molluscan species (Yeoman et al., 1993; Kehoe & McIntosh, 1998). The brain conditioned medium was replaced with normal Lymnaea saline prior to recordings (containing in mm: 51.3 NaCl; 1.7 KCl; 4.1 CaCl2; 1.5 MgCl2; 5 HEPES; 5 glucose, pH 7.9). The release probability was slowly changed in all experiments (unless stated otherwise) by perfusing either high-Ca2+ saline (10 mm Ca2+ ⁄ no added Mg2+), normal saline or normal saline with 30 lm Cd2+ to increase and decrease the transmitter release probability, respectively. Although a zero-Ca2+ saline (5 mm EGTA and Mg2+ increased to 5.6 mm) gave similar results, the whole-cell seals were most stable when Cd2+ was added to the normal saline.
Electrophysiology Sharp electrodes (35–55 MW) were back-filled with a saturated solution of K2SO4 for intracellular electrode recordings from the presynaptic VD4. Presynaptic action potentials and resting membrane potentials were controlled by current injection. Signals were amplified with a Cygnus intracellular amplifier (IR-283) and recorded with pclamp (Axon Instruments) with continuous acquisition at 5 kHz. Whole-cell voltage-clamp recordings of the postsynaptic cell (LPeAi) were carried out in most experiments in order to improve mPSC resolution. Signals were amplified with an Axopatch 1D (Axon Instruments) in soma–soma pairs, with an EPC-9 double patch amplifier (HEKA Elektronik) for recording from triple and quadruple soma configurations, and a Multiclamp 700B (Axon Instruments) for
the EGTA and ryanodine experiments (data acquired at 10 kHz). Postsynaptic patch electrodes were filled with a solution comprising (in mm): 35 CsCl; 10 HEPES; 2 ATP-Mg; 1 CaCl2; 10 EGTA, pH 7.4, elevating the intracellular chloride to enhance the driving force for the PSC. Patch electrodes were pulled on a Sutter P97 electrode puller and subsequently fire polished. These pipettes had tip resistances in the range 1.5–2.5 MW, leading to series resistance values (Rs) of 3– 8 MW. The series resistance was compensated 70–80% with the Axopatch and Multiclamp, and to optimal levels with the EPC-9 (avoiding oscillation). If the Rs increased over 8.5 MW or the seal resistance changed during a recording, then the experiment was terminated and the data were not included for further analysis. Liquid junctional potentials were corrected before seal formation and the leak current was not subtracted. Recordings typically lasted 20–30 min during which both evoked PSCs and mPSCs were measured while the probability of release was slowly changed by altering Ca2+ influx with Cd2+. LPeA cells varied slightly in size, with membrane capacitance ranging from 60 to 100 pF. Cells with >100 pF capacitance were not used for whole-cell experiments. For presynaptic whole-cell conditions, VD4 was held at )90 mV, and a whole-cell capacitance and access resistance were monitored every couple of minutes for changes. A voltage command from a prerecorded action potential in current clamp or a square pulse to +15 mV for 15 ms was used to elicit transmitter release. The access resistance was below 10 MW, the whole-cell capacitance was below 120 pF in all experiments and the patch electrodes were filled with (in mm): 25 caesium methanesulphonate; 10 CsCl; 10 HEPES; 2 ATP-Mg; 0.0001 CaCl2; 0.3 EGTA; pH 7.4. Experiments with ryanodine involved adding 30 lm ryanodine (Sigma Aldrich) to the presynaptic patch solution with a final concentration of 0.1% dimethylsulphoxide. Acetylcholine (10)5 m) was pressure applied directly on somata under a perfusion system as described previously (Feng et al., 2000).
Data analysis Evoked PSCs occurred within 35 ms of the action potential peak in VD4 and all other synaptic currents (conforming to the shape of the PSC) were judged to be mPSCs. The synaptic current rise-time was very slow (see Fig. 3) and with low access resistance and a short membrane time-constant (85% reduction with both). At the VD4–LPeA synaptic connections, the exogenously applied AChinduced current was observed to be sensitive only to tubocurarine but not to 100 lm Cd2+ (Fig. 2E). In some VD4–LPeA pairs (20–30%), we observed low mPSC variation and amplitude distributions that more closely approximated a normal distribution and much lower CVmPSC (Fig. 2F). Synaptic connections with a low CVmPSC in normal saline showed little or no mPSC amplitude Cd2+ sensitivity, whereas the mPSC amplitude was reduced at connections with high CVmPSC (Fig. 2G). The synaptic connections with CVmPSC 0.4) exhibited significant mPSC amplitude Ca2+ dependency, whereas this feature was absent in synaptic connections exhibiting low CVmPSC in normal saline (Fig. 2H). The mPSC frequency was reduced with Cd2+
saline at both the high-CVmPSC (reduced by 42.6 ± 13.6%, n ¼ 6, P < 0.05, Wilcoxon signed rank test) and the low-CVmPSC (reduced by 38.2 ± 25.9%, n ¼ 3) synapses. These data indicate that the mPSC amplitude was regulated presynaptically via extracellular Ca2+ at only some VD4–LPeA synaptic connections. The observed reduction in mPSC amplitude and variance with a reduction in Ca2+ influx at synaptic connections that exhibited a high initial CVmPSC suggests that these large-amplitude mPSCs are not truly spontaneous. Together with the lack of sensitivity of the postsynaptic receptors to Cd2+, this mPSC Ca2+ dependence indicates that the large-amplitude mPSCs may be MVR events.
Large-amplitude miniature postsynaptic currents are multivesicular release events Action potential-evoked transmitter release at VD4–LPeA synaptic connections occurs over a relatively long release asynchrony of up to 30 ms (Fig. 3A). As a result, low-amplitude evoked PSCs have an amplitude-dependent rise-time that increases until the full time-course of release asynchrony is reached. According to Wall & Usowicz (1998), the MVR is expected to show an increased rise-time because of temporal summation of the underlying single release events. Thus, the uniquantal events would probably show much faster rise-times than their multiquantal counterparts. The data presented here clearly show that mPSCs and evoked PSCs have similar amplitude rise-time relationships, suggesting that mPSCs (like the evoked PSCs) are indeed synchronized multiquantal events (Fig. 3B). The comparison of putative uniquantal mPSCs (smallest 20 mPSCs per trial, mean amplitude 29.4 ± 2.1 pA) and possible MVR mPSCs (largest 20 mPSCs in each trial, mean amplitude 147.9 ± 21.6 pA) shows a significant difference in rise-times (Fig. 3C). Reducing evoked
ª The Authors (2006). Journal Compilation ª Federation of European Neuroscience Societies and Blackwell Publishing Ltd European Journal of Neuroscience, 24, 1591–1605
Intersite multivesicular release affects quantal size 1595
Fig. 2. Large-amplitude miniature postsynaptic currents (mPSCs) are dependent upon external Ca2+ concentration. (A) mPSC amplitude histogram of a synaptic connection at which 1168 mPSCs were recorded. The mPSC amplitude mode was 25 pA but at most of the synaptic connections VD4 and LPeA, the mPSC amplitude skew is high with a mean amplitude of 60 pA and a coefficient of variation (CV) of 0.79. Whole-cell recordings of the postsynaptic cell enabled separation of mPSCs (black bars) from the noise (gray bars). Inset, postsynaptic recording with three spontaneous mPSCs (scale bars, 45 pA, 0.5 s). (B) mPSC amplitude histogram with currents recorded in normal saline (black bars) and with 30 lm Cd2+ saline (gray bars). Notice the reduction in skew with Cd2+. (C) Most VD4– LPeA synaptic connections exhibited high mPSC variance (CV > 0.4) and skew to large amplitudes, as represented here and in A and B. mPSC amplitudes at highCV synaptic connections show Ca2+ dependence (inset). (D) Postsynaptic currents induced from groups of ACh puffs and groups of 1-Hz presynaptic action potentials are reversibly blocked by tubocurarine, whereas only action potential-evoked release is blocked with Cd2+. Data from a representative trial and points are single postsynaptic currents. (E) Summary of the effect of 50 lm tubocurarine and 100 lm Cd2+ on evoked postsynaptic current (PSC) amplitude and exogenous ACh-induced PSCs. Data from four synapses. (F) Some synaptic connections have a much lower CV of the mPSC amplitude (CVmPSC) with less amplitude skew and Ca2+-independent mPSC amplitudes (inset). Note that the mode mPSC values for both high-CVmPSC and low-CVmPSC synaptic connections are similar. (G) Cd2+ sensitivity of mPSC amplitude at synaptic connections of different initial mPSC amplitude variation (CVmPSC). mPSC amplitudes at synapses with high initial CVmPSC show Cd2+ sensitivity. Each point is one synaptic connection. (H) Bar graph showing Ca2+ dependence of mean mPSC amplitudes at synaptic connections with high CVmPSC and low CVmPSC in normal-Ca2+ saline. Reducing Ca2+ influx with 30 lm Cd2+ significantly reduced mPSC amplitude at highCVmPSC synaptic connections (CVmPSC > 0.4) (*P < 0.05, Wilcoxon signed rank test, n ¼ 9 synaptic pairs). Only three of the 12 synaptic connections exhibited CVmPSC < 0.4 and all displayed Ca2+-insensitive mPSC amplitudes. ª The Authors (2006). Journal Compilation ª Federation of European Neuroscience Societies and Blackwell Publishing Ltd European Journal of Neuroscience, 24, 1591–1605
1596 T. W. Dunn and N. I. Syed
Fig. 3. Large-amplitude miniature postsynaptic currents (mPSCs) are multivesicular. Action potential-evoked transmitter release at visceral dorsal 4 synaptic connections is a highly asynchronous event occurring over 30 ms. However, postsynaptic current decay is also very slow with a time constant which is 3.4-fold longer than the total rise-time. (A) Low release probability evoked postsynaptic currents (PSCs) aligned by overlaying presynaptic action potentials (lower trace). The long duration of transmitter release (marked by the 30-ms box) is apparent in some of the smaller amplitude currents that have a delayed onset (marked by arrows) leading to much shorter rise-times. Bars, 200 pA ⁄ 50 mV, 50 ms. (B) Relationship between PSC rise-time and amplitude. Data points were averages from eight synapses where currents were grouped according to their amplitude. Both mPSC (filled squares) and PSC (diamonds) rise-time were highly dependent on amplitude (Spearman r ¼ 0.72, P < 0.01 and r ¼ 0.84, P < 0.0001, respectively). (C) The uniquantal mPSC rise-time was estimated from the mean rise-time averaged from the 20 smallest amplitude mPSCs per trial, whereas the multivesicular release mPSC rise-time was estimated from the 20 largest amplitude mPSCs per trial and the uniquantal PSC rise-time was estimated from the 20 smallest PSCs per trial (in 30 lm Cd2+). The release latency plateau is the average rise-time of all evoked PSCs with amplitudes greater than 500 pA in each trial (n ¼ 8 synaptic pairs, *P < 0.05 and ***P < 0.001, using repeated measures anova).
transmitter release with Cd2+ revealed a group of evoked PSCs with amplitudes and rise-times similar to those of the low-amplitude mPSCs (smallest 20 mPSCs per trial, mean amplitude 35.86 ± 10.7 pA) (n ¼ 8 synaptic connections). These data further indicate that large-amplitude mPSCs at highCVmPSC synaptic connections are MVR events that require extracellular Ca2+ for synchronized release. The mPSC mode is invariant from synapse to synapse, is Ca2+ independent (Fig. 2), and appears equal to the smallest and fastest mPSCs and PSCs (Fig. 3). Based upon these results, we next asked whether the phenomenon underlying the spontaneously synchronized MVR events also synchronizes multiple release sites during the action potential-evoked release event.
Multivesicular release affects quantal size If a high CVmPSC reflects the coupling of multiple vesicles to the same release event, then the quantum of transmitter (Q) must exceed the value of a single vesicle. Although many central synaptic connections exhibit large-amplitude mPSCs, in the case of some VD4–LPeA connections these mPSCs have extreme variance with a CV often greater than 0.7. Therefore, if the quantal size is increased beyond the value of a single vesicle then according to eqn 1 (see Materials and methods) the variance of evoked synaptic currents at a single release probability will also be expected to increase proportionally. Thus, synaptic connections with Ca2+-dependent, high mPSC amplitude
Fig. 4. Coefficient of variation (CV) of the miniature postsynaptic current (mPSC) amplitude (CVmPSC) correlates with variance-mean estimates of quantal size. (A) In representative postsynaptic current (PSC) traces from a high-CVmPSC (top trace) and a low-CVmPSC (bottom trace) synaptic connection with similar mean amplitudes, the difference in the amplitude variation between successive currents is apparent. Scale bars, 1 nA ⁄ 1 s. (B) Stationary PSCs at 1 Hz over an entire trial were divided into 20 PSC groups and normalized to a percentage of the maximum PSC in each group. Although reducing the release probability greatly changed the PSC amplitude, slow perfusion of Cd2+ saline, however, resulted in a gradual reduction in PSC with neither depression nor facilitation over the 20 PSC groups that were used to measure PSC variance and mean. (C) Variance-mean relationship of evoked PSCs at a high-CVmPSC synaptic connection (CV ¼ 0.74) with release probability changed slowly following the perfusion of Cd2+ saline. Q (quantal size) is estimated from eqn 3 (line) from stationary 1-Hz presynaptic stimulation (filled squares). Non-depressed PSCs (triangle) showed less variation than the higher probability 1-Hz PSCs with each point representing 20 PSCs. Parabolic line generated from eqn 1 (dashed line) with Q as 54.4 pA (Ca2+-independent mPSC mean for this trial) and N as 57, based on an estimated 4.780 nA Imax at this synaptic connection. Inset: a magnification of points at very low release probabilities, with a new estimate of quantal size from the slope of these points. (D) Variancemean relationship of evoked PSCs from a low-CVmPSC synaptic connection with release probability changed slowly with the perfusion of Cd2+ saline. Both stationary 1-Hz PSCs (filled squares) and non-stationary 5–10-Hz PSCs (diamonds, triangle) suggest similar values of Q, approx. 24 pA. As in C, the parabolic line is generated from eqn 1 (dashed line), with Q ¼ 39.1 pA [from the Ca2+-independent mPSC mean of 34.4 pA (CV ¼ 0.37)] and N ¼ 34 from a maximal observed current (Imax) of 1.34 nA for this synaptic connection. (E) PSC amplitude in high-Ca2+, normal-Ca2+ and Cd2+ salines. Data normalized in each trial to a percentage of the mean PSC amplitude in normal saline, for comparison of many trials with different PSC amplitudes under normal conditions. Increasing extracellular Ca2+ to 10 mm (and removing Mg2+) significantly increases PSC amplitude, whereas adding 30 lm Cd2+ to the saline reduces PSC amplitude. Significance calculated with repeated measures anova and Tukey’s multiple comparisons post-test, **P < 0.01, ***P < 0.001. (F) Reducing Ca2+ influx with Cd2+ greatly reduces the variance-mean estimate of quantal size. Increasing Ca2+ influx, which greatly increased PSC amplitude, did not change the estimate of quantal size (P > 0.05). Comparisons made with repeated measures anova and Tukey’s multiple comparison post-test, *P < 0.05. Data in E and F are from six synapses. (G) Relationship between CVmPSC, the mPSC amplitude mode value (triangles), mPSC mean (+) and the variance-mean estimate of Q from evoked PSCs (filled squares). The mPSC mode had no correlation to CVmPSC (Spearman r ¼ 0.3203, P > 0.05 and r ¼ 0.5333, P > 0.05, respectively), whereas mPSC mean (+) and variance-mean estimates of quantal size (filled squares) showed strong correlation to CVmPSC (Spearman r ¼ 0.7107, P < 0.005 and r ¼ 0.9109, P < 0.0001, respectively). Synapses with large-amplitude mPSCs that skew amplitude distributions leading to high CVmPSC show evoked PSC variation characteristic of synaptic connections with larger quantal sizes. Data are from 12 synapses, including the six used in E and F. ª The Authors (2006). Journal Compilation ª Federation of European Neuroscience Societies and Blackwell Publishing Ltd European Journal of Neuroscience, 24, 1591–1605
Intersite multivesicular release affects quantal size 1597 variance should also exhibit corresponding variance changes in evoked PSCs (eqn 2) if the mechanism for synchronization that occurs spontaneously truly affects quantal size. We found that some, but not all, VD4–LPeA synaptic connections displayed high variation from one evoked PSC to another (Fig. 4A). Induced action potentials at 1 Hz in VD4 produced PSCs at a stationary release probability without a trend toward depression or facilitation (Fig. 4B). To obtain an independent estimate of quantal size (Q), PSCs were measured while changing the release probability by slowly perfusing with Cd2+ (30 lm) saline. Means and variances
were calculated from 20 sequential PSCs, where release probability was changed slowly enough so that there was no trend in the 20 PSCs per group (Fig. 4B). VD4–LPeA synaptic connections undergo presynaptic, low-frequency depression, during which the difference between PSC1 and PSC2 is 250–300% but the difference between PSC3 and PSC4 is insignificant (data not shown). This synaptic depression (between PSC1 and PSC2) lasts for approximately 100 s and can be reversed by a short presynaptic tetanus. These nondepressed PSCs have a much larger mean (typically 300%) but less variance than PSCs elicited at 1 Hz (Fig. 4C). Thus, 1-Hz stationary
ª The Authors (2006). Journal Compilation ª Federation of European Neuroscience Societies and Blackwell Publishing Ltd European Journal of Neuroscience, 24, 1591–1605
1598 T. W. Dunn and N. I. Syed release occurs at a release probability of less than 0.5 (probably between 0.2 and 0.3) and with a mean maximal synaptic current (Imax) of 3.48 ± 0.90 nA, the average 1-Hz amplitude is close to 1 nA (n ¼ 12). As the release probability (P) is low at 1 Hz (0.2–0.3), eqn 3 can be applied to make a linear estimate of Q at these P-values and lower. CVmPSC values were estimated from mPSC amplitudes in normal saline. Application of a linear estimate will only underestimate Q. A representative high-CVmPSC synaptic connection has a greater slope and quantal size estimate when the PSC variance-mean is plotted over many release probabilities (Q ¼ 158 pA with CVmPSC measured at 0.74; Fig. 4C). However, the PSC variance at low-CVmPSC synaptic connections is indicative of a much smaller quantal size (average of both estimates Q ¼ 22 pA, with CVmPSC measured at 0.37; Fig. 4D). At very low release probabilities (release probability < 0.05) quantal size estimates at high-mPSC amplitude synaptic connections were reduced to lower values (Fig. 4C inset), suggesting some dependence of quantal size on release probability. PSCs at low-CVmPSC synaptic connections were evoked by both stationary and non-stationary methods, revealed similar variance-mean estimates of Q (17.4 and 27.1 pA, respectively) and the stationary estimate appeared low because PSCs at 1 Hz (in high-Ca2+ saline) occurred near a release probability of 0.5. Thus, a linear fit to all the data would be inappropriate as it would probably underestimate quantal size (Fig. 4D). The dashed lines in Fig. 4C and D were calculated using eqn 1 (see Materials and methods) with the Ca2+-insensitive mPSC amplitude mean value as Q (54.4 pA in Fig. 4C and 34.4 pA in Fig. 4D, measured from the mPSC mean in 30 lm Cd2+) and N estimated from the maximal current in high-Ca2+ saline at the synaptic connection as Imax (eqn 4). A quantal size based on the Cd2+insensitive mPSC mean fit very well to the PSC variance-mean relationship for the low-CVmPSC synaptic connection (dashed line Fig. 4D; non-linear regression, R2 ¼ 0.4450, runs test deviation P > 0.5) but not for the high-CVmPSC connection (dashed line Fig. 4C; R2 ¼ 0.0195, runs test P < 0.005). The PSC variance for the highCVmPSC synaptic connections was consistent with much higher quantal values than those estimated from the Ca2+-independent mPSC amplitude. An examination of changes in PSC amplitude with altered Ca2+ influx at high-CVmPSC connections (CV > 0.4) shows the expected Ca2+ dependence of evoked transmitter release (Fig. 4E). At these synaptic connections, variance-mean estimates of quantal size in both high-Ca2+ and normal saline were very similar, despite the difference in mean PSC amplitude between these two conditions (Fig. 4F). Variance-mean estimates of quantal size were, however, significantly reduced (P < 0.05) with Cd2+ saline (Fig. 4F), consistent
with the representative high-CVmPSC synaptic connection (Fig. 4C inset) and the Ca2+-dependent changes in mPSC amplitude (see Fig. 2). We also found that the mPSC mode amplitude was consistent at all of the VD4–LPeA synaptic connections measured (30–45 pA; Fig. 4G). The variance-mean estimate of quantal size was variable from trial to trial and was strongly correlated with CVmPSC (Spearman r ¼ 0.91, P < 0.0001) (Fig. 4G). The mPSC mean amplitudes in normal-Ca2+ saline also correlated with CVmPSC (r ¼ 0.71, P < 0.005). At CVmPSC values less than 0.4, the mPSC mode, mPSC mean and PSC variance-mean estimates of quantal size are all similar (Fig. 4G). These data suggest that the phenomenon underlying high CVmPSC (large-amplitude mPSCs, which, according to Fig. 3, is probably MVR) proportionally increases quantal size and thus greatly affects PSC variance at high-CVmPSC synaptic connections. The representative mPSC amplitude distributions and PSC variancemean relationships in Figs 2C and F, and 4C and D were obtained under identical experimental conditions (recorded on the same day and all the postsynaptic cells were from the same animal). This ensured that the cells were of the same size and maintained under identical culture conditions. This result is representative of all the data at the two extremes, i.e. high- and low-CVmPSC synaptic connections. It should, however, be noted that the representative high-CVmPSC synaptic connection (Figs 2C and 4C) had a larger amplitude than the representative low-CVmPSC synaptic connection (Figs 2F and 4D); this nevertheless was an exception and not a general trend over all the connections analysed. To clarify, although most (approx. 70%) of the VD4–LPeA synaptic connections exhibited high CVmPSC (>0.4), the maximum PSC amplitude of a connection did not correlate to CVmPSC at synapses with a CVmPSC < 0.7 (Spearman r ¼ 0.4833, P > 0.05, n ¼ 9). Multiple release sites share a release probability, multiplying quantal size The previous data suggest that presynaptic Ca2+ entry, both spontaneously and during an action potential, increases quantal size through the coupling of the release of multiple vesicles to a single release event. The very existence of the large-amplitude spontaneous event suggests that Ca2+ from a single source can trigger the release of multiple vesicles. We reasoned that if MVR was intrasite (MVR within the same active zone) it should be sensitive to 1,2-bis(2-aminophenoxy)ethane-N,N,N¢,N¢-tetraacetic acid; (BAPTA) and not EGTA, whereas intersite MVR (involving multiple release sites) involving the intracellular diffusion of Ca2+ over much longer distances would probably be both EGTA and BAPTA sensitive (Naraghi & Neher,
Fig. 5. Synaptic connections with high coefficient of variation of the miniature postsynaptic current amplitude (CVmPSC) and high initial quantal size estimates (Qi > 45 pA) show sensitivity to EGTA. (A) (i) Postsynaptic currents (PSCs) (bottom trace, scale bars, 400 pA ⁄ 1.5 s) were measured through whole-cell (WC) recordings of the postsynaptic cell and evoked by generating an action potential in visceral dorsal 4 (VD4) with a sharp electrode (top trace, scale bars, 40 mV ⁄ 1.5 s). (ii) After measuring PSC mean amplitude and variance at least twice (2 · 30 PSCs) for the calculation of initial quantal size (Qi), the sharp electrode is removed from VD4. Following removal of the sharp electrode, VD4 was whole-cell voltage clamped and PSCs generated by alternating between playback of a current-clamp recorded action potential (top left trace) or a square pulse to 15 mV for 15 ms (top right trace). Both methods of generating a PSC while WC on the presynaptic cell produced similarly sized PSCs (scale bars, 400 pA ⁄ 230 ms). (B) At the high-Qi synaptic connections with initial quantal size estimates of >45 pA, 10 mm EGTA in VD4 reduces quantal size within a few minutes of going WC (*P < 0.05, Wilcoxin signed rank test). Synaptic connections with low CVmPSC and corresponding low estimates of quantal size with variance-mean analysis (Qi < 45 pA) are not affected by 10 mm EGTA. (C) When 0.1–0.5 mm EGTA is included in the presynaptic pipette following intial sharp electrode stimulation, quantal size estimates with variance-mean analysis are not affected regardless of Qi at the synaptic connection. (D) PSC traces from a high-Qi (left pair of traces) and a low-Qi (middle three traces) synaptic connection before and after dialysis of the presynaptic cell with 10 mm EGTA (10 sequential PSCs overlaid, scale bars, 90 pA ⁄ 1 s). PCS’s evoked by playback of an action poteatial (a.p.) waveform (centre trace) are similar to those evoked by a presynaptic square pulse (right trace). PSC amplitude at the high-Qi synaptic connections is highly sensitive to 10 mm EGTA but is not affected by 0.1 mm EGTA in the presynaptic cell (right pair of traces, scale bars, 300 pA ⁄ 1 s). (E) The concentration-dependent relationship between presynaptic EGTA intracellular concentration [EGTA]i, PSC amplitude and variance-mean estimates of quantal size at synaptic connections with a high initial quantal size estimate (Qi > 45 pA). PSC amplitudes measured 5–10 min after going WC are normalized to the percentage of the initial PSC amplitude before going WC on the presynaptic cell. Quantal size estimated with the variance-mean relationship of the PSCs was normalized to the value estimated during sharp electrodeevoked release (n ¼ 3, 2, 4 and 5 synaptic pairs, for each concentrations from left to right). (F) PSC amplitude and quantal size estimates at synaptic connections with low initial Qi do not show concentration dependence with [EGTA]i (n ¼ 1, 3 and 3 synapses, left to right). ª The Authors (2006). Journal Compilation ª Federation of European Neuroscience Societies and Blackwell Publishing Ltd European Journal of Neuroscience, 24, 1591–1605
Intersite multivesicular release affects quantal size 1599 1997; Neher, 1998; Atwood & Karunanithi, 2002). Through wholecell voltage-clamp of the presynaptic neurone, the Ca2+ buffer EGTA was then used to determine whether this synchronization was intrasite (likely to be insensitive to EGTA) or intersite (involving multiple
release sites, which may be sensitive to EGTA). Initial recording with a sharp electrode in the presynaptic cell to evoke action potentials allowed for an estimate of PSC amplitude and quantal size under endogenous Ca2+ buffering conditions (Fig. 5A). This initial estimate
ª The Authors (2006). Journal Compilation ª Federation of European Neuroscience Societies and Blackwell Publishing Ltd European Journal of Neuroscience, 24, 1591–1605
1600 T. W. Dunn and N. I. Syed of quantal size (Qi) using eqn 3 (Materials and methods) and 20–30 stationary PSCs is used over mPSC estimates as it can be quickly attained, unlike the longer periods required for sufficient numbers of mPSCs. The amplitude of the variance-mean estimate of quantal size correlated well with the CVmPSC and mPSC mean (Fig. 4G), where the high-CVmPSC synaptic connection is also a high-Qi synaptic connection with large-amplitude mPSCs. Separation of synaptic connections by the initial quantal size estimate during the sharp electrode recording (Qi) is similar to separating connections into high and low CVmPSC in previous experiments, as at connections with CVmPSCs below 0.4 the PSC variance-mean estimate of quantal size was less than 45 pA (see Fig. 4G). After initial recordings with a sharp electrode in the presynaptic cell to evoke action potentials and control membrane potential, the sharp electrode was removed and a patch electrode with 0.1–10 mm EGTA was used for dialysis and voltage clamp of VD4 (Fig. 5A). Both playback of a prerecorded VD4 action potential and a square pulse were used in alternation to evoke transmitter release during whole cell presynaptic conditions (Fig. 5A far right traces). The synaptic connections with high initial quantal size estimates (Qi > 45 pA) show a significant reduction in quantal size with 10 mm EGTA in the presynaptic cell (Fig. 5B; P < 0.05, 7–10 min after membrane rupture for whole-cell control of the presynaptic neurone), whereas at connections with Qi < 45 pA the quantal size as estimated with the PSC variance-mean relationship (eqn 3) remained unchanged in the presence of 10 mm EGTA (Fig. 5B). When the EGTA concentration in the presynaptic patch pipette was reduced to 0.1 mm, the quantal size remained unchanged from initial estimates with sharp electrodes (endogenous buffering), regardless of the amplitude of Qi (Fig. 5C). The PSC amplitude was also very sensitive to 10 mm EGTA at the high-Qi (> 45 pA) but not the low-Qi (Fig. 5D left and middle traces) synaptic connections. The high-Qi synaptic connections experienced an increase in PSC amplitude in 0.1 mm EGTA (Fig. 5D right traces). Both PSC amplitude and quantal size show a concentration-dependent relationship with presynaptic EGTA at the high-Qi synaptic connections (Fig. 5E) that is not apparent at the low-Qi synaptic connections (Qi < 45 pA) (Fig. 5F). Furthermore, at the five high-Qi trials where 10 mm EGTA was dialysed in the presynaptic cell, the mean mPSC amplitude was reduced from 56.6 ± 7.0 to 27.46 ± 7.9 pA and the mean CVmPSC of 0.71 ± 0.22 with a sharp electrode in the presynaptic cell was reduced to 0.35 ± 0.05 with 10 mm EGTA (n ¼ 5 synaptic connections). The concentration of EGTA that does not affect quantal size and PSC amplitude (between 0.1 and 0.5 mm) suggests that Ca2+ must travel a long distance intracellularly to increase quantal size.
Ryanodine receptors synchronize release at multiple release sites to increase quantal size Ryanodine receptors have been implicated in the production of largeamplitude mPSCs at a variety of synapses (Llano et al., 2000; Sharma & Vijayaraghavan, 2003; Gordon & Bains, 2005). To examine whether these receptors are involved in increasing quantal size at VD4–LPeA synaptic connections, a protocol as depicted in Fig. 5A was followed with 0.3 mm EGTA and 30 lm ryanodine added to the presynaptic pipette. With synaptic connections grouped according to the amplitude of the initial variance-mean estimate of quantal size, high-Qi (> 45 pA) connections show a large reduction in quantal size within 10 min of presynaptic dialysis with 30 lm ryanodine (Fig. 6A, P < 0.05). At synaptic connections with low initial quantal size estimates (Qi < 45 pA), quantal size estimates do not change over the same time period with 30 lm ryanodine
(Fig. 6A). The PSC amplitude at these synaptic connections was also shown to decrease with ryanodine at the high-Qi but not at the lowQi synaptic connections (Fig. 6B). Most interesting in these experiments are the mPSC events, which clearly demonstrate dosedependent effects of ryanodine. At low concentrations (nanomolar), ryanodine increases the RyR open probability, stimulating Ca2+induced Ca2+ release; however, at micromolar concentrations ryanodine prevents channel opening, inhibiting Ca2+-induced Ca2+ release (Sutko et al., 1997). At both the high- and low-Qi synaptic connections, the mPSC frequency increased within the first few minutes of switching to the whole-cell configuration in VD4 (dialysis with ryanodine), prior to any effect on PSC amplitude or quantal size estimates (Fig. 6C and D). During and after the peak of the increase in mPSC frequency, the mPSC amplitude began to reduce at the high-Qi synaptic connections, whereas the mPSC amplitude remained constant during the changes in mPSC frequency at the low-Qi connections. Presynaptic intracellular ryanodine significantly reduced the variance-mean estimate of quantal size and mPSC amplitude at the high-CVmPSC, high-Qi synaptic connections (Fig. 6E, P < 0.01). At the low-Qi connections, variance-mean estimates of quantal size and mPSC amplitude were insensitive to 30 lm ryanodine (Fig. 6E). In addition to being Ca2+ and EGTA sensitive, CVmPSC was also affected by ryanodine at high-CVmPSC synapses reducing from 0.60 ± 0.05 to 0.38 ± 0.03 (n ¼ 6 synaptic connections, P < 0.05, Wilcoxon signed rank test), whereas at the low-CVmPSC synapses, CVmPSC remained stable (0.31 ± 0.02– 0.26 ± 0.05 in 30 lm ryanodine, n ¼ 3 synaptic connections). The PSC amplitude at the high-Qi synaptic connections was also highly sensitive to presynaptic ryanodine, with a reduction to 32 ± 6% of the PSC amplitude with a sharp electrode in VD4. The PSC amplitude at the low-Qi synaptic connections was still 83 ± 16% after 10 min with 30 lm ryanodine. Taken together, the results displayed in Figs 5 and 6 confirm the presynaptic nature of the large quanta observed at some synaptic connections and suggest that an intracellular Ca2+ signal between release sites, relayed via RyRs, produces the large quanta through MVR.
Target cell dependence of ryanodine-dependent multivesicular release at VD4–LPeA synaptic connections To address further whether or not trial-to-trial differences in mPSC and PSC amplitude variation may have resulted from the cellular variability (different cells, size, culture conditions, etc.), two pairs of cell ‘quadruples’ (VD4a–LPeAi–VD4b–LPeAii) or ‘triples’ (missing either VD4a or LPeAii) were cocultured in series (Fig. 7A). In this configuration, both VD4 cells (VD4a and VD4b) were from two different animals, whereas LPeAi and LPeAii were obtained from the homogeneous cluster of PeA neurones within the same ganglia. This culture configuration, in particular the quadruples, enabled us to ask whether synapse-to-synapse differences in Qi (the apparent level of release coupling) were contingent upon the identity of the postsynaptic cell. The maximum synaptic amplitude had no significant trend toward any of the connections, with some preparations showing wide ranges in Imax between synaptic connections, whereas others were very similar. Action potentials evoked in VD4a produced PSCs in LPeAi, whereas spikes in VD4b produced PSCs in both LPeAi and LPeAii (Fig. 7B). Action potentials in either VD4 did not affect the other VD4 and there was no electrical coupling between any of the cells. When variance-mean estimates of quantal size were compared, synaptic
ª The Authors (2006). Journal Compilation ª Federation of European Neuroscience Societies and Blackwell Publishing Ltd European Journal of Neuroscience, 24, 1591–1605
Intersite multivesicular release affects quantal size 1601
Fig. 6. Quantal size (Qi) is reduced at high-quantal size, coefficient of variation of the miniature postsynaptic current (mPSC) amplitude (CVmPSC) synaptic connections with ryanodine. (A) Variance-mean estimates of quantal size are reduced after going whole-cell (WC) in the presynaptic cell with 30 lm ryanodine included in the pipette. Synapses with a high initial Qi estimate show a reduction in quantal size following exposure to ryanodine (filled squares, n ¼ 6). At the synaptic connection with low Qi, ryanodine did not alter the estimate of quantal size in the 12 min of recording after going WC in the presynaptic cell (diamonds, n ¼ 3). Postsynaptic current (PSC) means and quantal size estimates calculated from groups of 30 PSCs at 1 Hz. (B) PSC amplitude is also reduced with 30 lm ryanodine in the presynaptic cell at high-Qi synapses (filled squares). However, PSC amplitude was unaltered in the presence of ryanodine at the low-Qi (CVmPSC) synaptic connection (*P < 0.05, Wilcoxin signed rank test). (C and D) mPSC amplitude at the high-Qi synaptic connection decreases in the presence of ryanodine, whereas mPSC amplitude is unaltered by ryanodine at the low-Qi synaptic connection. mPSC frequency transiently increases within a few minutes of going WC in the presynaptic cell and reduces back to pre-WC levels over the following few minutes. The increase in mPSC frequency occurred at both high- and low-Qi synaptic connections. Data are from one high-Qi (C) and one low-Qi (D) synaptic connection. (E) High-Qi, CVmPSC synaptic connections have a significantly reduced variance-mean estimate of quantal size (Qest) and mPSC amplitude with 30 lm ryanodine in the presynaptic cell. PSC variation and mPSC amplitude at low-Qi synaptic connections does not appear to be sensitive to ryanodine. Data from the six high- and three low-Qi synapses used in A and B. Qest, estimated Q. ª The Authors (2006). Journal Compilation ª Federation of European Neuroscience Societies and Blackwell Publishing Ltd European Journal of Neuroscience, 24, 1591–1605
1602 T. W. Dunn and N. I. Syed
Fig. 7. Quantal size is postsynaptic cell dependent. (A) Photomicrograph of quadruple somata preparation. Cells were soma–soma paired overnight as shown in Fig. 1A. The cells labelled as a and b refer to the same specific cell type from two different animals, and i and ii are two different postsynaptic cells from the homogeneous PeA cluster located with the left pedal ganglia of the same animal. [Both visceral dorsal 4s (VD4s) were taken from different animals (as there is only one VD4 ⁄ animal) than those used to obtain LPeA) and LPeAii.] (B) Representative traces from three synaptic connections at a quadruple soma preparation (A) recorded with intracellular (presynaptic) and whole-cell (postsynaptic) recordings. Induced action potentials in VD4a and VD4b with current clamp, and the corresponding postsynaptic currents (PSCs) in LPeAi and LPeAii as measured with whole-cell recordings (cells configured as in A and bathed in normal saline). The break in traces between VD4b and VD4a action potentials is from the removal of a 5-s period when neither cell was firing action potentials. Scale bars, 40 mV ⁄ 0.5 nA ⁄ 2 s. (C) Stationary PSC variance-mean relationship of three synaptic connections in a quadruple configuration with release probability changed slowly with Cd2+ saline perfusion. All three synaptic connections had very similar PSC amplitude means; however, PSC variance was very different between synaptic connections with the same presynaptic cell. Data points are from 20–30 PSCs evoked at 1 Hz. (D) Comparison of PSC variance-mean estimates of quantal size between two synaptic connections sharing the same LPeA cell and the two synaptic connections sharing the same VD4. Data from four triple and eight double soma–soma synaptic pairs (four soma and three soma, respectively). As miniature PSCs (mPSCs) cannot be attributed as coming from VD4a or VD4b on LPeAi connections, coefficient of variation of the mPSC amplitude (CVmPSC) cannot be estimated at this synapse. No quantal size estimates can be made using eqn 3 and thus values in pA are not corrected for CVmPSC and are thus overestimates by a factor of 1.09–1.64 (CVmPSC of 0.3 and 0.8, respectively). Two synaptic connections on the same LPeA cell (two different VD4 cells) had very similar quantal size estimates (even though mean PSC amplitude can be quite different between the two connections), whereas two synapses sharing the same presynaptic cell (VD4b) most often exhibited very different quantal size estimates.
connections sharing the same postsynaptic cell were found to be very similar (Fig. 7C). When the two (or three) connections were compared with variance-mean estimates of quantal size, we found a strong correlation (Spearman r ¼ 0.9429, P < 0.05) between connections with the same postsynaptic cell but no correlation between the two synaptic connections with the same presynaptic cell (Spearman r ¼ 0.2364, P > 0.05) (Fig. 7D). Therefore, it seems likely that the variation in quantal size between synaptic connections has a presynaptic origin but also that the postsynaptic cell is specifically recognized by VD4 and thus determines the level of release site coupling at that particular connection.
Discussion In this study, we have demonstrated that the large-amplitude mPSCs at the VD4–LPeA synaptic connection (at high-CVmPSC connections): (i) are Ca2+-dependent events (Figs 2, 4 and 5); (ii) they constitute the synchronized release of many vesicles (MVR) (Figs 3 and 5); (iii) reflect changes in quantal values as measured by PSC variance (Fig. 4); (iv) involve RyRs (Fig. 6); and (v) are postsynaptic celldependent (Fig. 7). The reduction in both the mPSC amplitude (Fig. 2B, C and F) and PSC variance-mean estimate of quantal size (Fig. 4C and F) in the presence of Cd2+ suggests that Ca2+ influx
ª The Authors (2006). Journal Compilation ª Federation of European Neuroscience Societies and Blackwell Publishing Ltd European Journal of Neuroscience, 24, 1591–1605
Intersite multivesicular release affects quantal size 1603 synchronizes transmitter release from many release sites. Intracellular dialysis of the presynaptic neurone VD4 with EGTA and ryanodine indicates that the large multivesicular quantal events (both spontaneously occurring as the large-amplitude mPSC and during evoked release as a statistical release unit) represent the coupling of multiple release sites to the same release probability. Although the evidence would suggest a purely presynaptic mechanism that is scaled through recognition of the postsynaptic cell (Fig. 7), we cannot fully exclude the more remote possibility that presynaptic Ca2+ indirectly controls release site coupling through a postsynaptic mechanism. Differences in the function of multiple synaptic connections from a single presynaptic neurone have been described previously (see Atwood & Karunanithi, 2002 for review). Many of the presynaptic, synapse-specific differences affect average release probability or the number of release sites (Bittner, 1968; Sherman & Atwood, 1972; Bradacs et al., 1997; Reyes et al., 1998; Gupta et al., 2000; Millar et al., 2002). Recent analysis of transmitter release in RyR mutants in Caenorhabditis elegans (C. elegans) suggests a role for presynaptic RyRs in maintaining normal quantal size as estimated through mPSC amplitude (Liu et al., 2005). Although the authors provided evidence that the involvement is not through MVR, presynaptic RyRs do appear to influence normal mPSC frequency and amplitude in C. elegans, as observed in Lymnaea. To the best of our knowledge, such synapsespecific differences in the quantal size of two synaptic connections from the same presynaptic cell have not previously been reported. Alteration in quantal size has been considered with respect to single release site synapses, either through differences in vesicle diameter, postsynaptic receptor density and saturation or a kiss-and-run-like mechanism (the difference in quantal size in all of these cases is a fraction of a vesicle) (Atwood & Karunanithi, 2002). At the VD4– LPeA synaptic connections, the RyR ⁄ Ca2+-dependent MVR increases quantal size by multiples of the current induced by the release of a single vesicle, which in turn multiplies the variance in stationary evoked PSCs. A potential implication of altering the variation in transmitter release relates to the work of Chance et al. (2002) who have demonstrated that variation in an input signal will lead to different levels of gain modulation to the relationship between driving input amplitude and the firing pattern of a postsynaptic neurone with multiple inputs. This suggests that the described intersite MVR represents not only a potential target for modulation (Sharma & Vijayaraghavan, 2003; Gordon & Bains, 2005) but also differentiates information flow in a single neurone with multiple synaptic connections through differential levels of transmitter release site coupling. Previous consideration of possible sources of measured quantal variation suggested that both intra- and intersite variation contribute minimally (fractions of a quantum) to evoked PSC variation at low release probabilities (Silver, 2003). The soma–soma synapse model reduces intersite variation that may arise from large electrotonic differences between release sites and alleviates voltage-clamp issues. Furthermore, under- or over-correction of series resistance also exerts only a limited effect on PSC variance when the release probability is low ( 0.4), the variance-mean relationship was not linear at very low release probabilities (
