An excess-calcium-binding-site model predicts neurotransmitter release at the neuromuscular junction

Abstract

Despite decades of intense experimental studies, we still lack a detailed understanding of synaptic function. Fortunately, using computational approaches, we can obtain important new insights into the inner workings of these important neural systems. Here, we report the development of a spatially realistic computational model of an entire frog active zone in which we constrained model parameters with experimental data, and then used Monte Carlo simulation methods to predict the Ca(2+)-binding stoichiometry and dynamics that underlie neurotransmitter release. Our model reveals that 20-40 independent Ca(2+)-binding sites on synaptic vesicles, only a fraction of which need to bind Ca(2+) to trigger fusion, are sufficient to predict physiological release. Our excess-Ca(2+)-binding-site model has many functional advantages, agrees with recent data on synaptotagmin copy number, and is the first (to our knowledge) to link detailed physiological observations with the molecular machinery of Ca(2+)-triggered exocytosis. In addition, our model provides detailed microscopic insight into the underlying Ca(2+) dynamics during synapse activation.

Figure 1

Overview of the frog NMJ model. (A) Rendered simulation snapshot of the complete AZ model. Visible are the two double rows of synaptic vesicles (large red spheres) as well as diffusing free and buffer-bound Ca²⁺ ions (small colored spheres). For visual clarity, unbound buffer sites are not shown. (B and C) Close-ups of synaptic vesicles, revealing the Ca²⁺-sensor sites at their bottom (the 40-sensor model is shown). The cylindrical glyphs directly in front of synaptic vesicles represent closed or open VGCCs (red, closed; yellow, open). Open VGCCs release Ca²⁺ ions (yellow spheres) into the presynaptic space, which can bind to endogenous buffer sites (cyan spheres; only Ca²⁺-bound buffer sites are shown) or sensor sites on synaptic vesicles. Unbound and bound Ca²⁺-sensor sites on vesicles are colored black and yellow, respectively. (D and E) Important model dimensions (drawings are not to scale).

Figure 2

Experimental and computed whole-cell and single-channel current integrals. (A) The action potential waveform used to drive the voltage-dependent rate constants between closed and open states in our four-state kinetic VGCC model (see inset). (B) Comparison of the experimental and computed whole-cell Ca²⁺ currents obtained using the action potential and kinetic model shown in panel A. Initial deviations were due to nonlinear leak subtraction of the complex action potential waveform used to activate Ca²⁺ current. The slightly slower measured deactivation was due to incompletely clamped long neurites extending on either side of the varicose presynaptic bouton. (C) Histogram of the computed single-channel current. (D) Corresponding histogram of the experimental single-channel current from cell-attached patch-clamp recordings in the chick ciliary ganglion. Inset: Sample single-channel openings (bottom trace) evoked by action potential waveforms (top trace). The experimental single-channel currents are larger than the computed ones due to the presence of a high barium concentration in the patch pipette solution (see Supporting Material) (24).

Figure 3

Comparison of vesicle-release latencies. (A) Histograms of vesicle-release latencies for a model with n_s = 10 and n_sb = 4 for simultaneous (blue, ind-sim) and sequential (green, ind-seq) fusion mechanisms. For comparison, the red graph depicts the data from Katz and Miledi (44) showing that sequential binding leads to a significantly broadened latency distribution. The sudden cutoff in the histogram of the sequential model at 2.35 ms is an artifact due to the 3 ms simulation window and the fact that the histogram was shifted left to overlap with the Katz data (the actual latency extended well beyond 2.35 ms). (B) Latency distribution for n_s = 20, n_sb = 5 with the ind-sim fusion mechanism, and n_s = 40, n_sb = 6 with the syn-sim mechanism, both of which agree well with the data from Katz and Miledi (44). See Table 2 legend for definition of n_s and n_sb.

Figure 4

Computed and measured CRRs. (A–D) Fits for the CRR from simulation data. The inset in each panel shows the arrangement of Ca²⁺-binding sites on the bottom of synaptic vesicles. (C and D) For the syn-sim fusion mechanism, identically colored regions of five-sensor sites each represent individual synaptotagmin molecules. (A and B) Results for a 10- and 20-sensor arrangement using the ind-sim fusion mechanism. Although the 10-sensor model was not sensitive enough to changes in [Ca²⁺]_ext, the 20-sensor model provided a good match with a CRR of 4.12. (C) Results for a 20-sensor arrangement, n_sb = 4, and the syn-sim fusion model, which was too insensitive to changes in [Ca²⁺]_ext with a CRR of 3.65. However, as shown in D, a further increase in the number of available Ca²⁺-sensor sites to 40, n_sb = 6, combined with the syn-sim fusion mechanism led to a model that agreed well both in terms of the CRR (4.65) and the number of released vesicles (n_r = 0.49). (E and F) Experimentally measured CRRs. (E) Recordings from a representative NMJ (averages of 15 EPPs each recorded at extracellular Ca²⁺ concentrations of 0.3, 0.4, 0.5, 0.6, 0.7 mM Ca²⁺, in order of increasing peak height). (F) Log-log plot and linear regression of the representative data shown in E; the slope of this linear regression is 4.2. When examined in 12 NMJs, the average slope of the linear regression was 4.24 ± 0.76 (mean ± SD). See Table 2 legend for definition of n_s, n_sb, and n_r.

Figure 5

Subvesicular Ca²⁺ concentration and VGCC contribution to release. (A) Average number and concentration of free Ca²⁺ in the confined space just below released synaptic vesicles (close to Ca²⁺-sensor sites, average over ∼4900 release events). Although the Ca²⁺ concentration can reach micromolar values, the average number of discrete Ca²⁺ that are present at any given point in time is very small. This emphasizes the extreme sparseness of free Ca²⁺ and thus the need for an excess of available Ca²⁺-binding sites on synaptic vesicles to achieve experimentally measured rates of release and CRR. (B) Fractional contribution of increasing numbers of VGCCs to the release of individual synaptic vesicles. The large majority of release events are triggered by Ca²⁺ ions from one or two Ca²⁺ channels, highlighting the highly localized (nanodomain (48)) coupling of VGCCs to synaptic vesicles.