Keeping Ca²⁺ channels at some distance from docked vesicles enables domain overlap control of release.

<p>(<b>A</b>) Illustration of one spatial sample of n = 14 Ca²⁺ channels located in active zone # 5 in the "exclusion zone" model (minimal distance from docked vesicle edge; 30 nm). <i>Bottom</i> shows the near-membrane [Ca²⁺]_i at 1.1 ms. (<b>B</b>) [Ca²⁺]_i reached at each docked vesicle during the standard AP (<i>top</i>), and the resulting release rates (<i>bottom</i>). (<b>C</b>) Plot of p_ves for the individual vesicle docking sites (<i>top</i>), and distribution of the number of released vesicles over the entire active zone (bottom), both computed for n = 8000 trials with a standard AP. (<b>D</b>) Double-logarithmic plot of p_ves versus Ca²⁺ entry for the simulation of the Ca²⁺ current—release cooperativity experiment. Note the high slope of 2.8 predicted for this spatial sample (see A; n = 2000–4000 repetitions for each AP width). On average, a slope value of 2.8 ± 0.1 resulted (n = 4 independent spatial samples). (<b>E</b>) Simulation of the EGTA—sensitivity of release driven by the standard AP. Note the biphasic sensitivity of release to EGTA, as observed experimentally [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004253#pcbi.1004253.ref015" target="_blank">15</a>]. (<b>F</b>) Dependence of p_ves on the exclusion zone size, measured as the minimal distance from vesicle edge. Note that an exclusion zone size of 30 nm produces a physiologically plausible p_ves of 0.1 (grey line).</p

The Ca²⁺ current—Release, cooperativity stays elevated in mature calyx of Held synapses.

<p>(<b>A</b>) Representative example traces of paired pre- and postsynaptic voltage-clamp experiments at a calyx of Held synapse of a P8 mouse (<i>left</i>), and at a P16 mouse (<i>right</i>). Panels from top to bottom show the voltage-clamp protocol, the presynaptic Ca²⁺ tail current, and the resulting EPSCs. The insets show the peaks of the presynaptic Ca²⁺ tail currents at higher resolution. (<b>B</b>) Plot of EPSC amplitudes versus integrated presynaptic Ca²⁺ charge for all data (n = 6 and 5 paired recordings at P8–P11 and at P15–P16 respectively). Note the double-logarithmic coordinates, and the steep slopes but slight leftward shift in older mice (red symbols). (<b>C</b>) Individual and average values for the slopes (<i>left</i>), and for the presynaptic Ca²⁺ charge needed to evoke an EPSC of 2 nA (<i>right</i>). Although both values were significantly lower at P15–P16 (p < 0.05 for both data sets), the slope value was still high in the more mature mice, suggesting release control by multiple channels.</p

Neither the supercluster nor the exclusion zone model predict slow release in response to long depolarizations.

<p>Simulations in response to a long depolarizing step to 0 mV [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004253#pcbi.1004253.ref045" target="_blank">45</a>] were made both for the supercluster arrangement (<i>left</i>) and for the exclusion zone arrangement (<i>right</i>) for the large active zone (active zone # 11; see Fig <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004253#pcbi.1004253.g005" target="_blank">5A</a> and <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004253#pcbi.1004253.g005" target="_blank">5D</a> for the spatial arrangements). (<b>A</b>) Voltage step from -70 mV to 0 mV and resulting Ca²⁺ current for the supercluster model (left) and the exclusion zone model (<i>right</i>). (<b>B</b>) The resulting aggregate cumulative release rate, averaged over all n = 11 vesicles at this active zone. The data traces (<i>black</i>) were fitted with a single exponential with time constant of 1.52 ms (<i>left</i>, supercluster arrangement) and 0.78 ms (<i>right</i>, exclusion zone model). (<b>C</b>) The cumulative release rate traces of the individual vesicles, for the supercluster and exclusion zone model. Note the larger spread of release delays in the supercluster model (<i>left</i>) as compared to the exclusion zone model (<i>right</i>). (<b>D</b>) Analysis of the delay (time needed to reach 10% of cumulative release), and the 20–80% rise times of the cumulative release rates as a function of Ca²⁺ channel—vesicle distance. For the supercluster model (<i>left</i>), an unequivocal distance between the supercluster and each vesicle can be computed. In the case of the exclusion zone model, the distance is given as the average distance of each vesicle to the three nearest Ca²⁺ channels. In C and D, numbers indicate some relevant vesicle positions (see Fig <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004253#pcbi.1004253.g005" target="_blank">5A</a> and <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004253#pcbi.1004253.g005" target="_blank">5D</a>).</p

Simulations at a larger example active zone show more drastically that placement of all Ca²⁺ channels in a single supercluster produces excessive heterogeneity of p_ves.

<p>(<b>A</b>) Active zone # 11 (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004253#pcbi.1004253.g001" target="_blank">Fig 1A</a>, triangle) was used for the simulations. We assumed the presence of n = 25 Ca²⁺ channels to maintain a constant Ca²⁺ channel density across active zones. One spatial seed is shown for an exclusion zone rule for Ca²⁺ channels (red dots) with minimal distance of 30 nm from the edge of each vesicle. (<b>B</b>) Resulting distribution of p_ves values in response to release triggered by the standard AP, for the spatial seed illustrated in (<b>A</b>). The number on the abscissa ("site") corresponds to the vesicle number in (<b>A</b>). (<b>C</b>) The plot of vesicular release probability versus Ca²⁺ influx, for the spatial seed illustrated in (<b>A</b>). Note the reasonably high slope value (2.7). (<b>D-F</b>) Model of the same active zone as in (<b>A-C</b>), but now with all Ca²⁺ channels (n = 25) placed in a single supercluster (red spot). Note the large heterogeneity in p_ves and the small values of p_ves for far-away vesicles (<b>E</b>). A high slope value of 3.3 was apparent in this simulation (<b>F</b>). (<b>G</b>) Dependence of p_ves on the distance of each vesicle from the Ca²⁺ channel supercluster.</p

Extracellular ion-concentration profiles at selected time points.

<p>Spatial profiles of the ECS ion concentrations over the depth of the piece of tissue at selected time points. Deviances from baseline concentrations (<i>t</i> = 0) increase throughout the 84 second simulation. Simulations shown for the case with diffusion set to zero (<b>A</b>) and with diffusion included (<b>B</b>).</p

Output from the neuronal population.

<p>Transmembrane currents into selected extracellular volumes, including (column <b>A</b>) the subvolume containing the neuronal somata (<i>n</i> = 3), (column <b>B</b>) the subvolume containing the trunk of the apical dendrite (<i>n</i> = 7), and (column <b>C</b>) the subvolume where the apical dendrites branched out (<i>n</i> = 13). Currents were subdivided into ion specific currents (row <b>1</b>–<b>4</b>) and the capacitive current (row <b>5</b>). The sum of all currents into a subvolume <i>n</i> is shown in row <b>6</b>. The location of the midpoint of a neural segment determined which ECS subvolume <i>n</i> it belonged to, and currents were summed over all neural segments (of all neurons) that occupied a given ECS-subvolume (<i>n</i>). The transmembrane currents were defined as positive when crossing the membrane in the outward direction. The total transmembrane currents of the neuron as a whole (summed over all <i>N</i> − 2 subvolumes) were also calculated (column <b>D</b>). Results are shown for a 7 second excerpt of simulations.</p

Randomly distributed Ca²⁺ channels in a realistic active zone cannot explain domain overlap control of release.

<p>(<b>A</b>) Illustration of the elements of the computational model (see main text, and <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004253#sec014" target="_blank">Material and Methods</a> for details). (<b>B</b>) The standard AP used for the simulation (upper panel), and the distribution of Ca²⁺ channel opening and closing times (<i>red</i> and <i>black</i> histogram bars, respectively). (<b>C</b>) Illustration of one spatial sample in which n = 14 Ca²⁺ channels (red dots) were placed randomly in active zone #5 (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004253#pcbi.1004253.g001" target="_blank">Fig 1A</a>; star symbol). The bottom panel shows a map of the near-membrane [Ca²⁺]_i at 1.1 ms, close to the peak of the Ca²⁺ current. (<b>D</b>) APs used for simulating the "Ca²⁺ current—release cooperativity" (<i>top</i>); and the resulting Ca²⁺ currents (<i>bottom</i>). The standard AP, and the resulting active zone Ca²⁺ current are shown by black traces. (<b>E</b>) Simulated transmitter release rates (<i>top</i>) for three selected AP widths (black trace corresponds to AP with standard width), and double-logarithmic plot of average vesicular release probability (p_ves) versus Ca²⁺ influx for the different AP widths (<i>bottom</i>). Note the low slope value of n = 1.3 ± 0.2 (blue symbols are average data points of n = 5 independent spatial seeds), indicating that a random localization of Ca²⁺ channel is unlikely to explain domain overlap control. (<b>F</b>) Plot of vesicular release probability (p_ves) at each release site (<i>top</i>), and simulated release rates for the n = 6 vesicle docking sites (<i>bottom</i>; same color codes as in C). Note the unrealistically high values of p_ves. (<b>G</b>) Simulations with a single supercluster of n = 14 channels (red dots, <i>top</i>) and a single vesicle placed at 100 nm distance (black circle, <i>top</i>). Note the high slope which can be reached in this arrangement (<i>bottom</i>; slope value = 2.8).</p

Extracellular flux densities of ions and net charge.

<p>Time-averaged extracellular flux densities in the cases without (<b>A</b>) and with (<b>B</b>) extracellular diffusion. In the latter case, the total flux density <b>(B3)</b> was subdivided into the field-driven <b>(B1)</b> and the diffusive <b>(B2)</b> component. When the curves are to the right/left of the dashed vertical lines, they represent fluxes in the positive/negative <i>z</i>-direction, respectively. The flux densities were computed as the temporal mean over time intervals indicated in the legend. The scale bar was the same for all flux densities, including the electrical current density (rightmost column), which was given in units of the unit charge: <i>i</i>/<i>F</i> = <i>j</i>^<i>K</i>+ + <i>j</i>^<i>Na</i>+ + 2<i>j</i>^<i>Ca</i>2+ − <i>j</i>^<i>X</i>−.</p

Analysis of the spatial distributions of docked vesicles at the mouse calyx of Held synapse.

<p>(<b>A</b>) Top-down views of n = 15 completely reconstructed active zones from a P11 mouse [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004253#pcbi.1004253.ref029" target="_blank">29</a>], with indicated docked vesicle positions (blue). Star- and triangle symbols indicate active zones #5 and # 11 used for simulations here (see below, Figs <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004253#pcbi.1004253.g002" target="_blank">2</a>–<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004253#pcbi.1004253.g005" target="_blank">5</a>). (<b>B</b>) Plot of the number of docked vesicles versus active zone area. Note the reasonable correlation (r = 0.74). The values for active zones # 5 and # 11, used for subsequent simulations, are highlighted by the vertical and horizontal arrow, respectively. (<b>C</b>) Analysis of the clustering of docked vesicles based on the nearest neighbor distance between vesicles. <i>Left image</i> shows the experimentally determined docked vesicle localization at active zone # 5 as an example; <i>right image</i> shows a single spatial sample of randomly localized docked vesicles. (<b>D</b>) Histograms of the distribution of distances for the random case (blue bars; n = 4800 repetitions for each active zone) and for the experimentally observed case (black; average ± S.D. 67.6 ± 19.0 nm; n = 88 docked vesicles from all N = 15 active zones). The experimental value was slightly smaller than the simulated random case (blue bars; 79.8 ± 20.2 nm; average ± S.D.; p = 8.5 10^–4; paired t-test), which indicates some clustering of docked vesicles. The right panel shows cumulative histograms. (<b>E</b>) Analysis of the clustering of docked vesicles based on a largest radius method. For each active zone, we computed the maximal radius of a circle whose center was in the active zone and did not overlap any vesicles (<i>left image</i>, for the example active zone). This was compared to distributions of circle radii for the same active zone, but with randomly placed vesicles (<i>right image</i>, example of a random seed of vesicle localization). (<b>F</b>) The distribution of circle radii when the vesicles are randomly distributed within all active zones (blue; n = 150 independent seeds for each active zone; 151.8 ± 39.2 nm), compared to the data distribution (black; 160 ± 44.7 nm). The cumulative distribution for the data (black) and random vesicle arrangements (blue; all 15 active zones) are similar. The mean of all 15 active zones for which the random configurations were tested, was statistically indistinguishable from the data mean (paired t-test; p = 0.25). (<b>G, H</b>) Analysis of the clustering of docked vesicles based on comparing areas included within a 30 nm exclusion zone. For each active zone, docked vesicles were placed in random positions, and the area within a 30 nm exclusion zone was calculated. The mean of the areas calculated from random placements (n = 3000 for each active zone) was plotted against the measured exclusion zone area for all N = 15 active zones (<b>I</b>). This follows a line with slope of 1, indicating little clustering at this exclusion zone size. (<b>I</b>) We used Ripley’s K function as a metric for detecting deviations from spatial homogeneity [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004253#pcbi.1004253.ref040" target="_blank">40</a>]. The quantity r-L (r) was computed (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004253#pcbi.1004253.s001" target="_blank">S1 Text</a>), and then plotted versus radius and normalized to the 99% confidence interval (dashed horizontal line). The mean for all active zones is shown in blue, while individual active zones are shown in gray. The plotted measure is below the 99% confidence interval for all radii tested, indicating no significant vesicle clustering.</p

Fast transmitter release at the calyx synapse remains sensitive to the slow Ca²⁺ buffer EGTA-AM up to adulthood.

<p>(<b>A1</b>) Example EPSC traces before (<i>black</i>) and after application of EGTA-AM (<i>red</i>; 200 μM) in a P8 mouse. The inset shows the EPSC trace before and after EGTA-AM normalized to their peak amplitudes. Note the largely unchanged kinetics of the EPSCs following EGTA-AM application (<i>red</i> trace). (<b>A2</b>), Plot of EPSC amplitude versus recording time, for the same cell as illustrated in A1. (<b>B</b>) Another representative example for application of 100 μM EGTA-AM in a different recording from an immature synapse; note that 100 μM EGTA-AM suppresses EPSC amplitudes more slowly, and to a lesser final degree. (<b>C</b>), Concentration-dependence of the EPSC suppression by EGTA-AM, measured in P8–P11 old mice. Suppression of EPSCs was measured at three concentrations of EGTA-AM (50, 100 and 200 μM), and the data was fitted with a Hill equation, indicating a half maximal effective concentration of 87 μM. (<b>D1–D2</b>) Same as (<b>A1-A2</b>), but now for MNTB neurons recorded in adult mice (P60–P100). Note that similar to the measurements at P8–P11, EPSCs were strongly (~80%) blocked by acute application of 200 μM EGTA-AM. (<b>E, F</b>) An example of EPSC suppression by 100 μM EGTA-AM in an adult synapse (<b>E</b>), and the dose-response relation measured at 50, 100, and 200 μM EGTA-AM, which indicated a half maximal effective concentration of 92 μM EGTA-AM. Note the similar concentration-dependent effects of EGTA-AM in immature (<b>A-C</b>), and adult synapses (<b>D-F</b>).</p