Quantitation and Simulation of Single Action Potential-Evoked Ca2+ Signals in CA1 Pyramidal Neuron Presynaptic Terminals

Abstract Presynaptic Ca2+ evokes exocytosis, endocytosis, and synaptic plasticity. However, Ca2+ flux and interactions at presynaptic molecular targets are difficult to quantify because fluorescence imaging has limited resolution. In rats of either sex, we measured single varicosity presynaptic Ca2+ using Ca2+ dyes as buffers, and constructed models of Ca2+ dispersal. Action potentials evoked Ca2+ transients with little variation when measured with low-affinity dye (peak amplitude 789 ± 39 nM, within 2 ms of stimulation; decay times, 119 ± 10 ms). Endogenous Ca2+ buffering capacity, action potential-evoked free [Ca2+]i, and total Ca2+ amounts entering terminals were determined using Ca2+ dyes as buffers. These data constrained Monte Carlo (MCell) simulations of Ca2+ entry, buffering, and removal. Simulations of experimentally-determined Ca2+ fluxes, buffered by simulated calbindin28K well fit data, and were consistent with clustered Ca2+ entry followed within 4 ms by diffusion throughout the varicosity. Repetitive stimulation caused free varicosity Ca2+ to sum. However, simulated in nanometer domains, its removal by pumps and buffering was negligible, while local diffusion dominated. Thus, Ca2+ within tens of nanometers of entry, did not accumulate. A model of synaptotagmin1 (syt1)-Ca2+ binding indicates that even with 10 µM free varicosity evoked Ca2+, syt1 must be within tens of nanometers of channels to ensure occupation of all its Ca2+-binding sites. Repetitive stimulation, evoking short-term synaptic enhancement, does not modify probabilities of Ca2+ fully occupying syt1’s C2 domains, suggesting that enhancement is not mediated by Ca2+-syt1 interactions. We conclude that at spatiotemporal scales of fusion machines, Ca2+ necessary for their activation is diffusion dominated.

Presynaptic Ca 2ϩ transients are resolvable with Ca 2ϩ dyes (DiGregorio and Vergara, 1997;Cochilla and Alford, 1998;Koester and Sakmann, 2000) at millisecond times and over the size of the entire terminal. However, Ca 2ϩ is used too locally and rapidly to be imaged within the dimensions of Ca 2ϩ -binding molecules that cause exocytosis Sabatini and Regehr, 1996). Nevertheless, dyes can quantify presynaptic Ca 2ϩ entry, buffering and removal (Neher and Augustine, 1992;Koester and Sakmann, 2000;Jackson and Redman, 2003;Brenowitz and Regehr, 2007). This approach requires calibration of dye concentrations, fluorescence, and Ca 2ϩbinding properties within cells.
To understand how much presynaptic Ca 2ϩ enters presynaptic terminals, how it interacts with presynaptic Ca 2ϩ buffers and with fusogenic targets such as syt1, we have quantified [Ca 2ϩ ] i in CA1 presynaptic terminals during action potentials. This allowed us to simulate actionpotential-evoked Ca 2ϩ entry, binding, buffering and dispersal at individual terminals using Monte Carlo (MCell) simulation (Kerr et al., 2008) and investigate its interaction with syt1 at resolutions that evoke exocytosis. Combining our results from quantitative analysis of exogenous dye/ buffers and computational modeling demonstrate the complex impacts of temporo-spatial scales on Ca 2ϩ diffusion Ca 2ϩ buffering, buffer saturation during evoked presynaptic Ca 2ϩ entry.

The preparation
Experiments were performed on hippocampal slices (300 m) of male or female 20-to 22-d-old Sprague Dawley rats anesthetized with isoflurane and decapitated. Hippocampi were isolated under semi-frozen Krebs-Henseleit solution: 124 mM NaCl, 26 mM NaHCO 3 , 1.25 mM NaH 2 PO 4 , 3 mM KCl, 2 mM CaCl 2 , 1 mM MgCl 2 , and 10 mM D-glucose, bubbled with 95% O 2 -5% CO 2 , sliced using a Vibratome. The recording chamber was superfused at 2 ml/min and maintained at 28 Ϯ 2°C. Experiments were performed in accordance with institutional guidelines of the University of Illinois at Chicago and the Association for Assessment and Accreditation of Laboratory Animal Care.
were recorded under whole-cell conditions but were held under voltage clamp to record synaptic inputs. In these latter neurons access resistance was monitored with a 10 mV voltage step before each episode. Focal stimuli (0.2 ms, 20 A or less) were applied over CA1 axons using glass-insulated monopolar tungsten microelectrodes. Cells were labeled with dye by allowing sufficient time for diffusion from the patch pipette in the live cell. Axons were tracked from the soma to their presynaptic terminals in the subiculum ( Fig. 1A; Hamid et al., 2014).

Imaging
Confocal microscopy was used to image individual varicosities of CA1 pyramidal neurons, with a 60 ϫ 1.1 NA water-immersion lens using a modified Bio-Rad MRC 600 confocal microscope with excitation wavelengths at 488 and 568 nm (Bleckert et al., 2012). Ca 2ϩ -sensitive dyes of one of two different affinities to Ca 2ϩ were visualized in each experiment. Dye concentration was determined by pairing these dyes with a Ca 2ϩ -insensitive dye (Alexa Fluor 594 hydrazide, molecular weight, 736 g mol Ϫ1 , identical to Fluo-5F and almost identical to that of Fluo-4, 737 g mol Ϫ1 ). Co-diffusion of the Fluo-4 and Alexa Fluor 594 hydrazide was demonstrated by recording absolute values of the fluorescence at axonal varicosities at rest over time. Alexa Fluor 594 hydrazide was excited with a 568-nm laser and imaged in longpass (Ͼ580 nM). Fluo dyes were separately excited with a 488-nm laser and imaged in bandpass (510 -560 nm). Images were taken separately to ensure no cross channel bleed-through.
Ca 2ϩ -binding properties of Fluo-4 and Fluo-5F were determined using Ca 2ϩ standards (Invitrogen) at 28 Ϯ 2°C (the temperature at which experiments were performed) and pH 7.2 (to which the intracellular patch solutions were buffered). Log plots of these data points were used to determine K d (Fig. 1B). Calibrated measurements of dye fluorescence within neurons were also made for each dye (n ϭ 2 for Fluo-5F and n ϭ 2 for Fluo-4) using whole-cell recordings obtained when the patch electrode contained either Fluo-4 or Fluo-5F. Whole-cell access was main- neurons were whole-cell patch-clamped with electrodes containing Fluo-4 (or 5F) and Alexa Fluor 594 hydrazide. Axons and varicosities were traced to the subiculum by imaging Alexa Fluor 594 hydrazide and Ca 2ϩ was imaged using the Fluo dye. B, Calibration of the Ca 2ϩ -sensitive dyes. Fluo-4 (circles) and Fluo-5F (squares) were imaged on the confocal system used for all measurements. Fluorescence intensity was measured over a range of Ca 2ϩ standard concentrations in fixed concentrations of EGTA. Log-log plots gave a slope (Hill coefficient) of 1. Ca 2ϩ concentrations were applied to a patch-clamped cell by application of ionomycin. From saturated Ca 2ϩ concentrations, zero Ca 2ϩ and a fixed value of Ca 2ϩ (0.78 M in EGTA-buffered Ca 2ϩ solution), the closed circle (Fluo-4) and closed square (Fluo-5F) values in the graphs were calculated. These values were used to correct the plots to values in the intracellular environment (solid lines) and to calculate values of K d for the two dyes in the cells (0.44 and 1.49 M). C, Dyes introduced from the patch pipette showed equal diffusion rates into axon varicosities. Intensities of Fluo-4 and Alexa Fluor 594 hydrazide measured by separate illumination at 488 and 568 nm, respectively, were normalized to the value of the fluorescence obtained following identification of a varicosity (20 min after whole-cell access) and plotted against one another for points measured over the next 20 min. The slope of a line fitted to this data (through 0,0, because both dye concentrations were zero at the experiment start) is close to unity. D, Fluorescence intensities of varicosities from all neurons in which Alexa Fluor 594 hydrazide was loaded with Fluo-4 (11 neurons; filled black circles). Overlaid on this data are results of simulations of diffusion of modeled Fluo-4 molecules (mol wt 736 g mol Ϫ1 , thick gray line) and Alexa Fluor 594 (mol wt 737 g mol Ϫ1 ; thick black line). These were detected 250 m from the somata. The thin gray lines indicate the Alexa Fluor 584 concentrations simulated closest to the soma (70 m) and at the extreme range of distances (600 m from the soma).
tained until soma and dendrites were clearly labeled. The electrode was then carefully withdrawn. Baseline fluorescence intensities were measured. The Ca 2ϩ ionophore, ionomycin (5 M) was added to the superfusate. Fluorescence intensities were measured at 2-min intervals until the signal reached a stable maximum. The superfusate was then replaced with a solution containing 0 Ca 2ϩ and 10 mM EGTA and images taken until the fluorescence intensity reached a stable minimum. This solution was then replaced with a solution containing buffered Ca 2ϩ -EGTA ([Ca 2ϩ ] ϭ 0.78 M) and fluorescence in the neuron was measured. Ratios of maxima to minima were very close to those obtained with standards. The standard data points were then plotted over the log plots obtained in vitro. A small correction was applied to the calculated K d for Fluo-4 ( Fig. 1B, black line) but the data obtained with Fluo-5F gave a value of K d that was not measurably different from that obtained in vitro. These values (Fluo-4 kDa ϭ 0.44 M, F min /F max ϭ 0.066 and Fluo-5F K d ϭ 1.49 M, F min /F max ϭ 0.023) were used in all subsequent calculations.
To determine whether Ca 2ϩ dyes and Alexa Fluor dyes diffused at similar rates, Fluo-4 and Alexa Fluor 594 hydrazide signals at varicosities were identified within 20 min of whole-cell access in 10 neurons. Signal strength was normalized to this time point for both dyes. A comparison of the increase in dye intensity over the following 20 min with no stimulation reveals strong correlation with a slope of 1.01 (Fig. 1C, this fit was forced through the origin because both dyes must be at a concentration of zero at the start of the experiment. Without this, the slope was 0.94).
As an independent control to confirm that the slight difference in molecular weights alone does not alter rates of diffusion of the two dyes in the axon, experimentally measured diffusion of Alexa Fluor 594 hydrazide was compared to diffusion of dye in a MCell simulation. Fluorescence intensities of varicosities from all recorded neurons in which Alexa Fluor 594 hydrazide was co-loaded with Fluo-4 (11 neurons; filled black circles) were measured (Fig. 1D). Overlaid on this data are results of simulations (MCell; Kerr et al., 2008) of diffusion of modeled dyes. For these simulations a 3D mesh model cell was created in which a spherical volume (10 m diameter) contained molecules with diffusion constants to simulate Fluo-4 (mol wt 736 g mol Ϫ1 ) and Alexa Fluor 594 hydrazide (mol wt 737 g mol Ϫ1 ). These concentrations were kept constant at this site. Contiguous with this site was a cylindrical mesh of diameter 0.12 m to simulate the axon diameter, interspersed with 1-m diameter varicosities at 4-m intervals. The axon diameter was derived from two sources. (1) Imaging allowed the ratio of total varicosity intensity to be compared with axon intensity. Thus, relative diameter of the axons and varicosities can be calculated from the ratios of the fluorescence intensities (varicosity/axon ϭ 8.3) and the measured diameters of the varicosities (1 m) assuming dye concentrations are the same in both compartments. The resultant ratio allowed calculation of the axon diameter as a ratio of the varicosity diameter.
(2) This result agreed closely with electron mi-croscopy of pyramidal cell axons (Harris and Weinberg, 2012). Resultant simulated dye concentrations were calculated at a distance of 250 m from the somata (Fig. 1D, thick black and gray lines). This represents the median range of the distance of experimentally imaged varicosities. The thin gray lines indicate the Alexa Fluor 584 concentrations simulated in varicosities closest to the soma (70 m; top) or furthest from the soma (600 m from the soma: bottom).
Note that the small difference in diffusion rate simulated between Alexa Fluor 594 (Fig. 1D, gray) and Fluo-4 ( Fig.  1D, black) made no measurable difference to the simulated dye diffusion rates. Additionally, the accumulation of these simulated dyes was overlapping with the experimentally measured fluorescence increase of Alexa Fluor 594 hydrazide (black circles) indicating that the rate of rise of dye concentration in the varicosities is consistent with simple diffusion. Thus, both dyes reach the varicosity at the same rate, which allows the use of Alexa Fluor 594 hydrazide as a "standard candle" for measuring dye concentration. Thus, Alexa Fluor 594 hydrazide fluorescence in axon varicosities was used to determine the concentration of Ca 2ϩ -sensitive dye in the terminal by calculation of that fluorescence as a fraction of its fluorescence in the recording pipette where its concentration was known.
The fluorescence intensity of Alexa Fluor 594 hydrazide fluorescence was measured throughout the experiment in the terminal using fixed parameters on the imaging system. A plot of intensity against time approached an asymptote toward 60 min after obtaining whole-cell access. The absolute fluorescence at the electrode tip was compared to that of the axon varicosities. At the end of the experiment the axon typically blebbed to ϳ5 m, large enough for the microscope point spread function to allow for absolute fluorescence of the axon to be measured. This phenomenon was never present during the recording of stimulation-evoked Ca 2ϩ transients. Its occurrence was observed subsequent to a rise in resting Ca 2ϩ seen after about an hour of recording. Fluorescence in the tip of the pipette where the dye concentration was known was measured in the tissue at the same depth as the axon. This allowed calculation of the axon dye concentration after the experiment ended. It was then straightforward to compare all previously measured values of Alexa Fluor 594 fluorescence, to give absolute dye concentrations throughout the experiment. Recordings in which all of these criteria could not be met were rejected from analysis. Absolute Ca 2ϩ concentrations were calculated in each varicosity using Equations 1, 2 (below). For these calculations we obtained saturated Fluo-4 or Fluo-5F intensity values in varicosities at the end of the experiment by repetitive stimulation and calculated minimum fluorescence values determined from the data in Figure 1B.

Effects of introduction of buffers to cell compartments
It is possible to calculate the intracellular Ca 2ϩ concentration ([Ca 2ϩ ] i ). For a non-ratiometric dye with a Hill coefficient of 1, [Ca 2ϩ ] i is determined from Equation 1: (1) The Ca 2ϩ dye minimum fluorescence intensity (F min ) was calculated as a ratio of F max determined from the dye calibration results (Fig. 1B), and from each cell at the end of the experiment. Absolute values of F min and F max were corrected by the observed value of Alexa Fluor 594 for each time point as a ratio of its value at the end of the experiment when F max was measured. A corrected value of Ca 2ϩ dye fluorescence in the varicosity (F) was calculated from the measured varicosity fluorescence (F meas ) at each time point used for analysis and then re-expressed as a ratio of F max , corrected by comparison to the Alexa Fluor 594 signal throughout the experiments. This is because F max was determined at the end of the experiment and consequently needed to be scaled for each time point at which measurements were made during the experiment. Thus, F is given by: These experiments required constant laser intensity and recording parameters throughout the experiment. To minimize photobleaching, imaging was performed only transiently during evoked responses (1 s per stimulus, Ͻ15 s total per experiment). To use calcium-sensitive dyes as buffers to investigate the fate of Ca 2ϩ that enters presynaptic terminals on stimulation, we must calculate their buffering capacities ( dye ) in the cytosol of the terminal. Since each molecule of dye binds just one Ca 2ϩ ion, the Hill equation with a coefficient of one can be used to calculate dye over a change in Ca 2ϩ concentration  (Neher and Augustine, 1992).
When a rapid Ca 2ϩ pulse enters a cell compartment, free Ca 2ϩ may be removed first by binding to intracellular endogenous buffers, and possibly by diffusion into neighboring compartments, and then by pumps. We have used methods used by Jackson and Redman (2003) originally described by Melzer et al. (1986) to determine the buffering characteristics of Ca 2ϩ in CA1 pyramidal neuron presynaptic varicosities. From these methods we can determine the quantity of calcium entering the varicosity, the mean free [Ca 2ϩ ] i within the varicosity immediately after the stimulus, the endogenous Ca 2ϩ buffering capacity, and the rate of removal of Ca 2ϩ from the cytosol. From this we have developed simulations of Ca 2ϩ entry, diffusion, and buffering in the presynaptic terminal.
The relationship between Ca 2ϩ unbinding rates from the dye and rebinding either to dye or endogenous buffers can be used to calculate endogenous buffering capacity ( end ) of the terminal. If the value of dye varies during the experiment then we assume a constant rate of Ca 2ϩ extrusion from the terminal ( ext ). The decay rate () of a pulse-like Ca 2ϩ signal in a cell compartment is described by the equation: Thus, we obtained values of end by fitting Equation 5 to plots of from experimental data vs dye from Equation 4. This approach does have drawbacks, if processes modifying Ca 2ϩ removal or adding to cytosolic Ca 2ϩ occur after action potentials. Such processes include diffusion of the Ca 2ϩ -dye complex from the measured compartment, or release of Ca 2ϩ from internal stores. In Equation 5, these effects are grouped into a single variable end . Nevertheless, the result ( end ) can be obtained independently of computed absolute values of Ca 2ϩ , or even of background fluorescence measurement errors. It therefore serves as an independent measure of whether the alternative following measurements of end are reasonable.
By measuring the peak amplitude of the free Ca 2ϩ transient throughout the varicosity over a range of values of dye , we may assume that the total change in Ca 2ϩ concentration due to a stimulus is described by the equation: and ⌬͓Ca end ͔ ϭ end •⌬͓Ca 2ϩ ͔i, where [Ca end ] is the concentration of endogenous buffer bound to Ca 2ϩ and ⌬[Ca] total is the total stimulus-evoked change in calcium concentration in the cell compartment. Thus, combining these equations, we may state: . For each action potential, as the value of dye rises it will come to dominate binding of Ca 2ϩ entering the cell compartment. This approach is useful because the value of ⌬[Ca dye ] can be calculated for each action potential in each presynaptic terminal as the value of dye increases by diffusion of dye from the soma. Equations 6-8 can also give: Values of ⌬[Ca] total , and end can be determined by extracting constants from fits of either Equation 9 or Equation 10. The true value of peak ⌬[Ca 2ϩ ] I in the varicosity when no dye is present is obtained by extrapolating the fit to the y intercept in Equation 9, where dye ϭ 0. To calculate total Ca 2ϩ entering the terminal from the concentrations obtained from either Equation 9 or Equation 10, we calculated varicosity volumes from images using Alexa Fluor 594 hydrazide. Varicosities are larger than the smallest structures that can be imaged in our microscope. Point spread data from 0.2-m latex microspheres were determined by imaging under the same light path as all data in this study (568-nm excitation, longpass emission). The point spread was Gaussian in x-y and z dimensions with an x-y dimension half maximal width of 0.45 m.
Varicosities approximated ellipsoids with the long axis along the line of the axon. We measured length (l) and width (w), assuming depth was similar to the width because it was not possible to obtain sufficient z-plane resolution to accurately determine depth. Mean measured varicosity length (l) was 2.3 Ϯ 0.2 m and width (w) was 1.2 Ϯ 0.1 m. These values are quite similar to terminal sizes obtained from electron microscopic images (Harris and Weinberg, 2012).
Assuming the varicosities were ellipsoid, volume of the varicosity is given by: Chemicals were obtained as follows: Alexa Fluor dyes, Fluo-4, Fluo-5F, and Ca 2ϩ standards from Thermo Fisher; salts, buffers, etc. from Sigma.

Simulations
MCell simulations were applied to Ca 2ϩ buffering within a model of the CA1 axon varicosity based on the data obtained experimentally in this study. Simulations were run in the MCell environment (Kerr et al., 2008) in which a 3D mesh model of the presynaptic terminal was created based on measurements determined from these experiments and from electron microscopic images of hippocampal presynaptic varicosities (Harris and Weinberg, 2012). Ca 2ϩ entry, diffusion binding and removal from the terminal were modeled using initial parameters obtained from experimental data in this study, and from the literature and from published sources. Possible Ca 2ϩ -binding proteins and their concentrations were investigated by comparing multiple parameters from experimental data and the results of simulations. All of the parameters used are outlined in Tables 1-3. An animated visualization of these simulations are viewable: https://anatomy.uic.edu/ faculty/index.html?facϭsimontalford&catϭall. Similarly, MCell parameter sets are available on this website.

Statistics
Data were combined from numerous recordings from a total of 18 neurons to calculate values indicated in tabular form. Fits to datasets over for a number of equations were performed in Igor Pro (Wavemetrics). Errors intervals from fitted data represent the 90% confidence limits of those fits. To compare simulation results to experimental data, results were considered to validate the model if these simulation datasets fell within the 95% confidence intervals of the experimental data. In fact, for each of these validations, simulations which fell within the 90% confidence interval indicated a stronger correlation. Otherwise errors are reported as the SEM. Significance was tested with two-tailed Student's t test or two-factor ANOVAs where appropriate. We used an ␣ level of 0.05 for significance for statistical tests.

Resting Ca 2؉ concentrations in axonal varicosities
To measure presynaptic Ca 2ϩ , Ca 2ϩ sensitive and insensitive dyes were introduced to CA1 pyramidal neurons from somatic whole-cell pipettes containing Ca 2ϩsensitive dye, and Alexa Fluor 594 hydrazide (250 M). After 20 min, the axon was traced by imaging Alexa Fluor 594 (Hamid et al., 2014). We initially used Fluo-4 (1 mM) as a Ca 2ϩ sensor. Alexa Fluor 594 fluorescence was used to measure dye concentration. We assume co-diffusion of the dyes which have similar molecular weights. Thus, Ca 2ϩ dye concentrations were calculated throughout each experiment (Materials and Methods) using Alexa Fluor 594 hydrazide as a standard.
To further illustrate co-diffusion of the two dyes, Alexa Fluor 594 hydrazide and Fluo-4 fluorescence ( Fig. 2Aa) were normalized to their values when the first varicosity image (inset 1) was obtained (20 min after whole cell). For 70 min (until Fig. 2Aa, inset 2), fluorescence ratios between the dyes remained constant. Resting [Ca 2ϩ ] i was calculated from these data and the F max of Fluo-4 fluorescence (obtained by repetitive stimulation), applied to Equation 3 (Materials and Methods). [Ca 2ϩ ] i remained stable for Ͼ1 h as dye concentrations rose (mean resting [Ca 2ϩ ] i ϭ 81 Ϯ 5 nM; 11 cells; Fig. 2Ab). At 80 min, Fluo-4 fluorescence increased more rapidly than Alexa Fluor 594's revealing an increase in resting [Ca 2ϩ ] i (Fig. 2Aa, green circles). Therefore, we did not sample time points later than 80 min.

Dependency of the Ca 2؉ signal on dye buffering capacity ( dye )
Single CA1 axon varicosities loaded with low-affinity Ca 2ϩ -sensitive dye (200 M Fluo-5F pipette concentration, K d ϭ 1.49 M; n ϭ 30) were imaged by line scanning (500 Hz) single action potential evoked Ca 2ϩ transients Bd, Responses as ⌬F/F ϩ 1 (F ϭ pre-stimulus Fluo-5F fluorescence). Ca 2ϩ transients are invariant. Be, Color-coded representation of line scan as ⌬F/F ϩ 1 from analyzed region in Bb after background subtraction. Bf, Single Ca 2ϩ transient 37 min after whole cell. Data fit by a single exponential. From fits, decay rates and peak responses were calculated. Ca, In varicosities filled with Alexa Fluor 594 hydrazide and higher affinity Fluo-4 (1 mM), Ca 2ϩ transients were evoked and Fluo-4 line scanned. The first recording (20 min after whole cell) was made as dye diffused into the varicosity (decay rate, ϭ 0.53 s, Cb pink); 25 min later the amplitude was reduced and increased ( ϭ 1.7 s, red). Cc, In other varicosities, at higher dye concentrations reduced ROI imaging (5 Hz) minimized bleaching. Transient intensity was plotted versus time and fitted with single exponentials to calculate and peak amplitude. Inset -varicosity imaged 80 min after whole-cell access at time points indicated by numbers. Da, Comparison of effect of Fluo-4 and Fluo-5F on transients. Values of from fits to plotted versus time after whole-cell access. Data from each varicosity with Fluo-4 is linked with lines. The line through the Fluo-5F data are a least squares fit. Db, Similar comparison of peak amplitudes. Values of and peak in Fluo-5F are constant those with Fluo-4 are time dependent. (Fig. 2B). Responses were evoked by single action potentials through the recording pipette ( Fig. 2Ba) during rising dye concentrations (Fig. 2Bb,Bc). Normalized as (⌬F/F ϩ 1), these Ca 2ϩ transients were invariant in amplitude and throughout the experiment (Fig. 2Bd), and the fluorescence transient was uniform across the varicosity within 6 ms of the stimulus (Fig. 2Be). Means of transients from sequential stimuli were plotted, and single exponentials fit to decays (Fig. 2Bf). From these fits, in all cells, transients from different varicosities at different axon locations gave reproducible amplitudes and values of decay time constant [; mean ⌬[Ca 2ϩ ] i ϭ 677 Ϯ 10 nM (Materials and Methods; Eq. 3), mean ϭ 119 Ϯ 1.4 ms, n ϭ 30].
Similar experiments were performed substituting the high affinity Ca 2ϩ dye (Fluo-4, K d , 0.44 M; 1 mM pipette concentration). Transient peak amplitudes reduced, and decay time constants () increased as dye concentrations rose (Fig. 2C). This is consistent with Ca 2ϩ buffering by Fluo-4, because the amplitude represents a proportion of the dye that is Ca 2ϩ -bound. As dye concentrations rise a smaller dye fraction binds Ca 2ϩ entering. Unbound dye competes for Ca 2ϩ with endogenous buffers, consequently, increases as rebinding to dye becomes more likely in cells (Neher and Augustine, 1992) or nerve terminals (Koester and Sakmann, 2000;Jackson and Redman, 2003;Brenowitz and Regehr, 2007). Indeed, as dye concentrations rose during the experiment, decay times became long enough that line scanning was not necessary. Axon terminals were instead imaged with sequential frames in two dimensions (Fig. 2Cc). When values of rose above 1 s, this imaging was used because it limited bleaching to repeat exposures.
An alternative explanation for increased is diffusional loss of endogenous buffers during whole-cell recording (Müller et al., 2007). However, this would occur regardless of dye concentration or affinity, be dependent on recording duration, and be accompanied by increased peak amplitudes. These effects did not occur (Fig. 2D). Indeed, during extended recording times, we compared Ca 2ϩ transient 's and peak amplitudes from Fluo-4 (n ϭ 11 neurons) versus Fluo-5F (n ϭ 30 neurons). As dye concentrations rose, the value of recorded with Fluo-4 increased, but in contrast the value obtained with Fluo-5F remained almost constant (Fig. 2Da). Similarly, the peak amplitude of the response measured as ⌬F/F ϩ 1, decreased over time when measured with Fluo-4 but again remained constant when recorded with Fluo-5F (Fig.  2Db). Thus, it is increasing dye buffering capacity ( dye ) not loss of endogenous buffer that causes the changes in peak ⌬F/F and . Calculated dye concentrations combined with calibrated dye properties (Fig. 1) and Ca 2ϩ transient amplitudes were therefore used to relate dye buffering to varicosity Ca 2ϩ transients.

Use of dyes to calculate Ca 2؉ entry and buffering
We determined dye (Eq. 4) for each Ca 2ϩ transient from varicosity dye concentrations, changes in varicosity-free Ca 2ϩ (⌬[Ca 2ϩ ] i ) calculated from this data, and Equation 3. This value was plotted against time after obtaining wholecell access for one example (Fig. 3Aa, inset). In 18 neu-rons (seven Fluo-5F, 11 Fluo-4) a linear fit to vs dye (single cell example in Fig. 3Aa; data from all cells, Fig.  3Ab) gave an x intercept of -58 Ϯ 40 and an estimate of the endogenous buffering capacity of the varicosity ( end ) of 57 (Eq. 5).
A plot of ⌬[Ca 2ϩ ] i (Eq. 3) against dye (Fig. 3Ba single example; data from all cells, Fig. 3Bb) demonstrated the relationship between dye and the Ca 2ϩ transient. A fit of Equation 9 to this data, or a linear fit to 1/⌬[Ca 2ϩ ] i vs dye (Fig. 3B, insets), gives a peak free change in Ca 2ϩ concentration (⌬[Ca 2ϩ ] I ) in the absence of dye throughout the terminal of 0.76 Ϯ 0.03 M. This is obtained from the y-axis intercept of the fit where dye ϭ 0. Constants from the same fit give total Ca 2ϩ entry of 58 Ϯ 6 M and end of 75 Ϯ 6.
Total dye bound Ca 2ϩ ([Ca dye ]) was calculated for each transient either from the product of [Ca 2ϩ ] I and dye, or from proportions of dye bound to Ca 2ϩ calculated from the Hill equation. These gave values that differed by Ͻ5%. Data in Figure 3C are from the former (single cell Fig. 3Ca; combined data, Fig. 3Cb). If total Ca 2ϩ entering each varicosity were constant for each action potential, then these data are represented by Equation 10, in which the asymptotic value of total Ca 2ϩ entering the varicosity was 45 Ϯ 3 M. From this and each measured varicosity dimensions (volume mean ϭ 1.7 Ϯ 0.3 m 3 , median ϭ 1.2 m 3 , n ϭ 18) we determined total molar Ca 2ϩ entering the varicosity (Table 1). end is taken from fits of Equation 9 to ⌬[Ca 2ϩ ] i (Fig. 3B). Peak [Ca 2ϩ ] i is for Ca 2ϩ throughout the varicosity and total [Ca 2ϩ ] entering is from fits to Equation 10 of data in Figure 3C. Results with the least errors were used and summarized (Table 1).

Ca 2؉ source and removal from the terminal
Internal stores might contribute to Ca 2ϩ transients (Cochilla and Alford, 1998;Emptage et al., 2001;Scott and Rusakov, 2008). Calculations of Ca 2ϩ entering, and end will be distorted if secondary Ca 2ϩ sources exist. In recordings with Fluo-5F, ryanodine (5 M; to block store release) was superfused, and five action potentials (50 Hz; Fig. 4A) evoked a response on which ryanodine had no effect (to 111 Ϯ 12% of control, 95% confidence interval of 90 -132%, n ϭ 5). Thus, ryanodine does not meaningfully alter Ca 2ϩ transients even during trains of stimuli.
If Ca 2ϩ extrusion is mediated by pumps with linear rates versus peak [Ca 2ϩ ] I , then as the transient varies with dye , removal rates can be calculated. As dye concentration increases, dye dominates end , and peak [Ca 2ϩ ] i available to pumps is reduced. Removal will be inversely proportional to available [Ca 2ϩ ] i . The slope of 1/ of the transient against peak [Ca 2ϩ ] i allows calculation of Ca 2ϩ removal. Thus, these data obtained with Fluo-4 were plotted (Fig.  4B), and the extrusion rate [7.6 ϫ 10 6 ϫ (total #Ca 2ϩ ions) M Ϫ 1 s Ϫ1 ] calculated from the slope. The linearity of these data also provide evidence that secondary Ca 2ϩ sources do not contribute to the transient, at least at these values of dye . A summary of experimentally determined properties of the varicosity is given in Table 1.

Modeling of Ca 2؉ transients in varicosities
Imaging experiments provided resting [Ca 2ϩ ] i , varicosity volumes, their endogenous buffering capacity, the peak free [Ca 2ϩ ] i , the total Ca 2ϩ entering, and its removal rate. The principal Ca 2ϩ buffer in CA1 pyramidal somata is calbindin 28K and its concentration in somata and dendrites has been determined to be 40 M (Müller et al., 2005), making it a candidate buffer in varicosities (Arszovszki et al., 2014) with well-characterized Ca 2ϩbinding properties (Nägerl et al., 2000). Calmodulin with similarly well-characterized properties (Faas et al., 2011) has also been proposed as a dominant binding protein in these neurons. We constructed 3D models in the simulation environment MCell (Kerr et al., 2008;Tables 2, 3), to investigate Ca 2ϩ entry, diffusion, buffering, and removal during action potential stimulation. Parameters and buffers (either calbindin 28k or calmodulin), used in this model were determined in this study, obtained from the literature, or varied to obtain best fits to the data (Table 2). A 3D mesh model was developed (Blender), from published data and from this study. Varicosities were represented by ellipsoids (Fig. 5A), 2 ϫ 1 m (volume ϭ 1.2 ϫ 10 Ϫ11 l, the median measured varicosity volume) en passant to an axon (0.12 m in diameter). They contained 320 40-nm diameter vesicles and an internal structure mimicking organelles (Fig. 5A). We modeled Ca 2ϩ extrusion with a rate of 2.2 ϫ 10 11 M Ϫ 1 s Ϫ1 (from the number of Ca 2ϩ ions entering and the slope from Fig. 4B) distributed to 2500 pumps over the plasma membrane and 1000 on the internal organelle mesh structure. A Ca 2ϩ leak (1.77 ϫ 10 5 ions s Ϫ 1 ) similarly distributed achieved resting free [Ca 2ϩ ] i of 81 nM. Ca 2ϩ buffering was modeled with three models of buffers (calbindin 28K 3:1 ratio, calbindin 28K 2:2 ratio or calmodulin). Calbindin 28K possesses four Ca 2ϩ -binding sites and models have been proposed for its Ca 2ϩ binding (Nägerl et al., 2000) with 3:1 or 2:2 ratios of high-affinity and medium-affinity non-cooperative sites. The former model was slightly but not significantly favored in data fits in vitro, but the latter fit experimental data significantly better in a model of cerebellar Purkinje neurons (Schmidt et al., 2012) in which a correction to the on-rate accounted for intracellular Mg 2ϩ (rates indicated in Table 2). Ca 2ϩ -calmodulin binding was also modeled using published parameters (Faas et al., 2011; Table 2). In our simulations, we used the same Mg 2ϩ on-rate correction in our models for calbindin 28K and calmodulin. Evoked Ca 2ϩ entry was modeled as a total of 45 M Ca 2ϩ entering the terminal in 2 ms (Table 1) Buffer concentrations were first estimated by solving the Hill equation for values of total Ca 2ϩ entry, and resting, and stimulated peak free [Ca 2ϩ ] i . This assumes equilibrium at peak, and was expected to underestimate true buffer concentrations because Ca 2ϩ transients are too rapid for equilibration. This gave 92.8 M for calmodulin and 24.8 M calbindin 28K (2:2 ratio of high-affinity and medium-affinity sites), or 19.7 M (3:1 ratio).
To determine buffer parameters, simulated endogenous buffer concentrations were varied starting at steadystate results to compare simulations to experimentally determined peak free ⌬[Ca 2ϩ ] i and ( Fig. 5B; parameters in Tables 2, 3). Transient decays were fit with single exponentials omitting the first 4 ms of the simulation to avoid initial Ca 2ϩ inhomogeneities. From these fits, peak free ⌬[Ca 2ϩ ] i and were plotted against simulated buffer concentrations (Fig. 5C). Intersection of simulated and experimental values for and ⌬[Ca 2ϩ ] i implies that model parameters are accurate and provides an estimate for buffer concentration and type. Models of calbindin 28K with a 2:2 binding ratio converge to within the 95% confidence interval of the experimental data (Fig. 5C, red line and markers). A least squares fit for this convergence predicts   (Müller et al., 2005). Neither the calbindin 28K 3:1 ratio nor calmodulin converged (Fig. 5C). Note, in cerebellar Purkinje neurons, models for calbindin 28K also favor 2:2 ratios (Schmidt et al., 2012). While other Ca 2ϩ buffers are present, we conclude that simulating calbindin 28K with a 2:2 ratio of binding site has validity.

Model validation of experimental results in a small terminal
We used simulations to determine if our experimental approach derived from (Neher and Augustine, 1992) is valid for small terminals. Effects of Fluo-4 (0 -670 M) were simulated and dye calculated as for experimental data. As for experimental data, rising values of simulated dye reduced peak [Ca 2ϩ ] i and increased . Peak [Ca 2ϩ ] i and were measured from single exponentials fitted to simulated data (Fig. 5Da) ommitting the initial 4 ms. Results were plotted with experimental data as versus dye (Fig. 5Db), peak [Ca 2ϩ ] i versus dye (Fig. 5Dc), and total Ca 2ϩ entry captured by the dye vs dye (Fig. 5Dd). In all cases, simulations fell within the 90% confidence limits of experimental data supporting the use of this approach in small varicosities and providing a validation of the simulation by simulating an uncontrolled variable.  Fluo-5F K d /k on /k off 1.49 M/5 ϫ 10 8 M -1 s Ϫ1 /750 s Ϫ1 Fig. 1

Varied in model
Varied in model (Nägerl et al., 2000;Schmidt et al., 2012) Calmodulin concentration N-terminal k on/off T N-terminal k on/off R C-terminal k on/off T C-terminal k on/off R 15 -60 M 7.7 ϫ 10 8 M -1 s Ϫ1 /1.6 ϫ 10 5 s Ϫ1 3.2 ϫ 10 10 M -1 s Ϫ1 /2.2 ϫ 10 4 s Ϫ1 8.4 ϫ 10 7 M -1 s Ϫ1 /2.6 ϫ 10 3 s Ϫ1 2.5 ϫ 10 7 M -1 s Ϫ1 /6.5 s Ϫ1   (Fig. 3), to a hypothetical zero dye concentration where dye ϭ 0 (Fig. 3), compared with results for recordings using Fluo-5F shows a close match indicating that the dye did not significantly buffer the Ca 2ϩ transient. Therefore, we used Fluo-5F to investigate Ca 2ϩ signaling in detail and to further validate simulations with experimental data. In four prep-arations the orientation of the axon and varicosity allowed simultaneous line scanning of both, to compare the relative amplitudes of their Ca 2ϩ transients. In axons farther than 1 m from the varicosity no Ca 2ϩ transient was observed (Fig. 5Eb,Ee, blue), indicating that Ca 2ϩ does not escape from varicosities by diffusion. An equivalent simulation was performed, in which

Ec Ed
Ee (a) Simulated Varicosity Figure 5. MCell simulation of Ca 2ϩ transients and validation against experimental data. A, The varicosity was modeled as an ellipsoid 2 ϫ 1 ϫ 1 m and contained 320 synaptic vesicles, and one large internal structure to provide sites for Ca 2ϩ intrusion (i.e., ER/mitchondrion). A variable quantity of Ca 2ϩ buffer was modeled. Images show free Ca 2ϩ ions (green) and Ca 2ϩ -bound states of calbindin 28K as per the color scheme in the kinetic model (B). Times indicated by letters in B. Parameter from Table 1 and from varying buffer concentrations. Pre-stimulus state (Aa) at peak of stimulus (Ab) at first time point resolveable with fluorescence imaging (Ac). B, Simulated total varicosity-free [Ca 2ϩ ] i following stimuli at three calbindin 28K concentrations (15 M, pink; 40 M, red; 60 M, black). Single exponential fits (blue) were applied to these simulations and values of peak ⌬[Ca 2ϩ ] i and decay () were obtained from these fits. Inset shows kinetic scheme for the calbindin 28K 2:2 ratio. Parameters in Table 2. C, 3D plot of simulated , peak ⌬Ca 2ϩ against varying buffer concentrations (15-60 M) following simulated varicosity stimulation. Blue, 3:1 ratio model of calbindin 28K ; red, 2:2 model of calbindin 28K ; green, model of calmodulin. Parameters in Table 2. The vertical black line and gray shading represent experimentally obtained , peak ⌬Ca 2ϩ and their standard errors. These data converge only with the 2:2 ratio of calbindin 28K at a concentration of 39.7 M. D, Varying Ca 2ϩ -sensitive dye concentrations (Fluo-4; Table 1) were simulated and resultant Ca 2ϩ transients graphed. Da, Responses shown with dye concentrations of 50, 200, and 670 M. Db-Dd, Decay time, peak ⌬Ca 2ϩ , and total Ca 2ϩ entry from these simulated transients over values of dye from 0 to 1121 (red circles and lines) is plotted as per Figure 3C and overlaid on the fits and 90% confidence intervals of that experimental data. E, Comparison to experimental data of simulation in axons. Action potentials (Ea) evoked varicosity Ca 2ϩ transients (Eb) recorded with Fluo-5F that also allowed recording from axons. Such events were also simulated by calculating Ca 2ϩ concentration along the axon and varicosity axis (Ec, yellow). Ed, Simulated line scan. Ee, top, Overlay of experimental ⌬F/F ϩ 1 from a varicosity (blue) and the simulated result (red). Bottom, Similar overlay but from adjacent axons. F, Comparison to experimental data of simulations of trains of stimuli. Fa, Five actions potentials at 50 Hz evoked Ca 2ϩ transients recorded with Fluo-5F (Fb) quantified as Ca 2ϩ concentrations (Fc, blue, gray lines 90% confidence interval from five varicosities). The same train was simulated (Fc, red). Simulation data fell within the 90% confidence interval of the data. Ca 2ϩ -Fluo-5F binding was simulated in discrete volumes along the model axis (Fig. 5Ec, yellow), and ⌬F/F ϩ 1 calculated from simulated bound/unbound ratio of Fluo-5F. Results (mean, 20 random seeds) were plotted with overlaid experimental data (Fig. 5Ee, red). The simulated transient, like the experimental was confined to the varicosity with negligible signal seen 1 m from the varicosity (Fig. 5Ee, lower traces).
We also tested simulations by comparing their results to train-evoked Ca 2ϩ transients in Fluo-5F (200 M)labeled varicosities. Ca 2ϩ transients were recorded during 5 action potentials (50 Hz; n ϭ 5 cells; Fig. 6Ca). This caused a summating Ca 2ϩ transient (Fig. 5F). Absolute Ca 2ϩ concentrations were calculated and expressed as the mean of all responses (Fig. 5Fc, blue; seven responses) bounded by the 90% confidence interval (gray). Ca 2ϩ transients simulated using MCell (five stimuli at 50 Hz; 10 seeds; Fig. 5Fc; red) fall within the 90% confidence intervals of the experimental data for the cell shown and for all five neurons.

Spatiotemporal distribution of Ca 2؉ entry to the terminal
Calculations of varicosity [Ca 2ϩ ] and its buffering assume that Ca 2ϩ rapidly reaches spatial uniformity within varicosities. The overlap between single exponential fits to experimental data and fits to simulations (Fig. 5D indicates this approach is valid to calculate total Ca 2ϩ entry and its buffering; however, in five neurons recorded with sufficiently high resolution, we observed repeatable, but non-uniform, Ca 2ϩ distributions immediately after stimulation; Fig 6).
In each varicosity (Fig. 6A), line scans (mean of four transients in each of the five terminals; ⌬F/F ϩ 1 vs time; Fig. 6B), reveal brighter regions immediately post-stimulus ( Fig. 6Ca; hotspots arrowed at faster time base, lower panel). However, these spots are close to the resolution limit of the microscope, and their intensity might have been affected by errors in background or prestimulus intensity. If hotspots represent localized Ca 2ϩ entry then a faster local decay, that will not be altered by these errors, would represent diffusion from this site (mean overall ϭ 119.5 Ϯ 1.4 ms). Therefore, fits to exponentials were analyzed in line scan subregions. In the case illustrated, a single exponential well-fit Ca 2ϩ transients away from hotspots (Fig. 6Cb,Ce), but did not adequately fit regions at hotspots. The hotspots were well-fit by double exponentials (s of 6 -11 and 105-135 ms; Fig. 6Cc,Cd). Similar results were obtained in all five neurons (mean 1 ϭ 9.0 Ϯ 2.9 ms; 2 ϭ 124.5 Ϯ 19.1 ms; sum of squares of residuals were significantly different between single and double exponential fits at the hotspots, t (4) ϭ 3.25, p ϭ 0.015, but were not significantly different away from hotspots, t (4) ϭ 1.42, p ϭ 0.11; the ratio of amplitudes of the first and second exponentials at the hotspots ϭ 0.92. This was significantly higher than values obtained from double exponentials fit to data away from hotspots ϭ 0.47, t (4) ϭ 3.82, p ϭ 0.009). To illustrate the peak [Ca 2ϩ ] i recorded by Fluo-5F, experimental data are replotted (Fig. 6D, black) as [Ca 2ϩ ] I versus time, and is well-fit with a double exponential (red; residual above also in red, fast ϭ 2.1 ms, peak [Ca 2ϩ ] i of 1.8 M; vs 0.8 M for the rest of the varicosity). In all five neurons, the mean peak free [Ca 2ϩ ] i ϭ 2.7 Ϯ 0.57 M and mean fast ϭ 3.3 Ϯ 1.3 ms. By comparison, the data were poorly fit by a single exponential (blue, residual above, goodness of fit was again determined by comparing sums of squares of residuals. The sum of squares of these residuals were significantly different between single and double exponential fits at hotspots; t (4) ϭ 3.25, p ϭ 0.016, but not away from hotspots, t (4) ϭ 2.00, p ϭ 0.060).
These Ca 2ϩ hotspots are repeatable. Examples from two locations (arrowed Fig. 6C) with an early fast Ca 2ϩ transient (Fig. 6Ea) or lacking one (Fig. 6Eb) were analyzed in four sequential stimuli (five cells). As for the values obtained from values of ⌬F/F at hotspots or non-hotspot regions, each [Ca 2ϩ ] i response was fit with a double exponential. Fast exponential amplitudes for the two regions were significantly different (the fast exponential amplitude at hotspots, 592 Ϯ 170 nM and slow, 331 Ϯ 68 nM, whereas at non-hotspots these amplitudes were 230 Ϯ 141 nM and 303 Ϯ 48 nM, p ϭ 0.0052, two-factor ANOVA, respectively), but there was no significant difference between slower exponential amplitudes (p ϭ 0.08).

Simulation of localized Ca 2؉ entry
We determined whether discrete placement of Ca 2ϩ entry within the simulation could reproduce the experimental non-uniform Ca 2ϩ distribution. In simulations, Ca 2ϩ entry was located at one to six plasma membrane sites. However, in all cases, the total Ca 2ϩ entry summed to 45 M (Table 2) over the whole varicosity. Experimental line scanning was simulated (20 random seeds) by simulating values of Fluo-5F ⌬F/F ϩ 1 (Fig. 7A) in a line of discrete volumes across the model varicosity (Fig. 7B, vertical yellow band). One end of this band always included only one Ca 2ϩ entry site. ⌬F/F ϩ 1 values, were resampled to rates obtained during experimental line scanning (500 Hz) to create a simulated line scan matrix (Fig. 7A) equivalent to the experimental data.
Simulation results were plotted from the two ends of the yellow band, obtained when all Ca 2ϩ entry (45 M) was at one point (Fig. 7B, top, point of simulated Ca 2ϩ entry; bottom, away from Ca 2ϩ entry; Fig. 7C, overlaid with experimental data, blue). There is a substantial difference between amplitudes of the earliest peak at the Ca 2ϩ entry site (Fig. 7Ca, red) compared to the other side of the simulated varicosity (Fig. 7Cb, black). Similar simulation results were plotted where Ca 2ϩ was evenly distributed at six locations, one of which was at the same location as above. Little difference in peak amplitude was seen at the Ca 2ϩ entry site and away from it (Fig. 7D).
Double exponentials were fit to the simulations. 's of fast exponentials were within the 90% confidence limits of fits of early components of experimental data (simulations from 3 to 4 ms; experimental data; Fig. 6D, 3.3 Ϯ 1.3 ms). Peak amplitudes of simulated Fluo-5F ⌬F/F early components were obtained for fits to all distributions of Ca 2ϩ entry at the site of entry and across the varicosity at the opposite end of the yellow band (Fig. 7B) from this site. Substantial differences in peak amplitudes at a point of Ca 2ϩ entry compared to the opposite side of the varicosity away from Ca 2ϩ entry, were observed only when Ca 2ϩ entry was at one or two sites (that is when at least 50% of total varicosity Ca 2ϩ entry was localized to one site; Fig.  7E). Thus, to obtain experimental local peaks in Ca 2ϩ (Fig.  7), clustering of VGCCs may occur.
We then determined time-courses of paired-pulse facilitation with EPSCs in subicular pyramidal neurons (Fig. 8C). In three of the preparations treated with EGTA-AM (20 M) the paired-pulse interval was varied (20 -500 ms; Fig. 8Ca). In EGTA-AM, facilitation was abolished at intervals Ͼ50 ms. In contrast in controls, facilitation was recorded at intervals from 20 to 500 ms (Fig. 8Cb). Facilitation ratios from controls (n ϭ 7) and after EGTA-AM (n ϭ 3) were plotted from 20-to 1000-ms intervals (approximate duration of varicosity Ca 2ϩ transients; Fig. 8Cc). In contrast to this facilitation of postsynaptic responses, presynaptic Ca 2ϩ transients did not show augmentation at 20-or 200-ms interpulse intervals (although at 20 ms the responses summed) and showed no summation at 200-ms intervals. Ca 2ϩ transients were recorded and evoked following wholecell recording as for Figure 2B, except that paired pulses of action potentials were evoked at 20-or 200-ms intervals. Amplitudes of the paired evoked Ca 2ϩ transients (⌬[Ca 2ϩ ] i ) were not significantly altered   ( Fig. 8D; at 20-ms intervals 2nd response was 115 Ϯ 19% of 1st, n ϭ 7, t (6) ϭ 0.98, p ϭ 0.18; at 200-ms intervals 2nd response was 100 Ϯ 10% of the 1st, n ϭ 3, t (2) ϭ 0.03, p ϭ 0.49). Thus, while paired pulse facilitation is Ca 2ϩ dependent, as indicated by its sensitivity to EGTA, Ca 2ϩ transients do not measurably augment at the scale of the entire terminal to cause this potentiation.

Simulating paired-pulse presynaptic Ca 2؉ transients
To address experimental limitations of analyzing Ca 2ϩ at the spatiotemporal resolutions of the vesicle fusion machinery and its activation, we simulated Ca 2ϩ , Ca 2ϩ buffer states, and effects of repetitive stimulation on unbound and bound Ca 2ϩ (Fig. 9) using parameters previously determined. Within the simulation, at rest, Ͼ90% of calbindin 28K is unbound (Fig. 9Aa,B). Stimulation causes partial occupancy of all calbindin 28k states (Fig. 9A). However, 2/3 of all bound states remain unoccupied even at peak occupancy (Fig. 9Ab,B). Nevertheless, unbinding is slow and full recovery takes longer than 1 s (Fig. 9Ad,B). We then determined the effect of paired pulses over intervals from 20 to 1000 ms. Although calbindin 28K was not saturated at any intervals (Fig. 9B, blue), the second pulse achieved higher peak free [Ca 2ϩ ] than the first (Fig.  9C, difference between 2nd peaks, black, and red dashed line, that represents linear summation) and showed a slower decay (Fig. 9Cb; of exponential increased from 423 s on the first stimulus to 767 on the second). This enhanced second peak, only resolvable by simulation is seen despite the fact that the Ca 2ϩ signal recorded at the base of this initial transient resolvable with imaging is only enhanced by Ͻ200 nm and only at the very shortest intervals (linear summation of the component resolvable by experimental imaging is demonstrated by the blue dashed line). The increased amplitude and decay rate is driven by higher occupancy of calbindin 28K by Ca 2ϩ . We conclude that the transient Ca 2ϩ signal resulting from diffusion of Ca 2ϩ throughout the varicosity does show an enhanced amplitude due to partial Ca 2ϩ buffer saturation. However, this signal is computed from a much larger volume than the Ca 2ϩ transients within tens of nanometers of the VGCCs that evokes fusion by interacting with syt1.

Activation of syt1 by evoked presynaptic Ca 2؉ entry
Syt1, the Ca 2ϩ sensor for exocytosis in CA1 pyramidal neurons, has two C2 domains with five Ca 2ϩ -binding sites, some of which have mM affinities for Ca 2ϩ (Südhof and Rizo, 2011). This requires syt1 to be Ͻ100 nm from the Ca 2ϩ source Augustine et al., 1991) as demonstrated also here (Fig. 8). It is unclear whether all sites must bind Ca 2ϩ to evoke exocytosis (Radhakrishnan et al., 2009), although there is evidence that very low affinity interactions at the C2A domain (Ubach et al., 1998) is important for syt1 interactions with syntaxin and for vesicle fusion. We simulated syt1 Ca 2ϩ binding (for parameters, see Table 2) at the plasmalemma ( Fig. 10A) using data that membrane interaction of the C2A domain enhances its Ca 2ϩ binding (Radhakrishnan et al., 2009). Ca 2ϩ entry and buffering were again simulated. To determine the requirements for Ca 2ϩ entry in the immediate vicinity of syt1 for full binding to occur, simulations were performed with six Ca 2ϩ entry sites across the surface of the varicosity such that a total of 45 M entered at each stimulus. Syt1 molecules were placed at 20, 100, and 200 nm from one of these sites (Fig. 10A), adjacent to a vesicle. This proximal Ca 2ϩ site varied from containing an equivalent of zero to five simulated channels (0.25 pA each, 0.5-ms open time).
More than 20 nm from the proximal Ca 2ϩ site no full syt1 binding events were recorded (100 random seeded simulations). Thus, the peak free [Ca 2ϩ ] i throughout the varicosity (9.3 M; Fig. 9C, red) is insufficient to occupy all five syt1-binding sites. However, even one simulated VGCC within 20 nm of syt1 allowed this binding ( Fig.  10Ba-Bc, black) and more channels increased the prob-   . continued of calbindin 28K binding were simulated and displayed as state diagrams from before a simulated stimulus (Aa) as well as during and after the stimulus (Ab, Ac, Ad) from time points indicated in B. Concentrations of calbindin 28K in each of its possible Ca 2ϩbound or unbound states throughout the varicosity is plotted on the vertical axis and color coded to concentration. The horizontal axes display Ca 2ϩ binding to high-affinity (B1) and mediumaffinity (B2) sites (C, single Ca 2ϩ bound; CC, two Ca 2ϩ bound). B, Graph of total concentration of vacant Ca 2ϩ -binding sites on calbindin 28K throughout the varicosity (black) and total bound Ca 2ϩ (blue) after a stimulus and 2nd pulse in light blue at varying interpulse intervals. Free Ca 2ϩ concentration is also shown (red) to the same scale for a single pulse. Ca, Graph of free Ca 2ϩ concentration after a single stimulus (red) throughout the varicosity and after 2nd stimuli at varying paired-pulse intervals     (Fig. 10Ba-Bc, red). With five channels, there was a small probability of syt1 fully binding Ca 2ϩ at five binding sites simultaneously when it was 100 nm from the Ca 2ϩ source. Within 20 nm from the Ca 2ϩ source, one channel raised the peak transient concentration to 110 M; five channels to 560 M (Fig. 10Bb,Bc). At this proximity full Ca 2ϩ occupancy of all five syt1 Ca 2ϩ sites occurred transiently throughout the stimulus. The narrow spatial half-widths (Fig. 10C) and rapid decay of Ca 2ϩ within tens of nm of VGCCs indicate rapid Ca 2ϩ removal from these volumes. Plots of total Ca 2ϩ entering the 20-nm scale region, Ca 2ϩ bound to calbindin 28K within the region, and free Ca 2ϩ are shown on a log scale (Fig. 10D) to encompass the range of concentrations when activation of three VGCCs was simulated at this site (similar results were obtained by clustering all Ca 2ϩ entry at these points). The arithmetic difference between Ca 2ϩ entry to this region, the Ca 2ϩ source by simulating three open channels (Fig.  10D, black curve), and Ca 2ϩ remaining in the region which is the sum of [Ca 2ϩ ] i (red trace) and Ca 2ϩ bound to buffer (blue trace) is the Ca 2ϩ that leaves the region by diffusion. This latter amount is 99.8% of the Ca 2ϩ that enters the region indicating that at this spatial scale, removal of Ca 2ϩ is dominated by diffusion. Thus, local Ca 2ϩ concentrations (tens of nanometers from the channels) are also dominated by diffusion during paired pulse stimulation when Ca 2ϩ buffers throughout the varicosity are not close to saturation (Fig. 9). Consequently, no significant pairedpulse facilitation (20-and 200-ms intervals) of the local Ca 2ϩ signal (within 200 nm of VGCCs) and no change in the decay rate from the peak of the Ca 2ϩ signal (Fig. 10Eb, insets) was seen at these scales. Similarly full syt1-Ca 2ϩ binding at all five sites was the same for the first and second stimuli (Fig. 10Ec,Ed, 20-ms intervals; Fig.  10Fb,Fc, 200-ms intervals; Fig. 10G).

Discussion
CA1 pyramidal neurons make en-passant synapses at subicular varicosities (Finch et al., 1983;Tamamaki and Nojyo, 1990). We show that evoked Ca 2ϩ transients are reliably activated in these varicosities, regardless of distance from the stimulated soma. Using a low affinity dye that did not significantly buffer entering Ca 2ϩ (Fluo-5F), Ca 2ϩ transients recorded over Ͼ1 h showed consistent amplitudes and decay rates. This implies quantal fluctuation of neurotransmission is not mediated by fluctuations in total CA1 varicosity Ca 2ϩ entry, although full Ca 2ϩ occupancy of syt1 is very sensitive to local Ca 2ϩ placement and we cannot distinguish total Ca 2ϩ in the varicosity from that entering at active zones. The result is not broadly applicable across all neurons. Evoked Ca 2ϩ entry in cerebellar granule cell varicosities vary (Brenowitz and Regehr, 2007), whereas responses in hippocampal dentate granule cells (Jackson and Redman, 2003), cortical pyramidal cells (Koester and Sakmann, 2000), and lamprey axons (Photowala et al., 2005) are reliable.

Quantitation and simulation of Ca 2؉ entry and buffering
This reliability, alongside our ability to introduce known Ca 2ϩ dye concentrations, allowed calculations of Ca 2ϩ buffering capacity, molar Ca 2ϩ entering, and extrusion rates. If we assume a VGCC current of 0.25 pA for 1 ms during action potentials (Weber et al., 2010), then on average 27 channels open per action potential per varicosity with a mean channel density of 7 m Ϫ2 . This is consistent with findings that either single channels evoke release (Stanley, 1993(Stanley, , 2015Haydon et al., 1994;Bertram et al., 1996) or few channels are necessary (Bucurenciu et al., 2008(Bucurenciu et al., , 2010, and allow efficient coupling of Ca 2ϩ to exocytosis (Scimemi and Diamond, 2012). Interestingly channel clustering and distance to the fusion apparatus can vary, giving synaptic responses with different probabilities even within one Calyx (Fekete et al., 2019).
Calculated properties of the Ca 2ϩ transient enabled creation of MCell simulations (Kerr et al., 2008) to investigate Ca 2ϩ entry, diffusion, and buffering. Calbindin 28K dominates Ca 2ϩ buffering in CA1 pyramidal neurons (Müller et al., 2005) and its binding properties are known (Nägerl et al., 2000) enabling its simulation. Experimentally determined peak [Ca 2ϩ ] i and were well-described by simulating calbindin 28K with a 2:2 ratio of high-affinity and medium-affinity Ca 2ϩ sites. Remarkably, 3D plots of vs peak [Ca 2ϩ ] i , vs calbindin 28K concentrations converge with experimental data at a calbindin 28K concentration (39.7 M) identical to these neurons' somata and dendrites (40 M for somata; Müller et al., 2005). This 2:2 ratio of binding sites (Nägerl et al., 2000) also well fit data from cerebellar Purkinje neurons (Schmidt et al., 2012). Two other buffer configurations, a 3:1 ratio of sites for calbindin 28K , or of calmodulin failed to converge with experimental data (Fig. 5). With the caveat that Ca 2ϩ buffering utilizes a mix of buffers, our findings are consistent with calbindin 28k as the dominant buffer. The model also reproduced independent features of experimental data; responses to repetitive stimulation and a failure to detect Ca 2ϩ diffusion from varicosities to axons. Simulations also validated use of dye as buffer within small varicosities. Simulating rising concentrations of Fluo-4 recapitulated experimental data showing effects of buffer on measured Ca 2ϩ transient decays, peak amplitudes, and total Ca 2ϩ entering varicosities (Fig. 5).
continued A simulating three local channels located within 20 nm of syt1. Ea, Simulated line scans as for Ba, but with a second pulse simulated 20 ms after the first. Eb, Ca 2ϩ transients within 20 nm of local Ca 2ϩ entry repeated at a 20-ms interval. Insets show single exponential fits and decay rates (blue) of the paired pulse local Ca 2ϩ transient. Ec, Probability of syt1 binding five Ca 2ϩ ions. Ed, Cumulative number of syt1-five Ca 2ϩ -binding events to emphasize these are equal in both pulses. F, Paired pulse results (Fa-Fc) as per Eb-Ed but at a paired-pulse interval of 200 ms. G, Spatial distribution of the peak free Ca 2ϩ entry in pulse 1 (black) and the second pulse at 20 ms (red) and 200 ms (blue) from volume in A, B.

Localization and clustering of Ca 2؉ entry
We compared experimental data and simulations to investigate presynaptic Ca 2ϩ . Presynaptic VGCCs localize to active zones (Khanna et al., 2007) and bind SNARE complex proteins (Mochida et al., 1996;Harkins et al., 2004;Szabo et al., 2006). Furthermore, release may be activated by single VGCCs (Stanley, 1993;Bertram et al., 1996;Shahrezaei et al., 2006), although, it remains unclear whether presynaptic Ca 2ϩ entry occurs at channel clusters (Llinás et al., 1992b;Bertram et al., 1996;Shahrezaei and Delaney, 2005) or a uniform distribution of channels, where individual VGCCs associate with primed vesicles in a 1:1 ratio. However, because Ca 2ϩ signals are smaller and faster than our imaging resolution, Ca 2ϩ entering the terminal, even at discrete points, will appear closer to uniformity throughout the terminal. Additionally, dye-Ca 2ϩ -complex diffusion might smooth variations, although we have demonstrated that Fluo-5F (10 -35 M) caused little perturbation because most Ca 2ϩ binds endogenous buffers rather than dye. ( dye ϭ 10 -20 for Fluo-5F vs 75 for end ). Nevertheless, in recordings where signal-to-noise ratios were favorable, we recorded localized Ca 2ϩ signaling. These regions show faster early 's, close to 3 ms (as fast as we can record). Peak free [Ca 2ϩ ] i within these regions reached 4 M. While this does not represent concentrations causing exocytosis Augustine et al., 1991;von Gersdorff and Matthews, 1994;Schneggenburger and Neher, 2000), it indicates non-uniform VGCC distributions, and channel clustering. We used MCell simulations of various VGCC distributions to explain localized Ca 2ϩ transients. Substantial spatial variation was only seen in simulated Fluo-5F responses if half or more of the channels in model synapses were clustered at one site.

Summation of Ca 2؉ transients and short-term plasticity
These synapses show paired-pulse facilitation that, as in other synapses (Katz and Miledi, 1967;Kamiya and Zucker, 1994;Zucker and Regehr, 2002), is Ca 2ϩ dependent (Kamiya and Zucker, 1994;Mukhamedyarov et al., 2009) and follows the time course of presynaptic residual Ca 2ϩ . However, although peak evoked Ca 2ϩ transients of 4 M, and simulated concentrations of 10 M throughout the varicosity may sum, Ca 2ϩ concentrations local to syt1 exceed 100 M. This suggests that summating Ca 2ϩ throughout the varicosity cannot modify paired-pulse responses by acting directly at syt1. Alternatively Ca 2ϩ , during stimulus trains, might saturate endogenous buffers (Neher, 1998) to evoke larger transients (Jackson and Redman, 2003), or subsequent Ca 2ϩ entry might be enhanced (Müller et al., 2008). In CA1 varicosities, experimentally applied paired pulse stimuli at 20-or 200-ms intervals reveal no significant alteration of the 2nd Ca 2ϩ transient amplitude. Later responses in stimulus trains of five stimuli do show non-linear summation, perhaps attributable to buffer saturation (Neher, 1998) or secondary Ca 2ϩ sources (Cochilla and Alford, 1998;Llano et al., 2000;Emptage et al., 2001;Scott and Rusakov, 2006), although notably, we recorded no effect of ryanodine at a dose that unloads Ca 2ϩ stores (Alford et al., 1993).
To investigate Ca 2ϩ at spatiotemporal scales relevant to molecular interactions, simulation was used. Our Ca 2ϩdye buffering data, supported by simulations, demonstrate that most Ca 2ϩ entering the varicosity is buffered endogenously at imaging time scales, similar to results from other synapses (Koester and Sakmann, 2000;Jackson and Redman, 2003). Simulations also indicate that endogenous buffers re-release Ca 2ϩ over seconds, and subsequent stimuli force occupancy of most Ca 2ϩ buffer binding sites. Supralinear rises in imaged and simulated Ca 2ϩ transients after more than two stimuli are due to buffer saturation. Simulation data indicate that total free Ca 2ϩ concentrations averaged throughout the varicosity reach 9.3 M after a single stimulus, and that buffer saturation indeed allows whole-terminal, paired-pulse enhancement of millisecond scale Ca 2ϩ transients up to 1 s after the first stimulus (Fig. 9). However, this does not account for Ca 2ϩ at scales of tens of nanometers and picoseconds in which Ca 2ϩ binds to syt1.
Simulation at these nanometer scales shows Ca 2ϩ dispersal from them is clearly dominated by diffusion and consequently there was no detectable difference in the amplitudes or distribution of two transients in paired pulses at intervals of 20 or 200 ms at this scale. Indeed, modeling binding of five Ca 2ϩ ions to syt1 indicates that Ca 2ϩ entry within Ͻ50 nm causes its full occupancy. This result, also indicates clustering of Ca 2ϩ channels may contribute to release at this synapse. Indeed, clusters of channels that are constrained to be further than 30 nm from the fusion apparatus has been proposed in calyceal synapses (Keller et al., 2015), although in those synapses Ca 2ϩ requirements for release are as low as 25 M (Schneggenburger and Neher, 2000). However, full Ca 2ϩ occupancy of the syt1 model is not enhanced by paired pulses. If residual Ca 2ϩ is responsible for paired pulse facilitation (Zucker and Regehr, 2002), then these data point to a Ca 2ϩ -binding site distinct from syt1, such as syt7 (Jackman et al., 2016;Jackman and Regehr, 2017). This effect might alternatively be consistent with an effect of residual bound Ca 2ϩ on vesicle priming (Neher and Sakaba, 2008) and the size of the readily releasable pool (Thanawala and Regehr, 2013).
We conclude that the Ca 2ϩ responsible for evoked release at CA1 neuron varicosities reaches hundreds of micromolar at small clusters of Ca 2ϩ channels local to the release machinery. These clusters may represent up to half of the Ca 2ϩ entry in the terminal for which fewer than 30 Ca 2ϩ channels open. As at most synapses, the Ca 2ϩ channels must be within tens of nanometers of the fusogenic Ca 2ϩ sensors, and simulations of Ca 2ϩ indicate that diffusion dominates its dispersal at this scale. Thus, neither paired pulse Ca 2ϩ accumulation (Wu and Saggau, 1994), nor buffer saturation (Neher, 1998;Matveev et al., 2004), nor Ca 2ϩ pumps substantially impact Ca 2ϩ binding to syt1. Nevertheless, buffer saturation during repetitive stimulation causes a varicosity wide enhancement of Ca 2ϩ transient amplitudes which may impact short-term enhancement by recruiting other Ca 2ϩ -binding proteins.