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

Edaeni Hamid; Emily Church; Simon Alford

doi:10.1523/ENEURO.0343-19.2019

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 calbindin_28K 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.

Significance Statement

Presynaptic Ca²⁺ influx, buffering and removal is essential to evoke synaptic transmission and therefore fundamental to nervous system function. It is also responsible for many forms of synaptic plasticity. Thus, it is important to understand fluxes of Ca²⁺ at the scale of the molecules with which it interacts. However, physical limitations prevent its imaging at such temporo-spatial scales. By combining a quantitative approach using Ca²⁺ dyes as buffers to determine characteristics of Ca²⁺ entry, buffering and removal from presynaptic varicosities, with simulation of Ca²⁺, its binding partners in and removal from varicosities, we provide a detailed quantitative analysis of Ca²⁺ at molecular scales. This enables insights into its molecular targets, and its effects on SNARE complexes and interacting proteins.

Introduction

Presynaptic Ca²⁺ entry through voltage-gated Ca²⁺ channels (VGCCs) causes exocytosis (Katz and Miledi, 1967). Exocytosis may require just one VGCC (Stanley, 1993; Bucurenciu et al., 2010; Weber et al., 2010; Eggermann et al., 2012; Scimemi and Diamond, 2012) or their clustering at microdomains (Llinás et al., 1992a; Shahrezaei and Delaney, 2004; Oheim et al., 2006), and their numbers may vary at active zones (Lübbert et al., 2019). Additionally, Ca²⁺ plays other roles in presynaptic terminals including modifying repetitive neurotransmission (Delaney et al., 1989; Zucker and Regehr, 2002), and receptor-mediated neuromodulation (Yoon et al., 2007; Gerachshenko et al., 2009).

Presynaptic Ca²⁺ transients are resolvable with Ca²⁺ 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, Ca²⁺ is used too locally and rapidly to be imaged within the dimensions of Ca²⁺-binding molecules that cause exocytosis (Adler et al., 1991; Sabatini and Regehr, 1996). Nevertheless, dyes can quantify presynaptic Ca²⁺ 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 Ca²⁺-binding properties within cells.

Neuronal Ca²⁺ binding requires various intracellular proteins. Bulk binding is dominated by EF-hand Ca²⁺-binding proteins (Burgoyne, 2004), but also occurs at C2 domains on numerous signaling proteins, including PKC (Farah and Sossin, 2012) and synaptotagmin1 (syt1; Chapman, 2002). CA1 pyramidal neuron somata and dendrites contain ∼40 µM of the Ca²⁺-binding protein calbindin_28K (Baimbridge et al., 1992; Müller et al., 2005), which may represent their dominant buffer (Yi, 2013), although other buffers are present. Indeed, calmodulin is present at presynaptic terminals (Llinás et al., 1991; Hinds et al., 2003). Buffering characteristics of these EF-hand proteins have been characterized in vitro (Nägerl et al., 2000; Faas and Mody, 2012) and by modeling in situ (Schmidt et al., 2005), allowing their impact on local Ca²⁺ signaling to be modeled.

Syt1 is widely considered the principal Ca²⁺ sensor for evoked release in pyramidal synapses (Geppert et al., 1994). In many synapses, exocytosis requires close association (<100 nm) between Ca²⁺ entry and synaptotagmin (Adler et al., 1991; Martens et al., 2007; Chapman, 2008; Südhof and Rizo, 2011). Ca²⁺ buffers modify Ca²⁺ diffusion, and Ca²⁺-synaptotagmin interactions. Although widely accepted (DiGregorio and Vergara, 1997; Koester and Sakmann, 2000) this is poorly characterized in presynaptic terminals. Syt1 has two Ca²⁺-binding domains (C2A and C2B; Perin et al., 1991), which bind three and two Ca²⁺ ions and is the Ca²⁺ sensor in CA1 axons. However, it is unclear whether all syt1 Ca²⁺ sites must bind Ca²⁺ given very low affinities for the C2B domain. Indeed, only one domain is necessary for membrane interaction (Davletov and Südhof, 1993), although this low affinity increases on association with lipid membranes containing phosphatidylinositol 4,5-bisphosphate PI(4,5)P₂ (Radhakrishnan et al., 2009; van den Bogaart et al., 2012).

To understand how much presynaptic Ca²⁺ enters presynaptic terminals, how it interacts with presynaptic Ca²⁺ buffers and with fusogenic targets such as syt1, we have quantified [Ca²⁺]_i in CA1 presynaptic terminals during action potentials. This allowed us to simulate action-potential-evoked Ca²⁺ 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 Ca²⁺ diffusion Ca²⁺ buffering, buffer saturation during evoked presynaptic Ca²⁺ entry.

Materials and Methods

The preparation

Experiments were performed on hippocampal slices (300 µm) 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 NaHCO₃, 1.25 mM NaH₂PO₄, 3 mM KCl, 2 mM CaCl₂, 1 mM MgCl₂, and 10 mM D-glucose, bubbled with 95% O₂-5% CO₂, sliced using a Vibratome. The recording chamber was superfused at 2 ml/min and maintained at 28 ± 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.

Electrophysiology

CA1 pyramidal neurons were whole-cell clamped following visual identification using an upright microscope with an Axopatch 200A amplifier (Molecular Devices). Patch pipettes (4–5 MΩ) contained the following: 146 mM potassium methane sulphonate, 2 mM MgCl₂, 0.025 mM EGTA, 9.1 mM HEPES, 5 mM ATP, and 2.5 mM GTP, pH adjusted to 7.2 with KOH. Pipettes were also filled with either Fluo-4 (1 mM) or Fluo-5F (200 µM) and Alexa Fluor 594 hydrazide (250 µM). Subicular pyramidal neurons 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 µA 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).

Figure 1.

Calibration of dye diffusion and Ca²⁺ response. A, Recording arrangement for imaging presynaptic varicosities. CA1 pyramidal 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 Ca²⁺ was imaged using the Fluo dye. B, Calibration of the Ca²⁺-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 Ca²⁺ standard concentrations in fixed concentrations of EGTA. Log-log plots gave a slope (Hill coefficient) of 1. Ca²⁺ concentrations were applied to a patch-clamped cell by application of ionomycin. From saturated Ca²⁺ concentrations, zero Ca²⁺ and a fixed value of Ca²⁺ (0.78 µM in EGTA-buffered Ca²⁺ 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 µM). 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⁻¹, thick gray line) and Alexa Fluor 594 (mol wt 737 g mol⁻¹; thick black line). These were detected 250 µm from the somata. The thin gray lines indicate the Alexa Fluor 584 concentrations simulated closest to the soma (70 µm) and at the extreme range of distances (600 µm from the soma).

Imaging

Confocal microscopy was used to image individual varicosities of CA1 pyramidal neurons, with a 60 × 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). Ca²⁺-sensitive dyes of one of two different affinities to Ca²⁺ were visualized in each experiment. Dye concentration was determined by pairing these dyes with a Ca²⁺-insensitive dye (Alexa Fluor 594 hydrazide, molecular weight, 736 g mol⁻¹, identical to Fluo-5F and almost identical to that of Fluo-4, 737 g mol⁻¹). 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 (>580 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.

Ca²⁺-binding properties of Fluo-4 and Fluo-5F were determined using Ca²⁺ standards (Invitrogen) at 28 ± 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 = 2 for Fluo-5F and n = 2 for Fluo-4) using whole-cell recordings obtained when the patch electrode contained either Fluo-4 or Fluo-5F. Whole-cell access was maintained until soma and dendrites were clearly labeled. The electrode was then carefully withdrawn. Baseline fluorescence intensities were measured. The Ca²⁺ ionophore, ionomycin (5 µM) 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 Ca²⁺ 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 Ca²⁺-EGTA ([Ca²⁺] = 0.78 µM) 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 = 0.44 µM, F_min/F_max = 0.066 and Fluo-5F K_d = 1.49 µM, F_min/F_max = 0.023) were used in all subsequent calculations.

To determine whether Ca²⁺ 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 µm diameter) contained molecules with diffusion constants to simulate Fluo-4 (mol wt 736 g mol⁻¹) and Alexa Fluor 594 hydrazide (mol wt 737 g mol⁻¹). These concentrations were kept constant at this site. Contiguous with this site was a cylindrical mesh of diameter 0.12 µm to simulate the axon diameter, interspersed with 1-µm diameter varicosities at 4-µm 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 = 8.3) and the measured diameters of the varicosities (1 µm) 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 microscopy of pyramidal cell axons (Harris and Weinberg, 2012). Resultant simulated dye concentrations were calculated at a distance of 250 µm 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 µm; top) or furthest from the soma (600 µm 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 Ca²⁺-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 ∼5 µm, 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 Ca²⁺ transients. Its occurrence was observed subsequent to a rise in resting Ca²⁺ 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 Ca²⁺ 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 Ca²⁺ concentration ([Ca²⁺]_i). For a non-ratiometric dye with a Hill coefficient of 1, [Ca²⁺]_i is determined from Equation 1: (1)

The Ca²⁺ 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 Ca²⁺ 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: (2)where D is the Alexa Fluor 594 fluorescence at each time, and D_F is the final Alexa Fluor 594 fluorescence. Thus, for experiments using Fluo-4 or Fluo-5F, where F and F_min in Equation 1 are ratios of F_max, and F_max = 1, [Ca²⁺]_I was calculated as follows: (3)

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, <15 s total per experiment). To use calcium-sensitive dyes as buffers to investigate the fate of Ca²⁺ that enters presynaptic terminals on stimulation, we must calculate their buffering capacities (κ_dye) in the cytosol of the terminal. Since each molecule of dye binds just one Ca²⁺ ion, the Hill equation with a coefficient of one can be used to calculate κ_dye over a change in Ca²⁺ concentration (Δ[Ca²⁺]_i) from [Ca²⁺]₁ to [Ca²⁺]₂. (4)where [Ca_Dye] is the concentration of Ca²⁺-bound dye, and [Dye_total] is the total dye concentration. Note that this approach takes into account the change in [Ca²⁺]_i in the pyramidal cell terminals during the stimulus which is large (approximately 1 µM). Other approaches with smaller Ca²⁺ changes use resting [Ca²⁺]_i as a basis for calculating κ_dye (Neher and Augustine, 1992).

When a rapid Ca²⁺ pulse enters a cell compartment, free Ca²⁺ 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 Ca²⁺ in CA1 pyramidal neuron presynaptic varicosities. From these methods we can determine the quantity of calcium entering the varicosity, the mean free [Ca²⁺]_i within the varicosity immediately after the stimulus, the endogenous Ca²⁺ buffering capacity, and the rate of removal of Ca²⁺ from the cytosol. From this we have developed simulations of Ca²⁺ entry, diffusion, and buffering in the presynaptic terminal.

The relationship between Ca²⁺ unbinding rates from the dye and rebinding either to dye or endogenous buffers can be used to calculate endogenous buffering capacity (κ_end) of the terminal. If the value of κ_dye varies during the experiment then we assume a constant rate of Ca²⁺ extrusion from the terminal (τ_ext). The decay rate (τ) of a pulse-like Ca²⁺ signal in a cell compartment is described by the equation: (5)

Thus, we obtained values of κ_end by fitting Equation 5 to plots of τ from experimental data vs κ_dye from Equation 4. This approach does have drawbacks, if processes modifying Ca²⁺ removal or adding to cytosolic Ca²⁺ occur after action potentials. Such processes include diffusion of the Ca²⁺-dye complex from the measured compartment, or release of Ca²⁺ from internal stores. In Equation 5, these effects are grouped into a single variable κ_end. Nevertheless, the result (κ_end) can be obtained independently of computed absolute values of Ca²⁺, or even of background fluorescence measurement errors. It therefore serves as an independent measure of whether the alternative following measurements of κ_end are reasonable.

By measuring the peak amplitude of the free Ca²⁺ transient throughout the varicosity over a range of values of κ_dye, we may assume that the total change in Ca²⁺ concentration due to a stimulus is described by the equation:

(6)

(7) and (8)

where [Ca_end] is the concentration of endogenous buffer bound to Ca²⁺ and Δ[Ca]_total is the total stimulus-evoked change in calcium concentration in the cell compartment. Thus, combining these equations, we may state: (9)

where Δ[Ca²⁺]_i varies with κ_dye. Values of Δ[Ca²⁺]_i are computed from our data using Equation 3 and values of κ_dye from Equation 4. For each action potential, as the value of κ_dye rises it will come to dominate binding of Ca²⁺ entering the cell compartment. This approach is useful because the value of Δ[Ca_dye] can be calculated for each action potential in each presynaptic terminal as the value of κ_dye increases by diffusion of dye from the soma. Equations 6 –8 can also give: (10)

Values of Δ[Ca]_total, and κ_end can be determined by extracting constants from fits of either Equation 9 or Equation 10. The true value of peak Δ[Ca²⁺]_I in the varicosity when no dye is present is obtained by extrapolating the fit to the y intercept in Equation 9, where κ_dye = 0. To calculate total Ca²⁺ 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-µm 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 µm.

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 ± 0.2 µm and width (w) was 1.2 ± 0.1 µm. 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: (11)

Chemicals were obtained as follows: Alexa Fluor dyes, Fluo-4, Fluo-5F, and Ca²⁺ standards from Thermo Fisher; salts, buffers, etc. from Sigma.

Simulations

MCell simulations were applied to Ca²⁺ 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). Ca²⁺ 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 Ca²⁺-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?fac=simontalford&cat=all. 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 α level of 0.05 for significance for statistical tests.

Results

Resting Ca²⁺ concentrations in axonal varicosities

To measure presynaptic Ca²⁺, Ca²⁺ sensitive and insensitive dyes were introduced to CA1 pyramidal neurons from somatic whole-cell pipettes containing Ca²⁺-sensitive dye, and Alexa Fluor 594 hydrazide (250 µM). 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 Ca²⁺ sensor. Alexa Fluor 594 fluorescence was used to measure dye concentration. We assume co-diffusion of the dyes which have similar molecular weights. Thus, Ca²⁺ 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 [Ca²⁺]_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). [Ca²⁺]_i remained stable for >1 h as dye concentrations rose (mean resting [Ca²⁺]_i = 81 ± 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 [Ca²⁺]_i (Fig. 2Aa, green circles). Therefore, we did not sample time points later than 80 min.

Figure 2.

Effects of high- and low-affinity dyes on presynaptic Ca²⁺ transients. Aa, CA1 pyramidal neurons whole-cell recorded and filled with Alexa Fluor 594 hydrazide (red, 250 µM) and Fluo-4 (green, 1 mM) from pipettes. Dye intensities normalized to values 20 min after whole-cell was plotted against time in one varicosity. Insets: green, Fluo-4; red, Alexa Fluor 594 in the same varicosity 20 and 70 min later. Ab, Resting [Ca²⁺] for all cells calculated from Equations 1, 2 plotted over time after whole-cell access. Green circles from Aa. B, Ca²⁺ transients measured with low affinity dye. Ba, Whole-cell-evoked action potentials evoked Ca²⁺ transients measured by line scans (Bb) through varicosities filled with Alexa Fluor 594 hydrazide and Fluo-5F. Line scan through the red bar in inset (Bc) showing intensities of five sequential line scans from the analyzed region in Bb. Colors indicate time after whole-cell access. Bd, Responses as ΔF/F + 1 (F = pre-stimulus Fluo-5F fluorescence). Ca²⁺ transients are invariant. Be, Color-coded representation of line scan as ΔF/F + 1 from analyzed region in Bb after background subtraction. Bf, Single Ca²⁺ 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), Ca²⁺ 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, τ= 0.53 s, Cb pink); 25 min later the amplitude was reduced and τ increased (τ = 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 τ 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 τ 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 τ and peak in Fluo-5F are constant those with Fluo-4 are time dependent.

Dependency of the Ca²⁺ signal on dye buffering capacity (κ_dye)

Single CA1 axon varicosities loaded with low-affinity Ca²⁺-sensitive dye (200 µM Fluo-5F pipette concentration, K_d = 1.49 µM; n = 30) were imaged by line scanning (500 Hz) single action potential evoked Ca²⁺ transients (Fig. 2B). Responses were evoked by single action potentials through the recording pipette (Fig. 2Ba) during rising dye concentrations (Fig. 2Bb,Bc). Normalized as (ΔF/F + 1), these Ca²⁺ transients were invariant in amplitude and τ 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 [τ; mean Δ[Ca²⁺]_i = 677 ± 10 nM (Materials and Methods; Eq. 3), mean τ = 119 ± 1.4 ms, n = 30].

Similar experiments were performed substituting the high affinity Ca²⁺ dye (Fluo-4, K_d, 0.44 µM; 1 mM pipette concentration). Transient peak amplitudes reduced, and decay time constants (τ) increased as dye concentrations rose (Fig. 2C). This is consistent with Ca²⁺ buffering by Fluo-4, because the amplitude represents a proportion of the dye that is Ca²⁺-bound. As dye concentrations rise a smaller dye fraction binds Ca²⁺ entering. Unbound dye competes for Ca²⁺ with endogenous buffers, consequently, τ 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 τ rose above 1 s, this imaging was used because it limited bleaching to repeat exposures.

An alternative explanation for increased τ 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 Ca²⁺ transient τ's and peak amplitudes from Fluo-4 (n = 11 neurons) versus Fluo-5F (n = 30 neurons). As dye concentrations rose, the value of τ 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 ΔF/F + 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 (κ_dye) not loss of endogenous buffer that causes the changes in peak ΔF/F and τ. Calculated dye concentrations combined with calibrated dye properties (Fig. 1) and Ca²⁺ transient amplitudes were therefore used to relate dye buffering to varicosity Ca²⁺ transients.

Use of dyes to calculate Ca²⁺ entry and buffering

We determined κ_dye (Eq. 4) for each Ca²⁺ transient from varicosity dye concentrations, changes in varicosity-free Ca²⁺ (Δ[Ca²⁺]_i) calculated from this data, and Equation 3. This value was plotted against time after obtaining whole-cell access for one example (Fig. 3Aa, inset). In 18 neurons (seven Fluo-5F, 11 Fluo-4) a linear fit to τ vs κ_dye (single cell example in Fig. 3Aa; data from all cells, Fig. 3Ab) gave an x intercept of –58 ± 40 and an estimate of the endogenous buffering capacity of the varicosity (κ_end) of 57 (Eq. 5).

Figure 3.

Analysis of Ca²⁺ transients and buffering using Ca²⁺-sensitive dyes. A, From the fits to Ca²⁺ transients obtained with Fluo-4 and Fluo-5F at various values of κ_dye, decay time constants (τ) were plotted against κ_dye. Aa, Example neuron. Inset, Increase in κ_dye over period of recording. Ab, Recordings from all neurons (each symbol used represents a different cell). The negative intercept on the abscissa is a measure of endogenous buffering capacity (κ_end) of the terminal (from Eq. 5). B, Evoked change in [Ca²⁺]_i calculated from Equation 3 is plotted against dye buffering capacity (κ_dye) for the same data. The curved line represents a fit of Equation 9. The inset represents the equivalent linear fit to the inverse of Δ[Ca²⁺]_i where the convergence of the fit with the abscissa represents κ_end and the slope is a function of Δ[Ca²⁺]_total. The fits give values for the peak free Ca²⁺ concentration, the varicosity κ_end and total Ca²⁺ entering. Ba, Example neuron. Bb, Recordings from all neurons. C, Values of total peak [Ca²⁺] bound to dye calculated from the product of measured Δ[Ca²⁺] and the κ_dye were plotted against κ_dye. These data were fit to Equation 10. As the curve reaches an asymptote at high values of κ_dye, this allows calculation of the total molar quantity of Ca²⁺ entering the varicosity following one action potential. Ca, Example neuron. Cb, Recordings from all neurons. Error bands are for 90% confidence intervals.

A plot of Δ[Ca²⁺]_i (Eq. 3) against κ_dye (Fig. 3Ba single example; data from all cells, Fig. 3Bb) demonstrated the relationship between κ_dye and the Ca²⁺ transient. A fit of Equation 9 to this data, or a linear fit to 1/Δ[Ca²⁺]_i vs κ_dye (Fig. 3B, insets), gives a peak free change in Ca²⁺ concentration (Δ[Ca²⁺]_I) in the absence of dye throughout the terminal of 0.76 ± 0.03 µM. This is obtained from the y-axis intercept of the fit where κ_dye = 0. Constants from the same fit give total Ca²⁺ entry of 58 ± 6 µM and κ_end of 75 ± 6.

Total dye bound Ca²⁺ ([Ca_dye]) was calculated for each transient either from the product of [Ca²⁺]_I and κ_dye, or from proportions of dye bound to Ca²⁺ calculated from the Hill equation. These gave values that differed by <5%. Data in Figure 3C are from the former (single cell Fig. 3Ca; combined data, Fig. 3Cb). If total Ca²⁺ entering each varicosity were constant for each action potential, then these data are represented by Equation 10, in which the asymptotic value of total Ca²⁺ entering the varicosity was 45 ± 3 µM. From this and each measured varicosity dimensions (volume mean = 1.7 ± 0.3 µm³, median = 1.2 µm³, n = 18) we determined total molar Ca²⁺ entering the varicosity (Table 1). κ_end is taken from fits of Equation 9 to Δ[Ca²⁺]_i (Fig. 3B). Peak [Ca²⁺]_i is for Ca²⁺ throughout the varicosity and total [Ca²⁺] entering is from fits to Equation 10 of data in Figure 3C. Results with the least errors were used and summarized (Table 1).

View this table:

Table 1.

Parameters of the varicosity and Ca²⁺ signaling

Ca²⁺ source and removal from the terminal

Internal stores might contribute to Ca²⁺ transients (Cochilla and Alford, 1998; Emptage et al., 2001; Scott and Rusakov, 2008). Calculations of Ca²⁺ entering, and κ_end will be distorted if secondary Ca²⁺ sources exist. In recordings with Fluo-5F, ryanodine (5 µM; 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 ± 12% of control, 95% confidence interval of 90–132%, n = 5). Thus, ryanodine does not meaningfully alter Ca²⁺ transients even during trains of stimuli.

Figure 4.

The Ca²⁺ transient is unaffected by block of release of Ca²⁺ from internal stores, and its peak amplitude is correlated with the inverse of its decay. A, Repetitive stimulation evokes summating Ca²⁺ transients that are unaffected by ryanodine. Aa, Five action potentials at 20 Hz evokes a summating Ca²⁺ transient measured using Fluo-5F in a CA1 neuron varicosity (Ab), which was unaffected by a 30-min application of ryanodine (5 µM; Ac, gray). B, Inverse of the Ca²⁺ transient decay rate versus peak Δ[Ca²⁺]_i for varicosities in which the value of κ_dye exceeded 150. From the slope, the extrusion rate of Ca²⁺ from the varicosity was determined (equal to slope × total molar Ca²⁺ entry). Each symbol used represent a different cell.

If Ca²⁺ extrusion is mediated by pumps with linear rates versus peak [Ca²⁺]_I, then as the transient varies with κ_dye, removal rates can be calculated. As dye concentration increases, κ_dye dominates κ_end, and peak [Ca²⁺]_i available to pumps is reduced. Removal will be inversely proportional to available [Ca²⁺]_i. The slope of 1/τ of the transient against peak [Ca²⁺]_i allows calculation of Ca²⁺ removal. Thus, these data obtained with Fluo-4 were plotted (Fig. 4B), and the extrusion rate [7.6 × 10⁶ × (total #Ca²⁺ ions) M^{− 1} s⁻¹] calculated from the slope. The linearity of these data also provide evidence that secondary Ca²⁺ sources do not contribute to the transient, at least at these values of κ_dye. A summary of experimentally determined properties of the varicosity is given in Table 1.

Modeling of Ca²⁺ transients in varicosities

Imaging experiments provided resting [Ca²⁺]_i, varicosity volumes, their endogenous buffering capacity, the peak free [Ca²⁺]_i, the total Ca²⁺ entering, and its removal rate. The principal Ca²⁺ buffer in CA1 pyramidal somata is calbindin_28K and its concentration in somata and dendrites has been determined to be 40 µM (Müller et al., 2005), making it a candidate buffer in varicosities (Arszovszki et al., 2014) with well-characterized Ca²⁺-binding 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 Ca²⁺ 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 × 1 µm (volume = 1.2 × 10⁻¹¹ l, the median measured varicosity volume) en passant to an axon (0.12 µm in diameter). They contained 320 40-nm diameter vesicles and an internal structure mimicking organelles (Fig. 5A). We modeled Ca²⁺ extrusion with a rate of 2.2 × 10¹¹ M^{− 1} s⁻¹ (from the number of Ca²⁺ 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 Ca²⁺ leak (1.77 × 10⁵ ions s^{− 1}) similarly distributed achieved resting free [Ca²⁺]_i of 81 nM. Ca²⁺ buffering was modeled with three models of buffers (calbindin_28K 3:1 ratio, calbindin_28K 2:2 ratio or calmodulin). Calbindin_28K possesses four Ca²⁺-binding sites and models have been proposed for its Ca²⁺ 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 Mg²⁺ (rates indicated in Table 2). Ca²⁺-calmodulin binding was also modeled using published parameters (Faas et al., 2011; Table 2). In our simulations, we used the same Mg²⁺ on-rate correction in our models for calbindin_28K and calmodulin. Evoked Ca²⁺ entry was modeled as a total of 45 µM Ca²⁺ entering the terminal in 2 ms (Table 1)

Figure 5.

MCell simulation of Ca²⁺ transients and validation against experimental data. A, The varicosity was modeled as an ellipsoid 2 × 1 × 1 µm and contained 320 synaptic vesicles, and one large internal structure to provide sites for Ca²⁺ intrusion (i.e., ER/mitchondrion). A variable quantity of Ca²⁺ buffer was modeled. Images show free Ca²⁺ ions (green) and Ca²⁺-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 [Ca²⁺]_i following stimuli at three calbindin_28K concentrations (15 µM, pink; 40 µM, red; 60 µM, black). Single exponential fits (blue) were applied to these simulations and values of peak Δ[Ca²⁺]_i and decay (τ) 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 τ, peak ΔCa²⁺ against varying buffer concentrations (15–60 µM) 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 τ, peak ΔCa²⁺ and their standard errors. These data converge only with the 2:2 ratio of calbindin_28K at a concentration of 39.7 µM. D, Varying Ca²⁺-sensitive dye concentrations (Fluo-4; Table 1) were simulated and resultant Ca²⁺ transients graphed. Da, Responses shown with dye concentrations of 50, 200, and 670 µM. Db–Dd, Decay time, peak ΔCa²⁺, and total Ca²⁺ entry from these simulated transients over values of κ_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 Ca²⁺ transients (Eb) recorded with Fluo-5F that also allowed recording from axons. Such events were also simulated by calculating Ca²⁺ concentration along the axon and varicosity axis (Ec, yellow). Ed, Simulated line scan. Ee, top, Overlay of experimental ΔF/F + 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 Ca²⁺ transients recorded with Fluo-5F (Fb) quantified as Ca²⁺ 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.

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Table 2.

Parameters used in the MCell model

View this table:

Table 3.

MCell model-specific parameters

Buffer concentrations were first estimated by solving the Hill equation for values of total Ca²⁺ entry, and resting, and stimulated peak free [Ca²⁺]_i. This assumes equilibrium at peak, and was expected to underestimate true buffer concentrations because Ca²⁺ transients are too rapid for equilibration. This gave 92.8 µM for calmodulin and 24.8 µM calbindin_28K (2:2 ratio of high-affinity and medium-affinity sites), or 19.7 µM (3:1 ratio).

To determine buffer parameters, simulated endogenous buffer concentrations were varied starting at steady-state results to compare simulations to experimentally determined peak free Δ[Ca²⁺]_i and τ (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 Ca²⁺ inhomogeneities. From these fits, peak free Δ[Ca²⁺]_i and τ were plotted against simulated buffer concentrations (Fig. 5C). Intersection of simulated and experimental values for τ and Δ[Ca²⁺]_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 a calbindin_28K 2:2 concentration of 39.7 µM, in close agreement to 40–45 µM calbindin_28K obtained experimentally for rat CA1 pyramidal neuron somata (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 Ca²⁺ 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 µM) were simulated and κ_dye calculated as for experimental data. As for experimental data, rising values of simulated κ_dye reduced peak [Ca²⁺]_i and increased τ. Peak [Ca²⁺]_i and τ were measured from single exponentials fitted to simulated data (Fig. 5Da) ommitting the initial 4 ms. Results were plotted with experimental data as τ versus κ_dye (Fig. 5Db), peak [Ca²⁺]_i versus κ_dye (Fig. 5Dc), and total Ca²⁺ entry captured by the dye vs κ_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.

Extrapolations of τ and Δ[Ca²⁺]_i (Fig. 3), to a hypothetical zero dye concentration where κ_dye = 0 (Fig. 3), compared with results for recordings using Fluo-5F shows a close match indicating that the dye did not significantly buffer the Ca²⁺ transient. Therefore, we used Fluo-5F to investigate Ca²⁺ signaling in detail and to further validate simulations with experimental data. In four preparations the orientation of the axon and varicosity allowed simultaneous line scanning of both, to compare the relative amplitudes of their Ca²⁺ transients. In axons farther than 1 µm from the varicosity no Ca²⁺ transient was observed (Fig. 5Eb,Ee, blue), indicating that Ca²⁺ does not escape from varicosities by diffusion. An equivalent simulation was performed, in which Ca²⁺-Fluo-5F binding was simulated in discrete volumes along the model axis (Fig. 5Ec, yellow), and ΔF/F + 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 µm from the varicosity (Fig. 5Ee, lower traces).

We also tested simulations by comparing their results to train-evoked Ca²⁺ transients in Fluo-5F (200 µM)-labeled varicosities. Ca²⁺ transients were recorded during 5 action potentials (50 Hz; n = 5 cells; Fig. 6Ca). This caused a summating Ca²⁺ transient (Fig. 5F). Absolute Ca²⁺ concentrations were calculated and expressed as the mean of all responses (Fig. 5Fc, blue; seven responses) bounded by the 90% confidence interval (gray). Ca²⁺ 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.

Figure 6.

Ca²⁺ or Ca²⁺ dye complex can show rapid diffusion from presynaptic terminal hotspots immediately after the stimulus. A, Axon varicosity containing both Alexa Fluor 594 hydrazide and Fluo-5F imaged using the Alexa Fluor dye. Bracketed region encompasses a single varicosity (center, red) and axon on either side (white) used for line scanning. B, Mean of four line scans from region in A. The varicosity exhibited a Ca²⁺ transient similar to those recorded in earlier figures (Ba). Mean intensity of the line scan through the varicosity (Bb, red bar), which showed a large increase in Ca²⁺ dye fluorescence following a single action potential (Bc). C, The mean of four line scans within the varicosity (red in B) displayed as ΔF/F + 1 (Ca, upper panel time scale as in graphs in D, E below). Immediately after the stimulus there is a rapidly decaying component of the transient. The lower panel of Ca shows the two hotspots (arrowheads) at a 10× time scale. Data were then analyzed in quadrants (Cb–Ce). Center quadrants (Cc, Cd). The center quadrants were well fit with double exponentials, the outer with single exponentials. D, Data in Cc replotted to demonstrate the amplitude of free [Ca²⁺]_i within this region of the varicosity. As with the data in Cd, this required a double exponential fit (single exponential and residual in blue, double exponential and residual in red). E, Ca²⁺ transients (gray) were plotted for each of the four sequential responses averaged in C. Ea, Plotted from the region labeled (Cc); and (Eb) from the region labeled (Ce) in Ca. Double exponentials were fit to these data for each of the four traces (colored traces).

Spatiotemporal distribution of Ca²⁺ entry to the terminal

Calculations of varicosity [Ca²⁺] and its buffering assume that Ca²⁺ 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 Ca²⁺ entry and its buffering; however, in five neurons recorded with sufficiently high resolution, we observed repeatable, but non-uniform, Ca²⁺ distributions immediately after stimulation; Fig 6).

In each varicosity (Fig. 6A), line scans (mean of four transients in each of the five terminals; ΔF/F + 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 Ca²⁺ entry then a faster local decay, that will not be altered by these errors, would represent diffusion from this site (mean τ overall = 119.5 ± 1.4 ms). Therefore, fits to exponentials were analyzed in line scan subregions. In the case illustrated, a single exponential well-fit Ca²⁺ transients away from hotspots (Fig. 6Cb,Ce), but did not adequately fit regions at hotspots. The hotspots were well-fit by double exponentials (τs of 6–11 and 105–135 ms; Fig. 6Cc,Cd). Similar results were obtained in all five neurons (mean τ₁ = 9.0 ± 2.9 ms; τ₂ = 124.5 ± 19.1 ms; sum of squares of residuals were significantly different between single and double exponential fits at the hotspots, t₍₄₎ = 3.25, p = 0.015, but were not significantly different away from hotspots, t₍₄₎ = 1.42, p = 0.11; the ratio of amplitudes of the first and second exponentials at the hotspots = 0.92. This was significantly higher than values obtained from double exponentials fit to data away from hotspots = 0.47, t₍₄₎ = 3.82, p = 0.009). To illustrate the peak [Ca²⁺]_i recorded by Fluo-5F, experimental data are replotted (Fig. 6D, black) as [Ca²⁺]_I versus time, and is well-fit with a double exponential (red; residual above also in red, fast τ = 2.1 ms, peak [Ca²⁺]_i of 1.8 µM; vs 0.8 µM for the rest of the varicosity). In all five neurons, the mean peak free [Ca²⁺]_i = 2.7 ± 0.57 µM and mean fast τ = 3.3 ± 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₎ = 3.25, p = 0.016, but not away from hotspots, t₍₄₎ = 2.00, p = 0.060).

These Ca²⁺ hotspots are repeatable. Examples from two locations (arrowed Fig. 6C) with an early fast Ca²⁺ transient (Fig. 6Ea) or lacking one (Fig. 6Eb) were analyzed in four sequential stimuli (five cells). As for the values obtained from values of ΔF/F at hotspots or non-hotspot regions, each [Ca²⁺]_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 ± 170 nM and slow, 331 ± 68 nM, whereas at non-hotspots these amplitudes were 230 ± 141 nM and 303 ± 48 nM, p = 0.0052, two-factor ANOVA, respectively), but there was no significant difference between slower exponential amplitudes (p = 0.08).

Simulation of localized Ca²⁺ entry

We determined whether discrete placement of Ca²⁺ entry within the simulation could reproduce the experimental non-uniform Ca²⁺ distribution. In simulations, Ca²⁺ entry was located at one to six plasma membrane sites. However, in all cases, the total Ca²⁺ entry summed to 45 µM (Table 2) over the whole varicosity. Experimental line scanning was simulated (20 random seeds) by simulating values of Fluo-5F ΔF/F + 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 Ca²⁺ entry site. ΔF/F + 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.

Figure 7.

Simulations of Fluo-5F transients and clustering of Ca²⁺ entry. Line scans (A) of Fluo-5F transients were simulated by determining its simulated Ca²⁺ binding in volumes (yellow boxes) across the varicosity (B). Ca, Simulated Fluo-5F ΔF/F + 1 transient (red) in the volume closest to Ca²⁺ entry (top of yellow band). Experimental data from Fig. 6Cc, blue. Cb, Simulated Fluo-5F ΔF/F + 1 transient in the volume at the bottom of the yellow band in B opposite the site of Ca²⁺ entry (black). Experimental data from Fig. 6Ce overlaid in blue. D, Ca²⁺ entry was simulated at six sites, including one placed at the plasmalemma, at the top of the yellow band in B. The Fluo-5F transient is shown from this site (red) and away from sites of Ca²⁺ entry from the bottom of the yellow band in B (black). E, Graph of peak amplitude of double exponential fit to the simulated transient at a site of Ca²⁺ entry (red) and away from these sites (black) in varicosities where Ca²⁺ entry was at one to six sites.

Simulation results were plotted from the two ends of the yellow band, obtained when all Ca²⁺ entry (45 µM) was at one point (Fig. 7B, top, point of simulated Ca²⁺ entry; bottom, away from Ca²⁺ entry; Fig. 7C, overlaid with experimental data, blue). There is a substantial difference between amplitudes of the earliest peak at the Ca²⁺ entry site (Fig. 7Ca, red) compared to the other side of the simulated varicosity (Fig. 7Cb, black). Similar simulation results were plotted where Ca²⁺ 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 Ca²⁺ entry site and away from it (Fig. 7D).

Double exponentials were fit to the simulations. τ’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 ± 1.3 ms). Peak amplitudes of simulated Fluo-5F ΔF/F early components were obtained for fits to all distributions of Ca²⁺ 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 Ca²⁺ entry compared to the opposite side of the varicosity away from Ca²⁺ entry, were observed only when Ca²⁺ entry was at one or two sites (that is when at least 50% of total varicosity Ca²⁺ entry was localized to one site; Fig. 7E). Thus, to obtain experimental local peaks in Ca²⁺ (Fig. 7), clustering of VGCCs may occur.

Proximity of the point of Ca²⁺ entry to the release machinery and paired-pulse facilitation

The proximity of Ca²⁺ entry to its molecular targets that cause vesicle fusion can be estimated by comparing effects of BAPTA (rapidly binds Ca²⁺) to EGTA (slower binding; Adler et al., 1991) on synaptic transmission. To record synaptic responses from CA1 synapses, their axons were stimulated (1/15 or 1/30 Hz; Hamid et al., 2014). Whole-cell recordings were made from their target subicular pyramidal neurons and EPSCs recorded (in bicuculline, 5 µM; AP5, 50 µM) to isolate AMPA receptor responses. BAPTA-AM was superfused (10–100 µM, 15–20 min) and reduced EPSC amplitudes dose dependently (to 34 ± 4% at 100 µM, n = 13; Fig. 8A). In contrast, EGTA-AM (20–100 µM was significantly less effective (100 µM, n = 12, to 83 ± 5% of control; Fig. 8A,B; t₍₂₂₎ = 8.0, p = 2.6 × 10⁻⁸). These results imply a close spatial association (tens of nanometers; Adler et al., 1991) between VGCCs and syt1 responsible for exocytosis.

Figure 8.

Paired-pulse potentiation is not explained by presynaptic residual Ca²⁺ concentration. A, EPSCs (in AP5 and bicuculline to block NMDAR and GABA_AR responses) recorded in subicular pyramidal neurons following stimulation of CA1 pyramidal axons. Effects on EPSC amplitudes of BAPTA-AM or EGTA-AM were recorded after 15–20 min of perfusion. Aa, BAPTA-AM (10–100 µM) caused dose-dependent inhibition of the EPSC (graphed in Ab). EGTA-AM (10–100 µM) had little effect. B, Paired-pulse responses were obtained at 10 Hz (six neurons) EGTA-AM (10 µM) was added to the superfusate (gray). Paired-pulse facilitation was prevented. Ca, In three neurons with EGTA-AM (10 µM), the interstimulus interval was varied from 20 to 500 ms. Paired pulse potentiation was prevented over intervals >50 ms. By contrast control paired-pulse potentiation was seen in all neurons tested over the same range of stimulus intervals (Cb). Cc, Graph showing paired pulse potentiation for these intervals in control (filled circles) and after superfusion of EGTA-AM (open circles). The dashed line represents the first stimulus amplitude. Errors expressed as SEM between preparations. D, Ca²⁺ transients were stimulated in paired pulses. Da, Line scan image of stimuli at 200-ms intervals. Db, Paired-pulse responses at 20-ms (gray) and 200-ms (black) intervals.

While Ca²⁺ evoked neurotransmitter release thus requires close coupling of Ca²⁺ channels to the Ca²⁺ target, repetitive stimulation evokes synaptic facilitation (Zucker and Regehr, 2002). This facilitation is thought to be caused by residual Ca²⁺, Ca²⁺-buffer saturation (Klingauf and Neher, 1997; Matveev et al., 2004), or Ca²⁺-dependent processes distinct from the fast exocytic machinery (Fioravante and Regehr, 2011), for example, by acting at syt7 (Jackman et al., 2016; Jackman and Regehr, 2017). At CA1 pyramidal cell presynaptic terminals we show that this facilitation is Ca²⁺ dependent. In similar recordings to Figure 8A, paired pulse stimuli were presented to CA1 pyramidal axons with interpulse intervals of 100 ms (Fig. 8B). This gave a mean facilitation ratio of 1.85 ± 0.191 (amplitude of EPSC 2/EPSC 1, n = 5, t₍₄₎ = 2.4, p = 0.03). The paired pulse enhancement was abolished by EGTA-AM (20 µM; facilitation ratio after EGTA-AM = 1.0 ± 0.1, t₍₄₎ = 0.4, p = 0.35).

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 µM) the paired-pulse interval was varied (20–500 ms; Fig. 8Ca). In EGTA-AM, facilitation was abolished at intervals >50 ms. In contrast in controls, facilitation was recorded at intervals from 20 to 500 ms (Fig. 8Cb). Facilitation ratios from controls (n = 7) and after EGTA-AM (n = 3) were plotted from 20- to 1000-ms intervals (approximate duration of varicosity Ca²⁺ transients; Fig. 8Cc). In contrast to this facilitation of postsynaptic responses, presynaptic Ca²⁺ 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. Ca²⁺ transients were recorded and evoked following whole-cell 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 Ca²⁺ transients (Δ[Ca²⁺]_i) were not significantly altered (Fig. 8D; at 20-ms intervals 2nd response was 115 ± 19% of 1st, n = 7, t₍₆₎ = 0.98, p = 0.18; at 200-ms intervals 2nd response was 100 ± 10% of the 1st, n = 3, t₍₂₎ = 0.03, p = 0.49). Thus, while paired pulse facilitation is Ca²⁺ dependent, as indicated by its sensitivity to EGTA, Ca²⁺ transients do not measurably augment at the scale of the entire terminal to cause this potentiation.

Simulating paired-pulse presynaptic Ca²⁺ transients

To address experimental limitations of analyzing Ca²⁺ at the spatiotemporal resolutions of the vesicle fusion machinery and its activation, we simulated Ca²⁺, Ca²⁺ buffer states, and effects of repetitive stimulation on unbound and bound Ca²⁺ (Fig. 9) using parameters previously determined. Within the simulation, at rest, >90% 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 [Ca²⁺] 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; τ of exponential increased from 423 µs on the first stimulus to 767 on the second). This enhanced second peak, only resolvable by simulation is seen despite the fact that the Ca²⁺ signal recorded at the base of this initial transient resolvable with imaging is only enhanced by <200 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 Ca²⁺. We conclude that the transient Ca²⁺ signal resulting from diffusion of Ca²⁺ throughout the varicosity does show an enhanced amplitude due to partial Ca²⁺ buffer saturation. However, this signal is computed from a much larger volume than the Ca²⁺ transients within tens of nanometers of the VGCCs that evokes fusion by interacting with syt1.

Figure 9.

Simulations of Ca²⁺ buffering in the varicosity. A, Using simulation parameters previously determined, the kinetics 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 Ca²⁺-bound or unbound states throughout the varicosity is plotted on the vertical axis and color coded to concentration. The horizontal axes display Ca²⁺ binding to high-affinity (B1) and medium-affinity (B2) sites (C, single Ca²⁺ bound; CC, two Ca²⁺ bound). B, Graph of total concentration of vacant Ca²⁺-binding sites on calbindin_28K throughout the varicosity (black) and total bound Ca²⁺ (blue) after a stimulus and 2nd pulse in light blue at varying interpulse intervals. Free Ca²⁺ concentration is also shown (red) to the same scale for a single pulse. Ca, Graph of free Ca²⁺ concentration after a single stimulus (red) throughout the varicosity and after 2nd stimuli at varying paired-pulse intervals (black). Red dashed line indicates theoretical value of linear summation of a second pulse. Blue dashed line represents the linear sum of the Ca²⁺ signal that is resolvable using imaging at 500 Hz. Cb, Expansion of the time course of paired pulses from Ca for pulses at 50 Hz. Color scheme as for Ca. Single exponential fits to the fast component of decay of the Ca²⁺ transients and their decay times (τ) are shown in blue.

Activation of syt1 by evoked presynaptic Ca²⁺ entry

Syt1, the Ca²⁺ sensor for exocytosis in CA1 pyramidal neurons, has two C2 domains with five Ca²⁺-binding sites, some of which have mM affinities for Ca²⁺ (Südhof and Rizo, 2011). This requires syt1 to be <100 nm from the Ca²⁺ source (Adler et al., 1991; Augustine et al., 1991) as demonstrated also here (Fig. 8). It is unclear whether all sites must bind Ca²⁺ 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 Ca²⁺ binding (for parameters, see Table 2) at the plasmalemma (Fig. 10A) using data that membrane interaction of the C2A domain enhances its Ca²⁺ binding (Radhakrishnan et al., 2009). Ca²⁺ entry and buffering were again simulated. To determine the requirements for Ca²⁺ entry in the immediate vicinity of syt1 for full binding to occur, simulations were performed with six Ca²⁺ entry sites across the surface of the varicosity such that a total of 45 µM 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 Ca²⁺ site varied from containing an equivalent of zero to five simulated channels (0.25 pA each, 0.5-ms open time).

Figure 10.

Paired pulses do not alter nanometer domains of Ca²⁺ entry. A, Characteristics of Ca²⁺ entry, buffering, and dispersal analyzed close to Ca²⁺ entry modeled within 20 nm of a vesicle at the plasmalemma. Left panel, View along axon axis including varicosity contents (blue dots, calbindin_28K; green, Ca²⁺, vesicles; light blue, organelle). Right panel, Magnified model showing volume at the membrane (yellow band, where simulated Ca²⁺ was determined) and vesicles (blue circles, one dark blue at Ca²⁺ entry site). The latter vesicle distorts the spatial symmetry of the Ca²⁺ signal (C, G; Shahrezaei and Delaney, 2004). Ba, Ca²⁺ transients expressed as a simulated line scan versus time from yellow band in A centered at one point of Ca²⁺ entry for five channels (red), one channel (black), and zero local channels (blue) active for 0.5 ms (dark gray) against a background of 45 µM entering the entire varicosity for 2 ms (light gray) in Bb, where data are from the center 20 nm of Ba. Bc, Probability (from 100 simulations) of syt1 model showing occupancy of all five Ca²⁺-binding sites for five (red) and one (black) local Ca²⁺ channels. Gray shaded regions as for Bb. C, Spatial distribution of the Ca²⁺ transient peaks from the end of the dark gray shading in B for 0 through five channels at the local site of Ca²⁺ entry. D, Total Ca²⁺ entering a volume within 20 nm of three channels (black), the free Ca²⁺ in this volume (red), and the Ca²⁺ in the volume bound to buffer. Loss of Ca²⁺ by diffusion is the difference between the black trace and the sum of the black and red traces (traces are on a logarithmic scale). Gray shaded regions as per B. E, Paired-pulse Ca²⁺ transients from yellow region in 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, Ca²⁺ transients within 20 nm of local Ca²⁺ entry repeated at a 20-ms interval. Insets show single exponential fits and decay rates (blue) of the paired pulse local Ca²⁺ transient. Ec, Probability of syt1 binding five Ca²⁺ ions. Ed, Cumulative number of syt1-five Ca²⁺-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 Ca²⁺ entry in pulse 1 (black) and the second pulse at 20 ms (red) and 200 ms (blue) from volume in A, B.

More than 20 nm from the proximal Ca²⁺ site no full syt1 binding events were recorded (100 random seeded simulations). Thus, the peak free [Ca²⁺]_i throughout the varicosity (9.3 µM; 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 probability of this binding (Fig. 10Ba–Bc, red). With five channels, there was a small probability of syt1 fully binding Ca²⁺ at five binding sites simultaneously when it was 100 nm from the Ca²⁺ source. Within 20 nm from the Ca²⁺ source, one channel raised the peak transient concentration to 110 µM; five channels to 560 µM (Fig. 10Bb,Bc). At this proximity full Ca²⁺ occupancy of all five syt1 Ca²⁺ sites occurred transiently throughout the stimulus.

The narrow spatial half-widths (Fig. 10C) and rapid decay of Ca²⁺ within tens of nm of VGCCs indicate rapid Ca²⁺ removal from these volumes. Plots of total Ca²⁺ entering the 20-nm scale region, Ca²⁺ bound to calbindin_28K within the region, and free Ca²⁺ 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 Ca²⁺ entry at these points). The arithmetic difference between Ca²⁺ entry to this region, the Ca²⁺ source by simulating three open channels (Fig. 10D, black curve), and Ca²⁺ remaining in the region which is the sum of [Ca²⁺]_i (red trace) and Ca²⁺ bound to buffer (blue trace) is the Ca²⁺ that leaves the region by diffusion. This latter amount is 99.8% of the Ca²⁺ that enters the region indicating that at this spatial scale, removal of Ca²⁺ is dominated by diffusion. Thus, local Ca²⁺ concentrations (tens of nanometers from the channels) are also dominated by diffusion during paired pulse stimulation when Ca²⁺ buffers throughout the varicosity are not close to saturation (Fig. 9). Consequently, no significant paired-pulse facilitation (20- and 200-ms intervals) of the local Ca²⁺ signal (within 200 nm of VGCCs) and no change in the decay rate from the peak of the Ca²⁺ signal (Fig. 10Eb, insets) was seen at these scales. Similarly full syt1-Ca²⁺ 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 Ca²⁺ 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 Ca²⁺ (Fluo-5F), Ca²⁺ transients recorded over >1 h showed consistent amplitudes and decay rates. This implies quantal fluctuation of neurotransmission is not mediated by fluctuations in total CA1 varicosity Ca²⁺ entry, although full Ca²⁺ occupancy of syt1 is very sensitive to local Ca²⁺ placement and we cannot distinguish total Ca²⁺ in the varicosity from that entering at active zones. The result is not broadly applicable across all neurons. Evoked Ca²⁺ 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 Ca²⁺ entry and buffering

This reliability, alongside our ability to introduce known Ca²⁺ dye concentrations, allowed calculations of Ca²⁺ buffering capacity, molar Ca²⁺ 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 µm⁻². This is consistent with findings that either single channels evoke release (Stanley, 1993, 2015; Haydon et al., 1994; Bertram et al., 1996) or few channels are necessary (Bucurenciu et al., 2008, 2010), and allow efficient coupling of Ca²⁺ 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 Ca²⁺ transient enabled creation of MCell simulations (Kerr et al., 2008) to investigate Ca²⁺ entry, diffusion, and buffering. Calbindin_28K dominates Ca²⁺ 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 [Ca²⁺]_i and τ were well-described by simulating calbindin_28K with a 2:2 ratio of high-affinity and medium-affinity Ca²⁺ sites. Remarkably, 3D plots of τ vs peak [Ca²⁺]_i, vs calbindin_28K concentrations converge with experimental data at a calbindin_28K concentration (39.7 µM) identical to these neurons’ somata and dendrites (40 µM 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 Ca²⁺ 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 Ca²⁺ 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 Ca²⁺ transient decays, peak amplitudes, and total Ca²⁺ entering varicosities (Fig. 5).

Localization and clustering of Ca²⁺ entry

We compared experimental data and simulations to investigate presynaptic Ca²⁺. 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 Ca²⁺ 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 Ca²⁺ signals are smaller and faster than our imaging resolution, Ca²⁺ entering the terminal, even at discrete points, will appear closer to uniformity throughout the terminal. Additionally, dye-Ca²⁺-complex diffusion might smooth variations, although we have demonstrated that Fluo-5F (10–35 µM) caused little perturbation because most Ca²⁺ binds endogenous buffers rather than dye. (κ_dye = 10–20 for Fluo-5F vs 75 for κ_end). Nevertheless, in recordings where signal-to-noise ratios were favorable, we recorded localized Ca²⁺ signaling. These regions show faster early τ’s, close to 3 ms (as fast as we can record). Peak free [Ca²⁺]_i within these regions reached 4 µM. While this does not represent concentrations causing exocytosis (Adler et al., 1991; 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 Ca²⁺ 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 Ca²⁺ 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 Ca²⁺ dependent (Kamiya and Zucker, 1994; Mukhamedyarov et al., 2009) and follows the time course of presynaptic residual Ca²⁺. However, although peak evoked Ca²⁺ transients of 4 µM, and simulated concentrations of 10 µM throughout the varicosity may sum, Ca²⁺ concentrations local to syt1 exceed 100 µM. This suggests that summating Ca²⁺ throughout the varicosity cannot modify paired-pulse responses by acting directly at syt1. Alternatively Ca²⁺, during stimulus trains, might saturate endogenous buffers (Neher, 1998) to evoke larger transients (Jackson and Redman, 2003), or subsequent Ca²⁺ 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 Ca²⁺ transient amplitude. Later responses in stimulus trains of five stimuli do show non-linear summation, perhaps attributable to buffer saturation (Neher, 1998) or secondary Ca²⁺ 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 Ca²⁺ stores (Alford et al., 1993).

To investigate Ca²⁺ at spatiotemporal scales relevant to molecular interactions, simulation was used. Our Ca²⁺-dye buffering data, supported by simulations, demonstrate that most Ca²⁺ 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 Ca²⁺ over seconds, and subsequent stimuli force occupancy of most Ca²⁺ buffer binding sites. Supralinear rises in imaged and simulated Ca²⁺ transients after more than two stimuli are due to buffer saturation. Simulation data indicate that total free Ca²⁺ concentrations averaged throughout the varicosity reach 9.3 µM after a single stimulus, and that buffer saturation indeed allows whole-terminal, paired-pulse enhancement of millisecond scale Ca²⁺ transients up to 1 s after the first stimulus (Fig. 9). However, this does not account for Ca²⁺ at scales of tens of nanometers and picoseconds in which Ca²⁺ binds to syt1.

Simulation at these nanometer scales shows Ca²⁺ 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 Ca²⁺ ions to syt1 indicates that Ca²⁺ entry within <50 nm causes its full occupancy. This result, also indicates clustering of Ca²⁺ 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 Ca²⁺ requirements for release are as low as 25 µM (Schneggenburger and Neher, 2000). However, full Ca²⁺ occupancy of the syt1 model is not enhanced by paired pulses. If residual Ca²⁺ is responsible for paired pulse facilitation (Zucker and Regehr, 2002), then these data point to a Ca²⁺-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 Ca²⁺ on vesicle priming (Neher and Sakaba, 2008) and the size of the readily releasable pool (Thanawala and Regehr, 2013).

We conclude that the Ca²⁺ responsible for evoked release at CA1 neuron varicosities reaches hundreds of micromolar at small clusters of Ca²⁺ channels local to the release machinery. These clusters may represent up to half of the Ca²⁺ entry in the terminal for which fewer than 30 Ca²⁺ channels open. As at most synapses, the Ca²⁺ channels must be within tens of nanometers of the fusogenic Ca²⁺ sensors, and simulations of Ca²⁺ indicate that diffusion dominates its dispersal at this scale. Thus, neither paired pulse Ca²⁺ accumulation (Wu and Saggau, 1994), nor buffer saturation (Neher, 1998; Matveev et al., 2004), nor Ca²⁺ pumps substantially impact Ca²⁺ binding to syt1. Nevertheless, buffer saturation during repetitive stimulation causes a varicosity wide enhancement of Ca²⁺ transient amplitudes which may impact short-term enhancement by recruiting other Ca²⁺-binding proteins.

Acknowledgments

Acknowledgements: We thank Dr. Janet Richmond and Dr. Nelson Spruston for helpful discussions throughout the course of this study.

Footnotes

The authors declare no competing financial interests.
This work was suported by National Institutes of Health Grants R01 MH084874 and R01 NS052699 (to S.A.) and F31 NS063662 (to E.H.).

This is an open-access article distributed under the terms of the Creative Commons Attribution 4.0 International license, which permits unrestricted use, distribution and reproduction in any medium provided that the original work is properly attributed.

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Reviewing Editor: Christian Hansel, University of Chicago

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

Abstract

Significance Statement

Introduction

Materials and Methods

The preparation

Electrophysiology

Imaging

Effects of introduction of buffers to cell compartments

Simulations

Statistics

Results

Resting Ca2+ concentrations in axonal varicosities

Dependency of the Ca2+ signal on dye buffering capacity (κdye)

Use of dyes to calculate Ca2+ entry and buffering

Ca2+ source and removal from the terminal

Modeling of Ca2+ transients in varicosities

Model validation of experimental results in a small terminal

Spatiotemporal distribution of Ca2+ entry to the terminal

Simulation of localized Ca2+ entry

Proximity of the point of Ca2+ entry to the release machinery and paired-pulse facilitation

Simulating paired-pulse presynaptic Ca2+ transients

Activation of syt1 by evoked presynaptic Ca2+ entry

Discussion

Quantitation and simulation of Ca2+ entry and buffering

Localization and clustering of Ca2+ entry

Summation of Ca2+ transients and short-term plasticity

Acknowledgments

Footnotes

References

Synthesis

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Neuronal Excitability

Subjects

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

Resting Ca²⁺ concentrations in axonal varicosities

Dependency of the Ca²⁺ signal on dye buffering capacity (κ_dye)

Use of dyes to calculate Ca²⁺ entry and buffering

Ca²⁺ source and removal from the terminal

Modeling of Ca²⁺ transients in varicosities

Spatiotemporal distribution of Ca²⁺ entry to the terminal

Simulation of localized Ca²⁺ entry

Proximity of the point of Ca²⁺ entry to the release machinery and paired-pulse facilitation

Simulating paired-pulse presynaptic Ca²⁺ transients

Activation of syt1 by evoked presynaptic Ca²⁺ entry

Quantitation and simulation of Ca²⁺ entry and buffering

Localization and clustering of Ca²⁺ entry

Summation of Ca²⁺ transients and short-term plasticity