Abstract
Presynaptic Ca2+ evokes exocytosis, endocytosis, and short-term synaptic plasticity. However, Ca2+ flux and interactions at presynaptic molecular targets are difficult to determine, because imaging has limited resolution. We measured single varicosity presynaptic Ca2+ using Ca2+ dyes as buffers, and constructed models of Ca2+ dispersal. Action potentials evoked Ca2+ transients (peak amplitude, 789±39 nM, within 2 ms of stimulation; decay times, 119±10 ms) with little variation when measured with low-affinity dye. Endogenous Ca2+ buffering capacities, action potential-evoked free [Ca2+]¡ and total amounts entering terminals were determined using high-affinity Ca2+ dyes to buffer Ca2+ transients. These data constrained Monte Carlo (MCell) simulations of Ca2+ entry, buffering, and removal. Data were well-fit with simulations of experimentally-determined Ca2+ fluxes, buffered by simulated Calbindin28K. Simulations were consistent with clustered Ca2+ entry followed within 2 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 diffusion rates were high. Thus, Ca2+ within tens of nanometers of entry, did not accumulate during sequential stimuli. A model of synaptotagmin1-Ca2+ binding indicates that even with 10 μM free varicosity Ca2+, synaptogmin1 must be within tens of nanometers of channels to ensure occupation of all its Ca2+ binding sites. Repetitive stimulation, which evokes short-term synaptic enhancement, does not modify probabilities of Ca2+ fully occupying synaptotagmin1’s C2 domains, suggesting that enhancement is not mediated by Ca2+-synaptotagmin1. We conclude that at spatio-temporal scale of fusion machines, Ca2+ necessary for their activation is diffusion dominated.
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 (Llinas et al., 1992; Shahrezaei and Delaney, 2004; Oheim et al., 2006). Additionally, Ca2+ plays other roles in presynaptic terminals including modifying repetitive neurotransmission (Zucker, 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). However, Ca2+ is utilized 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 and Ca2+ binding properties within cells.
CA1 pyramidal neuron somata and dendrites contain approximately 40 μM of the Ca2+ binding protein calbindin28K (Baimbridge et al., 1992; Müller et al., 2005) which may represent their dominant buffer (Yi, 2013) – although other buffers will have an impact. Indeed, calmodulin is present at presynaptic terminals (Llinas 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.
Synaptotagmin1 is idely 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. Though widely accepted (DiGregorio and Vergara, 1997; Koester and Sakmann, 2000) this is poorly characterized in presynaptic terminals. Synaptotagmin 1 (syt1) has two Ca2+ binding domains (C2A and C2B) (Perin et al., 1991) which bind 3 and 2 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 Sudhof, 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 presynaptic Ca2+ interacts with synaptotagmin, we have quantified [Ca2+]i in CA1 presynaptic terminals during single action potentials. This allowed us to simulate action-potential-evoked Ca2+ entry, binding, buffering and dispersal at individual terminals using Monte Carlo simulation (MCell (Kerr et al., 2008) and investigate its interaction with syt1 at resolutions that evoke exocytosis.
Results
Loading cells and resting Ca2+ concentrations in axonal varicosities
To measure presynaptic Ca2+, dye was introduced to CA1 pyramidal neurons from somatic whole cell pipettes containing Ca2+-sensitive dye (Fig 1B), and Alexa 594 hydrazide (250 μM; Fig 1A). After 20 mins, the axon was traced by imaging Alexa 594 (Hamid et al., 2014). We initially used Fluo-4 (1mM) as a Ca2+ sensor. Both dyes diffused into axon varicosities at similar rates (Fig 1C) and Alexa 594 fluorescence was used to measure dye concentration. We assume co-diffusion of the dyes which have similar molecular weights (736 and 737 g·mol−1). Thus, dye concentrations were calculated throughout each experiment (methods). MCell simulations of diffusion from these molecular weights and the axon morphology support this assumption (Supplemental Fig 1). To illustrate this, Alexa 594 hydrazide and Fluo-4 fluorescence (Fig 2Aa) were normalized to their values when the first varicosity image (inset 1) was obtained. For 70 mins (until Fig 2Aa inset 2), fluorescence ratios between the dyes remained constant. Resting [Ca2+]i was calculated from these data and the Fmax of Fluo-4 fluorescence (obtained by repetitive stimulation), applied to equation 3 (methods). [Ca2+]i remained stable for >1 hour as dye concentrations rose (Fig 2Ab; mean resting [Ca2+]i = 81± 5 nM; 11 cells). At 80 mins, Fluo-4 fluorescence increased more rapidly than Alexa 594’s revealing an increase in resting [Ca2+]i (Fig 2Aa, green circles). No data were used after this.
Dependency of the Ca2+ signal on dye buffering capacity (κdye)
Single CA1 axon varicosities loaded with high-affinity Ca2+-sensitive dye (Fluo-4, Kd, 0.44 μM; 1 mM) were imaged by line-scanning single action potential evoked Ca2+ transients (Fig 2B). Transient peak amplitudes reduced, and decay time constants (τ) increased as dye concentrations rose (Fig 2B). 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). 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 accompanied by increased peak amplitudes. These did not occur (supplemental Fig 2).
Similar experiments were performed substituting a low affinity Ca2+ dye (200 μM Fluo-5F, kd 1.49 μM; n = 30). Responses were recorded during rising dye concentrations (Fig 2Ca-b). Normalized as (ΔF/F+1), these Ca2+ transients were invariant in amplitude and τ throughout the experiment (Fig. 2Cd), and the fluorescence transient was uniform across the varicosity within 6 ms of the stimulus (Fig 2Ce). Means of transients from sequential stimuli were plotted, and single exponentials fit to decays (Fig 2Cf). In all cells, transients from different varicosities at different axon locations gave reproducible amplitudes and τ’s (mean Δ[Ca2+]i = 677 ± 10 nM (methods, equation 3), mean τ = 119 ± 1.4 ms, n = 30).
Comparing Ca2+ transient τ’s and amplitudes from Fluo-4 (n=11) vs. Fluo-5F (n = 7) at similar times after whole-cell access also indicates dye buffering (increasing κdye) not loss of endogenous buffer causes the changes in peak ΔF/F and τ. Using Fluo-4, as concentration increased, τ increased and peak amplitudes were reduced. However, Fluo-5F left both unaltered (Supplementary Fig 2). Calculated dye concentrations were therefore used to relate dye buffering to varicosity Ca2+ transients (example cell, Fig 3: Supplementary materials).
We determined κdye (equation 4) for each Ca2+ transient from varicosity dye concentrations, changes in varicosity free Ca2+ (Δ[Ca2+]i) calculated from this data, and equation (3). In 18 neurons (7 - Fluo-5F, 11 - Fluo-4) a linear fit to τ vs κdye (Fig 3A) gave an x intercept of −58 ± 40 and an estimate of the endogenous buffering capacity of the varicosity (kend) of 57 (equation 5). A plot of Δ[Ca2+]i (equation 3) against κdye (Fig 3B) demonstrated the relationship between κdye and the Ca2+ transient. A fit of equation (9) to this data or a linear fit to 1/Δ[Ca2+]i vs κdye (inset Fig 3B) gives a peak free Ca2+ concentration ([Ca2+]ι) 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 κdye = 0. Constants from the same fit give total Ca2+ entry of 58 ± 6 μM and κend of 75 ± 6.
Total dye bound Ca2+ ([Cadye]) was calculated for each transient either from the product of [Ca2+]i and κdye, or from proportions of dye bound to Ca2+ calculated from the Hill equation. These gave values that differed by less than 5%. Data in Fig 3C are from the former. 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). Ke⊓d 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 least errors were used and summarized in table 1.
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 κend 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 to 132 %, n=5). Thus ryanodine does not meaningfully alter Ca2+ transients.
If Ca2+ extrusion is mediated by pumps with linear rates vs peak [Ca2+]I, then as the transient varies with κdye, removal rates can be calculated. As dye concentration increases, κdye dominates κend, 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 κdye. A summary of experimentally determined properties of the varicosity is given (Table 1).
Modelling 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 calbindin28K (Müller et al., 2005)(40 μM), making it a candidate buffer in varicosities (Arszovszki et al., 2014) with well-characterised Ca2+ binding properties (Nägerl et al., 2000). Calmodulin with similarly characterized properties (Faas et al., 2011) has also been proposed as a dominant binding protein in these neurons. We constructed a 3D model in the simulation environment MCell (see methods) (Kerr et al., 2008), to investigate Ca2+ entry, diffusion, buffering, and removal during action potential stimulation. Paramaters and buffers (either calbindin28k 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, 2 by 1 μm (volume = 1.2×10−11 L, the median measured varicosity volume) en-passant to an axon (0.12 μm diameter). They contained 320 40 nm diameter vesicles and an internal structure mimicking organelles to position 1/3 of the Ca2+ extrusion pumps (Fig 5A; supplementary video 1 for Ca2+ transient simulation). We modeled Ca2+ extrusion with a rate of 2.2×1011 M−1·s−1 distributed to 3000 pumps over the plasma membrane and organelle meshes. A Ca2+ leak (1.77×105 s−1) similarly distributed achieved resting free [Ca2+]i of 81 nM. Ca2+ buffering was modeled with three models of buffers (calbindin28K 3:1 ratio, calbindin28K 2:2 ratio or calmodulin). Calbindin28K 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 and medium affinity non-cooperative sites. The former model was slightly but not significantly favored in data fits in vitro (Nägerl et al., 2000), but the latter significantly in a model of cerebellar Purkinje neurons (Schmidt et al., 2012) in which a correction to the on-rate accounted for intracellular Mg2+. Ca2+-calmodulin binding was also modeled using published parameters (Faas et al., 2011) (table 2). We utilized the same Mg2+ on-rate correction in our models for calbindin28K and calmodulin. Evoked Ca2+ entry was modeled as a total of 45 μM Ca2+ entering the terminal in 2 ms (table 1)
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 calbindin28K (2:2 ratio of high 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 - 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 calbindin28K with a 2:2 binding ratio converge to within the 95% confidence interval of the experimental data (Fig. 5C). A least squares fit for this convergence predicts a calbindin28K 2:2 concentration of 39.7 μM – in close agreement to 40-45 μM calbindin28K obtained experimentally for rat CA1 pyramidal neuron somata (Müller et al., 2005). Neither the calbindin28K 3:1 ratio nor calmodulin converged (Fig 5C, supplementary Fig 4). Note, in cerebellar purkinje neurons, models for calbindin28K also favor 2:2 ratios (Schmidt et al., 2012). While other Ca2+ buffers are present, we conclude that simulating calbindin28K 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 is valid for small terminals. Effects of Fluo-4 (0 to 670 μM) were simulated and κdye calculated as for experimental data. As for experimental data, rising values of simulated κdye 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 vs. κdye (Fig. 5Db), peak [Ca2+]i vs. κdye (Fig. 5Dc), and total Ca2+ entry captured by the dye vs κdye (Fig. 5Dd). In all cases simulations fell within the 90% confidence limits of experimental data supporting the use of this approach in small varicosities.
We then compared experimental Fluo-5F results to simulations of Fluo-5F-Ca2+ binding to validate simulations with experimental data. The simulation reproduced experimental measurements showing that Ca2+ transients remain isolated to varicosities (supplemental Fig 5A,B). Additionally, simulated responses to repetitive stimulation fell within the 90% confidence interval of the experimental data to equivalent stimuli (supplementary Fig 5C).
Spatio-temporal 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 indicate 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 4 transients in each of the 5 terminals; ΔF/F+1 vs time; Fig. 6B), reveal brighter regions immediately post-stimulus (Fig. 6Ca, hotspots arrowed at faster timebase - lower panel). However, these spots are close to the resolution limit, and their intensity might be affected by errors in background or prestimulus intensity. If hotspots represent localized Ca2+ entry then a faster local decay would represent diffusion from this site (mean τ overall = 119.5 ± 1.4 ms). Therefore, τ was analyzed in line-scan subregions. In the case illustrated, a single exponential well-fit Ca2+ transients away from hotspots (Fig 6Cb,e; sum of squares of residuals were not significantly different between single and double exponential fits, p = 0.11) but did not adequately fit regions at hotspots. These were well-fit by double exponentials (τ’s of 6 - 11 and 105 - 135 ms, Fig 6Cc,d). Similar results were obtained in all 5 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 these hotspots, p = 0.013). To illustrate the peak [Ca2+]i recorded by Fluo-5F, experimental data is replotted (Fig. 6D, black) as [Ca2+]i vs. 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 5 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 was poorly fit by a single exponential (blue, residual above, goodness of fit was again determined by comparing sums of squares of residuals. These were significantly different between single and double exponential fits at hotspots; p = 0.02, but not away from hotspots, p = 0.06).
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 4 sequential stimuli (5 cells). Each response was fit with a double exponential. Fast exponential amplitudes for the two regions were significantly different (p = 0.0052, two factor ANOVA), but there was no significant difference between slower exponential amplitudes (p = 0.08).
We determined whether discrete placement of Ca2+ entry within the simulation could reproduce the experimental Ca2+ distribution. In simulations, Ca2+ entry was located at 1 to 6 plasma membrane sites. 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.
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 (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 6 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 95% confidence limits of fits of early components of experimental data (simulations from 3-4 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
Proximity of Ca2+ entry to its molecular targets can be estimated by comparing effects of BAPTA (rapidly binds Ca2+) to EGTA (slower binding) (Adler et al., 1991). To record synaptic responses from CA1 synapses, their axons were stimulated (1/15 Hz) (Hamid et al., 2014). Whole-cell recordings were made from subicular pyramidal neurons and excitatory postsynaptic currents (EPSCs) recorded (in bicuculline, 5 μM; AP5, 50 μM) to isolate AMPA receptor responses. BAPTA-AM was superfused (10-100 μM, 20 mins) and reduced EPSCs dose-dependently (to 35 ± 13 %, 100 μM, n = 4; to 38 and 49%, 20 μM and to 80 ± 10 % of control, 10 μM, n = 3; Fig 8A). In contrast EGTA-AM (20 – 100 μM was ineffective (100 μM, n = 2, to 91 and 101%; 20 μM, n = 7 to 110 ± 30% of control, p = 0.86, Fig 8C). These results imply a close spatial association between VGCCs and syt1 responsible for exocytosis.
Repetitive stimulation may evoke Ca2+-dependent facilitation (Zucker and Regehr, 2002) caused by residual Ca2+, Ca2+-buffer saturation (Klingauf and Neher, 1997; Matveev et al., 2004), or Ca2+-dependent processes distinct from the exocytic machinery (Fioravante and Regehr, 2011). We determined time-courses of paired-pulse facilitation with EPSCs in subicular pyramidal neurons (Fig 8B; n=7). Intervals at 100 ms gave a mean facilitation ratio of 1.85 ± 0.191 (pulse 2/pulse 1, n=5, p = 0.014, Fig 8Ca) which was abolished by EGTA-AM (20 μM; ratio after EGTA-AM = 1.0 ± 0.1, p = 0.001). In three of these cells the paired-pulse interval was varied (20 to 500 ms, Fig 8B, C,D). In EGTA, facilitation was abolished at intervals >50 ms. Facilitation ratios from controls (n = 7) and after EGTA (n = 3) were plotted from 20 to 1000 ms intervals (∼duration of varicosity Ca2+ transients). The effect of paired-pulse stimulation on Ca2+ transients was measured at 20 and 200 ms intervals. Amplitudes of the paired evoked Ca2+ transients (Δ[Ca2+]i) was not significantly altered (n = 5 and 3, Fig 8E; p = 0.25 at 20 ms). Thus, paired pulse facilitation is Ca2+-dependent, but Ca2+ transients do not measurably summate.
Simulating Paired-Pulse Presynaptic Ca2+ transients
To address experimental limitations of analyzing Ca2+ at the spatio-temporal resolutions of the vesicle fusion machinery, we simulated Ca2+, Ca2+ buffer states, and effects of repetitive stimulation on free Ca2+ using parameters previously determined (Fig 9; in Supplementary video 2). Within the simulation, at rest, >90% of calbindin28K is unbound. Stimulation causes partial occupancy of all calbindin28k states (Fig 9A). However, 2/3 of all bound states remain unoccupied even at peak (Fig 9B, Supplementary Fig 6 shows all calbindin28k states). Nevertheless, unbinding is slow and full recovery takes longer than 1 s. We then determined the effect of paired pulses over intervals from 20 to 1000 ms. Though calbindin28K was not saturated at all intervals (Fig 9B), the second pulse achieved higher peak free [Ca2+] than the first (Fig 9C, difference between 2nd peaks, black, and red dashed line). This is in spite of 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 (summation of the component resolvable by experimental imaging is shown by the blue dashed line).
Activation of synaptotagmin 1 by evoked presynaptic Ca2+ entry
Synaptotagmin 1 (syt1), the Ca2+ sensor for exocytosis, has two C2 domains with 5 Ca2+ binding sites, some of which have mM affinities for Ca2+. This requires synaptotagmin to be <100 nm of the Ca2+ source (Fig 8) (Adler et al., 1991; Augustine et al., 1991a) and leaves unanswered whether all sites must bind Ca2+ to evoke exocytosis (Radhakrishnan et al., 2009). We simulated syt1 Ca2+ binding at the plasmalemma (table 2) 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 6 Ca2+ entry sources 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 sources (Fig 10A), adjacent to a vesicle. This proximal Ca2+ source varied from an equivalent of 0 to 5 simulated channels (0.25 pA each, 0.5 ms open time).
More than 20 nm from the proximal Ca2+ source 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 5 syt1 binding sites. However, even one simulated VGCC within 20 nm of syt1 allowed this binding (Fig 10Bc, black) and more channels increased this probability (Fig 10Bc, red). With 5 channels there was a small probability of syt1 full binding 100 nm from the Ca2+ source. Within 20 nm from the Ca2+ source, one channel raised the transient concentration to 110 μM; 5 channels to 560 μM (Fig 10Bb).
The narrow spatial halfwidths 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 calbindin28K within the region, and free Ca2+ are shown on a log scale (Fig 10D) to encompass the range of concentrations when activation of 3 VGCCs was simulated at this site (similar results were obtained by clustering all Ca2+ entry at these points). Calculations of the difference between Ca2+ entry and [Ca2+]i and CaDye indicate that at this scale removal is dominated by diffusion. Thus, local Ca2+ concentrations are 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) or of full syt1-Ca2+ binding occurred (Fig 10E,F).
Discussion
CA1 pyramidal neurons make en-passant synapses at subicular varicosities (Finch et al., 1983; Tamamaki and Nojyo, 1990). We show that single action-potential evoked Ca2+ transients were reliably activated in these varicosoties from somatic stimulation, regardless of distance from the soma (to 600 μm). Using a low affinity dye that did not significantly buffer entering Ca2+ (Fluo-5F), Ca2+ transients recorded over more than 1 hour did not vary in peak amplitude or decay τ. This result implies quantal fluctuation of neurotransmission is not mediated by fluctuations in total presynaptic Ca2+ entry in CA1-subicular synapses, although full Ca2+ occupancy of syt1 is very sensitive to local Ca2+ placement. This result is not broadly applicable across cell types. Cerebellar granule cell varicosities show variation in total evoked Ca2+ entry (Brenowitz and Regehr, 2007) whereas hippocampal dentate granule cells (Jackson and Redman, 2003), cortical pyramidal cells (Koester and Sakmann, 2000) and lamprey giant axons (Photowala et al., 2005) may not.
The reliability allows calculations of buffering capacity, molar Ca2+ entering, and extrusion rates. Thus, if we assume a VGCC conductance of 2 pS and mean current of 0.25 pA for 1 ms during action potentials (Weber et al., 2010), then the mean number of VGCCs per varicosity is 27 with a mean channel density of 7 μm−2. This is consistent with findings that single channels can evoke release during artificial voltage ramps (Stanley, 1993; Haydon et al., 1994; Bertram et al., 1996) and that few channels are necessary for evoked release (Bucurenciu et al., 2008; 2010). This number of channels may still allow efficient coupling of Ca2+ entry to exocytosis (Scimemi and Diamond, 2012). Using simulations of Ca2+ distribution in varicosities we investigated how this may be achieved.
We created Monte Carlo simulations (MCell) within a model varicosity to investigate Ca2+ entry, diffusion, and buffering. Calbindin28K dominates Ca2+ buffering in CA1 pyramidal neuron dendrites (Müller et al., 2005) and its binding properties have been quantified with unprecedented accuracy (Nägerl et al., 2000) enabling its simulation. From experimental data, we found the transient peak [Ca2+]i and τ were well-described by simulating calbindin28K with a 2:2 ratio of high and medium-affinity Ca2+ binding sites. Remarkably, 3D plots of τ vs peak [Ca2+]i, vs calbindin28K concentrations converge with experimental data at a calbindin28K concentration identical to these neurons’ somata and dendrites (39.7 μM for this study vs 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 calbindin28K, and of calmodulin failed to converge with experimental data (Fig 5). Our findings, while consistent with calbindin28k as a dominant buffer come with the caveat that Ca2+ buffering must be a function of a mix of buffers. The model also reproduced features of the experimental data, including responses to repetitive stimulation and the failure of detectable Ca2+ to diffuse from varicosities to their axons. Simulations were used to validate the use of exogenous dye as buffer within small varicosities. Simulating rising concentrations of the high affinity Fluo-4 dye recapitulated experimental data showing effects of buffer on measured Ca2+ transient decays, Ca2+ transient peak amplitudes, and total Ca2+ entering (Fig. 5).
Presynaptic VGCCs colocalize to active zones (Khanna et al., 2007) and bind SNARE complex proteins (Mochida et al., 1996; 2003; 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 is unclear whether presynaptic Ca2+ entry occurs through channel clusters (Llinas et al., 1992; Bertram et al., 1996; Shahrezaei and Delaney, 2005) or more diffusely through a uniform distribution of channels. In the latter, individual Ca2+ channels might associate with primed vesicles in a 1:1 ratio. However, because Ca2+ signals from single VGCCs are smaller and faster than our imaging resolution, Ca2+ entering the terminal, even at discrete points, will appear uniformly throughout the terminal. Additionally, dye-Ca2+-complex diffusion may rapidly smooth signal variation. However, we have demonstrated that Fluo-5F (at 10 - 35 μM) caused little perturbation of the evoked transient because most Ca2+ binds endogenous Ca2+ buffers rather than dye. (κdye = 10 to 20 for Fluo-5F vs. 75 for κend). Thus, in recordings, where the terminals were close to the surface of the slice and signal-to-noise ratios were favorable, we recorded reliable localized Ca2+ signaling in varicosities.
These regions show faster early τ’s, requiring double exponential fits. When plotted as [Ca2+]i vs. time, the early component τ was close to 3 ms (as fast as we can record). Peak experimental free [Ca2+]i within these regions reached 4 μM. While this does not represent concentrations responsible for exocytosis (Adler et al., 1991; Augustine et al., 1991b; Schneggenburger and Neher, 2000), the rapid decay from concentrations substantially greater than seen throughout the remainder of the varicosity indicate non-uniform VGCC distributions, consistent with channel clustering. We used MCell simulations to determine whether VGCC clustering explains stable hotspots of Ca2+ entry. 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, providing support to the hypothesis that channels cluster.
At CA1 pyramidal to subicular synapses, paired-pulse facilitation is apparent. This facilitation, as in other synapses (Katz and Miledi, 1968; Kamiya and Zucker, 1994; Zucker and Regehr, 2002), follows the time-course of presynaptic residual Ca2+. However, with measured peak evoked Ca2+ transients of 4 μM, simulated concentrations of 10 μM throughout the varicosity and local concentrations exceeding 100 μM, residual free [Ca2+]i cannot reach concentrations that will modify paired-pulse responses by a direct action on proteins that evoke synchronous release. This reiterates a number of earlier studies across many synapses (Blundon et al., 1993; Delaney and Tank, 1994; Zucker and Regehr, 2002), although Ca2+ signaling is necessary for short-term facilitation (Kamiya and Zucker, 1994; Mukhamedyarov et al., 2009) It has alternatively been proposed that Ca2+ entry following single action potentials saturates endogenous buffers (Neher, 1998) leading to enhanced subsequent transients (Jackson and Redman, 2003), or perhaps that subsequent Ca2+ entry is enhanced (Müller et al., 2008). In CA1 varicosities, experimentally applied paired pulse stimuli at 20 or 200 ms intervals revealed no alteration of the 2nd Ca2+ transient, either peak amplitude or decay. Later responses in stimulus trains of 5 stimuli do show non-linear summation, which might be attributable to buffer saturation (Neher, 1998) or a secondary source of Ca2+ (Cochilla and Alford, 1998; Llano et al., 2000; Emptage et al., 2001; Scott and Rusakov, 2006) though notably we recorded no effect of ryanodine.
To investigate this at molecular spatio-temporal scales, simulation was used to investigate evoked Ca2+ transients. Throughout the varicosity, our Ca2+-dye buffering data and simulations demonstrate that most Ca2+ entering the varicosity is buffered endogenously at the timescale of imaging, similarly to results from other synapses (Koester and Sakmann, 2000; Jackson and Redman, 2003). Simulations also indicate that buffers re-release Ca2+ over seconds, and second stimuli force occupancy of most Ca2+ buffer binding sites. Supralinear rises in imaged and simulated Ca2+ transients after more than two stimuli indicate this can be due to buffer saturation. Simulation data indicate that total free Ca2+ varicosity concentrations reach 9.3 μM after a single stimulus, and that buffer saturation allows a whole-terminal, paired-pulse enhancement of Ca2+ transients up to 1s after the first stimulus (Fig 10). However, this does not account for Ca2+ at scales of tens of nanometers and picoseconds in which Ca2+ binds to synaptotagmin1.
When Ca2+ transients were simulated at the nanometer scale local to syt1 molecules, it is clear that Ca2+ dispersal from such small regions is dominated by diffusion. Rates of removal due to buffering or local accumulation are three orders of magnitude less than this diffusion. Because diffusion dominated 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 5 Ca2+ to syt1 indicates that Ca2+ entry within less than 50 nm of synaptotagmin causes its full occupancy. This result, along with our experimental and modeling data indicate clustering of Ca2+ channels may contribute to release at this synapse. Indeed such clusters of channels that are constrained to be further than 30nm 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 synaptotagmin1 model is not enhanced by paired pulses. If residual Ca2+ is responsible for paired pulse facilitation, for which there exists a great deal of evidence (Zucker and Regehr, 2002), then these data, in addition to data indicating the prolonged binding of Ca2+ buffers, point to a Ca2+ binding site distinct from that involved in evoked release (i.e. synaptotagmin 1) as mediated by a short-term enhancement of neurotransmitter release at these synapses, such as synaptotagmin 7 (Jackson and Redman, 2003; Jackman et al., 2016). This effect is perhaps also 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 synchronous evoked release at en-passant pyramidal neuron varicosities reaches hundreds of micromolar concentrations at clusters of Ca2+ channels local to the release machinery. These clusters may represent up to half of the Ca2+ entry in the terminal as a whole for which the activation of fewer than 30 Ca2+ channels is required, but that dispersal from these sites is diffusion dominated and does not show accumulation during repetitive stimulation. Nevertheless, buffer saturation during repetitive stimulation does account for a varicosity wide enhancement of Ca2+ transient amplitudes which may impact short-term enhancement by recruiting other Ca2+ binding proteins.
Materials and Methods
The preparation
Experiments were performed on hippocampal slices (300 μm) of male or female 20-22-day-old Sprague-Dawley rats anesthetized with isoflurane and decapitated. Hippocampi were isolated under semi-frozen Krebs Henseleit solution (in mM): 124 NaCl, 26 NaHCO3, 1.25 NaH2PO4, 3 KCl, 2 CaCl2, 1 MgCl2, 10 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 Acreditation of Laboratory Animal Care.
Electrophysiology
CA1 pyramidal neurons were whole-cell clamped follwing visual identification using an upright microscope with an Axopatch 200A amplifier (Axon Instruments). Patch pipettes (4-5 MΩ) contained solution (in mM): potassium methane sulphonate 146, MgCl2 2, EGTA 0.025, HEPES 9.1, ATP 5 and GTP 2.5, pH adjusted to 7.2 with KOH. Pipettes were also filled with either Fluo-4 (1 mM) or Fluo-5F (200 μM) and Alexa 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).
Imaging
Confocal microscopy was used to image individual varicosities of CA1 pyramidal neurons, with a 60X 1.1 NA water-immersion lens using a modified Biorad 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 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 594 hydrazide was demonstrated by recording absolute values of the fluorescence at axonal varicosities at rest over time. Alexa 594 hydrazide was excited with a 568 nm laser and imaged in long-pass (>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.
Fluo-4 and Alexa 594 hydrazide signals at varicosities were identified within 20 mins 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 mins with no stimulation reveals strong correlation with a slope of 1.01 (Fig 10B, 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 an MCell model was constructed of axons (diameter, 0.12 μm, varicosities at 4 μm intervals). Release of dyes were simulated within a 10 μm diameter soma and diffusion to varicosities up to 500 μm from the soma were simulated. There was no significant difference between rates of diffusion of the two dyes and diffusion times to varicosities were within times seen for experimental data (supplementary Fig 1) in which dye diffusion into varicosities was monitored using the Alexa 594 hydrazide fluorescence signal. Thus, both dyes reach the varicosity at the same rate, which allows the use of Alexa 594 hydrazide as a “standard candle” for measuring dye concentration. Thus, Alexa 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 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 towards 60 mins 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 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 and 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 1C.
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 a pH of 7.2 (to which the intracellular patch solutions were buffered). Log plots of these data points were used to determine Kd (Fig 1C). Calibrated measurements of dye fluorescence within neurons were also made for each dye (n=2 for Fluo-5F and n=2 for Fluo-4). Whole-cell recordings were obtained in which 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 Kd for Fluo-4 (black line, Fig 1B) but the data obtained with Fluo-5F gave a value of Kd that was not measurably different than that obtained in vitro. These values (Fluo-4 Kd= 0.44 μM, Fmin/Fmax = 0.066 and Fluo-5F Kd = 1.49 μM, F min/F max = 0. 023) were used in all subsequent calculations.
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:
The Ca2+ dye minimum fluoresence intensity (Fmin) was calculated as a ratio of Fmax determined from the dye calibration results summarized in figure 1B, from each cell at the end of the experiment. Absolute values of Fmin and Fmax were corrected by the observed value of Alexa 594 for each time point as a ratio of its value at the end of the experiment when Fmax was measured. A corrected value of Ca2+ dye fluorescence in the varicosity (F) was calculated from the measured varicosity fluorescence (Fmeas) at each time point used for analysis and then re-expressed as a ratio of Fmax, corrected by comparison to the Alexa 594 signal throughout the experiments. This is because Fmax 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: where D is the Alexa 594 fluorescence at each time, and DF is the final Alexa 594 fluorescence. Thus, for experiments using Fluo-4 or Fluo-5F, where F and Fmin in equation (1) are ratios of Fmax, and Fmax = 1, [Ca2+]i was calculated as follows:
These experiments required constant laser intensity and recording parameters throughout the experiment. To minimise photobleaching, imaging was performed only transiently during evoked responses (1s 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 (kdye) 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 κdye over a change in Ca2+ concentration (Δ[Ca2+]i) from [Ca2+]1 to [Ca2+]2. where [CaDye] is the concentration of Ca2+-bound dye, and [Dyetotal] 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 (approx. 1 μM). Other approaches with smaller Ca2+ changes use resting [Ca2+]i as a basis for calculating κdye (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 (Jackson and Redman, 2003) originally described by Melzer et al (Melzer et al., 1986) to determine the buffering characteristics of Ca2+ in CA1 pyramidal neuron presyaptic varicosities. From these methods we can determine the quantity of calcium entering the varicosity, the mean free [Ca2+]¡ 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 (κend) of the terminal. If the value of κdye varies during the experiment then we assume a constant rate of Ca2+ extrusion from the terminal (τext). The decay rate (τ) of a pulse-like Ca2+ signal in a cell compartment is described by the equation:
Thus, we obtained values of κend by fitting equation (5) to plots of τ from experimental data vs κdye 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 kend. Nevertheless, the result (κend) can be obtained independently of computed absolute values of Ca2+, or even of background fluorescence meaurement errors. It therefore serves as an independent measure of whether the following measurements of kend are reasonable.
By measuring the peak amplitude of the free Ca2+ transient throughout the varicosity over a range of values of κdye, we may assume that the total change in Ca2+ concentration due to a stimulus is described by the equation:
Where [Caend] is the concentration of endogenous buffer bound to Ca2+ and Δ[Ca]totalis the total stimulus-evoked change in calcium concentration in the cell compartment. Thus combining these equations we may state:
Where Δ[Ca2+]i varies with kdye. Values of Δ[Ca2+]i are computed from our data using equation (3) and values of κdye from equation (4). For each action potential, as the value of κdye rises it will come to dominate binding of Ca2+ entering the cell compartment. This approach is useful because the value of Δ[Cadye] can be calculated for each action potential in each presynaptic terminal as the value of κdye increases by diffusion of dye from the soma. Equations (6), (7), and (8) can also give:
Values of Δ[Ca]total, and κend can be determined by extracting constants from fits of either equation (9) or (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 κdye = 0. To calculate total Ca2+ entering the terminal from the concentrations obtained from either equation (9) or (10), we calculated varicosity volumes from images using Alexa 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, long pass 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 elipsoids 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:
Chemicals were obtained as follows: Alexa dyes, Fluo-4, Fluo-5F, Ca2+ standards; (Thermo Fisher, Eugene OR), salts, buffers etc; Sigma (St Louis MO). Fits to datasets were performed in Igor Pro (Wavemetrics, IA USA). Errors bars from fitted data represent the 95% confidence limits of those fits. Otherwise errors are reported as the standard error of the mean. Significance was tested with Student’s t test or 2 factor ANOVAs where appropriate.
Simulations
Monte Carlo 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, 2, and 3. Animated visualizations of these simulations are shown in Supplementary materials.
Acknowledgements
We would like to thank Drs Janet Richmond and Nelson Spruston for helpful discussions throughout the course of this study. This work was funded by NIH grants R01 MH084874 and R01 NS052699 to SA and F31 NS063662 to EH.