A new kinetic framework for synaptic vesicle trafficking tested in synapsin knock-outs

Abstract

At least two rate-limiting mechanisms in vesicle trafficking operate at mouse Schaffer collateral synapses, but their molecular/physical identities are unknown. The first mechanism determines the baseline rate at which reserve vesicles are supplied to a readily releasable pool. The second causes the supply rate to depress threefold when synaptic transmission is driven hard for extended periods. Previous models invoked depletion of a reserve vesicle pool to explain the reductions in the supply rate, but the mass-action assumption at their core is not compatible with kinetic measurements of neurotransmission under maximal-use conditions. Here we develop a new theoretical model of rate-limiting steps in vesicle trafficking that is compatible with previous and new measurements. A physical interpretation is proposed where local reserve pools consisting of four vesicles are tethered to individual release sites and are replenished stochastically in an all-or-none fashion. We then show that the supply rate depresses more rapidly in synapsin knock-outs and that the phenotype can be fully explained by changing the value of the single parameter in the model that would specify the size of the local reserve pools. Vesicle-trafficking rates between pools were not affected. Finally, optical imaging experiments argue against alternative interpretations of the theoretical model where vesicle trafficking is inhibited without reserve pool depletion. This new conceptual framework will be useful for distinguishing which of the multiple molecular and cell biological mechanisms involved in vesicle trafficking are rate limiting at different levels of synaptic throughput and are thus candidates for physiological and pharmacological modulation.

Figure 1.

Development of a novel kinetic model for rate-limiting steps in vesicle trafficking. A, B, Markov models of single release sites. F states represent full states, meaning loaded with a docked and primed vesicle, whereas E states represent empty states. rel. denotes release events, which occur during all transitions from F to E states. A, Key preliminary models that led to the working model. Ai, Two state Markov model depicting an individual release site. The model can account for key aspects of depression during the first several seconds of heavy drive, but does not account for the slowly recovering supply-rate depression induced later on. Aii, An extension with a secondary, more deeply inhibited E state (E₂). This model does predict a form of supply-rate depression, but cannot account for the delayed onset during induction seen in experiments. Aiii, A further extension that can account for the delayed induction of supply-rate depression in addition to the double exponential RRP replenishment time courses described in Equation 1, but not the additional observations in C. B, Working model. The parameter r determines the length of the delay before onset of supply-rate depression by specifying the number of F and E state pairs. The total number of states would be r * 2. The difference compared to Aiii is that the only transitions allowed from states with higher numbers to lower numbers are transitions into the F₁ state, which is key for satisfying the third constraint. C, The third constraint is τ = τ_s recovery of the aggregate response during stimulation that induces the maximum amount of short-term depression. Maximal depression was induced at Schaffer collateral synapses two times with a pair of 20 Hz stimulus trains of 600 pulses, separated by an experimentally varied rest interval (ΔT) as diagrammed at the top. Plotted is the logarithm of 1 minus recovery of the sum of all responses during the second train versus the intertrain interval [n = 24 trials from 16 preparations, including the 12 used for Garcia-Perez et al. (2008, their Fig. 5)]. The dashed line is the single exponential function with τ = 70 s, matching τ_s in the previous study. Green diamonds are simulation results using the working model in B with r = 4. Squares are the incorrect predictions made by the model in Aiii. D, Schematic diagram of a reserve pool depletion interpretation of B. Top left, Each release site (green squares) docks a vesicle-tethering unit (red strands). The theoretical model in B pertains to a single one of these sites (dashed gray boxes). Only one of the attached vesicles at a given site may be primed (magenta) at any given time, whereas the other vesicles function as a local reserve pool (blue). Individual release sites are modeled as behaving independently, and thus different sites can be in different states as depicted. Nondocked tethers are in the immobile reserve. Bottom left, Replenishment of local reserve pools occurs when tethering units are spontaneously but infrequently replaced by new, fully loaded tethering units. Stochastic all-at-once replenishment such as this is a requirement of the result in C. Right, All possible states for a single release site/tethering unit complex in WT synapses during heavy drive, diagramed to match the scheme in B. Arrows indicate the sequence of transitions between states. A release site with a primed vesicle is in one of the F states and releases the vesicle at the rate specified by β, transitioning the site on to the next E state. Thereafter, a new vesicle will be primed from among the reserves attached to the tether at the rate specified by α if one is available. Stochastic replacement of tethering units is indicated here by the brown arrows pointing back to F₁ and occurs at the rate specified by γ. Priming (faster) and docking replacement tethers (slower) would be the two kinetic modes by which vesicles are supplied to the RRP. Instead of priming, α could alternatively be postfusion clearance of tangled SNAREs or physical translocation of vesicles along the tethers.

Figure 2.

The working model accurately predicts the induction of supply-rate depression. A, Left, Values for rate parameters in the working model that were constrained by previous experiments. Increasing the resting value for β to match the estimates of the spontaneous minirate (<0.0005/s per release site) made no detectable difference in the results. Single asterisks indicate that values for α in Wesseling and Lo (2002) correspond to α + γ here. The resting value for γ was calculated assuming τ_s = 1 min, which is close to both the value in cell culture using pairs of osmotic shocks (Stevens and Wesseling, 1999a) and the value newly estimated from Figure 5 in the present report, but slightly faster than the τ_s = 70 s value reported by Garcia-Perez et al. (2008). Double asterisks indicate that γ needed to be accelerated to 0.025/s during active periods for the working model to match observations exactly; this value was not included in the table because it was not highly constrained by data in previous reports, and is therefore a prediction of the working model, rather than a constraint. Right, Values for β(t) used during modeling throughout the present report. Values were calculated from the first 80 responses plotted in B using the kinetic scheme described in the appendix of the study by Wesseling and Lo (2002), assuming only that the RRP is depleted to a standing fullness of ∼5% by the end of the first 3 s of 20 Hz stimulation. B, Short-term plasticity during 30 s of 20 Hz Schaffer collateral stimulation in slices (n = 66 preparations). Response sizes were normalized by the mean size of the first 20 responses. The magenta line is the simulation of the working model with r = 4, γ = 0.017/s, and the other parameters with the values specified in A. The green line is the same model with γ accelerated to 0.025/s.

Figure 3.

Synapsin DKO synapses depress faster and more extensively during heavy stimulation. Responses during 30 s of 20 Hz Schaffer collateral stimulation in slices from strain-matched DKO and WT animals (n = 55 preparations for DKO; WT values are from Fig. 2B). Magenta symbols represent DKO, and blue represents WT. A, First 80 responses. Insets are the first responses averaged across all experiments. Calibration: 100 pA, 25 ms. B, All 600 responses versus pulse number, binned into groups of five for clarity. Error bars (SEM) are smaller than the symbols. Green lines are the working model with r = 2.6 (matching DKO) and r = 4 (WT). Left inset, Averaged traces across all experiments of responses 1 to 5 and 151 to 155, scaled by the mean size of responses 1 to 5. Scale bar, 25 ms. Middle inset, Magnified responses 151 to 155. Boxed inset, Overlaid, averaged traces from an additional set of experiments before and at least 4 min after 600 pulses (20 Hz; average of 5 experiments). Calibration: 100 pA, 20 ms. C, Cumulative responses. Green lines are the working model.

Figure 4.

Sixty-pulse trains are long enough to exhaust the RRP at DKO synapses. A, Schaffer collaterals were driven at 20 or 40 Hz for 60 s (1200 or 2400 pulses; 8 paired trials from 5 preparations). Ai, Traces from an example experiment after subtracting the stimulus artifacts (see Materials and Methods). Top, First 200 ms. Calibration: 100 pA, 50 ms. Middle, First 4 s. Calibration: 100 pA, 1 s. Bottom, All 60 s. Calibration: 100 pA, 10 s. Aii, Mean of the current integral per 100 ms bin during the first 6 s of stimulation across all experiments (bin values were normalized by the mean size during the fourth s of stimulation at 20 Hz). Note that the time-integrated response was greater at 40 Hz during the first 1 s of stimulation (140 ± 9%), which confirms that stimulation at 40 Hz can release neurotransmitter at a faster rate before the RRP has been exhausted. The difference disappeared during the first 3 s of stimulation (106 ± 5% at 40 Hz). Aiii, Mean of response integral per 1 s bin over the first 30 s of stimulation showing that after the fourth second the response integral matched at the two stimulation frequencies, even in the face of a more than threefold further decline. The individual responses at 40 Hz were half the size of the responses at 20 Hz, but there were twice as many. Overall, no difference was detected in the cumulative response integral over 30 s of stimulation (101 ± 8%). See Figure 1 of Garcia-Perez et al. (2008) for equivalent experiments at WT synapses. B, Stimulation frequency was doubled after the 200th pulse at 20 Hz. No increase in the time-integrated response was detected under standard conditions (top; n = 4), but a robust increase was detected in positive controls conducted at a reduced Ca²⁺/Mg²⁺ ratio (0.45/2.5 mm), where 20 Hz stimulation does not exhaust the RRP (bottom; n = 8). The response integral during the first 2 s following the frequency jump compared to first 2 s overall was 129 ± 18%, compared to 87 ± 9.5% with no jump (p < 0.01). Traces are from example experiments. Calibration: top, 30 pA, 5 s; bottom, 10 pA, 5 s.

Figure 5.

Slower RRP replenishment after moderate drive, but unaltered recovery kinetics of component exponentials. RRP replenishment time courses were measured after 80 or 600 pulses with pairs of 20 Hz stimulation trains separated in time by experimentally varied intervals as diagrammed at the top (WT after 80 pulses, n = 45 trials from 23 preparations; WT after 600, n = 24 trials from 16 preparations; DKO after 80, n = 47 trials from 34 preparations; DKO after 600, n = 42 trials from 31 preparations). A, Linear plots showing that RRP replenishment is slower after 80 pulses at DKO compared to WT synapses. Dashed lines are Equation 1 with τ_f = 6.7 s, τ_s = 55 s, and w as indicated. B, Semilogarithmic plots. Bi, Later time points gathered for ΔT values between 30 and 120 s. Dashed lines are the single exponential y(t) = (1 − w) · $\left(1-e^{\frac{-t}{\tau }}\right)$ + w, with τ = 55 s and w values as in A. Best-fitting time constants for just the later data points were calculated as 55 s (range of 46 to 69 s with 95% confidence) for WT after 600 pulses, 56 s (43 to 77 s) for DKO after 600 pulses, and 54 s (45 to 65 s) for DKO after 80 pulses. Bii, Earlier time points after first subtracting the slower exponential component assuming τ = 55 s. The dashed gray line is the single exponential with τ = 6.7 s. Deviations from the single exponential were expected because of the activity/residual Ca²⁺-dependent acceleration of α, which reverses as the Ca²⁺ is cleared during rest intervals. The solid green line is the deviation predicted by Wesseling and Lo (2002, their Eq. 2), with N = 1 and assuming α is accelerated from 0.10/s to 0.24/s by residual Ca²⁺ and that subsequent clearance during rest intervals follows the time course in Figure 2D of Garcia-Perez and Wesseling (2008). The WT data point after 80 pulses for ΔT = 15 s and the DKO data point after 80 pulses for ΔT = 2 s are shifted slightly along the horizontal axis to make them visible.

Figure 6.

Induction of supply-rate depression. A, Plot of w versus history of synaptic use. Synapses were stimulated with pairs of 20 Hz trains separated by fixed 20 s rest intervals as diagrammed (top). The length of the first train of each pair was varied experimentally, and subsequent RRP replenishment during the 20 s rest intervals was used to calculate w in Equation 1 assuming τ_f = 6.7 s and τ_s = 55 s. Plotted are fractional RRP replenishment (y-axis on left side) and w (right side) versus the cumulative response during the first train [DKO, n = 17 trials from 9 preparations; WT, n = 31 trials from 17 preparations; WT data are a subset of the data set published previously in the study by Garcia-Perez et al. (2008, their Fig. 7)]. The dashed lines (green) are the working model with values for r as indicated. The gray box labeled “single-point assay” contains the recovery values after trains of 120 pulses. The x-axis at the top is the cumulative release recalibrated into the number of RRP equivalents, which was calculated directly from the working model. B, Synapsin dosage dependence of induction of supply-rate depression. Bi, Recovery during 20 s rest intervals following 120 pulse trains for the indicated genotypes (n ≥ 10 trials from 6 preparations; **p < 0.01 compared to WT; ^##p < 0.01 compared to synapsin 2 heterozygote). Recovery was measured as the size of the aggregate response during the second train divided by the size of the aggregate response to the first 60 pulses of the first train, which is simpler than the fractional RRP replenishment measurements plotted in A (see Materials and Methods). Bii, Western blot analysis of synapsin 2 levels in hippocampal tissue homogenates showing that levels are decreased by about half. A representative blot is shown on the left. For quantification, optical density of synapsin 2 bands from synapsin 2 heterozygotes was normalized by the density of the corresponding bands from animals with both alleles (*p < 0.05; n = 3 for syn 1(+/+) background, n = 6 for syn 1(−/−) background). Error bars indicate SEM.

Figure 7.

Osmotic shock experiments in autapses. A, Confirmation of earlier onset of supply-rate depression. RRP replenishment was measured at cell culture autapses following 80 presynaptic action potentials as diagrammed at top. The first osmotic shock (Osm) was used to ensure RRP depletion, the second was used to measure RRP replenishment over the intervening rest interval, and the third, 3 min later, was used to estimate the fully replenished RRP size in a way that avoids erroneously ascribing rundown to incomplete RRP replenishment (Stevens and Wesseling, 1999a). Box, Example responses to the second and third osmotic shocks when ΔT = 20 s. Calibration: WT, 2 s, 50 pA; DKO, 2 s, 200 pA. The experiment was designed to recapitulate results for the single-point assay used in Figure 6B and the difference between DKO and WT matched predictions; see Results for quantification. Bottom, Full time course for DKO synapses. The filled circle is the DKO data from the trials where ΔT = 20 s (n = 6), used to extrapolate the value of w in Equation 1 (i.e., w = 0.60; n ≥ 3 for each data point). The dashed line is the resulting prediction generated by Equation 1. All recovery values were adjusted for the 5% rundown that typically occurs over the 3 min between the second and third osmotic shocks (Stevens and Wesseling, 1999a); see Stevens and Wesseling (1999a) for WT RRP replenishment time courses measured with osmotic shocks. B, Preservation of activity-dependent acceleration of vesicle trafficking. RRP replenishment during 2-s-long rest intervals was measured at fully rested DKO synapses with pairs of osmotic shocks as diagrammed at the top, without (baseline) and with (accelerated) 10 action potentials during the final 1 s of the first shock. Example traces are plotted; see Results for quantification. The dashed gray boxes contain the responses elicited by the second shocks of each pair, showing acceleration.

Figure 8.

Unaltered release parameters. A, Initial release probability. Use-dependent blockade of the NMDA component of synaptic responses was monitored every 8 s in the presence of MK801 (n = 10 for DKO; n = 9 for WT). Mean response sizes were normalized by the sum of all responses. The best-fitting double exponential for WT data (white line) had exponential components of 5 ± 1 and 37 ± 3 responses, with 57 ± 3% weighting for the faster exponential component. The same function fit the DKO data equally well (R² = 79 vs 78%), indicating that the initial release probability was similar. B, Early short-term plasticity. Bi, Responses to 20 pulses at 20 Hz, normalized by the mean size of all 20 responses (n = 66 for WT, 20 for syn 1(−/−), 25 for syn 2(−/−), 55 for DKO). Bii, Paired-pulse ratio calculated as the size of the second response divided by the size of the first for each experiment before calculating the mean (*p < 0.05 compared to WT; ^#p < 0.05 compared to DKO). C, Augmentation. Relative enhancement in the probability of release per readily releasable vesicle (P_VES enhancement) during rest intervals following 600-pulse trains were calculated as in Garcia-Perez and Wesseling (2008, their Fig. 4B), and the theoretical curve (dashed line) is identical to the one in their figure. Briefly, recovery from depression after each rest interval was measured in two ways from the responses elicited by a second stimulus train that was long enough to empty the RRP: RRP replenishment was estimated from the sum of all responses, as in Figure 5, whereas the substantially faster recovery of the response elicited by single pulses was calculated from the first response. P_VES enhancement for each time point was then calculated by dividing the single response recovery value by the RRP replenishment value. Error bars indicate SEM.

Figure 9.

Specific additional tests of the working model at DKO synapses. A, DKO synapses satisfy the third of the initial general constraints. The analogous result for WT is in Figure 1C. Plotted is the logarithm of 1 minus recovery of the sum of all responses during the second trains versus the intertrain interval (n = 22 trials from 29 preparations). The dashed line is the single exponential with τ = 55 s, which is the value of τ_s in Equation 1 that was extracted from Figure 5 for both WT and DKO. Green diamonds are simulation results using the working model with r = 2.6 and γ = 0.018/s. (i.e., 1/55 s). B, Replot of data in Figure 6A, except with the number of pulses of stimulation on the x-axis, showing that the working model with γ = 0.018/s (magenta) during activity does not fit results for either DKO or WT synapses, whereas γ = 0.025/s (green) does fit in both cases.

Figure 10.

Less residual FM1-43 accumulation argues against increased trapping of recycling vesicles. DKO and WT synapses in cell culture were stained with FM1-43 using electrical field stimulation and subsequently destained, as diagramed at the top. Images are of DKO synapses after staining and after subsequent destaining. ΔF versus time values are the mean of the median values after background subtraction starting 20 s before destaining and continuing for 20 s afterward (n = 10 fields for DKO; n = 15 fields for WT, each containing 22–97 fluorescent punctae). Both the total amount and residual level of staining were significantly reduced in DKO (p < 0.01), and the residual level as a relative quantity was not increased (see Results).