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The Journal of Neuroscience, April 1, 2000, 20(7):2480-2494
Release-Independent Short-Term Synaptic Depression in Cultured Hippocampal Neurons
David L. Brody and David T. Yue The Johns Hopkins University School of Medicine, Departments of Biomedical Engineering and Neuroscience, Program in Molecular and Cellular Systems Physiology, Baltimore, Maryland 21205
ABSTRACT
TOP
ABSTRACT
INTRODUCTION
Short-term synaptic plasticity may dramatically influence neuronal information transfer, yet the underlying mechanisms remain incompletely understood. In autapses (self-synapses) formed by cultured hippocampal neurons, short-term synaptic depression (STD) had several unusual features. (1) Reduction of neurotransmitter release probability with Cd2+, a blocker of voltage-gated calcium channels, did not change depression. (2) Lowering [Ca2+]o and/or raising [Mg2+]o had little effect on STD in cells with strong baseline depression, but in cells with more modest baseline depression, it reduced the depression. (3) Random variations in the size of initial EPSCs did not influence successive EPSC sizes. These findings were inconsistent with release-dependent mechanisms, such as vesicle depletion, post-synaptic receptor desensitization, and autoreceptor inhibition. Instead, other results suggested that changes in action potentials (APs) contributed to depression. The somatic APs declined in amplitude with repetitive stimulation, and modest reduction of AP amplitudes with tetrodotoxin inhibited EPSCs. Notably, tetrodotoxin also increased depression. Similar changes in axonal APs could produce STD in at least two ways. First, decreasing presynaptic spike amplitudes could reduce calcium entry and release probability. Alternatively, APs could fail to propagate through some axonal branches, reducing the number of active synapses. To explore these possibilities, we derived the expected variance of EPSCs for the two scenarios. Experimentally, the variance increased and then decreased on average with successive responses during trains of APs, confirming a unique prediction from the conduction failure scenario. Thus, STD had surprising properties, incompatible with commonly postulated mechanisms but consistent with AP conduction failure at axonal branches.
Key words: short-term synaptic plasticity; short-term synaptic depression; autapse; microisland; cell culture; hippocampus; cadmium; calcium; magnesium; correlation analysis; miniature EPSC; action potential; tetrodotoxin; variance analysis; simulation; branch-point failure; conduction failure; propagation failure
INTRODUCTION
Short-term synaptic plasticity (STP) refers to the changes in the efficacy of synaptic transmission that occur from one action potential to the next, depending on the recent history of presynaptic activity. Such plasticity, lasting from milliseconds to seconds, is believed to figure importantly in neuronal information transfer (Magleby, 1987
; Zucker, 1989
Much of what is known about short-term synaptic plasticity has come from experiments in brain slice preparations, which have been essential in defining its physiologically important features. But polysynaptic circuits, incomplete solution exchange, and the small sizes of individual synaptic responses in slices may complicate investigation of the mechanisms underlying plasticity. Cultured neuronal preparations may therefore be an important complement for in-depth investigations into the sources of STP. Hippocampal neurons grown in culture on glial microislands form synapses onto themselves (Furshpan et al., 1986
We have recently used these microcultured hippocampal neurons to provide evidence for a novel form of short-term synaptic facilitation attributable to relief of G-protein inhibition of presynaptic calcium channels (Brody and Yue, 2000
MATERIALS AND METHODS
Cultured neurons. Hippocampal neurons were cultured on glial microislands essentially as reported (Furshpan et al., 1986
The next day, neonatal (1-2 d old) Sprague Dawley rats were decapitated, and their brains were placed in ice-cold Earle's Balanced Salt Solution (EBSS, Life Technologies) with 10 mM HEPES. Oblique razor cuts were made from the anterior midline to the posterior temporal lobe, exposing portions of the hippocampi enriched in CA1 and CA3 neurons. The meninges were gently removed starting from the rostral end, and in the process, the exposed wedge of hippocampus flipped out of the bowl formed by the lateral ventricle. The tissue was further enriched in CA1 and CA3 pyramidal cells by clipping away a central portion of dentate gyrus that sometimes remained with the hippocampal wedge. Selective dissection of CA1 and CA3 increased the number of glutamate-releasing pyramidal cells relative to inhibitory interneurons. The tissue was minced into 1 mm3 pieces and digested in papain solution at 37°C for 50 min. Papain solution contained 20-25 U/ml papain (Worthington, Lakewood, NJ), 1 mM CaCl2, 0.5 mM EDTA, and 10 mM HEPES in EBSS, and was prewarmed to 37°C. DNAase (Calbiochem, San Diego, CA) was added to 0.1 µg/ml for 5 min further incubation. Then the tissue was washed twice with FCS media, triturated in NEU media, and passed through a 70 µm cell strainer (Beckton Dickinson) to isolate single cells. The cells were plated onto the astrocyte-containing microislands at a range of densities between 2,000 and 28,000 per milliliter. Usually one of these densities yielded a significant number of islands containing a single neuron. Plating onto astrocytes improved the health and longevity of the neurons and dramatically enhanced the number and strength of synapses that they formed. The day after plating, the proliferation of astrocytes was halted by adding 35 µM 5-fluoro-2-deoxyuridine (Sigma, St. Louis, MO) with 75 µM uridine. Patch-clamp recordings were made between 7 and 21 d in vitro. Media did not need to be exchanged for up to 21 d.
Leftover cells were placed in FCS media in an uncoated tissue culture flask. After 7 d, the flask was shaken on a laboratory shaker overnight at room temperature, and then the media was replaced. This rough treatment killed process-bearing and sensitive cells such as neurons and created a purified astrocyte culture. If fibroblasts were present, the culture was discarded.
Electrophysiology. Microislands containing one or more glia and a single neuron with extensive processes were selected for whole-cell patch-clamp recording. Pipets with resistance of 3-4 M
were pulled from borosilicate glass (TW150F-4, WPI, Sarasota, FL) and lightly fire-polished. Standard pipette solution contained (in mM): 137 K-gluconate, 12 NaCl, 10 HEPES, 4 EGTA, 0.5 CaCl2, 4 MgATP, and 0.3 LiGTP, pH 7.2 with KOH. Standard extracellular solution contained (in mM): 145 NaCl, 5.4 KCl, 2 CaCl2, 1 MgCl2, 10 HEPES, pH 7.4 with NaOH, adjusted to 310 mOsm with 15-25 mM glucose. All chemicals were from Sigma except NBQX from RBI (Natick, MA). Solutions were exchanged via gravity-fed lines connecting to a 1-mm-diameter glass tube placed 0.5 mm from the cell under study. Solutions flowed continuously at a rate of ~1 ml/min. A junction potential of
14 mV was corrected before sealing. All recordings were made at room temperature (23-25°C).
Data were acquired using an Axopatch 200B (Axon Instruments, Foster City, CA) patch-clamp amplifier and a DEC PDP-11 computer running custom software written in Basic 23. In voltage-clamp mode, the holding potential was
For current-clamp recordings, the fast mode of the Axopatch 200B was used. Baseline current injection was typically <100 pA, and adjusted to maintain a resting potential near
Analysis. In each cell with excitatory synaptic transmission, the EPSCs mediated by AMPA-type glutamate receptors were defined as the current sensitive to 2-5 µM of the AMPA receptor antagonist NBQX. Total EPSC charge transfer in windows extending 2-3 to 20 msec after each stimulus was calculated by integrating currents in this window and subtracting integrals of NBQX-resistant currents from the same cell in the same time window. NBQX-resistant currents were generally smaller than 10% of basal EPSC size and stable over time. In displayed traces, NBQX-insensitive currents have been subtracted from total currents, and 2-3 msec stimulus transients have been blanked for clarity except in Figure 1.
For very short interstimulus intervals, the first EPSC was still decaying during the second EPSC. To calculate the true amplitude of the second EPSC, we subtracted the expected contribution of the first EPSC to the total current in the second EPSC's integration window. Measurements of short-term synaptic plasticity were obtained by averaging 5-20 sweeps and normalizing by the amplitude of the first EPSC. This analysis was performed using custom software written in Matlab (The MathWorks, Natick, MA). Somatic action potential amplitudes and widths were measured automatically also using custom software written in Matlab.
All averages, variances, and statistical comparisons were calculated with Microsoft Excel. The p values given in the text were obtained from two-tailed, paired t tests or from two-tailed, unequal variance t tests as appropriate. Error values (±) cited in the text are standard errors. To check the stability of EPSCs over time (see Figs. 5, 9), we used the regression macro from the Microsoft Excel 7.0 Data Analysis tools. Data were accepted as sufficiently stable if the regression slope 95% confidence interval included zero. To look for inverse correlations between the first and second EPSCs for both simulated and experimental data (see Fig. 5), the same correlation tool was used. Final correlation coefficients were calculated after excluding rare outlying sweeps (16/431) with first EPSCs more than 3 SDs away from the means for their respective cells. Similar conclusions were reached before these exclusions.
The fits of mean versus variance data were performed using the Microsoft Excel 7.0 Solver tool, with the constraint that the fit had to include the data point corresponding to the initial mean and variance. In fitting the average normalized data to Equation 2 (see Fig. 9C), the parameters N and q were dropped, because they cannot be constrained by normalized data. The variance contributed by NBQX-insensitive currents was not subtracted from the total variance, because it was always <5% of the total variance and did not change with repetitive stimulation.
Simulations of correlations between pairs of EPSCs (see Fig. 5). Simulations were performed to assess our ability to experimentally resolve correlations that would result if release-dependent paired-pulse depression (PPD) were present (see Fig. 5). In principle, release-dependent depression should produce inverse correlations between the sizes of successive EPSCs, whereas release-independent depression should not produce any such correlations (Thomson et al., 1993
For each simulated EPSC the contributions from 500 model release sites were summed. We estimated that cultured autapses contained at least 500 sites from measurements of average EPSC amplitude (2000 pA), average quantal amplitude (15 pA), and upper-limit estimate of release probability [0.29, see Fig. 9A: 2000 pA/(15 pA × 0.29)
500]. Each release site was assumed to release either no vesicle or one vesicle with each stimulus, and quantal amplitudes were considered to be uniform. Because the results of interest were always relative EPSC sizes, quantal amplitudes were arbitrarily set to 1. For each simulation, we generated a new group of 500 heterogeneous initial release probabilities, which were drawn from a
distribution with parameters similar to those found experimentally in slices and cultured neurons (Dobrunz and Stevens, 1997
In simulations of PPD attributable to a release-dependent mechanism, if a given individual site successfully released on the first stimulus, its probability of releasing on the second stimulus was set to be a small, constant fraction (f) of its original release probability. If it did not release, its release probability was unchanged on the second trial. In release-independent depression, the release probability was decreased uniformly at all sites before the second stimulus. For each correlation trial, we generated 400 pairs of EPSCs, one with the initial set of release probabilities and the second using the modified release probabilities after depression. In the release-dependent depression simulations shown in Figure 5A, we used an f value of 0.02. Initial release probabilities were drawn from a
To address the question of how sensitive the correlation method used in Figure 5 was in detecting release-dependent depression, we performed a series of simulations with varying values of f. We increased f, decreasing the overall amount of release-dependent depression, until the statistical significance of the negative correlations approached our cutoff of p = 0.05. This cutoff was approached at f = 0.5, where the overall paired-pulse depression was 14.4 ± 0.17% (n = 11 simulations), and the p values for the slopes of the regression lines were between 0.00053 and 0.067 (mean 0.017). Thus, the correlation method was sensitive enough to detect much smaller amounts of release-dependent depression than were shown in Figure 5A, or in the electrophysiological data (32%).
Variance calculations for action potential conduction failure (see Figs. 8, 9). For derivations of analytical relations for homogeneous values of parameters used in Figures 8, A and B, and 9, see Appendix.
To explore the effects of relaxing some of the simplifying assumptions used in the Appendix, we numerically calculated the means and variances for populations of heterogeneous axonal branches (i.e., see results in Fig. 8C). For each simulation, we considered a population of 50-500 independent axonal branches and picked a random value for the number of sites per branch (SB) from a distribution of values. The distribution used was a clipped normal distribution, with SDs less than or equal to the value of the mean. Distributions were clipped in that values below 0 were taken to be equal to 0, and values above two times the mean were taken to be equal to two times the mean. To simulate depression attributable to conduction failures, conduction probabilities at each branch were decreased in discrete time steps. The rates of decrease were also heterogeneous and drawn from clipped normal distributions. These rates were held constant for each time step and were not correlated with the values of SB. The total mean and variance were calculated at each time step by calculating the mean and variance for each branch, according to Equation A6 in the Appendix, and summing across branches. Smooth curves displayed in Figure 8C were generated by interpolating between time steps. Release probabilities and quantal sizes were uniform across release sites, initial conduction probability (PC1) was set at 1, and all results were normalized by the initial values of mean and variance.
The heterogeneous rates of decrease in PC were used as a general representation for several possible scenarios. Differences between branches could arise from the variability in axonal dimensions or in the electrical excitability of the branch points. Similarly, variability in the axonal branching complexity could contribute to nonuniform depression of conduction probability. For example, even if all individual axonal branch points were equivalent, groups of release sites located distal to several sequential branch points would have lower total conduction probability than those found more proximally (see Fig. 8F).
RESULTS
Characteristics of short-term depression
Single, glutamatergic hippocampal neurons grown in culture on glial microislands were chosen for analysis of short-term depression. To record postsynaptic currents, we delivered brief voltage-clamp stimuli via a somatic, whole-cell patch pipette (Fig. 1A, top). Propagating action potentials were generated, with momentary loss of voltage-clamp control caused by large sodium and potassium currents corresponding to initial inward and outward currents. Slower inward currents followed, which flowed through AMPA-type glutamate receptors (Fig. 1A, total current). Subtraction of responses obtained with the AMPA antagonist NBQX (Fig. 1A, NBQX) isolated synaptic currents (Fig. 1A, total
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Figure 1. Short-term depression (STD) in microcultured hippocampal neurons. A, Voltage-clamp stimuli (stim.) were applied via a somatic patch pipette to single self-synaptic (autaptic) neurons in culture, and the resulting currents were recorded (total current). Synaptic currents were isolated by subtracting the current remaining in 2 µM NBQX (NBQX), from the total current (total
During 50 Hz trains of stimuli, short-term synaptic plasticity under control conditions was dominated by depression (Fig. 1B), similar to previous findings (Mennerick and Zorumski, 1995
The recovery from synaptic depression followed an apparently biexponential time course (Fig. 2), also consistent with a previous report (Mennerick and Zorumski, 1995
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Figure 2. Recovery from depression occurred in two phases. Interstimulus interval (d) between pairs of stimuli (S1, S2) was varied between 5 msec and 15 sec. Shown are single sweeps for intervals of 15 msec, 200 msec, and 15 sec (top). QEPSC averages after second stimuli (avg. S2) were normalized by QEPSC averages after first stimuli (avg. S1). Five to ten sweeps were averaged for each interstimulus interval. Error bars not shown when smaller than symbols. The sum of two exponentials (smooth curve) was fit to the recovery of the EPSCs (avg. S2/avg. S1); for this cell, time constants were 5.8 msec and 4.8 sec, with relative amplitudes 0.74 and 0.26.
To determine whether a release-dependent mechanism underlies the observed STD, we investigated the effects of reducing presynaptic calcium entry with Cd2+, a blocker of voltage-gated calcium channels. Cd2+ blocks at micromolar concentrations, so surface charge effects are minimal, and there is no significant change in the relative current-voltage relations of the channels (Leonard et al., 1987
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Figure 3. STD was not affected by reduction in release probability by Cd2+. A, Diary plot of QEPSC for first stimuli (solid diamonds, S1) and second stimuli (open squares, S2) of 50 Hz stimulus trains. Both NBQX and Cd2+ were readily reversible. B, Sample records after NBQX subtraction, acquired at the times indicated by ii and iii in the diary plot above. C, QEPSC averages across 29 cells. Left, Responses normalized by the first QEPSC in control (solid squares) for each cell, then averaged across cells, showing extent of inhibition by Cd2+ (open triangles). Right, Responses normalized by first QEPSC in each condition, to facilitate comparison of STD. There were no statistically significant differences between control and Cd2+. Error bars not shown when smaller than symbols. Time constant of smooth curve was 23.8 msec.
In a previous report, depression in a very similar preparation was altered by changing extracellular calcium and magnesium concentrations (Mennerick and Zorumski, 1995
To examine the basis of this apparent discrepancy, we also lowered release probability using a variety of different [Ca2+]o and [Mg2+]o solutions (
Ca/Mg). All solutions reduced initial EPSC amplitudes, as expected, but detailed consideration of the effects of these manipulations on STD proved complex. In some cells,
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Figure 4. Complex effects on depression with reduced [Ca2+]o and/or increased [Mg2+]o ( Ca/Mg/S1control), and paired-pulse plasticity in control (S2control/S1control). Relative
To test whether the effects of
To gauge the relative importance of these two factors, S1
The results with altered Ca2+ and Mg2+ were difficult to interpret in their entirety, but nonetheless, two conclusions could be reliably drawn. First, release-dependent depression cannot account for these effects. Second, there was a robust correlation between the extent of depression and the effects of altering calcium and/or magnesium. On the whole, the data were most consistent with changes in axonal excitability (perhaps because of a combination of surface charge screening and alterations in calcium-regulated conductances) superimposed upon release-independent short-term depression (see Discussion).
We next used an independent method (Fig. 5) to further test for the presence of release-dependent STD, taking advantage of the intrinsic fluctuations in the sizes of EPSCs from sweep to sweep (Thomson et al., 1993
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Figure 5. Sweep-to-sweep fluctuations in first EPSC sizes did not affect second EPSCs. For both simulations and experimental data, each first QEPSC was normalized by the first QEPSC average (normalized S1) and each second QEPSC was normalized by the second QEPSC average (normalized S2). A, Simulation of release-dependent depression. Four hundred pairs of EPSCs were generated using a model with 500 binary release sites (see Materials and Methods). There was a significant inverse correlation between successive, normalized EPSC sizes (open squares, individual simulated EPSC pairs; solid line, linear regression). Regression slope was
The correlation analysis for experimental data is shown in Figure 5C. We took 415 data sweeps from 28 cells, normalized the response amplitudes for each cell, and then pooled all of the normalized data across cells. All responses used in this analysis were recorded in control 2 Ca/1 Mg solutions. Only groups of at least eight traces in which neither the first EPSC amplitude nor the mean short-term plasticity were changing systematically with time were accepted (see Materials and Methods). In this pooled data, the second EPSC amplitudes were on average 68% of the first EPSC amplitudes. As in the release-independent simulations, there was no correlation between relative first and second EPSC sizes.
To screen for release-dependent depression in a specific subset of cells, we focused our correlation analysis on 6 of the 28 cells that showed the greatest decreases in depression with
Presynaptic action potential hypothesis
What sort of mechanism(s) could produce release-independent short-term depression? The source of depression is likely to be presynaptic, given that there were no substantial changes in the size of miniature EPSCs during depression in this preparation (Mennerick and Zorumski, 1995
Somatic APs were recorded in current-clamp mode (see Materials and Methods) to generate hypotheses about the presynaptic APs (Fig. 6). Single APs in control solutions plus NBQX peaked at 33.7 ± 2.5 mV (n = 12 cells) and were 1.47 ± 0.08 msec wide at half amplitude (Fig. 6A). With short interstimulus intervals, the second APs were broader but considerably lower in amplitude. When the interstimulus interval was varied, the second APs regained amplitude with a time constant of 8.2 ± 2.3 msec (n = 5) (Fig. 6B,C), similar to the fast time constant of recovery from STD (Fig. 2). Even with 60 msec intervals, the second AP amplitudes did not fully return to the size of the first spike but reached a plateau 3.1 ± 1.0 mV lower. This too was similar to the recovery from STD in these cells, which also had an apparent plateau attributable to the slow component of recovery (Fig. 2). The widths of the second action potentials relaxed similarly with varying interstimulus intervals; both the amplitude and width curves could be fit by single exponentials with the same time constant (Fig. 6C). The spikes recovered entirely within 15 sec, but we were not able to resolve the time course of the slower phase of recovery. Thus we hypothesized that if the presynaptic action potentials were similar to those recorded at the somata, changes in their amplitude could be responsible for some or all of the STD.
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Figure 6. Somatic APs. A, In current-clamp mode, current injection at the soma triggered brief APs. Measurement of peak (+35 mV) and half-amplitude width (1.8 msec) is illustrated. B, Four overlaid pairs of APs at varied interstimulus intervals. With pairs of current injections, peak amplitudes were lower and half-amplitude widths were greater for the second AP. C, The peak (left) and half-amplitude width (right) of the second AP recovered toward the values of the first AP with increasing interstimulus intervals. Recovery time courses for both parameters were well fit by single exponentials (solid lines) with the same time constant, 7.3 msec. Data from same cell as in A and B.
To support this hypothesis, we demonstrated that the EPSC sizes were sensitive to a manipulation that changed somatic AP amplitudes (Fig. 7). Low doses of tetrodotoxin (TTX), a specific blocker of voltage-gated sodium channels, reduced somatic AP peak height while leaving half-amplitude widths unchanged (Fig. 7A,B). A second spike triggered 20 msec later was also reduced in amplitude by a similar proportion, so that the ratio of second peak height to first peak height was not changed significantly in TTX (Fig. 7A,B). Synaptic efficacy, as reflected in the EPSC sizes (back in voltage-clamp mode), decreased considerably in TTX (Fig. 7C) with an average reduction of ~40% (Fig. 7D). Thus transmitter release was indeed sensitive to changes in the action potential amplitude. Furthermore, TTX increased depression (Fig. 7C,D), such that EPSCs were on average ~10% of their initial amplitudes after 10 pulses, whereas they were ~20% of initial size in control for this group of cells (Fig. 7D). The increase in depression in TTX provided further evidence that a presynaptic mechanism involving changes in the AP waveform produced the observed depression.
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Figure 7. Low doses of TTX reduced AP and EPSC amplitudes, while increasing STD. A, Two pairs of current-clamped APs from the same cell, one in control and the other in 10 nM TTX, illustrating reduction in AP peak amplitudes. B, AP parameters averaged across cells. APs peaked lower and widths were unchanged in TTX. C, Sample EPSCs from a cell with larger-than-average effects of TTX. EPSCs were reduced 79%, and paired-pulse depression was increased from 31 to 62% in this cell. D, Normalized QEPSC averages in control (solid squares) and TTX (open diamonds). Left, Normalized by the first EPSC in control. First EPSCs reduced 38 ± 13% in TTX. Right, Normalized by the first EPSC in each condition, to show increase in STD. Averages across seven cells, p values 0.02-0.12 for stimuli 2-10.
Three lines of experiments were performed to attempt to reduce short-term depression by strengthening presynaptic action potentials. First, lowering intracellular sodium to 4 mM decreased the extent of short-term depression: paired-pulse modulation, as gauged by the first two responses in a 50 Hz train, was 0.73 ± 0.03 (n = 4 cells; data not shown), whereas the paired-pulse modulation in control (12 mM Na+) was 0.57 ± 0.04, (data shown in Fig. 3). Depression was similarly affected during the remainder of the responses in 50 Hz trains. The differences in the extent of depression were statistically significant (p < 0.05) for each of the responses in the trains. This finding adds further to the evidence favoring action potential changes as a contributor to depression. In 4 mM [Na+]i, the remaining depression was still release independent, in that decreasing release probability with Cd2+ did not affect the extent of depression in three of the four cells.
Second, changing the membrane potential at the soma in the interstimulus intervals from
Finally, we applied the anemone toxin ATX II, which reduces sodium channel inactivation (Mantegazza et al., 1998
Evidence for action potential conduction failure
The somatic action potential results (Fig. 6), the effects of TTX (Fig. 7), and the findings with lowered [Na+]i pointed to a mechanism of depression involving decrements in the strength of axonal action potentials. This could occur in at least two ways. First, lower amplitude action potentials arriving at the presynaptic terminal could be less effective at opening the voltage-gated calcium channels that trigger vesicle release. Such changes would be expected to progressively decrease vesicle release probability (PR) in a release-independent manner. Alternatively, lower amplitude action potentials might be less likely to propagate through regions of high electrical impedance, such as through axonal branch points. If the probability of successful action potential conduction at axonal branches (PC) decreases with repetitive stimulation, net synaptic efficacy would be reduced, also in a release-independent manner. For the simplest formulation in which all branches and release sites are assumed to be identical and independent, these two alternatives would have indistinguishable effects on mean EPSC amplitudes. This is because the mean EPSC amplitudes are directly proportional to both PR and PC, as shown in Equation 1:
where NB represents the number of branches, SB is the number of release sites per branch, and q is the quantal EPSC size for each successful release.
(1) Therefore, to distinguish between reduction in release probability versus increases in conduction failures at axonal branches, we calculated the expected EPSC variances for the two scenarios (Figs. 8, 9; Appendix). Two experimental constraints were imposed on these calculations. First, the initial action potential conduction probability was taken to be close to 1 for all branches (Luscher et al., 1994b
The extent of the rise and fall in variance increased with the number of release sites per axonal branch (SB) (Fig. 8B) and also depended on the release probability (see Appendix). The sharper increases in peak variance for large values of SB occur because multiple release sites fail with conduction block of each axonal branch, creating stochastic "events" that are larger in amplitude than the release of individual vesicles. This feature is represented diagrammatically in Figure 8E. For a single release site for each branch (SB = 1), the two models were formally identical, because the equation reduced to the well known binomial variance formula (see Appendix) (del Castillo and Katz, 1954
![&sfgr;<SUP>2</SUP>=N<SUB><UP>B</UP></SUB> P<SUB><UP>C</UP></SUB> P<SUB><UP>R</UP></SUB> S<SUB><UP>B</UP></SUB> q<SUP>2</SUP>[1−P<SUB><UP>C</UP></SUB> P<SUB><UP>R</UP></SUB> S<SUB><UP>B</UP></SUB>+P<SUB><UP>R</UP></SUB> (S<SUB><UP>B</UP></SUB>−1)].](/content/vol20/issue7/fulltext/2480/img002.gif)
(2)
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Figure 8. Expected EPSC variance in two models of release-independent STD. A, Depression attributable to decreasing release probability (PR) at each vesicle release site. Variance fell monotically with decreasing PR when initial PR was constrained to be <0.29 (see Results). Curve plotted according to the binomial variance formula, 2 = NPR(1
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Figure 9. Experimentally measured EPSC variances during STD. A, Demonstration of acceptance criteria for variance measurements. Seventeen first and second EPSCs (solid diamonds, S1 and open squares, S2) were stable in amplitude over time (dashed lines: slope = 0). EPSCs were 2.7-fold larger in 4 mM Ca2+ plus 100 µM 4-AP, constraining initial PR to <0.37. B, QEPSC variance ( 8 and 2.5 × 10
For our analytic model of short-term depression caused by axonal branch point failure, we assumed that all axonal branches had the same number of sites (i.e., SB was constant) and the same probability of failing during depression (i.e., PC decreased uniformly at all branches). These assumptions were necessary for the derivation of an analytical relation between mean and variance (see Appendix). When we relaxed these assumptions and numerically computed the expected variance for several possible nonuniform distributions of numbers of sites per branch (SB) and rate of decline in action potential conduction probability (PC) (see Materials and Methods), we found that the trends illustrated by our analytic result were maintained; depression attributable to branch point failure led under many circumstances to near-parabolic relations between mean and variance (Fig. 8C). This sort of heterogeneity in the numbers of sites per branch and action potential conduction probability is represented in the diagram in Figure 8F. Interestingly, as the dispersion in the number of sites per branch increased, the rise and fall in variance with progressive conduction failure became more extreme (Fig. 8C). This may occur because of the nonlinear relationship between the number of sites per branch and the magnitude of the peak in variance (see Appendix, Eq. A11). Thus, the distinction in expected variance between depression arising from decreases in release probability and depression attributable to decreases in conduction probability did not depend critically on the simplifying assumptions used for the analytic solutions.
Experimentally, we observed a clear rise and fall in variance on average during short-term depression (Fig. 9). To ensure that rundown or patch instability did not contaminate variance estimates, cells were accepted for this analysis only if there were at least 10 continuous sweeps in control conditions with no systematic change in EPSC amplitudes over time (Fig. 9A). Also, EPSCs had to be at least twofold larger in 4 mM Ca2+ plus 100 µM 4-AP (Fig. 9A). This final requirement was met in all cells tested and was included to ensure that any nonmonotonic mean-variance relationships could not be caused by decreasing release probability (Silver et al., 1998
It is worth noting that interpretation of the variance data requires an assumption about the initial action potential conduction probabilities and vesicle release probabilities (see Appendix). In particular, we interpret the rise and fall of variance to mean that the probability of action potential conduction (PC) started close to 1 and declined with short-term depression; the maximal variance occurred for intermediate values of PC (see Appendix). Alternatively, however, this parabolic variance could have been caused by vesicle release probabilities (PR) initially near 1 that declined during depression (Silver et al., 1998
DISCUSSION
We have found that in hippocampal neurons grown in microisland cultures, short-term synaptic depression had several unusual features. The depression was not caused by a release-dependent mechanism such as vesicle depletion, because depression was unaffected by reduction of initial release probability with Cd2+. This was confirmed by the absence of an inverse correlation between successive, relative EPSC sizes that would be expected for release-dependent depression. Instead, one source of STD could be progressive increases in the probability of AP conduction failure along axonal branches. Four lines of evidence favored this mechanism. The somatic AP amplitudes declined with repetitive stimulation, modest reduction in AP amplitude with tetrodotoxin inhibited EPSCs significantly, lowering of [Na+]i decreased depression, and the variance of EPSCs rose and fell with monotonic depression of the EPSC mean.
Can the observed changes in APs account entirely for the depression in EPSCs? There are several factors that preclude a definitive answer. First, somatic APs may be different from those at branch points and terminals, because of differences in the geometry, membrane properties, and/or distribution of ionic channels at various subcellular locations (Hoffman et al., 1997
Recent experimental findings and detailed simulations (Streit et al., 1992
