A Slow Short-Term Depression at Purkinje to Deep Cerebellar Nuclear Neuron Synapses Supports Gain-Control and Linear Encoding over Second-Long Time Windows

S-STD of PC_DCN IPSCs

To explore the response of PC_DCN synapses to sustained activity, I used cerebellar slices from juvenile (P21–P32) or adult (P55–P72) mice maintained under conditions like those in situ(i.e., temperature: 36.5 ± 0.5°C and extracellular CaCl₂ concentration: 1.5 mm), as variations in these parameters and the developmental stage affect synaptic transmission and STP (Borst, 2010). Whole-cell patch-clamp or cell-attached recordings were obtained from large DCNs (>20 μm) in the lateral or the interpositus nuclei because this group of DCNs can be unambiguously identified as projecting, putative glutamatergic DCNs, while smaller DCNs may be part of different subgroups, potentially displaying different synaptic properties (Uusisaari et al., 2007; Uusisaari and Knopfel, 2008; Najac and Raman, 2015). To mimic the persistent discharge of PCs, I used protracted ES of PC axons in the surrounding white matter (≥2 min) at three different stimulating background frequencies (BF: 10, 29.5, and 67 Hz), which are within the PCs firing rate range in awake animals at rest (Thach, 1968; Zhou et al., 2014).

The responses to 2-min-long trains of stimuli confirmed an initial phase of rapid decrease in phasic IPSC peak amplitude with successive events, which slowed down and leveled after tens of events (Telgkamp and Raman, 2002; Pedroarena and Schwarz, 2003; Turecek et al., 2016) (representative traces from one neuron in Fig. 1A, and mean normalized peak amplitude as a function of time across neurons in Fig. 1B). However, the use of protracted stimulation unveiled a different slow phase of decay in IPSC peak amplitude ensuing the fast one, with time constants ranging from 18 to 47 s, most evident by analyzing the results in a compressed timescale (Fig. 1B, insets, fits using double exponential decay functions). Furthermore, the average IPSC amplitude at the end of the 2 min stimulation periods decreased with increasing stimulating BFs, suggesting divergence from the frequency-invariant phase described before at earlier stages of PC activation trains (Turecek et al., 2016) (Fig. 1B,C). Importantly, the population results reflected the results from single experiments, depicted individually in Figure 1D. Although the magnitude of depression varied among neurons, for each case, the normalized steady-state synaptic strength decreased with increasing BFs (mean values: 0.4 ± 0.02 [10 Hz], vs 0.26 ± 0.02 [29.5 Hz], n = 8, paired t test, p < 0.001; 0.26 ± 0.02 [29.5 Hz] vs 0.15 ± 0.015 [67 Hz], n = 9, paired t test, p < 0.001). Therefore, protracted activation of PC_DCNs revealed an S-STD, which at steady state appears as frequency-dependent. Because PCs are continuously active, the differences in mean IPSC amplitudes for different BFs (more than double comparing 10 vs 67 Hz) are likely functionally relevant.

• Download figure
• Open in new tab
• Download powerpoint

Figure 1.

Protracted PC stimulation unveils an S-STD. A, Top, Sketch of experimental configuration and stimulation paradigm. Bottom, Typical examples of IPSCs from the same neuron evoked by 2 min trains of stimuli applied to PC axons at the frequencies (BF) indicated on the left, at the beginning (left), and at the end of stimulation (right). Note the different time scales. B, Top to bottom, Mean normalized IPSC peak amplitude as a function of time for BFs 10 Hz (light blue, n = 11), 29.5 Hz (red, n = 9), and 67 Hz (dark blue, n = 9), and all three plots overlaid (symbols represent mean ± SEM) illustrate two phases of decay. Color code applies to all figures, unless otherwise stated. The double exponential decay fits in the insets: fast tau: 0.81 ± 0.04, 0.41 ± 0.012, and 0.33 ± 0.007 s and slow tau: 23 ± 1.9, 18 ± 0.5, and 47 ± 1.2 s for 10, 29.5, and 67 Hz BFs, respectively. C, Average normalized steady-state phasic IPSCs amplitude (IPSC_SS) versus BF (averages calculated over the last 100 events of the data plotted in B; 0.37 ± 0.002, 0.25 ± 0.002, and 0.15 ± 0.002 for 10, 29.5, and 67 Hz BFs, respectively: 10 versus 29.5 Hz [Mann–Whitney rank sum test] and 29.5 vs 67 Hz [t test], p < 0.001 for both comparisons). D, Results from individual neurons illustrate decreasing mean IPSC_SS with increasing BF (averages over 100 events). Top, IPSC amplitude for 29.5 versus 10 Hz. Bottom, IPSC amplitude for 67 versus 29.5 Hz. All points fall below the unity line. E, Typical examples from the same neuron in A of IPSCs evoked by the same ordinal stimuli but at different BFs (indicated on the left). The 10 Hz trace is the same shown in A for comparison. F, Summary of IPSC amplitude as in B, but as a function of the event number (color labeled as B). Top, Events 1-50. Bottom, Events 1-1200. G, Averages as in C, calculated over the events indicated on top of each bar plot. Top, Events 10-50: 0.49 ± 0.01, 0.47 ± 0.02, and 0.47 ± 0.03, for 10, 29.5, and 67 Hz, respectively; Wilcoxon signed rank sum test: 10 versus 29.5 Hz, p = 0.115; 29.5 versus 67 Hz, p = 0.7. Bottom, Events 1000-1100: 0.37 ± 0.002, 0.276 ± 0.002, and 0.236 ± 0.002, for 10, 29.5, and 67 Hz, respectively, t test, 10 versus 29.5 and 29.5 versus 67 Hz, p < 0.001 for both. H, Similar as in D, but for mean IPSCs amplitudes calculated over stimuli 1000-1100th for each neuron. Top, 29.5 Hz versus 10 Hz. Bottom, 67 versus 29.5 Hz. Data are mean ± SEM. **p < 0.001.

To confirm S-STD frequency dependence and to explore its buildup along the stimulating trains, I analyzed the changes in synaptic strength as a function of the event number (Fig. 1E–H). In agreement with previous studies using similar conditions as here, the IPSC amplitudes initially, over the first 10 events, depressed significantly but on average with slightly lower rates with increasing BFs (Fig. 1F, top), while later, after tens of events, the IPSCs evoked with different BFs displayed similar amplitudes (frequency-invariant phase; Fig. 1F,G, top plots) (Turecek et al., 2016). However, after hundreds of events, the IPSC amplitudes started to diverge, indicating dependence to the time interval between stimuli (Fig. 1F, bottom). The IPSCs further decayed, but at different rates for different BFs. The time constants of decay calculated after the first 100 events using single exponential fits were 216 ± 24, 612 ± 21, and 3305 ± 83 events for 10, 29.5, and 67 Hz BF, respectively. This is more than one order of magnitude slower than previously described forms of depression at PC_DCNs (Telgkamp and Raman, 2002; Pedroarena and Schwarz, 2003; Turecek et al., 2016), including a “slow” frequency-dependent depression (i.e., with time constant of 117 events for 100 Hz stimulus trains) found in smaller DCNs (15–20 µm) from younger animals (P13–P15), recorded at lower temperatures (31°C) (Telgkamp and Raman, 2002). Significant differences in average IPSC amplitudes as a function of the BFs could be detected considering events 1000-1100 or further (Fig. 1G, bottom). Moreover, the results from single experiments agreed with the population ones (Fig. 1H): in all but 1 case, the mean IPSCs amplitude decreased with increasing BFs (0.402 ± 0.02 vs 0.29 ± 0.02, n = 8, paired t test, p < 0.001 for 10 vs 29.5 Hz; and 0.29 ± 0.02 vs 0.24 ± 0.02, for 29.5 Hz vs 67 Hz, n = 9, paired t test, p = 0.003).

Similar results arose using Poisson-like trains of stimuli with mean frequencies 10 or 70 Hz (Fig. 2A), ruling out that the alternation of regular and irregular periods of firing in awake animals (Shin et al., 2007; Hong et al., 2016) could result in recovery from depression during long intervals abolishing the frequency differences in synaptic strength found here. Importantly, despite developmentally regulated PC_DCN STP (Turecek et al., 2016, 2017), I found similar late phase of slow frequency-dependent decay in IPSC amplitude along trains using slices from adult mice (P55–P72), albeit with shallower levels of depression at steady state than at younger ages (Fig. 2B). In addition, similar to previous studies using slices from mature animals (>P20), recordings from large DCNs, and close to physiological temperatures (Najac and Raman, 2015; Turecek et al., 2016) (33°C–34°C and 34°C–35°C, respectively), PC_DCN activation did not evoke prominent slow tonic currents, in contrast to recordings using smaller DCNs (15–20 µm), from younger mice (P13–P15), and lower recording temperatures (31°C) (Telgkamp and Raman, 2002). Type of cell, developmental stage, and temperature all influence PC-DCN kinetics and could explain differences in slow currents (Linnemann et al., 2004; Person and Raman, 2012; Najac and Raman, 2015; Turecek et al., 2016).

• Download figure
• Open in new tab
• Download powerpoint

Figure 2.

S-STD frequency dependence under irregular activation patterns and in DCNs from adult mice. A, Top, Representative traces of IPSCs evoked in the same neuron by 2 min Poisson-like stimulation at the mean frequencies indicated on the left. Bottom, Summary plots of mean IPSCs amplitudes calculated over the stimuli indicated on top of each graph as in Figure 1, but for Poisson-like stimulation at 10 Hz (n = 9) and 70 Hz (n = 7). Significance assessed using Mann–Whitney rank sum test (0.33 ± 0.002, 0.23 ± 0.003 for 10 and 70 Hz, for events 1000-1100th; and 0.33 ± 0.002, 0.15 ± 0.003 for 10 and 70 Hz, respectively, for steady-state IPSCs, p < 0.001). B, Left, Normalized average amplitude as a function of event number of PC_DCN IPSC recordings obtained from slices from P55-P72 animals (BF 10 Hz, n = 8, BF 67 Hz, n = 7). Right, Summary plots of mean IPSC amplitudes calculated from the graphs on the left, over the events indicated on top of each bar plot (1000-1100th for 10 and 67 Hz BFs: 0.45 ± 0.002 and 0.32 ± 0.002, t test, p < 0.001; average of 100 events at steady state: 0.45 ± 0.002 and 0.26 ± 0.003 for 10 and 67 Hz, respectively, t test, p < 0.001). **p < 0.001.

Together, these results strongly argue that regular or irregular sustained activity of young or adult PC_DCNs induces a previously undetected slow form of frequency-dependent STD (S-STD), requiring hundreds to thousands of events to reach steady-state level.

Because of the acknowledged difficulties in carrying large DCN recordings using slices from older animals (Uusisaari et al., 2007; Turecek et al., 2016) and the need of particularly long recordings for the present study, the rest of the experiments were performed using slices from juvenile mice (> P20) as in other studies (Turecek et al., 2016, 2017).

Sustained PC activation modulates IPSCs and DCN spike responses evoked by HFS trains

Given the typical PCs sustained activity found in awake-behaving animals (e.g., Schonewille et al., 2006), presumably S-STD continuously controls PC_DCN efficacy. This raises the question of whether and how S-STD modulates the responses to moretransient changes in PC rate associated to cerebellar controlled behaviors. To address this question experimentally, first, PC_DCN synapses were depressed to steady state using protracted stimulation at different BFs; and afterward, a brief, high frequency train of stimuli (HFS, 100 events, 180 Hz) was used to mimic behavior-driven transient signals. The HFS duration covers the length of usual discrete motor events (e.g., reaches, steps, saccades, etc.). To quantify and compare the synaptic output induced by HFSs preceded by different BFs, I measured the total charge transferred during the HFS (Q_HFS, see Materials and Methods), then normalized it to the charge transferred by corresponding control IPSCs (Q P_Ctrl) to be able to average across neurons, and expressed it per second. Analysis of changes in Q_HFS as a function of the preceding BF revealed a remarkable modulation (Fig. 3A). Specifically, the normalized Q_HFS decreased with increasing BF (no prior activity, 0 Hz: 72 ± 4.5, n = 22; BF 10 Hz: 61 ± 3.3, n = 16, 29.5 Hz: 40 ± 4.0, n = 9, and 67 Hz: 16 ± 1.9, n = 12, t test: 0 vs 10 Hz, p = 0.033, 1 tail; 10 vs 29.5 Hz; p < 0.001; 29.5 vs 67 Hz, p < 0.001). These Q_HFS values contrast with the expected for either, a nondepressing synapse (considering 1 the charge transfer of control IPSCs and 180 the HFS frequency: 1 × 180 = 180), or for synapses that after the first phase of depression remain stable and frequency-invariant (Fig. 1, ∼0.48 × 180 = 86). The mean Q_HFS for HFSs preceded by 2 min stimulation at 67 Hz was approximately one-fourth of the Q_HFS elicited by HFSs preceded by 10 Hz stimulation. These results strongly support the view that BFs modulates the output produced by behavior-driven PC signals.

• Download figure
• Open in new tab
• Download powerpoint

Figure 3.

PC background activity modulates the DCN synaptic and spiking responses to HFS trains. A, Top, Stimulation paradigm. Bottom, Mean charge transfer amplitude during HFS (100 events, 180 Hz), normalized to that of control IPSCs as a function of prior BF. B, Typical examples from two different neurons illustrating how prior BF (indicate on the left of each trace) modulates the amplitude of IPSCs evoked by the HFS (indicated by the gray box). C, Four typical examples of DCN cell-attached recordings used to investigate how BF modulates the suppression of DCN spontaneous firing rate induced by HFSs delivered after protracted stimulation at 10 Hz (left) or at 67 Hz (right). Each row corresponds to the same neuron. Vertical line indicates the occurrence of one spike. D, Scatter plot of changes in DCN firing rate induced by HFSs (HFS-Basal rate), for HFS preceded by BF 67 Hz versus HFSs preceded by BF 10 Hz. All points fall below the unity lines (diagonal), indicating stronger inhibition after BF 10 Hz. Inset, Mean values and SEM for BF 10 and 67 Hz. E, Effect of nonstationary BF stimulation on HFSs suppression of DCN rate. Top, Stimulation paradigm. Bottom, Mean HFS-induced changes in DCN firing rate as a function of the 67 Hz train duration, normalized to the responses evoked without switch to 67 Hz (top, dashed line, 100%). Bottom, Dashed line indicates the value of mean responses to HFS after 120 s at 67 Hz only. The data were fitted with a single exponential function (R² = 0.99, n = 6). F, Same as in E, but for a switch in BF from 120 s at 67 Hz to 10 Hz (R² = 0.94, n = 6). **p < 0.001, *p < 0.05.

To further probe the latter idea, I used cell-attached recordings of spontaneously firing DCNs and similar stimulating protocols as in Figure 3A, to investigate whether the changes in synaptic output translated to changes in DCN spiking activity (Fig. 3C,D). Large mature DCNs recorded in vitro at physiological temperatures fired spontaneously at high frequencies (mean firing rate 81.9 ± 3.5 Hz, range 48–121 Hz, n = 12), which are within the DCN firing rate range found in behaving mice at rest (e.g., Ten Brinke et al., 2017; Sarnaik and Raman, 2018). Furthermore, under cell-attached recordings, the intracellular content is not dialyzed, reflecting the conditions found in the intact animal/neuron. In a number of experiments, I used the same number of preceding stimuli (7000 stimuli at 10 or 67 Hz) to rule out that the number of stimuli (and not the stimulating frequency) determined the changes in synaptic strength. The results were similar to those using 120 s of sustained stimulation indicating that at steady state BF determined S-STD. Thus, the results were pooled together for statistical analysis. Individual and summary results show that HFSs preceded by sustained stimulation at 10 Hz completely suppressed or sharply decreased DCN firing rate, while HFSs delivered after 67 Hz only induced a moderate effect (Fig. 3C,D) (−67.7 ± 7.4 and −26.5 ± 6.6 Hz, respectively, paired t test, p < 0.001, n = 12). These results strongly suggest that the modulation induced by S-STD not only has an impact on the synaptic output but on DCN firing rate, and thus possibly on the cerebellar output in behaving animals.

Having found that S-STD modulates DCN responses to HFSs, I next explored the time course of this effect. This question is relevant because (1) it could provide information on the existence and duration of a time window for linear encoding; and (2) it could inform on the consequences of changes in PC background activity in different timescales. To explore the time course, I leveraged the above-described differential modulation of HFS spiking responses accordingto preceding BFs (Fig. 3C,D). Usingcell-attached recordings, as above, I interposed between the 2 min blocks of stimulation at 10 or 67 Hz and the HFSs, a switch in the stimulating frequency (to 67 or 10 Hz, respectively), for variable periods of time (ΔT, shown 1, 10, 50, or 100 s; Fig. 3E,F, top). The change in DCN firing rate for the 10 to 67 Hz switches (normalized to the response to HFSs preceded by 120 s at 10 Hz without switch to 67 Hz) decreased with increasing ΔT at 67 Hz, with a time constant of 22 s. The change was undetectable for 67 Hz periods of ≤1 s and, on average, only after 100 s the suppression reached the same level than after 2 min of stimulation at 67 Hz. For the switch from 67 to 10 Hz, the time constant of recovery was 14 s (i.e., the recovery from deeper depression seemed faster than the buildup), but within a similar time range, and it took also similar periods to reach a new steady-state level. Again, no changes were detected for periods of ≤1 s (Fig. 3F). The bidirectional amplitude modulation established in the course of tens of seconds highlight the time scale and flexibility of S-STD and consequent HFS response modulation. Moreover, the slow time course (from tens of seconds to minutes) contrasts with the rapid adaptation (in the millisecond range) of other forms of depression expressed earlier during the train (Telgkamp and Raman, 2002), strongly suggesting that S-STD is based on a different mechanism. The minor differences in buildup and recovery time course of S-STD could depend on differences in the activation or deactivation rates of faster synaptic forms of plasticity and/or S-STD itself.

Importantly, these results revealed a time window up to few seconds during which changes in BF did not significantly alter the response to subsequent HFS; in other words, the PC_DCN synaptic gain seemed unchanged over this period. Remarkably, this is the range of durations of common motor events controlled by cerebellum. If S-STD guaranteed stable synaptic gain during this time window for all functionally relevant PC rates, then S-STD could support linear encoding of behavior-related PC signals while still being able to adapt synaptic strength to the background activity.

Linear input/output transfer function for 0.5-s-long PC test trains with gain dependent on PC BF

To test the above-mentioned idea, I used 500 ms test trains of stimuli, with frequencies ranging between 10 and 300 Hz to match the usual PC signals related to common movements, preceded by protracted PC activation with different BFs (Fig. 4A, top). To estimate the synaptic output evoked by the test trains, I measured the charge transfer amplitude as in Figure 3A, B (Q test, normalized to Q P_Ctrl, and expressed per time unit; for further details, see Materials and Methods), and plotted it against the corresponding test train frequency for each explored BF (Fig. 4A). Indeed, in favor of the idea that S-STD provides a time window for linear encoding, the Q test values were proportional to the corresponding test train frequency, such that the relationship between these two parameters was approximately linear over the physiological range of PC rates (10-200 Hz), with slopes or gains decreasing for increasing BFs. In contrast, the transfer function corresponding to test trains applied from rest displayed a saturating type of curve characteristic of depressing synapses (0 Hz, black empty circles). The dashed unity line indicates the expected values for a nondepressing/nonfacilitating synapse. These results strongly support the view that S-STD provides a time window of hundreds of milliseconds to seconds over which PC rates can be linearly encoded in the synaptic output.

• Download figure
• Open in new tab
• Download powerpoint

Figure 4.

Linear PC_DCN transfer function of subsecond changes in PC rate with gain dependent on preceding BF. A, Top, Stimulation paradigm to investigate changes in PC_DCN input/output gain: 0.5 s test trains of stimuli at different frequencies (from 10 to 260 Hz) delivered after 120 s of stimulation at different BFs (0, 10, 29.5, or 67 Hz). Bottom, Summary of measured PC_DCN synaptic charge transfer during the test trains (Q _TEST), normalized to the charge transfer of corresponding control IPSCs (Q P_Ctrl), expressed per time unit, as a function of the test frequency. The plots corresponding to test trains applied from rest (0 Hz), or after 120 s at 10, 29.5, or 67 Hz are labeled on the right of each curve (color code as before). Note the almost linear relationship between 10 and 180 Hz and the different slopes for different BFs, indicative of different gains (gain of linear fits from 10 to 200 Hz: 0.34 ± 0.002, 0.23 ± 0.001, and 0.085 ± 0.004 for 10, 29.5, and 67 Hz, respectively). Dashed black line (unity line) indicates the expected values for nondepressing/nonfacilitating PSCs. B, Plots of changes in DCN firing rate (difference to steady state rate) as a function of the test train frequency from experiments using the same stimulation paradigm as in A, and DCN cell-attached recordings. Top, Two typical examples exhibit approximately linear relationships (lines correspond to linear fits to the data). Left, bottom, One unit exhibited nonlinear relationship after 10 Hz BF (points linked by straight lines). Right, bottom, Average changes in DCN firing rate from neurons with linear relationship (n = 6, lines correspond to linear fits; gain: −0.34 ± 0.005 and −0.22 ± 0.012 Hz/Hz and R² = 0.999 and 0.997 for 10 and 67 Hz BF, respectively). C, Scatter plots of gains (estimated by the slopes of linear fits as in B) for BF 67 Hz versus their corresponding values for BF 10 Hz (n = 6) for single neurons (Wilcoxon sign rank test, p = 0.031, n = 6; diagonal is the unity line). D, Same data from A, but normalized to the charge transferred by the corresponding IPSCs at steady state (Q P_SS). The responses to test stimuli applied from rest, 0 Hz, in empty black. The plots corresponding to different BFs overlap around the unity line indicating that the synaptic strength at steady state determines the BF-dependent gains (i.e., the slopes shown in A). Linear fits for the test frequency range 10-200 Hz (for clarity not shown). For BF 10 Hz: slope 1.0 ± 0.04, R² = 0.99; BF 29.5 Hz: slope 1.1 ± 0.06, R² = 0.99; BF 67 Hz: slope 0.9 ± 0.03, R² = 0.99. Dashed line indicates unity line. Inset, same plot as in A overlaid to colored dashed lines indicating the result of multiplying the corresponding mean Q P_ss by the test train frequency, for each BF. E, Average charge transfer amplitude for IPSCs at steady state normalized to control IPSCs (Q P_ss) as a function of the BF (n = 25). Curve indicates the fit with a rational function (n = 25, R² = 0.999). Inset, Averaged measured charge transfer amplitude at steady state per time unit, normalized to control IPSCs (Q ss) versus the BF (note different scale). F, Same as in D, but for the first 100 ms of the responses to the 500 ms test trains show gain > 1.

To assess the functional relevance of these results, a different series of experiments using DCN cell-attached recordings tested whether similar stimulation patterns as in Figure 4A induced equivalent changes in DCN firing rates (Fig. 4B,C). Although synchronous PC inputs are expected to be less effective than desynchronized ones in changing DCN firing rates (Sarnaik and Raman, 2018), 6 of 7 recorded DCNs (average basal rates preceding stimulation 83.7 ± 4.8 Hz, range 60–121 Hz, n = 7) displayed linear decreases in firing rates with increasing test frequencies (for examples, see Fig. 4B, top). Moreover, the gain of these relationships, that is, the decrease in DCN firing rate per increase in PC test frequency was in each case higher for test trains preceded by 10 Hz BF compared with those applied after 67 Hz (Fig. 4A, bottom right, C). Thus, these results strongly suggest that S-STD is able to support scaled linear encoding of PC rates in the DCN spike output, over behavior-relevant time windows. These results do not rule out that under different conditions (i.e., responsive state of DCNs, presence of other inputs, or other PC input patterns), DCNs could respond with other spike outputs, a matter for further studies but indicate that DCN spike output suppression can faithfully reflect PCs inhibitory drive, as suggested previously (Pedroarena, 2010).

The finding that the gain of PC_DCN transfer function depends on the preceding BF opens two types of questions: (1) about the origin and (2) about the consequences of BF-dependent gains. Regarding the first, different gains could derive simply from the differences in synaptic strength caused by S-STD. Alternatively or additionally, if S-STD involved modifications in fast forms of STP (e.g., decreased facilitation), different balance of fast facilitation/depression in response to the test trains could contribute to the different gains. To elucidate this issue, I renormalized the data in Figure 4A to the charge transferred by the corresponding IPSCs at steady state (Q P_ss; Fig. 4D). After this transformation, over the range of 10-200 Hz, the gain of the curves corresponding to different BFs collapsed, coinciding with the unity line, consistent with the notion that the different gains were exclusively dependent on the preceding level of synaptic strength. This is further illustrated in the inset, where the experimentally obtained Q _test values (plotted as in Fig. 4A) are similar to the values calculated by multiplying the average Q P_ss for different BFs (see later), and the test train frequencies (dashed lines, color code as before). Together with recent reports of linear transfer function of PC_DCN synapses after tens of events, when S-STD is not yet expressed (Turecek et al., 2016, 2017), this outcome strongly suggests that S-STD expression did not interfere with the mechanism(s) responsible for linear encoding, which could be the equilibrated fast facilitation and depression.

Regarding the question of the consequences of BF-dependent gain for PC-DCN function, it is important to note, first, that because the synaptic gain at steady state determines the gain for the test train periods, the gains are the same when considering changes from steady state and, thus, effective under the typical incessant PC activity. Inspection of the results in Figure 4A reveals one possible consequence of BF-dependent gain. A jump to 180 Hz from BF 10 Hz resulted in a change in synaptic output of 57 charge units, in contrast to the 9.1 units produced from BF 67 Hz. Thus, changes in background rate could represent a way for tuning the responses of different PCs to stereotyped signals (e.g., complex spikes). Further inspection of the same results illustrates another possible consequence. It has been previously shown that for many fast depressing synapses, changes in gain determine a Weber-Fechner effect (i.e., independently of the BF), equal fractional changes in frequency (ΔF/BF) produce equal absolute outputs, despite the difference in absolute presynaptic rate change (Abbott et al., 1997). Figure 4A shows that here, similarly, a change from BF 10–29.5 Hz (∼20 Hz, 200% of change) produced a change in output of 6.2 charge units, which is close to the 9.1 units resulting from changing BF 67 to 180 Hz (113 Hz, but ∼170% of change). For many fast depressing synapses, synaptic strength at steady state becomes proportional to 1/BF with increasing BFs (Abbott et al., 1997; Tsodyks and Markram, 1997), such that the response to a change in frequency becomes transiently proportional to ΔF/BF, explaining the Weber-Fechner effect. For PC_DCNs, the charge transfer produced by single IPSCs at steady state (Q P_ss) plotted as a function of the BF shows Q P_ss decreasing nonlinearly in proportion to 1/BF with increasing BFs (Fig. 4E, black line: a rational function fit). This finding suggests S-STD, too, could support a Weber-Fechner effect, but importantly, for time windows in the timescale of usual movements. Indeed, calculated from the data in Figure 4A, the changes in synaptic charge transfer as a function of ΔF/BF were similar for BFs > 10 Hz (6.69 ± 0.05 and 5.69 ± 0.26 charge units, for BF 29.5 and 67 Hz, respectively). Thus, S-STD could support similar impact on target DCNs from PCs with different BFs.

A different consequence of the BF-dependent gain is that, as indicated in the inset of Figure 4E, the charge transferred at steady state per time unit (Q SS) increases nonlinearly withthe BF (compare with Fig. 4A), signaling low sensitivity of PC_DCNs to BFs. This property could be useful to prevent silencing of DCNs with increasing BFs and in general to maintain DCNs within their working range_.

Overall, these results indicate the following: (1) the BF-dependent gain modulation reduces the sensitivity to steady PC rates; (2) PCs independently of their BF would produce equal outputs to equal fractional changes in rate; and (3) changes in PC BF could be used to tune the response to stereotyped signals (e.g., complex spikes).

Finally, the observation that changes in PC stimulation frequency often produced relative transient facilitation of IPSCs(e.g., Fig. 3B) (Pedroarena and Schwarz, 2003; Turecek et al., 2016, 2017), and that some cerebellar signals are short-lasting, raised the question of whether the linear transfer holds for signals shorter than the test trains used here. I analyzed the charge transferred during the first 100 ms of the test trains when relative facilitation is predominant (Fig. 4F; Q, test normalized to Q P_ss as in Fig. 4D). The transfer function for the 100 ms periods was approximately linear within the 10–200 Hz range but with slopes slightly >1, suggesting linear and preferential transfer of brief signals or the onset of longer ones. In addition, for the higher test frequencies (260 Hz), the plots deviated from linearity depending on the preceding BF: after 10 or 29.5 Hz, the responses were often supralinear, although variable (note the high SEM). The variability is in line with the idea that similar type of synapses differ mainly by the degree of facilitation (Fekete et al., 2019), but other mechanisms cannot be ruled out and should be addressed in further studies. These results unveil a new role of facilitation at PC_DCN synapses in promoting the transfer of short signals, in addition to its possible role in linear encoding.

Together, these findings strongly suggest that, in the timescales of usual motor behaviors, S-STD enables scaled linear encoding of PC rates in both the synaptic output and the DCN rates while producing adaptation at longer timescales.

Evidence that S-STD mechanism is input-specific, presynaptic, and independent of fast forms of plasticity

To understand the basis of the apparently opposing S-STD effects at different timescales, first, I set out to explore the S-STD mechanism. S-STD input specificity was investigated by combining OG and ES in slices from mice expressing channelrhodopsin in PCs under the L7 promoter (L7-ChR2-eYFP; for further details, see Materials and Methods) (Chaumont et al., 2013). I adjusted the stimulation intensities to obtain OG IPSCs larger than the ES IPSCs under control conditions and assumed this reflects a larger number of OG activated synapses. If depression was input-specific, tonic ES should depress transmission at ES-activated synapses but spare those exclusively (or mainly) activated by light. Indeed, after 2 min of repetitive ES at 67 Hz, the depression of OG IPSCs was significantly less than for ES IPSCs, supporting the idea that depression is input-specific (Fig. 5A,B). The much lower depression of OG IPSCs suggested that the OG and ES stimuli were largely nonoverlapping. This is likely, since OG activation was submaximal (see Materials and Methods). The possibility that OG activation modified synaptic function(e.g., by inducing prolonged depolarization of terminals and branches or calcium influx promoting alternative release pathways) could not be completely ruled out. However, in one experiment where the degree of occlusion of OG and ES IPSCs was monitored, the degree of depression of the OG IPSC coincided with the expected depression of the overlapping component (not shown), supporting the idea that the results reflectedS-STD input specificity.

• Download figure
• Open in new tab
• Download powerpoint

Figure 5.

Exploration of S-STD mechanism. A, Combined OG and ES to explore input specificity. Top, Experimental paradigm. Bottom, Representative examples of OG IPSCs and ES IPSCs before (control, black) and after (test, red) 2 min ES at 67 Hz. B, Plot showing significant differences in average OG and ES IPSC amplitudes after 2 min ES at 67 Hz (normalized to the corresponding controls: IPSCs induced after 2 min without ES; 0.81 ± 0.078 and 0.21 ± 0.03 for OG and ES IPSCs, respectively, paired t test, p < 0.001, n = 8) suggests input specificity. C, Plot of CV⁻² versus their corresponding mean amplitudes (M) for IPSCs depressed to steady state steady using 120 s stimulation at 10, 29.5, or 67 Hz, normalized to the values of their corresponding control IPSCs (n = 8). Inset, Expected CV⁻² versus M values for changes in the parameters N (red line), p (green), or q (blue) of a binomial release model. D, Same as in C, but for IPSCs depressed using BF 29.5 or 67 Hz normalized the corresponding BF 10 Hz values (n = 7). Dashed line indicates unity line. Fit of data using a linear function (R² = 0.78, slope 1.07 ± 0.13, n = 7; data not shown). E, Left, Plot of mean IPSC peak amplitude normalized to control IPSCs as a function of the HFS event number for HFSs (100 events, 180 Hz) applied from rest (black, n = 17) or after 120 s of stimulation at 10 Hz (light blue, n = 11), 29.5 Hz (red, n = 9), and 67 Hz (dark blue, n = 9). Continuous lines indicate exponential fits to the curves. Note the faster decay for the HFS applied from rest but similar slower values for the other curves, suggesting similar probability of release after the first events. Right, Plot of IPSC peak amplitudes normalized to the value of the first IPSC of the HFS, illustrates relative facilitation during the first events for BFs 10 and 30 Hz, but similar decay rate and percentage of decay for different BFs afterward. F, Left, Same as in E (left), but for HFSs applied after 50 events at 10 or 67 Hz (color code as in E). Note the relative facilitation of the first events for BF 10 Hz, but similar degree of depression at the end of the HFS for 10 and 67 Hz BF. Continuous lines indicate exponential fits. The data correspond to a different set of neurons than those shown in E. Right, Same data as on the left, but normalized to the corresponding first IPSC of the HFS. Bottom, Plots represent superimposed mean IPSC amplitude normalized to the first HFS event for HFSs delivered after 120 s of stimulation (red circles) or 50 events (empty circles) after BF 10 Hz (left) or 67 Hz (right) as a function of the HFS event number. The similarity in the IPSC amplitude time course after 120 s or 50 events suggests that S-STD did not alter the relative proportion of fast synaptic facilitation and depression evoked by the HFSs. **p < 0.001.

Another important conclusion drawn from the small changes induced by 120 s ES in OG IPSCs compared with ES IPSCs is that changes in chloride gradient is unlikely the cause for S-STD (as OG IPSCs recorded from the same DCNs would have been expected to change if this were the case).

To gain further insight into the basis of S-STD, I investigated changes in the inverse squared CV⁻² of IPSCs, an index of synaptic variability useful to clarify the mechanism underlying changes in synaptic efficacy (Bekkers and Stevens, 1990; Malinow and Tsien, 1990) (for details, see Materials and Methods). Briefly, specific changes in CV⁻² versus the respective changes in M are expected from changes in each one of the factors assumed to explain the mean IPSC amplitude (M = N.p.q), that is, the number of presynaptic releasable vesicles (N), the probability of each one to be released (p), and the postsynaptic response to one vesicle (q) (for guidance, see Fig. 5C, inset). Figure 5C illustrates how the CV⁻² of PC_DCNs IPSCs depressed to steady state (normalized to control IPSCs) decreased more than the corresponding means. This result is compatible (1) with a presynaptic locus because changes in q would have caused no change in CV⁻²; and (2) with a reduction in p, because changes in N would have caused proportional changes in the CV⁻² and M (see inset). Next, to explore the specific basis of S-STD, I compared IPSCs depressed with steady state using different BFs (Fig. 5D). The CV⁻² of IPSCs evoked by BF 29.5 or 67 Hz normalized to the values corresponding to BF 10 Hz decreased proportionally to their means, a result consistent with a presynaptic mechanism and particularly with a change in the number of available quanta (N). Overall, this analysis suggests that repetitive stimulation from rest induces first a decrease in the probability of release and that S-STD depends on a presynaptic mechanism, specifically, a decrease in the available quanta (N). Moreover, the present results are incompatible with S-STD being dependent on changes in q, for example, due to changes in the postsynaptic chloride gradient by sustained stimulation or in the amount of NT contained in each quantum (Fig. 5C, inset, blue line).

To verify the CV⁻² analysis outcome, an alternative estimation of the release probability was obtained. The rate with which the peak amplitude of synaptic responses decay during a train is in part dependent on the release probability, as larger use of the available quanta would deplete faster the remaining pool (Buchs and Senn, 2002). Because S-STD adjusts slowly (Fig. 3), one would expect persistent changes in the release probability if this were the basis for S-STD. Thus, I analyzed the rate of decay of peak amplitudes of IPSCs evoked by HFSs (180 Hz) applied from rest or after different periods of protracted PC stimulation. For HFSs delivered after 120 s at different BFs, the IPSC peak amplitudes decayed to different steady-state levels depending of the preceding BF (Fig. 5E), in agreement with the idea that S-STD adjust slowly to new levels (see later for details). The rate of decay for HFSs preceded by 120 s stimulation at different BFs was similar but slower than for HFSs applied from rest (Fig. 5E; exponential fits to the data, tau: 18.6 ± 0.53, 27.9 ± 3.1, 28.7 ± 3.6, and 27.7 ± 5.1 for rest [n = 34], and BFs 10 [n = 11], 29.5 [n = 10], and 67 [n = 9] Hz, respectively). This is consistent with a decrease in release probability at the beginning of the train but not between different S-STD levels of depression. Moreover, normalizing the amplitudes to the first IPSC of the HFS more clearly illustrates the similarity in decay rate and proportion of decay for HFSs preceded by different BFs (Fig. 5E, right). In contrast, in a different set of experiments using HFSs applied after 50 events at 10 or 67 Hz, the IPSC peak amplitude decayed to similar steady-state levels (Fig. 5F; IPSC amplitude averaged over the last 30 events, normalized to control IPSC: 0.247 ± 0.079 and 0.23 ± 0.07 for 10 or 67 Hz, respectively, paired t test, n = 5, p = 0.162). These results demonstrate that the synaptic strength can be rapidly adjusted to new levels before S_STD expression (Telgkamp and Raman, 2002) (compare with Fig. 5E, mean IPSC peak amplitude over the last HFS 30 events after 2 min stimulation: 0.185 ± 0.25 vs 0.067 ± 0.09 for 10 or 67 Hz BF, respectively, n = 11 and n = 9, Mann–Whitney rank sum test, p = 0.001). The rates of decay for HFS after 50 events at different BFs were similar (tau: 27.8 ± 3 and 31.2 ± 5.1 events for BF 10 [n = 5] and 67 [n = 5] Hz, respectively), and similar to rates of decay for HFS delivered after 120 s of stimulation (Fig. 5E), but slower than the rate of decay from rest. This is congruent with the main decrease in probability of release occurring during the first 50 events. Finally, the bottom plots illustrate how the time course of IPSC amplitudes normalized to the first HFS event is similar after 50 events or 120 s of stimulation, although different for BF 10 or 67 Hz (left and right, respectively, i.e., higher relative facilitation at the beginning of HFS delivered from BF 10 Hz than from 67 Hz). These results suggest that the proportions of fast facilitation and depression recruited by changes in rate differ depending on the BF (10 or 67 Hz), but importantly, this proportion is not altered by S-STD expression. This supports the view that the S-STD mechanism is distinct and behaves independently from the processes underlying faster forms of plasticity.

Together, these results strongly suggest that S-STD is input-specific, involves a presynaptic mechanism, probably a change in the number of available quanta (N), and its mechanism does not interfere with the balance of faster forms of synaptic plasticity.

A model with an independent slow-depression component explains well the experimental results

Computer simulations were used to further gain insight into how different synaptic processes could interact to explain the present results. As a starting point, I tested a version of previously published models with two different pools of ready-to-be-released vesicles (RRPs) (Trommershauser et al., 2003), which successfully explained PC_DCN responses to trains of hundreds of stimuli (Turecek et al., 2016). Briefly, this model requires two different RRPs (RRPA with high probability of release (Pr) and slow recovery time constant (Tau_R); and RRPB with low Pr, fast Tau_R, and facilitation) to explain PC_DCNs initial fast phase of depression, the substantial output with continuous activation, and the phase of frequency invariance (Turecek et al., 2016) (for further details, see Materials and Methods; Fig. 6, scheme). This model (hereafter D + F model; Fig. 6) explained well the present PC_DCN responses to the first 100 stimuli of trains with frequencies 10, 29.5, and 67 Hz (Fig. 6, same data as in Fig. 1), including frequency invariance phases and approximately linear encoding explained by the counteracting fast facilitation and depression of release, confirming previous results (Turecek et al., 2016).

• Download figure
• Open in new tab
• Download powerpoint

Figure 6.

Experimental and simulated responses of a two-pool and facilitation model of PC_DCNs to different BFs. A, Top, D + F model scheme. Synapses contain two different pools of vesicles A and B, which differ in release probability (Pr), time constant of recovery (Tau_R), and presence of facilitation. Bottom, The predicted output of a two-pool and facilitation model (D + F model) explains the experimental responses to the first 100 events of stimulation trains at 10, 29.5, and 67 Hz (same data as in Fig. 1). B, Detail of the model responses to the first 8 events of the trains at 10 and 67 Hz using a semilogarithmic plot to illustrate slower decaying rates with higher stimulating frequencies. C, Left and right plots (for 10 and 67 Hz stimulation rates, respectively) represent, from top to bottom, the data (circles) and model output (continuous lines), the predicted IPSC amplitudes for Pools A and B (PA, PB, red and blue), and the size of the ready to be released A and B pools (RRPA, RRPB, red and blue, respectively). D, The relationship of the predicted synaptic output at steady state (estimated by the product of the predicted IPSC amplitude and the stimulation frequency) versus the stimulation frequency is almost linear. E, Summary of results predicted by the D + F model at steady state as a function of the stimulation frequency: the predicted output of the Pool B (PB, blue circles), the total probability of release of the Pool B normalized to Event 1 (P_rB + facilitation, black circles), and the change in RRPB (yellow circles), normalized to Event 1. RRPA₀ = 7, RRPB₀ = 25, Pr A = 0.098, Pr B = 0.017, Tau_R A = 12, Tau_R B = 0.5, f1 = 0.0005, Tauf1 = 0.007, f2 = 0.001, Tauf2 = 0.1.

However, the D + F model could not explain the further decay in IPSC amplitude with protracted stimulation (Fig. 7A), even when facilitation was omitted. The mechanism(s) of slow depression is debated, but it has been recently proposed that, under intense or sustained synaptic activity, the most sensitive bottleneck for the availability of vesicles for release is the number of release sites that after undergoing exocytosis are cleared and prepared to receive new vesicles or quanta (Neher, 2010). Considering the latter idea, the frequency dependence of S-STD, the evidence that S-STD depends on decrease in available quanta, and that is independent from fast forms of plasticity, I implemented a slow-depression component simulated by an activity-dependent decrease in active release sites of Pool B (R_SitesB), recovering with fixed time constant (Fig. 7B) (see Materials and Methods). The properties of the release sites remaining active are unchanged by this process. Inclusion of this component extended the D + F model. The extended model (hereafter, SD_RS model) was able to explain the changes in IPSC amplitude observed during 120-s-long stimulation trains (Fig. 7B). Importantly, this model explained as well the results from a different set of experiments using a switch in the protracted stimulation frequency within the same trial (i.e., from 10 to 67 Hz) (Fig. 7C, details in Fig. 8). The experimental results in Figure 7C confirmed those obtained using cell-attached recordings (Fig. 3E,F), further demonstrating that S-STD adjusts slowly to new levels, requiring several tens of seconds to reach a new steady state. In the model, the slow changes in the number of “active release sites” after the switch correlated with the slow time course of depression (R_Sites B, Fig. 8D, inset). Note the similarity in the time course of the amplitudes of the experimental and predicted responses: first, a relative facilitation of IPSCs amplitude follows the switch, recovers, and afterward slowly readapts up to a new (lower) steady-state level.

• Download figure
• Open in new tab
• Download powerpoint

Figure 7.

A two-pool and facilitation model extended by a slow-depression component (SD) explains experimental S-STD and scaled linear encoding of responses to 0.5 s steps of changes in rate. A, Predictions from a two-pool and facilitation model (D + F model) (yellow line, same fitting parameters as in Fig. 6) fail to explain S-STD (experimental data: blue and violet circles represent 10 and 67 Hz, respectively; same data as in Fig. 1). B, Instead, both, early and late experimental responses were explained by a model featuring a slow-depression (SD) component simulating an activity-dependent decrease in number of active release sites of Pool B (ready to be refilled after use and filled), schematized on top. Bottom, Data and model output (SD-RS model: dark blue line; see Materials and Methods, data as in A). In lower rows from top to bottom (Pool A in red and Pool B in blue): the predicted IPSC amplitudes of Pools A and B (PA, PB), the size of (filled) ready-to-be-released A and B pools (RRPA, RRPB), and the number of active release sites of Pool B (R_SitesB). C, Experimental (light blue) and SD-RS model predictions (dark blue line) to a sustained change in stimulation frequency (120 s at 10 Hz followed by 50 s at 67 Hz, indicated by the top scheme). Right, Detail in expanded time scale, around the switch time. Data from a different set of neurons than A and B (n = 6); the model estimated parameters are in Figure 8. D, Left, Summary of predicted steady-state normalized values of RRPB (NRRPB, filled squares) and PB (open circles) by the D + F (yellow) and SD_RS (dark blue) models and of the slow-depression component (red triangles, R_SitesB of the RS-SD model, normalized to the value at P0) as a function of the BF from experiments as in A and B. Right, a multiplicative effect of the SD component explains the differences between the models. Light blue curves indicate the product of the D + F curves (yellow) times the corresponding fractional R_SitesB (shown on the left plot in red). Dark blue traces (SD_RS model predictions) are occluded by the light blue curves. E₁, Model predictions to steps of change in stimulating frequency (proxy for the test trains in Fig. 4). Top, Stimulation paradigm. Bottom, Examples of SD_RS model responses. Red dashed line indicates beginning of the step. E₁, Plots of the integral of predicted IPSCs (proxy for charge transfer) as a function of the step frequency, for different BFs (labeled on the right). The D + F and SD_RS model outputs correspond to the left and right plots, respectively. E₃, Multiplicative effect of SD: predicted input/output functions by the D + F (yellow) and SD-RS (dark blue) models as in E₂, for 10 and 67 Hz BF (left and right plots, respectively). Light blue traces were obtained by dividing the output of the SD-RS model (dark blue) by the corresponding fraction of R_SitesB available before the frequency step. (SD-RS: RRPA₀ = 7, RRPB₀ = 25, PrA=0.098, PrB = 0.017, Tau_RA = 12, Tau_RB = 0,5, f1 = 0.0005, Tauf1 = 0.007, f2 = 0.001, Tauf2 = 0.1, ARSB = 0.47, F_RS = 29, TauRSr = 30, apply to all panels except Fig. 6C, see details in main text).

The comparison of steady-state values of the normalized RRPB size (NRRPB, diamonds) and the output of Pool B (PB, circles) predicted by the SD_RS (blue) and the D + F (yellow) models, which differ only by the presence or absence of the slow-depression component, highlights the effect of the latter (Fig. 7D, left). The plot also illustrates the frequency-dependent change in the slow-depression component represented by the fractional size of active release sites of Pool B (R_SitesB_ss normalized to the value at P_0, NR_SitesB, red triangles). The scaling effect of S-STD (Fig. 4A) suggested a multiplicative relationship of the slow-depression component. The here implemented inactivation of sites does not interfere with the properties of the remaining active ones, predicting a pure scaling effect. Indeed, the product of the NRRPB or the PB values of the D + F model, times the slow-depression component (NR_SitesB_ss), returned the RRPB and PB values of the SD_RS model, respectively (Fig. 7D, right, respective products shown in light blue), graphically illustrating the multiplicative operation of the slow-depression component for steady-state conditions. Noteworthy, due to the minimal contribution of Pool A to the total output at steady state, similar results emerged from the analysis of the total output (PA + PB) (Fig. 8E). Therefore, the extended model explained both the changes in amplitude and the time course of these changes during protracted stimulation and after a switch in BF.

• Download figure
• Open in new tab
• Download powerpoint

Figure 8.

Predicted responses of the SD-RS model. A, SD-RS model predictions to synapse activation at 10 Hz (120 s) followed by 67 Hz (50 s) PA and PB (red and blue, respectively, as in Fig. 7). B, RRPA and RRPB (red and blue, respectively, as in Fig. 7). C, Total facilitation for Pool B. D, Number of release sites active (R_SitesB). Inset, In expanded scale, the values around the switch time (red arrow). RRPA₀ = 7, RRPB₀ = 25, PrA = 0.098, PrB = 0.01, Tau_RA = 12, Tau_RB = 1.55, f1 = 0.0005, Tauf1 = 0.007, f2 = 0.0024, Tauf2 = 0.1, ARSB = 0.74, F_RS = 29, TauRSr = 30. E, Plot represents the predictions of the total synapse output (PoolA+PoolB) at steady state (P_ss) by the D + F and the SD_RS models (yellow and dark blue circles, respectively) as a function of BF. Red triangles represent the normalized values of the number of active release sites of the RS_SD model (R_SitesB). Light blue (almost occluding the dark blue trace) represents the result of multiplying the P_ss values of the D + F model by the normalized R_SitesB of the SD_RS model.

Next, I checked whether this model accounted as well for the BF-dependent changes in gain for the responses to test trains(e.g., Fig. 4A). The predictions of both models to steps of changes in activation rate (duration: 0.5 s) induced after sustained activation, as applied experimentally to PC_DCN synapses (Fig. 7E1), were investigated. As expected, the integral of the predicted output over the step duration (proxy for the charge transfer amplitude) by the D + F model increased almost linearly as a function of the step frequency up to 200 Hz; however, in contrast to the experimental results, the slopes or gains for different BFs were almost coincident (Fig. 7E2, left vs Fig. 4A). Instead, the predictions by the SD_RS model (Fig. 7E2, right) showed similar linear increases in output but clearly distinct slopes for different BFs, indicating that the model captures the changes in gain mediated by the different BFs. Moreover, dividing the values obtained with the SD_RS model by the normalized number of release sites present at steady state before the step returned the values of the D + F model (Fig. 7E3), indicating that the multiplicative effect of this slow-depression component of Pool B was sufficient to explain the effect. Furthermore, the number of active release sites changed slowly (Fig. 8D), explaining that the number of sites available just before the step determines the gain during the post-ceding subsecond-to-few seconds periods of the steps in frequency. The fast STP components (given by the total facilitation and RRP depletion) led to opposing effects during the step (Fig. 8), contributing to the linear encoding during this time window.

Summarizing, a model of synaptic transmission, including a slow-depression component with a multiplicative relationship to the simulated fast plasticity components, explains well the experimental data. Moreover, these results demonstrate that an activity-dependent change in release sites is a plausible molecular mechanism for slow depression at PC_DCN synapses and consequent gain control.