In this paper, a computational model of neurotransmission and excitation in the cerebellar glomerulus is developed and a series of routines to investigate the parameter space is implemented. A single-compartment model of the granule cell [(D'Angelo et al., 2001) updated in Nieus et al. (2006)] was implemented with advanced representations of inhibitory synapses and run using the NEURON simulator (NEURON version 7.3; Hines and Carnevale, 2001). The model was coupled to a recording electrode to reproduce realistic current-clamp conditions and simulations were compared to cellular responses corrected for 10 mV liquid-junction potential. The ionic mechanism were the same as reported in Nieus et al. (2006) and Solinas et al. (2010). The granule cells are extremely compact also when channels are open in the dendrites during synaptic transmission. Calculations based on cable equation (D'Angelo et al., 1993, 1995; Rossi et al., 1994) and tests using bio-realistic compartmental models (Silver et al., 1992; Diwakar et al., 2009) showed that dendritic electrotonic length was around L = 0.04 and the maximum current and membrane potential loss was <5%. Therefore, the results would not be different using single or multi-compartment models.

Short high-frequency bursts represent a fundamental pattern of mossy fiber activity (Chadderton et al., 2004). Bursts co-activate granule cells and Golgi cells (D'Angelo et al., 1995; Mapelli et al., 2014). While granule cells depolarization begins, the progressive increase of activity in the inhibitory circuit tends to modulate their response. An early component of inhibition passes through the mossy fiber—Golgi cell—granule cell circuit (feed-forward inhibition), while a late component passes through the mossy fiber—granule cell—Golgi cell—granule cell circuit (feed-back inhibition) (Cesana et al., 2013; D'Angelo et al., 2013).

The impact of inhibitory neurotransmission was investigated by measuring how it modulated granule cell excitation following mossy fiber burst stimulation in acute cerebellar slices (a condition in which feed-forward inhibition prevails). Since metabotropic mechanisms can influence granule cell responses (see (Mapelli et al., 2014) for review), ionotropic effects were isolated using a cocktail of antagonists for mGluRs and GABA-B receptors (CGP35348, CGP55845, MCPG, CPPG) (Figure 1B). Following application of these blockers, on average the number of spikes increased (sn change 39.8 ± 10.5%, p < 0.034, n = 7), the discharge time-window increased (tw change 93.4 ± 43.1% p < 0.034, n = 7) while the time-to-first-spike and first spike standard deviation did not vary significantly (ttfs change −2.3 ± 17.5%, n = 7, p = 0.79; fssd change −1.17 ± 1.34%, n = 7, p = 0.97) (Figure 1C). These results show that metabotropic receptors could modify burst transmission to granule cells indicating that the data to be compared to our cerebellar microcircuit model simulations had to be those obtained in the presence of metabotropic receptor blockers.

Inhibitory neurotransmission between Golgi cells and granule cells is mediated by GABA-A receptors, which can be selectively blocked by the GABA-A receptor antagonist, gabazine (Rossi et al., 2003). This receptor antagonist is normally used in a variety of experimental conditions and blocks the phasic and tonic inhibitory processes altogether (Hamann et al., 2002; Nusser and Mody, 2002; Mitchell and Silver, 2003; Rossi et al., 2003; Mapelli et al., 2010a,b; Gandolfi et al., 2013). Following metabotropic receptor blockage (see above), the application of 10 μM gabazine significantly increased number of spikes (68.9 ± 41.1%, p < 0.05, n = 7) and time window (112.6 ± 45.0%, p < 0.04, n = 7) but did not significantly change the time to first spike (2.74 ± 10.83%, p < 0.79, n = 7) or first spike standard deviation (23.4 ± 80.0%, p < 0.32, n = 7) (Figure 1C). Thus, as a whole, GABA-A receptor-mediated inhibition reduced the intensity and duration of granule cell responses without significantly changing the average time of occurrence and precision of the first spike. This was expected considering that Golgi cell inhibition through the feed-forward circuit usually occurs after the granule cell has emitted the first spike.

In each of the recorded granule cells, measurements of EPSCs and IPSCs were obtained at the reversal potential of IPSCs and EPSCs, respectively (Figure 1D). Moreover, the tonic GABA current was estimated by measuring the leakage current before and after gabazine application (not shown). We did not found any significant correlations between the tonic current and the estimated number of active Golgi cell axons (Figure 1F), suggesting that the tonic current was regulated by ambient GABA rather than by phasic neurotransmitter release (for review see Mapelli et al., 2014). Specific simulations showed that changes in the tonic current in the range observed experimentally did not significantly affect the model outcome (<5% difference for spike number, first-spike delay, time-window; data not shown). Therefore, in the model tonic inhibition was set as a fixed value, not correlated with the number of active synapses.

The number of active synapses was estimated by comparing EPSCs and IPSCs with the average single-site responses measured previously in identical experimental conditions (Figure 1D) (Sola et al., 2004; Mapelli et al., 2009). The estimated number of active mossy fibers ranged from 1 to 5 and that of active Golgi cell synapses ranged from 1 to 10 (Figure 1E). Therefore, for each recorded granule cell, the most relevant parameters required to determine its inhibitory control were available and this allowed a direct comparison with simulated data (see Figure 6).

A model of cerebellar glomerular inhibition should be able to predict the different kinds of synaptic inhibitory responses observed experimentally in granule cells.

A raise in release probability was proposed to explain the changes in synaptic responses caused by GABA-B receptor blockage by CGP55845 (Mapelli et al., 2009). Here, these changes were simulated by increasing the release probability from pI = 0.42 to pI = 0.67 (Figure 2C). This transiently enhanced GABA concentration in the synaptic cleft, but within 4 impulses the concentration settled toward similar levels with both p values. While the α₁ receptors followed the GABA concentration changes, the α₆ receptors developed similar kinetics at both release probabilities. The slow reaction of α₆ receptors and their early saturation explained the invariance of temporal summation and total charge transfer despite the clear changes caused by pI on the α₁ receptor-mediated response.

In order to test whether a p change could indeed provide a global interpretation of IPSC changes during trains, control and CGP55845 eIPSC trains reported by Mapelli et al. (2009) were simultaneously fitted with the model and pI was left free to vary (Figure 3A). The fittings yielded pI = 0.42 ± 0.12 in control and pI = 0.67 ± 0.13 in CGP55845 (n = 5), in close agreement with experimental determinations (n = 5; p = 0.14, paired t-test). The normalized eIPSC amplitude showed a significant difference on the first pulse but then recovered to control values and the total electrical charge transferred during the IPSC train was in good agreement with the experimental one and did not change significantly by raising pI (from 1.19 ± 0.20 to 1.46 ± 0.24 pC; n = 5; p = 0.31 paired t-test) (Figure 3B). These simulations indicate that a raise in release probability can indeed explain a consistent set of changes in composite α₁–α₆ receptors-mediated synaptic currents during repetitive neurotransmission suggesting appropriate setting of synaptic transmission parameters.

In order to quantify granule cell responsiveness in different activation regimens, several series of simulations were run using the dendritic microcircuit model (Figure 4A) and the spiking parameters (number of spikes, time-window, time to first spike and first spike standard deviation) were calculated from raster plots and PSTHs of the responses (see Methods). An exhaustive exploration over all possible excitatory/inhibitory (E/I) synapse combinations and release probabilities was performed generating multiparametric color plots (Figure 4B).

Some regularities emerged from this representation. First of all, the parameters varied in a predictable manner with respect to the E/I balance: number of spikes and time window apparently increased by several times while time to first spike and first spike standard deviation showed modest changes by raising E/I. On a macro-scale, in all graphs an ideal bisectrix separated a low response region (top left, low E/I) from a high response region (bottom right, high E/I). Moreover, a micro-pattern emerged inside each sub-quadrant determined at each E/I by varying excitatory and inhibitory release probabilities, pE/pI. Thus, in principle, by combining different numbers of fibers with different release probabilities, a broad set of response combinations could be obtained generating an extended response space. A quantitative insight on its properties was obtained by considering representative areas. For example, by comparing parameters in the quadrants E1,2/I3,4 (low E/I) and E3,4/I1,2 (high E/I) there was a nearly 10-fold increase in number of spikes, a 3-fold increase in time window and a modest changes in time to first spike and first spike standard deviation (Figure 5A).

The inspection of the graphs reported in Figure 4B showed that, after switch-off of the phasic components of inhibitory synaptic transmission, number of spikes and time window increased in all quadrants, while time to first spike and first spike standard deviation increased only at low E/I. Interestingly, the effect of α6-receptor switch-off dominated over that of α1-receptor switch-off in all cases. It should also be noted that the effects of changing E/I and pE/pI, as well as the effects of α1 and α6-receptors switch-off, tuned first-spike timing and precision over the sub-millisecond time-scale and that the spike number varied in discrete units of a few spikes, making the system highly sensitive to activity variations. The complete switch-off of all forms (phasic and tonic) of GABAergic inhibition (simulating a gabazine application see Figure 1) caused a proportionate increase only in spike number and time-window duration without changing time to first spike and first spike standard deviation.

Finally, the model showed that raising pI caused a modest decrease (≤20%) of number of spikes, time window, time to first spike and first spike standard deviation. Conversely, raising pE remarkably increased number of spikes (≤80%) and decreased time to first spike and first spike standard deviation (≤80%) with a limited effect on time window (≤20%) (Figure 5B). Therefore, the effect of synaptic inhibition on burst parameters were more related to the number of active inhibitory synapses and to E/I than to the inhibitory release probability.

The simulated parameters were compared to those measured experimentally (cf. Figure 1). The points were reported in their sub-quadrant following the indications derived from Figure 1E and located at the corresponding pE/pI intersection (Figure 6A). In this comparison we used only the 5 granule cells with E, I = 4 in order to fit into the simulated parameter space. For these cells, the pE and pI values closely corresponded to those reported previously (Sola et al., 2004; Mapelli et al., 2009) (Figure 6B). The parameter variation caused by gabazine was then compared to that caused by switch-off of both tonic and phasic synaptic inhibition in the model (Figure 6C). The data measured for the different parameters showed a variation similar to that of the model (linear fitting with slope 0.95, R² = 0.914). It should be noted that this data distribution was not significantly different from the unitary diagonal (X² p < 2.6 e⁻¹⁰). Finally, it should be noted that time to first spike and first spike standard deviation showed modest changes compared to number of spikes and time window, in agreement with experimental results matched for the E/I balance (experimental E/I = 2.2 compared to simulated E/I = 2.6). Therefore, the model was able to capture the main quantitative properties of glomerular transmission and the impact of synaptic inhibition on granule cell firing.

In order to assess the impact of inhibition on information coding (i.e., to what extent the same responses could be obtained with different parameters), the coding fraction (actually the ratio between mutual information and entropy, see Methods) was calculated (Borst and Theunissen, 1999; Sadeghi et al., 2007; Ince et al., 2009). The coding fraction of number of spikes, time window, and time to first spike was relatively small (see Table 4) demonstrating a remarkable redundancy in the parameter space. Once inhibition was removed by blocking α1 and α6 receptors, the coding fraction increased for time window and time to first spike, but not apparently so for the number of spikes (Table 4), indicating a preferential control of inhibition over spike patterning and timing rather than on spike number per se.

Beside the coordinated action of excitation and inhibition caused by concurrent mossy fiber activation of granule cells and Golgi cells shown in Figure 4, the excitatory and inhibitory synapses impinging on granule cells can work in any arbitrary phase relationship. Given their different time-course and temporal integration during trains (cf. Figures 2, 3), α1 and α6 receptor-mediated currents might have differential impact on firing depending on the E/I phase (Figure 7A). Therefore, we have performed simulations using different phase-lags of inhibition with respect to excitation generating tuning curves for the spiking parameters (in these simulations pE and pI were not changed since we used single stimulation pulses preventing their impact on short-term train dynamics). The most apparent changes occurred when α6 receptors were switched off. Interestingly, number of spikes, time window, time to first spike and first spike standard deviation showed resonance around −10 ms phase-lag. When α1 receptors were switched off, resonance appeared around 10 ms phase-lag. The impact of the E/I phase was evaluated also for currents generated by NMDA channels and voltage-dependent calcium channels (VDCCs) (Figure 7B). Again, the most apparent changes occurred when the α6 receptor was turned off. The VDCC current decreased monotonically with positive phase-lag while the NMDA current showed broad tuning distributed between −20 and +30 ms phase-lag. When the α1 receptor was turned off, resonance peaked around +10 ms phase-lag.

These simulations showed that α1 and α6 receptor-mediated effects combined in tuning spike generation toward specific phase-lags and that α6 receptor-mediated effects were larger and broader than α1 receptor-mediated effects.

The tuning curves reported in Figure 7 revealed dependence of granule cell responses on the E/I phase-lag. This effect was evaluated by fitting the tuning curves with Lorentzian functions yielding Q = A/ω, a parameter indicating the tendency of the response to peak at a certain phase-lag θ_max with area A and broadness ω (Equation 4, see Methods; Figure 8A).

Lorentzian parameters, which report the effectiveness of tuning toward a preferential phase-lag, showed specific properties (Figure 8B). For all parameters, Q(α6) > Q(α1) reflected the larger impact of α6 than α1 receptor-mediated charge transfer, ω(α6) > ω(α1) reflected the longer duration of α6 than α1 receptor-mediated responses, and θ_max(α6) < 0 and θ_max(α1) > 0 reflected the slower raise of α6 than α1 receptor-mediated responses (cf. Figures 2, 3). Interestingly, Q(α6) was much larger for time window, time to first spike and first spike standard deviation than for number of spikes (Figure 8B). This pattern was opposite to that observed for burst transmission (cf. Figure 5A), implying that only the time-dependent parameters were tuned by the E/I phase difference. It should also be noted that Q(α6) of the NMDA current was very small, reflecting the slow time course of this current and its broad integration times (D'Angelo et al., 1995; Schwartz et al., 2012).

Modulation of Q(α6) for time window, time to first spike and first spike standard deviation tended to decrease with E/I, according to the powerful effect of phasic inhibition in controlling time-dependent parameters (Figure 8C). Modulation of Q(α6) with E/I for the VDCC current followed strictly that of the number of spikes (D'Angelo et al., 1999; Gandolfi et al., 2014). Modulation of Q(α6) with E/I for the NMDA current was marginal but, specifically, θ_max (α6) shifted progressively from −20 to +30 ms (phase-lag precession, cf. Figure 7B) with increasing E/I (Figure 8D) unveiling a complex influence of α6 receptor-mediated inhibition on voltage-dependent NMDA channel unblock.

Finally, in order to determine the effect of tonic inhibition on granule cell responses to dynamic patterns, tuning curves were generated with tonic inhibition blocked. The plot in Figure 8C shows the difference between the cases in which tonic inhibition was on or off. The tonic current biased the effect of inhibition proportionately to the E/I balance without altering the dynamics of inhibition substantially. Therefore, the model predicts that tonic inhibition simply scales the effect of phasic inhibition on firing parameters.

The glomerular microcircuit model could fit and explain the firing patterns observed in experimental data following mossy fiber burst stimulation. Once experimental granule cell firing parameter (time to first spike, first spike standard deviation, number of spikes and time window) values were reported on the simulated response space, the glomerular microcircuit model yielded pE and pI values corresponding to those observed experimentally (average pE = 0.51 vs. 0.55 in (Sola et al., 2004); average pI = 0.42 vs. 0.42 in Mapelli et al., 2009). Moreover, the model properly fitted the spiking parameters changes caused by gabazine, a drug that blocks both phasic and tonic inhibition. Therefore the model was endowed with mechanisms capable of capturing the impact of inhibitory neurotransmission on granule cell firing parameters and could be used to predict the effect of different E/I phase lags.

It should be noted that in our model the effect of metabotropic receptors was excluded to isolate the ionotropic component of inhibition. Experimentally, the application of mGluRs and GABA-B receptor blockers caused a net dis-inhibitory effect (cf. Figure 1), which could reflect multiple mechanisms. The mGluRs on presynaptic Golgi cell terminals might have reduced GABA release, and this would suffice to explain the increased number of spikes and duration of discharge in most of the recordings. Conversely, GABA-B receptor blockage on granule cells and on Golgi cell terminals (Rossi et al., 2006; Mapelli et al., 2009) would reduce granule cell excitability and enhance inhibitory neurotransmission, thereby sorting the opposite effect. Future models of glomerula neurotransmission may be designed to include metabotropic receptor control (Mapelli et al., 2014).

The inhibitory neurotransmission model was based on GABA-A receptor kinetics and was fitted to voltage-clamp recordings. Simulations of glomerular inhibition were consistent with a mechanism in which α₁ receptors determine the rapid response to released GABA characterizing the direct component, while α₆ receptors determine the slow temporal integration of spillover currents characterizing the indirect component (Cherubini and Conti, 2001; Farrant and Nusser, 2005; Glykys and Mody, 2007). The model predicts that, while α₁ receptor-mediated responses can precisely follow GABA concentration changes, α₆ receptor-mediated responses tend to saturate early during the train. Thus, as observed experimentally, raise in p determined minor changes in synaptic charge transfer matching experimental observations (Mapelli et al., 2009).

The adherence of the inhibitory neurotransmission model to the microscopic properties of the synapse could be defined at different levels. First, the GABA-A receptor kinetic schemes (derived from Pugh and Raman, 2005) appropriately reproduced eIPSCs and their changes in different functional conditions, suggesting that GABA affinities and the balance between open, closed and desensitized states were in the physiological range for granule cell receptors. Secondly, by setting the same diffusion coefficient for GABA and glutamate (DiGregorio et al., 2002), the number of diffusing molecules and the diffusion distance were similar to those estimated for the mossy fiber—granule cell synapse (Nieus et al., 2006). This was not unexpected, given the substantial similarity in the number of releasing sites involved and the common diffusion space for the two neurotransmitters. Thirdly, the p values obtained by fitting the model to experimental data were almost identical to those estimated experimentally with quantal analysis and no changes in the rate of vesicle recycling or in any other model parameters were needed to fit the experimental eIPSC trains.

Model simulations explained the complex effect of phasic inhibition on the burst-burst transmission modality of the granular layer (Chadderton et al., 2004; Rancz et al., 2007; Arenz et al., 2008). The E/I balance was most effective in controlling granule cell tonic discharge (the ~9-fold number of spikes increase was associated with a ~3-fold time window increase, so that the output spike frequency increased by about 3 times) but had minor effects on time-related parameters, time to first spike and first spike standard deviation. The pE/pI balance was most effective in controlling number of spikes, time to first spike and first spike standard deviation. Raising pE specifically increased number of spikes and reduced time to first spike, consistent with the fact that AMPA and NMDA receptor activation shows a remarkable modulation with pE (Nieus et al., 2006). Raising pI depressed all parameters but its effect was small, probably because inhibition during a burst largely depends on the charge carried by α6 receptors, which are early saturated (see above and cf. Figures 2, 3). The first spike standard deviation was almost equally reduced by raising pE and pI, probably reflecting reduction of synaptic noise determined by the larger number of released quanta (Sola et al., 2004; Mapelli et al., 2009). It turns out that, during burst transmission, the major effect of inhibition is to control the number and frequency of spikes emitted by granule cells through a regulation of the relative number of active Golgi cell synapses. Both E/I and pE/pI effects were enhanced by GABA receptor switch-off, but the contribution of α6 was always much larger than that of α1 receptors reflecting the fact that α6 receptors controlled most of the inhibitory charge transfer.

The tonic GABA leakage in the model did not contribute to the effect of inhibitory transmission substantially beside proportionately increasing number of spikes and time window. The tonic GABA leakage was modeled on the basis of experimental observations in cerebellar slices. The cerebellar glomerulus is an ideal structure to preserve tonic inhibition in slices provided that the glial sheath is intact (Hamann et al., 2002; Mitchell and Silver, 2003; Mapelli et al., 2014). Although the topic is still debated, tonic inhibition was reported in vivo revealing properties similar as in slices (Chadderton et al., 2004), suggesting that predictions made by our model could apply to synaptic transmission in natural conditions.

Model simulations predicted a specific role for phasic inhibition in controlling granule cell responses with different E/I phases lags. The most apparent regulatory effects on granule cell firing occurred when the α6 receptor-mediated current was turned off. This was due to the long time course and large charge transfer of α6 receptor-mediated responses, extending the influence of inhibition for about ±50 ms around granule cell excitation. When the α1 receptor-mediated current was turned off, the effects were smaller and resonance was restricted over about ±10 ms. Interestingly, time-related firing parameters (time window, time to first spike, first spike standard deviation) showed much sharper tuning than tonic firing (number of spikes). Moreover, tuning of time-related parameters decreased with E/I along with the decreasing inhibitory control, while GABA leakage did not alter the dynamics of inhibition substantially.

The model also predicted how VDCC and NMDA currents would be regulated by α1 and α6 receptors. VDCC current regulation strictly followed the number of spikes, as these channels open during the upstroke (D'Angelo et al., 1997, 2001; Gandolfi et al., 2014). The α6 receptor-mediated regulation of the NMDA current showed a broad tuning extending over ±50 ms and reflecting the slow NMDA current kinetics (D'Angelo et al., 1995; Schwartz et al., 2012). Puzzlingly, the effect of inhibition on the NMDA current showed a precession with E/I (from −20 to +30 ms phase-lag) suggesting a complex voltage-dependent interaction between NMDA channel unblock, depolarization and inhibitory control.

The dynamic control of inhibition by α6 and α1 receptors could have specific consequences during local microcircuit activation. Feed-forward inhibition affects granule cell excitation around 5 ms after mossy fiber activation (D'Angelo and De Zeeuw, 2009). With 5 ms phase-lag, the model predicted a higher impact for α6 mediated inhibition (except for the number of spikes at low E/I, where α6 and α1 affected the response in a similar way). Feed-back inhibition occurs after about 10 ms. With 10 ms phase-lag, the overall effect was also dominated by α6 mediated inhibition, but α1 and α6 effects were similar for time-to-first spike and first-spike standard deviation (and also on the number of spikes at low E/I). Therefore, in summary, the α6 component dominated on feed-forward inhibition, while the α1 component gained relevance in controlling the timing of granule cell output firing at low E/I during feed-back inhibition. Interestingly, during feedback inhibition at low E/I the α1 component is often more effective than the α6 component. Concerning the NMDA current, phase-lag precession suggested that the maximum impact of α6 mediated inhibition at 5–10 ms phase-lag was also achieved at low E/I. The multiple combinations of these effects and the complex inhibitory patterns provided by α1 and α6 subunit-containing GABA-A receptors make phasic inhibition particularly suitable to finely regulate the delay and precision of granule cell firing.

These properties may have an impact on spike-timing dependent plasticity (STDP) induction and on its interaction with low-frequency coherent oscillations reported in the cerebellar granular layer (Pellerin and Lamarre, 1997; Hartmann and Bower, 1998) and deserve future experimental assessment.

The extensive simulation strategy adopted in this paper suggests how phasic inhibition provided by Golgi cells controls information transfer through the granular layer. For each E/I value, release probabilities generated a complex subspace, such that similar firing parameter values could be found with different E/I and pE/pI combinations with a redundancy of 80 ÷ 90% (CF = 0.1 ÷ 0.2) (Borst and Theunissen, 1999; Sadeghi et al., 2007; Ince et al., 2009). The actual number of excitatory synapses may be relatively unimportant, provided that the number of inhibitory synapses is properly set, suggesting that the granular layer has intrinsic re-scaling properties with respect to the intensity of the inputs. Synaptic plasticity, mostly through pE, could allow to select points in this computational landscape for any specific E/I and pE/pI combination.

The amount of transmitted information (MI; Borst and Theunissen, 1999; Sadeghi et al., 2007; Ince et al., 2009), depends on the signal-to-noise (S/N) ratio. Since short bursts (1–3 spikes: see Figure 4B) at the mossy fiber—granule cell synapse carry the largest fraction of MI (Arleo et al., 2010), it is expected that regulation of first-spike delay and precision by phasic inhibition contributes substantially to regulate MI transfer through the cerebellum input stage (Garrido et al., 2013). It should also be noted that quantal fluctuations in GABA release generate synaptic noise, which should be smaller the larger the number of active synapses and the higher their release probabilities. Therefore, redundant E/I and pE/pI combinations giving same granule cell output patterns may not be equivalent in terms of MI transfer.

In summary, simulations identify five main reasons why phasic inhibition is needed for dynamic control of spike transmission at the mossy fiber—granule cell relay. (1) During burst transmission, tonic inhibition simply scales the effect of phasic inhibition on tonic spike discharge (number of spikes) without affecting time-related parameters (time to first spike and time window) significantly. (2) During inhibition with variable E/I phase, the pattern observed during bursts is reversed, so that phasic inhibition specifically affects time-related parameters without affecting tonic spike discharge significantly. (3) During inhibition with variable E/I phase, tonic GABA leakage does not alter the dynamics of inhibition substantially, so that tonic inhibition simply scales the effect of phasic inhibition on firing parameters. (4) The differential kinetics imposed by α1 and α6 receptors during inhibition with bursts or with variable E/I phase may not be explained by tonic inhibitory effects. (5) Phasic inhibition reduced redundancy specifically for time-related parameters.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.