Stellate cell computational modeling predicts signal filtering in the molecular layer circuit of cerebellum

The functional properties of cerebellar stellate cells and the way they regulate molecular layer activity are still unclear. We have measured stellate cells electroresponsiveness and their activation by parallel fiber bursts. Stellate cells showed intrinsic pacemaking, along with characteristic responses to depolarization and hyperpolarization, and showed a marked short-term facilitation during repetitive parallel fiber transmission. Spikes were emitted after a lag and only at high frequency, making stellate cells to operate as delay-high-pass filters. A detailed computational model summarizing these physiological properties allowed to explore different functional configurations of the parallel fiber—stellate cell—Purkinje cell circuit. Simulations showed that, following parallel fiber stimulation, Purkinje cells almost linearly increased their response with input frequency, but such an increase was inhibited by stellate cells, which leveled the Purkinje cell gain curve to its 4 Hz value. When reciprocal inhibitory connections between stellate cells were activated, the control of stellate cells over Purkinje cell discharge was maintained only at very high frequencies. These simulations thus predict a new role for stellate cells, which could endow the molecular layer with low-pass and band-pass filtering properties regulating Purkinje cell gain and, along with this, also burst delay and the burst-pause responses pattern.


Ionic channels
Nav1.1 -Nav1.6. Expression and distribution of SC sodium channels were determined experimentally 1,2 . Nav1.1 channel was placed on the soma and Nav1.6 on the AIS and axonal compartment.
The gating mechanism was taken from 3,4 .
Kv3.4. This ionic channel with delayed rectifier properties was distributed on the soma, AIS and axon to repolarize the Na + spikes 8-10 . The gating mechanism was taken from 7 .

Supplementary Table 1. Ionic mechanisms in stellate cell models
The table shows the main properties of ionic channels used in the SC models. For each ionic channel type, the columns specify the maximum ionic conductance (G i -max), ionic channels reversal potential (E rev ). The corresponding gating equations were written either in Hodgkin-Huxley (HH) style or in Markovian style.

Supplementary Table 2. Electrotonic compartments in stellate cell models
The table shows the morphological analysis with NEURON software of the four morphologies used for the multi-compartment SC models. The table reports the sections of the multi-compartment SC model along with their number, their length and the soma area.

Supplementary Table 3. Synaptic model parameters
The table summarizes the parameters used for modeling the AMPA, NMDA and GABA A receptors [41][42][43] .

Supplementary Table 4, 5. Spike features
The tables show exemplar values of features, obtained from experimental traces (n = 9 used for the spontaneous firing recordings and n = 5 used for the current injection experimental protocols) and from simulations (n = 4) using eFEL and Clampfit software.

Supplementary Figure 1. Ionic currents in stellate cell model sections
The traces show the ionic currents and calcium concentration changes generated by membrane channels in the SC model when a spike occurs during autorhythmic firing. Note the localization of channels in different sections and the different calibration scales.

Supplementary Figure 2. Ionic currents in the somatic compartment in response to current injection
The traces show the model response recorded from the soma during alternated phases of pacemaking, hyperpolarization and depolarization. The upper traces shows membrane potential (V m ) and [Ca 2+ ] i , the other traces show the ionic currents. It should be noted that marked changes in current size are correlated with rebound bursts, adaptation and pauses.

Supplementary Figure 4. Dendritic currents in response to current injection
The figure shows the main dendritic mechanisms correlated with injected current pulses of different duration.
(A) The trace shows the model response during alternated phases of pacemaking, hyperpolarization and depolarization (as in Supplementary Fig. 2).

Supplementary Figure 5. Dendritic currents in response to repetitive synaptic transmission
The figure shows the main dendritic mechanisms correlated with bursts of synaptic activity.
(A) After a short burst (10 pulses @ 100 Hz; the trace is replotted from Fig. 6A), the SC model does not make any pause. After a long duration burst (50 pulses @ 100 Hz), the SC model shows a pause. These properties resemble those appearing at the end of a prolonged depolarizing current injection of the same duration (cf. Fig. 3 and Supplementary Fig. 4). For comparison, the figure compares the PC model, which shows a pause following bursts of both short and long duration demonstrating that the behavior of stellate cells reflects the specific balance, composition and localization of their ionic channels. (D) Top, the trace shows the SC model response during inhibitory burst duration (@100Hz , 32 synapses SC→ SC). Bottom, the 3D plots show rebound burst (ISI2/ISI1) increases with the inhibitory burst duration (@100Hz , 32 synapses SC→SC) and the size of the Cav3.2 current.

Supplementary Figure 6. Simulation of long-duration EPSC trains in SCs
Simulated synaptic currents in a SC evoked by activation of 3 PF-SC synapses with long input bursts. Note that, at all tested frequencies, the spike amplitude decreases after the initial increase but remains over the control level.

Supplementary Movie 1. Stellate cell morphology
The movie shows a SC morpho-electrical equivalent (morphology 1 in Fig. 1). The dendritic tree was flatted on the sagittal plane of the folium and the axon, after an initial part travelling parallel to the dendrite, advanced along the transverse plane.

Supplementary Movie 2. Stellate cell pacemaker activity
The movie shows the SC model spontaneous activity (membrane potential in the soma).

Supplementary Movie 3. Parallel fibers -stellate cell -Purkinje cell activity
SC model activation by a PF burst (10 impulses @ 200 Hz). The PC receives SC inhibition and generates a pause. The plots show membrane potential traces taken in the SC and PC soma.