Spike burst-pause dynamics of Purkinje cells regulate sensorimotor adaptation

Cerebellar Purkinje cells mediate accurate eye movement coordination. However, it remains unclear how oculomotor adaptation depends on the interplay between the characteristic Purkinje cell response patterns, namely tonic, bursting, and spike pauses. Here, a spiking cerebellar model assesses the role of Purkinje cell firing patterns in vestibular ocular reflex (VOR) adaptation. The model captures the cerebellar microcircuit properties and it incorporates spike-based synaptic plasticity at multiple cerebellar sites. A detailed Purkinje cell model reproduces the three spike-firing patterns that are shown to regulate the cerebellar output. Our results suggest that pauses following Purkinje complex spikes (bursts) encode transient disinhibition of target medial vestibular nuclei, critically gating the vestibular signals conveyed by mossy fibres. This gating mechanism accounts for early and coarse VOR acquisition, prior to the late reflex consolidation. In addition, properly timed and sized Purkinje cell bursts allow the ratio between long-term depression and potentiation (LTD/LTP) to be finely shaped at mossy fibre-medial vestibular nuclei synapses, which optimises VOR consolidation. Tonic Purkinje cell firing maintains the consolidated VOR through time. Importantly, pauses are crucial to facilitate VOR phase-reversal learning, by reshaping previously learnt synaptic weight distributions. Altogether, these results predict that Purkinje spike burst-pause dynamics are instrumental to VOR learning and reversal adaptation.


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The cerebellum controls fine motor coordination including online adjustments of eye 56 movements [1]. Within the cerebellar cortex, the inhibitory projections of Purkinje cells 57 to medial vestibular nuclei (MVN) mediate the acquisition of accurate oculomotor 58 control [2,3]. Here, we consider the role of cerebellar Purkinje cells in the adaptation of 59 the vestibular ocular reflex (VOR), which generates rapid contralateral eye movements 60 that maintain images in the fovea during head rotations (Fig 1A). The VOR is crucial to 61 preserve clear vision (e.g., whilst reading) and maintain balance by stabilising gaze 62 during head movements. The VOR is mediated by the three-neuron reflex arc comprised 63 of connections from the vestibular organ via the medial vestibular nuclei (MVN) to the 64 eye motor neurons [3][4][5]. VOR control is purely feed-forward [6] and it relies on several 65 cerebellar-dependent adaptive mechanisms driven by sensory errors (Fig 1B). Because 66 of its dependence upon cerebellar adaptation, VOR has become one of the most 67 intensively used paradigms to assess cerebellar learning [6]. However, very few studies 68 have focused on the relation between the characteristics spike response patterns of 69 Purkinje cells and VOR adaptation, which is the main focus of this study. with high-frequency spikelet components up to 600 Hz), and post-complex spike pauses 159 (Fig 2A). In the model, CF discharges trigger transitions between the Purkinje cell Na + 160 spike output, CF-evoked bursts, and post-complex spike pauses. As evidenced in [37], 161 in in-vitro slice preparations at normal physiological conditions, 70% of Purkinje cells 162 spontaneously express a trimodal oscillation: a Na + tonic spike phase, a Ca-Na + bursting 163 phase, and a hyperpolarised quiescent phase. On the other hand, Purkinje cells also show 164 spontaneous firing consisting of a tonic Na + spike output without Ca-Na + bursts [37-165 39]. McKay et al. [37] report Purkinje cell recordings exhibiting a tonic Na + phase 166 sequence followed by CF-evoked bursts (via complex spikes) and the subsequent pause 167 (Fig 2A). The frequency of Purkinje cell Na + spike output decreases with no correlation 168 with the intervals between CF discharges. The model mimics this behaviour under 169 similar CF discharge conditions (Fig 2B). 170 The duration of model post-complex spike pauses increases linearly with burst 171 duration ( Fig 2C; R

Role of cerebellar Purkinje spike burst-pause dynamics in VOR adaptation 210
We assessed h-VOR adaptation by simulating a 1 Hz horizontal head rotation to be 211 compensated by contralateral eye movements ( Fig 1A). First, we tested the role of 212 Purkinje spike burst-pause dynamics in the absence of cerebellar learning, i.e. by 213 blocking synaptic plasticity across all model projections (i.e., MF-MVN, PF-Purkinje 214 cell, Purkinje cell-MVN). Synaptic weights were initialised randomly and equally within 215 each projection set. The CF input driving Purkinje cells was taken as to signal large 216 retina slips, which generated sequences of complex spikes made of 4 to 6 burst spikelets 217 [14] (Fig 3A, top). The elicited Purkinje spike burst-pause sequences shaped the 218 temporal disinhibition of targeted VN neurons, allowing the incoming input from MFs 219 to drive MVN responses (Fig 3A, middle). This facilitated a coarse baseline eye motion 220 ( Fig 3A, bottom). Blocking complex spiking in the Purkinje cell model (through the 221 blockade of muscarinic voltage-dependent channels, see Methods) prevented MF 222 activity from eliciting any baseline MVN compensatory output (Fig 3B). These results 223 suggest that the gating mechanism mediated by Purkinje spike burst-pause sequences, 224 which encode transient disinhibition of MVN neurons, is useful for early and coarse 225 VOR, prior to the adaptive consolidation of the reflex through cerebellar learning. 226  reversed. Here, we first simulated an h-VOR adaptation protocol (1 Hz) during 10000 s 303 (as before). Then, h-VOR phase reversal took place during the next 12000 s. Finally, the 304 normal h-VOR had to be restored during the last 12000 s (Fig 5). Our results suggest 305 that Purkinje spike burst-pause dynamics were instrumental to phase-reversal VOR gain 306 adaptation (Fig 5A), allowing for fast VOR learning reversibility consistently with 307 experimental recordings [3] (Fig 5B). Conversely, the absence of Purkinje complex 308 spiking led to impaired VOR phase-reversal learning with significant interference (  Consequently, the cerebellar model kept 'forgetting' the memory traces as during the 367 reversal VOR learning of day 1 (Fig 7, blue curve). In the second scenario, we considered 368 an average MF activity of 2.5 Hz, which made the LTP driven by vestibular activity to 369 counterbalance the LTD driven by the CFs. Under this condition, the cerebellar model 370 consolidated reversal VOR adaptation thus maintaining the synaptic weights at PF-371 Purkinje and MF-MVN synapses (Fig 7, green curve). Finally, we considered a low level 372 of MF activity (average 1 Hz), which made LTD to block the LTP action driven by the 373 vestibular (MF) activity. Under this third scenario, the cerebellar model showed a 374 consistent tendency for weights at PF-Purkinje and MF-MVN synapses to decay back 375 towards their initial value (Fig 7, red curve). Therefore, the model predicts that LTP 376 blockade during REMs stages might underlie the reversal VOR gain discontinuities in-377 between training sessions, in agreement with experimental data [3] (Fig 7, black curve). 378 379

Figure 7. LTP blockades (due to dominant LTD) during REMs explain reversal VOR 380
gain discontinuities between training sessions. We simulated 6 REMs stages (for a total 381 of 18000 s of simulation) between day 1 and 2 of VOR phase-reversal learning. High 382 Purkinje cell complex spike-pauses were elicited at high frequency during adaptation 396 ( Fig 8A). As the VOR error decreased, the frequency of CF-evoked Purkinje bursts 397 decayed to ~1 Hz upon completion of adaptation ( Fig 8B) However, a direct (and error independent) high-frequency stochastic stimulation of CFs 409 would lead to VOR impairment. To illustrate this, we simulated a protocol similar to the 410 one used by [46]. As expected, the number of CF-evoked Purkinje burst-pauses 411 increased as the CF frequency was artificially incremented through a 7 Hz direct 412 stimulation ( Fig 8A).Therefore, the VOR gain error tended to increase indicating an 413 impairment/blockade of the acquired reflex ( Fig 8B) and a decrease in VOR gain even 414 with similar CFs discharges observed during VOR adaptation. can regulate the adaptive output of the cerebellum, we also use a Purkinje neuron model 456 that cannot express complex spike firing (i.e., it can only operate in tonic mode). The 457 main finding of this study is that the CF-evoked spike burst-pause dynamics of the 458 Purkinje cell is a key feature for supporting both early and consolidated VOR learning. 459

Hz) leads to a balance of LTP (driven by vestibular activity) and LTD (driven by the
The model predicts that properly timed and sized Purkinje spike burst-pause sequences 460 are critical to: (1) gating the contingent association between vestibular inputs (about 461 head rotational velocity) and MVN motor outputs (to determine counter-rotational eye 462 movements), mediating an otherwise impaired VOR coarse acquisition; (2)   The results point towards a key role of CF-evoked Purkinje cell spike burst-pause 538 dynamics in driving adaptation at downstream neural stages. This testable prediction 539 may help to better understanding the cellular-to-network principles underlying 540 cerebellar-dependent sensorimotor adaptation. 541

VOR Analysis and Assessment 543
We simulated horizontal VOR (h-VOR) experiments with mice undertaking sinusoidal 544 (~1 Hz) whole body rotations in the dark [36]. The periodic functions representing eye 545 and head velocities (Fig 1A) were analysed through a discrete time Fourier transform. 546 The VOR gain was calculated as the ratio between the first harmonic amplitudes of the 547 forward Fourier eye-and head-velocity transforms: 548

Cerebellar Spiking Neural Network Model 556
The cerebellar circuit was modelled as a feed-forward loop capable of compensating 557 head movements by producing contralateral eye movements (Fig 1B).
(3) 579 with K g denoting a delayed rectifier potassium current, Na g a transient inactivating 580 sodium current, Ca g a high-threshold non-inactivating calcium current, L g a leak 581 current, and M g a muscarinic receptor suppressed potassium current (see Table 1). 582 583 584   (Table 2). 591

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The sodium activation variable was replaced and approximated by its equilibrium 594 function [ ] 0 m V . M-current presents a temporal evolution significantly slower than the 595 rest of the five variables thus provoking a slow-fast system able to reproduce the 596 characteristic Purkinje cell spiking modes (Fig 2). 597 The final voltage dynamics for the Purkinje [62, 63]cell model was given by: 598 where C m denotes the membrane capacitance, E AMPA and E GABA are the reversal potential 622 of each synaptic conductance, E rest is the resting potential, and G rest indicates the 623 conductance responsible for the passive decay term towards the resting potential. 624 Conductances g AMPA and g GABA integrate all the contributions received by each receptor 625 type (AMPA and GABA) through individual synapses and they are defined as decaying 626 exponential functions [81, 96]: 627   Table 5). 660

Granular cells (GCs). The granular layer included N=2000
Note that a delay is introduced in the generated analogue signal. This delay is 703 related to the number of filter coefficients and to the shape of the filter kernel h(t). In 704 order to mitigate this effect, we used an exponentially decaying kernel: where M is the number of filter taps (one per integration step) and τ M is a decaying factor. 707 At each time step, the output signal value only depends on its previous value and on the 708 input spikes in the same time step. Therefore, this filter is implemented by recursively 709 updating the last value of the output signal. Importantly, this kernel is similar to 710 postsynaptic current functions [121, 122], thus facilitating a biological interpretation. 711 Furthermore, this FIR filter is equivalent to an integrative neuron [123] . 712 where ∆W PFj-PCi (t) denotes the weight change between the j th PF and the target i th 725 Purkinje cell; is the time constant that compensates for the sensorimotor delay 726 (100ms); is the Dirac delta function corresponding to an afferent spike from a PF 727 fixed (Ito, 1982;[92, 125]   sampling of the error ensures that the entire error region is accurately represented over 1157 trials with a constrained CF activity below 10 spikes per second, per fibre (CF activated 1158 between 1-10 Hz). Hence, the error evolution is accurately sampled even at a low 1159 frequency [115,117]