High frequency burst firing of granule cells ensures transmission at the parallel fiber to purkinje cell synapse at the cost of temporal coding

Model cerebellar granule cells can faithfully transmit modulated firing rate signals

A crucial assumption of many high-level system models of the cerebellum is that information in the granular layer is encoded in a linear manner. However, granule cells are known for their non-linear and resonant synaptic and intrinsic properties that could potentially impede linear signal transmission. In this modeling study we analyse how electrophysiological granule cell properties and spike sampling influence information coded by firing rate modulation, assuming no signal-related, i.e., uncorrelated inhibitory feedback (open-loop mode). A detailed one-compartment granule cell model was excited in simulation by either direct current or mossy-fiber synaptic inputs. Vestibular signals were represented as tonic inputs to the flocculus modulated at frequencies up to 20 Hz (approximate upper frequency limit of vestibular-ocular reflex, VOR). Model outputs were assessed using estimates of both the transfer function, and the fidelity of input-signal reconstruction measured as variance-accounted-for. The detailed granule cell model with realistic mossy-fiber synaptic inputs could transmit information faithfully and linearly in the frequency range of the vestibular-ocular reflex. This was achieved most simply if the model neurons had a firing rate at least twice the highest required frequency of modulation, but lower rates were also adequate provided a population of neurons was utilized, especially in combination with push-pull coding. The exact number of neurons required for faithful transmission depended on the precise values of firing rate and noise. The model neurons were also able to combine excitatory and inhibitory signals linearly, and could be replaced by a simpler (modified) integrate-and-fire neuron in the case of high tonic firing rates. These findings suggest that granule cells can in principle code modulated firing-rate inputs in a linear manner, and are thus consistent with the high-level adaptive-filter model of the cerebellar microcircuit.

Network structure within the cerebellar input layer enables lossless sparse encoding

The synaptic connectivity within neuronal networks is thought to determine the information processing they perform, yet network structure-function relationships remain poorly understood. By combining quantitative anatomy of the cerebellar input layer and information theoretic analysis of network models, we investigated how synaptic connectivity affects information transmission and processing. Simplified binary models revealed that the synaptic connectivity within feedforward networks determines the trade-off between information transmission and sparse encoding. Networks with few synaptic connections per neuron and network-activity-dependent threshold were optimal for lossless sparse encoding over the widest range of input activities. Biologically detailed spiking network models with experimentally constrained synaptic conductances and inhibition confirmed our analytical predictions. Our results establish that the synaptic connectivity within the cerebellar input layer enables efficient lossless sparse encoding. Moreover, they provide a functional explanation for why granule cells have approximately four dendrites, a feature that has been evolutionarily conserved since the appearance of fish.

A cerebellar learning model of vestibulo-ocular reflex adaptation in wild-type and mutant mice

Mechanisms of cerebellar motor learning are still poorly understood. The standard Marr-Albus-Ito theory posits that learning involves plasticity at the parallel fiber to Purkinje cell synapses under control of the climbing fiber input, which provides an error signal as in classical supervised learning paradigms. However, a growing body of evidence challenges this theory, in that additional sites of plasticity appear to contribute to motor adaptation. Here, we consider phase-reversal training of the vestibulo-ocular reflex (VOR), a simple form of motor learning for which a large body of experimental data is available in wild-type and mutant mice, in which the excitability of granule cells or inhibition of Purkinje cells was affected in a cell-specific fashion. We present novel electrophysiological recordings of Purkinje cell activity measured in naive wild-type mice subjected to this VOR adaptation task. We then introduce a minimal model that consists of learning at the parallel fibers to Purkinje cells with the help of the climbing fibers. Although the minimal model reproduces the behavior of the wild-type animals and is analytically tractable, it fails at reproducing the behavior of mutant mice and the electrophysiology data. Therefore, we build a detailed model involving plasticity at the parallel fibers to Purkinje cells' synapse guided by climbing fibers, feedforward inhibition of Purkinje cells, and plasticity at the mossy fiber to vestibular nuclei neuron synapse. The detailed model reproduces both the behavioral and electrophysiological data of both the wild-type and mutant mice and allows for experimentally testable predictions.

Dendritic SK channels convert NMDA-R-dependent LTD to burst timing-dependent plasticity

Feedback and descending projections from higher to lower brain centers play a prominent role in all vertebrate sensory systems. Feedback might be optimized for the specific sensory processing tasks in their target brain centers, but it has been difficult to connect the properties of feedback synapses to sensory tasks. Here, we use the electrosensory system of a gymnotiform fish ( Apteronotus leptorhynchus) to address this problem. Cerebellar feedback to pyramidal cells in the first central electrosensory processing region, the electrosensory lateral line lobe (ELL), is critical for canceling spatially and temporally redundant electrosensory input. The ELL contains four electrosensory maps, and we have previously analyzed the synaptic and network bases of the redundancy reduction mechanism in a map (centrolateral segment; CLS) believed to guide electrolocation behavior. In the CLS, only long-term depression was induced by pairing feedback presynaptic and pyramidal cell postsynaptic bursts. In this paper, we turn to an ELL map (lateral segment; LS) known to encode electrocommunication signals. We find remarkable differences in synaptic plasticity of the morphologically identical cerebellar feedback input to the LS. In the LS, pyramidal cell SK channels permit long-term potentiation (LTP) of feedback synapses when pre- and postsynaptic bursts occur at the same time. We hypothesize that LTP in this map is required for enhancing the encoding of weak electrocommunication signals. We conclude that feedback inputs that appear morphologically identical in sensory maps dedicated to different tasks, nevertheless display different synaptic plasticity rules contributing to differential sensory processing in these maps.

T-type channel blockade impairs long-term potentiation at the parallel fiber-Purkinje cell synapse and cerebellar learning

CaV3.1 T-type channels are abundant at the cerebellar synapse between parallel fibers and Purkinje cells where they contribute to synaptic depolarization. So far, no specific physiological function has been attributed to these channels neither as charge carriers nor more specifically as Ca(2+) carriers. Here we analyze their incidence on synaptic plasticity, motor behavior, and cerebellar motor learning, comparing WT animals and mice where T-type channel function has been abolished either by gene deletion or by acute pharmacological blockade. At the cellular level, we show that CaV3.1 channels are required for long-term potentiation at parallel fiber-Purkinje cell synapses. Moreover, basal simple spike discharge of the Purkinje cell in KO mice is modified. Acute or chronic T-type current blockade results in impaired motor performance in particular when a good body balance is required. Because motor behavior integrates reflexes and past memories of learned behavior, this suggests impaired learning. Indeed, subjecting the KO mice to a vestibulo-ocular reflex phase reversal test reveals impaired cerebellum-dependent motor learning. These data identify a role of low-voltage activated calcium channels in synaptic plasticity and establish a role for CaV3.1 channels in cerebellar learning.

Reevaluation of the beam and radial hypotheses of parallel fiber action in the cerebellar cortex

The role of parallel fibers (PFs) in cerebellar physiology remains controversial. Early studies inspired the "beam" hypothesis whereby granule cell (GC) activation results in PF-driven, postsynaptic excitation of beams of Purkinje cells (PCs). However, the "radial" hypothesis postulates that the ascending limb of the GC axon provides the dominant input to PCs and generates patch-like responses. Using optical imaging and single-cell recordings in the mouse cerebellar cortex in vivo, this study reexamines the beam versus radial controversy. Electrical stimulation of mossy fibers (MFs) as well as microinjection of NMDA in the granular layer generates beam-like responses with a centrally located patch-like response. Remarkably, ipsilateral forepaw stimulation evokes a beam-like response in Crus I. Discrete molecular layer lesions demonstrate that PFs contribute to the peripherally generated responses in Crus I. In contrast, vibrissal stimulation induces patch-like activation of Crus II and GABAA antagonists fail to convert this patch-like activity into a beam-like response, implying that molecular layer inhibition does not prevent beam-like responses. However, blocking excitatory amino acid transporters (EAATs) generates beam-like responses in Crus II. These beam-like responses are suppressed by focal inhibition of MF-GC synaptic transmission. Using EAAT4 reporter transgenic mice, we show that peripherally evoked patch-like responses in Crus II are aligned between parasagittal bands of EAAT4. This is the first study to demonstrate beam-like responses in the cerebellar cortex to peripheral, MF, and GC stimulation in vivo. Furthermore, the spatial pattern of the responses depends on extracellular glutamate and its local regulation by EAATs.