A comparison of methods to determine neuronal phase-response curves

The phase-response curve (PRC) is an important tool to determine the excitability type of single neurons which reveals consequences for their synchronizing properties. We review five methods to compute the PRC from both model data and experimental data and compare the numerically obtained results from each method. The main difference between the methods lies in the reliability which is influenced by the fluctuations in the spiking data and the number of spikes available for analysis. We discuss the significance of our results and provide guidelines to choose the best method based on the available data.Comment: PDFLatex, 16 pages, 7 figures

GlyT2+ Neurons in the Lateral Cerebellar Nucleus

The deep cerebellar nuclei (DCN) are a major hub in the cerebellar circuitry but the functional classification of their neurons is incomplete. We have previously characterized three cell groups in the lateral cerebellar nucleus: large non-GABAergic neurons and two groups of smaller neurons, one of which express green fluorescence protein (GFP) in a GAD67/GFP mouse line and is therefore GABAergic. However, as a substantial number of glycinergic and glycine/GABA co-expressing neurons have been described in the DCN, this classification needed to be refined by considering glycinergic neurons. To this end we took advantage of a glycine transporter isoform 2 (GlyT2)-eGFP mouse line that allows identification of GlyT2-expressing, presumably glycinergic neurons in living cerebellar slices and compared their electrophysiological properties with previously described DCN neuron populations. We found two electrophysiologically and morphologically distinct sets of GlyT2-expressing neurons in the lateral cerebellar nucleus. One of them showed electrophysiological similarity to the previously characterized GABAergic cell group. The second GlyT2+ cell population, however, differed from all other so far described neuron types in DCN in that the cells (1) are intrinsically silent in slices and only fire action potentials upon depolarizing current injection and (2) have a projecting axon that was often seen to leave the DCN and project in the direction of the cerebellar cortex. Presence of this so far undescribed DCN neuron population in the lateral nucleus suggests a direct inhibitory pathway from the DCN to the cerebellar cortex

Purkinje cell input to cerebellar nuclei in tottering: Ultrastructure and physiology

Homozygous tottering mice are spontaneous ataxic mutants, which carry a mutation in the gene encoding the ion pore of the P/Q-type voltage-gated calcium channels. P/Q-type calcium channels are prominently expressed in Purkinje cell terminals, but it is unknown to what extent these inhibitory terminals in tottering mice are affected at the morphological and electrophysiological level. Here, we investigated the distribution and ultrastructure of their Purkinje cell terminals in the cerebellar nuclei as well as the activities of their target neurons. The densities of Purkinje cell terminals and their synapses were not significantly affected in the mutants. However, the Purkinje cell terminals were enlarged and had an increased number of vacuoles, whorled bodies, and mitochondria. These differences started to occur between 3 and 5 weeks of age and persisted throughout adulthood. Stimulation of Purkinje cells in adult tottering mice resulted in inhibition at normal latencies, but the activities of their postsynaptic neurons in the cerebellar nuclei were abnormal in that the frequency and irregularity of their spiking patterns were enhanced. Thus, although the number of their terminals and their synaptic contacts appear quantitatively intact, Purkinje cells in tottering mice show several signs of axonal damage that may contribute to altered postsynaptic activities in the cerebellar nuclei

Rebound Discharge in Deep Cerebellar Nuclear Neurons In Vitro

Neurons of the deep cerebellar nuclei (DCN) play a critical role in defining the output of cerebellum in the course of encoding Purkinje cell inhibitory inputs. The earliest work performed with in vitro preparations established that DCN cells have the capacity to translate membrane hyperpolarizations into a rebound increase in firing frequency. The primary means of distinguishing between DCN neurons has been according to cell size and transmitter phenotype, but in some cases, differences in the firing properties of DCN cells maintained in vitro have been reported. In particular, it was shown that large diameter cells in the rat DCN exhibit two phenotypes of rebound discharge in vitro that may eventually help define their functional roles in cerebellar output. A transient burst and weak burst phenotype can be distinguished based on the frequency and pattern of rebound discharge immediately following a hyperpolarizing stimulus. Work to date indicates that the difference in excitability arises from at least the degree of activation of T-type Ca2+ current during the immediate phase of rebound firing and Ca2+-dependent K+ channels that underlie afterhyperpolarizations. Both phenotypes can be detected following stimulation of Purkinje cell inhibitory inputs under conditions that preserve resting membrane potential and natural ionic gradients. In this paper, we review the evidence supporting the existence of different rebound phenotypes in DCN cells and the ion channel expression patterns that underlie their generation

The generation of phase differences and frequency changes in a network model of inferior olive subthreshold oscillations

This is an open-access article, free of all copyright, and may be freely reproduced, distributed, transmitted, modified, built upon, or otherwise used by anyone for any lawful purpose. The work is made available under the Creative Commons CC0 public domain dedicationIt is commonly accepted that the Inferior Olive (IO) provides a timing signal to the cerebellum. Stable subthreshold oscillations in the IO can facilitate accurate timing by phase-locking spikes to the peaks of the oscillation. Several theoretical models accounting for the synchronized subthreshold oscillations have been proposed, however, two experimental observations remain an enigma. The first is the observation of frequent alterations in the frequency of the oscillations. The second is the observation of constant phase differences between simultaneously recorded neurons. In order to account for these two observations we constructed a canonical network model based on anatomical and physiological data from the IO. The constructed network is characterized by clustering of neurons with similar conductance densities, and by electrical coupling between neurons. Neurons inside a cluster are densely connected with weak strengths, while neurons belonging to different clusters are sparsely connected with stronger connections. We found that this type of network can robustly display stable subthreshold oscillations. The overall frequency of the network changes with the strength of the inter-cluster connections, and phase differences occur between neurons of different clusters. Moreover, the phase differences provide a mechanistic explanation for the experimentally observed propagating waves of activity in the IO. We conclude that the architecture of the network of electrically coupled neurons in combination with modulation of the inter-cluster coupling strengths can account for the experimentally observed frequency changes and the phase differences.Peer reviewedFinal Published versio

Cerebellar Nuclear Neurons Use Time and Rate Coding to Transmit Purkinje Neuron Pauses

Copyright: © 2015 Sudhakar et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are creditedNeurons of the cerebellar nuclei convey the final output of the cerebellum to their targets in various parts of the brain. Within the cerebellum their direct upstream connections originate from inhibitory Purkinje neurons. Purkinje neurons have a complex firing pattern of regular spikes interrupted by intermittent pauses of variable length. How can the cerebellar nucleus process this complex input pattern? In this modeling study, we investigate different forms of Purkinje neuron simple spike pause synchrony and its influence on candidate coding strategies in the cerebellar nuclei. That is, we investigate how different alignments of synchronous pauses in synthetic Purkinje neuron spike trains affect either time-locking or rate-changes in the downstream nuclei. We find that Purkinje neuron synchrony is mainly represented by changes in the firing rate of cerebellar nuclei neurons. Pause beginning synchronization produced a unique effect on nuclei neuron firing, while the effect of pause ending and pause overlapping synchronization could not be distinguished from each other. Pause beginning synchronization produced better time-locking of nuclear neurons for short length pauses. We also characterize the effect of pause length and spike jitter on the nuclear neuron firing. Additionally, we find that the rate of rebound responses in nuclear neurons after a synchronous pause is controlled by the firing rate of Purkinje neurons preceding it.Peer reviewedFinal Published versio

Variability and directionality of inferior olive neuron dendrites revealed by detailed 3D characterization of an extensive morphological library

The inferior olive (IO) is an evolutionarily conserved brain stem structure and its output activity plays a major role in the cerebellar computation necessary for controlling the temporal accuracy of motor behavior. The precise timing and synchronization of IO network activity has been attributed to the dendro-dendritic gap junctions mediating electrical coupling within the IO nucleus. Thus, the dendritic morphology and spatial arrangement of IO neurons governs how synchronized activity emerges in this nucleus. To date, IO neuron structural properties have been characterized in few studies and with small numbers of neurons; these investigations have described IO neurons as belonging to two morphologically distinct types, “curly” and “straight”. In this work we collect a large number of individual IO neuron morphologies visualized using different labeling techniques and present a thorough examination of their morphological properties and spatial arrangement within the olivary neuropil. Our results show that the extensive heterogeneity in IO neuron dendritic morphologies occupies a continuous range between the classically described “curly” and “straight” types, and that this continuum is well represented by a relatively simple measure of “straightness”. Furthermore, we find that IO neuron dendritic trees are often directionally oriented. Combined with an examination of cell body density distributions and dendritic orientation of adjacent IO neurons, our results suggest that the IO network may be organized into groups of densely coupled neurons interspersed with areas of weaker coupling