Role of olivary electrical coupling in cerebellar motor learning

The level of electrotonic coupling in the inferior olive is extremely high, but its functional role in cerebellar motor control remains elusive. Here, we subjected mice that lack olivary coupling to paradigms that require learning-dependent timing. Cx36-deficient mice showed impaired timing of both locomotion and eye-blink responses that were conditioned to a tone. The latencies of their olivary spike activities in response to the unconditioned stimulus were significantly more variable than those in wild-types. Whole-cell recordings of olivary neurons in vivo showed that these differences in spike timing result at least in part from altered interactions with their subthreshold oscillations. These results, combined with analyses of olivary activities in computer simulations at both the cellular and systems level, suggest that electrotonic coupling among olivary neurons by gap junctions is essential for proper timing of their action potentials and thereby for learning-dependent timing in cerebellar motor control.     

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

It 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.     

Development of ionic conductances in neurons of the inferior olive in the rat: an in vitro study

Neurons of the inferior olive of the rat were studied at different stages of their postnatal (PN) development by using the current clamp technique in slices maintained in vitro. Antidromic and synaptic activation of inferior olivary neurons could be achieved in preparations as young as PN day 2. Neurons at this age already exhibited a variety of ionic conductances which included fast sodium-dependent spikes, high-threshold and low-threshold calcium spikes, potassium-dependent currents, Ca-dependent after-hyperpolarizing potentials (AHPS), and both instantaneous and time-dependent inward rectification at hyperpolarized levels of membrane potential. The two types of Ca-dependent responses recorded in olivary neurons during the first postnatal week were graded with the magnitude of the depolarization imposed on the cells. Furthermore, the high-threshold Ca spikes were only clearly observed during this early period when K conductances were depressed by the injection of caesium into the cells or by bath application of 4-aminopyridine. In contrast, the high-threshold Ca spikes could be obtained without suppression of K currents and were all-or-none in character in some neurons after PN day 8 and in all neurons after PN day 11. The observations suggest that the balance between K and Ca currents changes throughout maturation and is largely in favour of the K current until about the end of the first PN week. At all ages studied, the low-threshold Ca spikes were much less sensitive to the Ca channel blocker cadmium than were the high-threshold Ca spikes. Finally, spontaneous, regular oscillations of the membrane potential were observed for the first time at PN day 16 and were only commonly observed after PN day 19, suggesting a late development of electrotonic coupling between olivary neurons.     

Predicting single spikes and spike patterns with the Hindmarsh–Rose model

Most simple neuron models are only able to model traditional spiking behavior. As physiologists discover and classify different electrical phenotypes, computational neuroscientists become interested in using simple phenomenological models that can exhibit these different types of spiking patterns. The Hindmarsh–Rose model is a three-dimensional relaxation oscillator which can show both spiking and bursting patterns and has a chaotic regime. We test the predictive powers of the Hindmarsh–Rose model on two different test databases. We show that the Hindmarsh–Rose model can predict the spiking response of rat layer 5 neocortical pyramidal neurons on a stochastic input signal with a precision comparable to the best known spiking models. We also show that the Hindmarsh–Rose model can capture qualitatively the electrical footprints in a database of different types of neocortical interneurons. When the model parameters are fit from sub-threshold measurements only, the model still captures well the electrical phenotype, which suggests that the sub-threshold signals contain information about the firing patterns of the different neurons.     

Hypertrophy of inferior olivary neurons: a degenerative, regenerative or plasticity phenomenon

After contralateral hemi-cerebellectomy, neurons in the cat inferior olive may either degenerate, appear unchanged (affected) or become hypertrophic. Morphological and physiological aspects of the latter two cell types are studied by means of intracellular recording and injection techniques and compared to normal olivary neurons. It is demonstrated that affected and hypertrophic olivary neurons can be activated by mesodiencephalic stimulation. Affected olivary neurons are morphologically very similar to normal cells. However, they may respond with long latency action potentials only to mesodiencephalic stimulation. Hypertrophic olivary neurons have an enlarged dendritic tree and soma. The soma and proximal dendrites are studded with spine-like processes. Their reaction to mesodiencephalic stimulation is very diverse and may consist of short and/or long latency action potentials that may or may not trigger dendritic spikes. It is argued that olivary hypertrophy does not present either a degenerative or regenerative state, but that both hypertrophic as well as affected olivary neurons can survive axotomy due to a strong and continuous electrotonic coupling, made possible by destruction of the GABAergic cerebellar afferents.     

Emergent properties of electrically coupled smooth muscle cells

Asynchronous and synchronous calcium oscillations occur in a variety of cells. A well-established pathway for intercellular communication is provided by gap junctions which connect adjacent cells and can mediate electrical and chemical coupling. Several experimental studies report that cells presenting only a transient increase when freshly dispersed may oscillate when they are coupled. Such observations suggest that the role of gap junctions is not only to coordinate calcium oscillations of adjacent cells. Gap junctions may also be important to generate oscillations. Here we illustrate the emergent properties of electrically coupled smooth muscle cells using a model that we recently proposed. A bifurcation analysis in the case of two cells reveals that synchronous and asynchronous calcium oscillations can be induced by electrical coupling. In a larger population of smooth muscle cells, electrical coupling may result in the creation of groups of cells presenting synchronous calcium oscillations. The elements of one group may be distant from each other. Moreover, our results highlight a general mechanism by which gap junctional electrical coupling can give rise to out of phase calcium oscillations in smooth muscle cells that are non-oscillating when uncoupled. All these observations remain true in the case of non-identical cells, except that the solution corresponding to synchronous calcium oscillations disappears and that the formation of groups is sensitive to the degree of heterogeneity. The first two authors contributed equally to this work.     

A model for feature linking via collective oscillations in the primary visual cortex

A neural network model for explaining experimentally observed neuronal responses in cat primary visual cortex is proposed. In our model, the basic functional unit is an orientation column which is represented by a large homogeneous population of neurons modeled as integrate-and-fire type excitable elements. The orientation column exhibits spontaneous collective oscillations in activity in response to suitable visual stimuli. Such oscillations are caused by mutual synchronization among the neurons within the column. Numerical simulation for various stimulus patterns shows that as a result of activity correlations between different columns, the amplitude and the phase of the oscillation in each column depend strongly on the global feature of the stimulus pattern. These results satisfactorily account for experimental observations.     

Inferior olive mirrors joint dynamics to implement an inverse controller

To produce smooth and coordinated motion, our nervous systems need to generate precisely timed muscle activation patterns that, due to axonal conduction delay, must be generated in a predictive and feedforward manner. Kawato proposed that the cerebellum accomplishes this by acting as an inverse controller that modulates descending motor commands to predictively drive the spinal cord such that the musculoskeletal dynamics are canceled out. This and other cerebellar theories do not, however, account for the rich biophysical properties expressed by the olivocerebellar complex’s various cell types, making these theories difficult to verify experimentally. Here we propose that a multizonal microcomplex’s (MZMC) inferior olivary neurons use their subthreshold oscillations to mirror a musculoskeletal joint’s underdamped dynamics, thereby achieving inverse control. We used control theory to map a joint’s inverse model onto an MZMC’s biophysics, and we used biophysical modeling to confirm that inferior olivary neurons can express the dynamics required to mirror biomechanical joints. We then combined both techniques to predict how experimentally injecting current into the inferior olive would affect overall motor output performance. We found that this experimental manipulation unmasked a joint’s natural dynamics, as observed by motor output ringing at the joint’s natural frequency, with amplitude proportional to the amount of current. These results support the proposal that the cerebellum—in particular an MZMC—is an inverse controller; the results also provide a biophysical implementation for this controller and allow one to make an experimentally testable prediction.     

Climbing Fiber Burst Size and Olivary Sub-threshold Oscillations in a Network Setting

The inferior olivary nucleus provides one of the two main inputs to the cerebellum: the so-called climbing fibers. Activation of climbing fibers is generally believed to be related to timing of motor commands and/or motor learning. Climbing fiber spikes lead to large all-or-none action potentials in cerebellar Purkinje cells, overriding any other ongoing activity and silencing these cells for a brief period of time afterwards. Empirical evidence shows that the climbing fiber can transmit a short burst of spikes as a result of an olivary cell somatic spike, potentially increasing the information being transferred to the cerebellum per climbing fiber activation. Previously reported results from in vitro studies suggested that the information encoded in the climbing fiber burst is related to the occurrence of the spike relative to the ongoing sub-threshold membrane potential oscillation of the olivary cell, i.e. that the phase of the oscillation is reflected in the size of the climbing fiber burst. We used a detailed three-compartmental model of an inferior olivary cell to further investigate the possible factors determining the size of the climbing fiber burst. Our findings suggest that the phase-dependency of the burst size is present but limited and that charge flow between soma and dendrite is a major determinant of the climbing fiber burst. From our findings it follows that phenomena such as cell ensemble synchrony can have a big effect on the climbing fiber burst size through dendrodendritic gap-junctional coupling between olivary cells.     

Spatial and temporal changes in natural and target deprivation-induced cell death in the mouse inferior olive

The survival of inferior olive neurons is dependent on contact with cerebellar Purkinje cells. There is evidence that this dependence changes with time. Because inferior olivary axons, called climbing fibers, already show significant topographical ordering in cerebellar target zones during late embryogenesis in mice, the question arises as to whether olive neurons are dependent on target Purkinje cells for their survival at this early age. To better characterize this issue, inferior olive development was studied in two transgenic mouse mutants, wnt-1 and L7ADT, with embryonic and early postnatal loss of cerebellar target cells, respectively, and compared to that in the well-studied mutant, Lurcher. Morphological criteria as well as quantitative measures of apoptosis were considered in this developmental analysis. Survival of inferior olive neurons is observed to be independent of Purkinje cells throughout embryogenesis, but dependence begins immediately at birth in both wild types and mutants. Thereafter, wild types and mutants show a rapid increase in olive cell apoptosis, with a peak at postnatal day 4, followed by a period of low-level, but significant, apoptosis that continues to at least postnatal day 11; the main difference is that apoptosis is quantitatively enhanced in the mutants compared to wild types. The multiphasic course of these effects roughly parallels the known phases of climbing fiber synaptogenesis. In addition, despite significant temporal differences among the mutants with respect to absolute numbers of dying cells, there are common spatial features suggestive of distinct intrinsic programs linking different olivary subnuclei to their targets.     

Regulating synchronous oscillations of cerebellar granule cells by different types of inhibition

Synchronous oscillations in neural populations are considered being controlled by inhibitory neurons. In the granular layer of the cerebellum, two major types of cells are excitatory granular cells (GCs) and inhibitory Golgi cells (GoCs). GC spatiotemporal dynamics, as the output of the granular layer, is highly regulated by GoCs. However, there are various types of inhibition implemented by GoCs. With inputs from mossy fibers, GCs and GoCs are reciprocally connected to exhibit different network motifs of synaptic connections. From the view of GCs, feedforward inhibition is expressed as the direct input from GoCs excited by mossy fibers, whereas feedback inhibition is from GoCs via GCs themselves. In addition, there are abundant gap junctions between GoCs showing another form of inhibition. It remains unclear how these diverse copies of inhibition regulate neural population oscillation changes. Leveraging a computational model of the granular layer network, we addressed this question to examine the emergence and modulation of network oscillation using different types of inhibition. We show that at the network level, feedback inhibition is crucial to generate neural oscillation. When short-term plasticity was equipped on GoC-GC synapses, oscillations were largely diminished. Robust oscillations can only appear with additional gap junctions. Moreover, there was a substantial level of cross-frequency coupling in oscillation dynamics. Such a coupling was adjusted and strengthened by GoCs through feedback inhibition. Taken together, our results suggest that the cooperation of distinct types of GoC inhibition plays an essential role in regulating synchronous oscillations of the GC population. With GCs as the sole output of the granular network, their oscillation dynamics could potentially enhance the computational capability of downstream neurons.     

Properties of the Nucleo-Olivary Pathway: An In Vivo Whole-Cell Patch Clamp Study

The inferior olivary nucleus (IO) forms the gateway to the cerebellar cortex and receives feedback information from the cerebellar nuclei (CN), thereby occupying a central position in the olivo-cerebellar loop. Here, we investigated the feedback input from the CN to the IO in vivo in mice using the whole-cell patch-clamp technique. This approach allows us to study how the CN-feedback input is integrated with the activity of olivary neurons, while the olivo-cerebellar system and its connections are intact. Our results show how IO neurons respond to CN stimulation sequentially with: i) a short depolarization (EPSP), ii) a hyperpolarization (IPSP) and iii) a rebound depolarization. The latter two phenomena can also be evoked without the EPSPs. The IPSP is sensitive to a GABA_A receptor blocker. The IPSP suppresses suprathreshold and subthreshold activity and is generated mainly by activation of the GABA_A receptors. The rebound depolarization re-initiates and temporarily phase locks the subthreshold oscillations. Lack of electrotonical coupling does not affect the IPSP of individual olivary neurons, nor the sensitivity of its GABA_A receptors to blockers. The GABAergic feedback input from the CN does not only temporarily block the transmission of signals through the IO, it also isolates neurons from the network by shunting the junction current and re-initiates the temporal pattern after a fixed time point. These data suggest that the IO not only functions as a cerebellar controlled gating device, but also operates as a pattern generator for controlling motor timing and/or learning.     

Spatial and temporal changes in natural and target deprivation‐induced cell death in the mouse inferior olive

The survival of inferior olive neurons is dependent on contact with cerebellar Purkinje cells. There is evidence that this dependence changes with time. Because inferior olivary axons, called climbing fibers, already show significant topographical ordering in cerebellar target zones during late embryogenesis in mice, the question arises as to whether olive neurons are dependent on target Purkinje cells for their survival at this early age. To better characterize this issue, inferior olive development was studied in two transgenic mouse mutants, wnt‐1 and L7ADT, with embryonic and early postnatal loss of cerebellar target cells, respectively, and compared to that in the well‐studied mutant, Lurcher. Morphological criteria as well as quantitative measures of apoptosis were considered in this developmental analysis. Survival of inferior olive neurons is observed to be independent of Purkinje cells throughout embryogenesis, but dependence begins immediately at birth in both wild types and mutants. Thereafter, wild types and mutants show a rapid increase in olive cell apoptosis, with a peak at postnatal day 4, followed by a period of low‐level, but significant, apoptosis that continues to at least postnatal day 11; the main difference is that apoptosis is quantitatively enhanced in the mutants compared to wild types. The multiphasic course of these effects roughly parallels the known phases of climbing fiber synaptogenesis. In addition, despite significant temporal differences among the mutants with respect to absolute numbers of dying cells, there are common spatial features suggestive of distinct intrinsic programs linking different olivary subnuclei to their targets. © 2000 John Wiley & Sons, Inc. J Neurobiol 43: 18–30, 2000     

Synchronization in a network of fast-spiking interneurons

Experimental results revealed that in neocortex inhibitory fast-spiking (FS) interneurons interact also by electrical synapses (gap-junctions). They receive sensory information from thalamus and transfer it to principal cells by feedforward inhibition. Moreover, their synchronous discharge enhances their inhibitory control of pyramidal neurons. By using a biophysical model of FS interneurons the synchronization properties of a network of two synaptically coupled units are investigated. In the case they interact only by inhibitory synapses, well defined regions exist in the parameters space described by the strength and duration of the synaptic current, where synchronous regimes occur. Then an empirical protocol is proposed to determine approximately the borders of the synchronization manifold (SM). When electrical synapses are included, the region of synchronous discharge of the two interneurons becomes larger. In both cases, the coherent states are characterized by discharge frequencies in the gamma range. Lastly, the effects of heterogeneity, either obtained by using different stimulation currents or unidirectional inhibitory coupling, are studied.     

Cortical Resonance Frequencies Emerge from Network Size and Connectivity

Neural oscillations occur within a wide frequency range with different brain regions exhibiting resonance-like characteristics at specific points in the spectrum. At the microscopic scale, single neurons possess intrinsic oscillatory properties, such that is not yet known whether cortical resonance is consequential to neural oscillations or an emergent property of the networks that interconnect them. Using a network model of loosely-coupled Wilson-Cowan oscillators to simulate a patch of cortical sheet, we demonstrate that the size of the activated network is inversely related to its resonance frequency. Further analysis of the parameter space indicated that the number of excitatory and inhibitory connections, as well as the average transmission delay between units, determined the resonance frequency. The model predicted that if an activated network within the visual cortex increased in size, the resonance frequency of the network would decrease. We tested this prediction experimentally using the steady-state visual evoked potential where we stimulated the visual cortex with different size stimuli at a range of driving frequencies. We demonstrate that the frequency corresponding to peak steady-state response inversely correlated with the size of the network. We conclude that although individual neurons possess resonance properties, oscillatory activity at the macroscopic level is strongly influenced by network interactions, and that the steady-state response can be used to investigate functional networks.     

Diffusion of calcium and metabolites in pancreatic islets: killing oscillations with a pitchfork

Cell coupling is important for the normal function of the beta-cells of the pancreatic islet of Langerhans, which secrete insulin in response to elevated plasma glucose. In the islets, electrical and metabolic communications are mediated by gap junctions. Although electrical coupling is believed to account for synchronization of the islets, the role and significance of diffusion of calcium and metabolites are not clear. To address these questions we analyze two different mathematical models of islet calcium and electrical dynamics. To study diffusion of calcium, we use a modified Morris-Lecar model. Based on our analysis, we conclude that intercellular diffusion of calcium is not necessary for islet synchronization, at most supplementing electrical coupling. Metabolic coupling is investigated with a recent mathematical model incorporating glycolytic oscillations. Bifurcation analysis of the coupled system reveals several modes of behavior, depending on the relative strength of electrical and metabolic coupling. We find that whereas electrical coupling always produces synchrony, metabolic coupling can abolish both oscillations and synchrony, explaining some puzzling experimental observations. We suggest that these modes are generic features of square-wave bursters and relaxation oscillators coupled through either the activation or recovery variable.     

Spontaneously active cells induce state transitions in a model of olfactory cortex

The existence of neurons with intrinsic oscillations does not in itself explain the synchronization of local populations of neurons, but it is likely to pace population rhythms when the neurons are suitably coupled by chemical and/or electrical synapses. In the present study, we have investigated the role of spontaneously active cells as noisy or pacemaker units in setting global oscillations in a three-layered cortical model. The presence of a small number of noisy (spontaneously active) units induce oscillations at the network level in the range of the gamma rhythm. The number of noisy units in the network and their type (excitatory or inhibitory or excitatory and inhibitory together) determines the emergence of regular oscillations or aperiodic (chaotic) behaviour. It also determines the onset of the global behaviour. On replacing a noisy unit by a pacemaker unit, similar gamma oscillations were generated. With both noisy and pacemaker units, we found that certain characteristics of the spontaneous activity determine the delay period for the onset of global activity. Preliminary studies have been carried out with spontaneously active units having a chaotic dynamics but the results are much similar to that with a noisy burst. Different functional roles have been suggested for cortical oscillations, such as determining global functional states and specifying connectivity during development. Oscillations at different frequency bands, in particular in the gamma band (around 40 Hz), have also been associated with memory and attention. The presence of spontaneously active neurons, either with noisy or oscillatory activity, could be responsible for global oscillations in the absence of external stimuli in certain cortical areas in the mature brain.     

Specificity of a target cell-derived stop signal for afferent axonal growth.

With a novel model culture system in which afferents are co-cultured with purified populations of target neurons, we have demonstrated that a target cell within the central nervous system (CNS), the cerebellar granule neuron, poses a "stop-growing signal" for its appropriate afferents, the mossy fibers. To ask whether this stop signal is afferent specific, we co-cultured granule neurons with another cerebellar afferent system, the climbing fibers from the inferior olivary nuclei, which normally contact Purkinje neurons, and with retinal ganglion cell afferents, which never enter the cerebellum. Granule neurons do not pose a stop signal to either of these afferents. In contrast to pontine mossy afferents that grow well on laminin and showed reduced outgrowth on granule neurons, both olivary and retinal fibers displayed similar growth on laminin alone or on granule neurons. In addition, each afferent showed different degrees of fasciculation and growth cone morphology on laminin. Thus, the growth arrest signal sent by granule neurons is specifically recognized by their appropriate afferents. Moreover, these three types of afferents exhibit varying growth patterns on the same noncellular and cellular substrates, implicating distinct molecular characteristics of growth regulation for different classes of neurons that would contribute to specificity of synapse formation.     

Interspike interval densities of resonate and fire neurons

The subthreshold dynamics of a neuron can follow one of the two patterns: resonant neurons generate intrinsic subthreshold membrane potential oscillations, whereas in nonresonant neurons these oscillations are not observed. Here, we investigate how these subthreshold behaviors affect the suprathreshold response. Both types of neurons are described by a resonate and fire model, with the stable fixpoint being either a focus or a node. Using analytic expression for a linear oscillator model with threshold and reset, we calculate the multimodal interspike interval densities. We show that a change in model parameters induces qualitative changes in the interspike interval densities.