Solution to the inverse problem of estimating gap-junctional and inhibitory conductance in inferior olive neurons from spike trains by network model simulation

Electrical coupling controls dimensionality and chaotic firing of inferior olive neurons

We previously proposed, on theoretical grounds, that the cerebellum must regulate the dimensionality of its neuronal activity during motor learning and control to cope with the low firing frequency of inferior olive neurons, which form one of two major inputs to the cerebellar cortex. Such dimensionality regulation is possible via modulation of electrical coupling through the gap junctions between inferior olive neurons by inhibitory GABAergic synapses. In addition, we previously showed in simulations that intermediate coupling strengths induce chaotic firing of inferior olive neurons and increase their information carrying capacity. However, there is no in vivo experimental data supporting these two theoretical predictions. Here, we computed the levels of synchrony, dimensionality, and chaos of the inferior olive code by analyzing in vivo recordings of Purkinje cell complex spike activity in three different coupling conditions: carbenoxolone (gap junctions blocker), control, and picrotoxin (GABA-A receptor antagonist). To examine the effect of electrical coupling on dimensionality and chaotic dynamics, we first determined the physiological range of effective coupling strengths between inferior olive neurons in the three conditions using a combination of a biophysical network model of the inferior olive and a novel Bayesian model averaging approach. We found that effective coupling co-varied with synchrony and was inversely related to the dimensionality of inferior olive firing dynamics, as measured via a principal component analysis of the spike trains in each condition. Furthermore, for both the model and the data, we found an inverted U-shaped relationship between coupling strengths and complexity entropy, a measure of chaos for spiking neural data. These results are consistent with our hypothesis according to which electrical coupling regulates the dimensionality and the complexity in the inferior olive neurons in order to optimize both motor learning and control of high dimensional motor systems by the cerebellum.

Computational theory suggests that the cerebellum must decrease the dimensionality of its neuronal activity to learn and control high dimensional motor systems effectively, while being constrained by the low firing frequency of inferior olive neurons, one of the two major source of input signals to the cerebellum. We previously proposed that the cerebellum adaptively controls the dimensionality of inferior olive firing by adjusting the level of synchrony and that such control is made possible by modulating the electrical coupling strength between inferior olive neurons. Here, we developed a novel method that uses a biophysical model of the inferior olive to accurately estimate the effective coupling strengths between inferior olive neurons from in vivo recordings of spike activity in three different coupling conditions. We found that high coupling strengths induce synchronous firing and decrease the dimensionality of inferior olive firing dynamics. In contrast, intermediate coupling strengths lead to chaotic firing and increase the dimensionality of the firing dynamics. Thus, electrical coupling is a feasible mechanism to control dimensionality and chaotic firing of inferior olive neurons. In sum, our results provide insights into possible mechanisms underlying cerebellar function and, in general, a biologically plausible framework to control the dimensionality of neural coding.

The Roles of the Olivocerebellar Pathway in Motor Learning and Motor Control. A Consensus Paper

For many decades, the predominant view in the cerebellar field has been that the olivocerebellar system's primary function is to induce plasticity in the cerebellar cortex, specifically, at the parallel fiber-Purkinje cell synapse. However, it has also long been proposed that the olivocerebellar system participates directly in motor control by helping to shape ongoing motor commands being issued by the cerebellum. Evidence consistent with both hypotheses exists; however, they are often investigated as mutually exclusive alternatives. In contrast, here, we take the perspective that the olivocerebellar system can contribute to both the motor learning and motor control functions of the cerebellum and might also play a role in development. We then consider the potential problems and benefits of it having multiple functions. Moreover, we discuss how its distinctive characteristics (e.g., low firing rates, synchronization, and variable complex spike waveforms) make it more or less suitable for one or the other of these functions, and why having multiple functions makes sense from an evolutionary perspective. We did not attempt to reach a consensus on the specific role(s) the olivocerebellar system plays in different types of movements, as that will ultimately be determined experimentally; however, collectively, the various contributions highlight the flexibility of the olivocerebellar system, and thereby suggest that it has the potential to act in both the motor learning and motor control functions of the cerebellum.

New insights into olivo-cerebellar circuits for learning from a small training sample

Artificial intelligence such as deep neural networks exhibited remarkable performance in simulated video games and 'Go'. In contrast, most humanoid robots in the DARPA Robotics Challenge fell down to ground. The dramatic contrast in performance is mainly due to differences in the amount of training data, which is huge and small, respectively. Animals are not allowed with millions of the failed trials, which lead to injury and death. Humans fall only several thousand times before they balance and walk. We hypothesize that a unique closed-loop neural circuit formed by the Purkinje cells, the cerebellar deep nucleus and the inferior olive in and around the cerebellum and the highest density of gap junctions, which regulate synchronous activities of the inferior olive nucleus, are computational machinery for learning from a small sample. We discuss recent experimental and computational advances associated with this hypothesis.

Segmental Bayesian estimation of gap-junctional and inhibitory conductance of inferior olive neurons from spike trains with complicated dynamics

The inverse problem for estimating model parameters from brain spike data is an ill-posed problem because of a huge mismatch in the system complexity between the model and the brain as well as its non-stationary dynamics, and needs a stochastic approach that finds the most likely solution among many possible solutions. In the present study, we developed a segmental Bayesian method to estimate the two parameters of interest, the gap-junctional (gc ) and inhibitory conductance (gi ) from inferior olive spike data. Feature vectors were estimated for the spike data in a segment-wise fashion to compensate for the non-stationary firing dynamics. Hierarchical Bayesian estimation was conducted to estimate the gc and gi for every spike segment using a forward model constructed in the principal component analysis (PCA) space of the feature vectors, and to merge the segmental estimates into single estimates for every neuron. The segmental Bayesian estimation gave smaller fitting errors than the conventional Bayesian inference, which finds the estimates once across the entire spike data, or the minimum error method, which directly finds the closest match in the PCA space. The segmental Bayesian inference has the potential to overcome the problem of non-stationary dynamics and resolve the ill-posedness of the inverse problem because of the mismatch between the model and the brain under the constraints based, and it is a useful tool to evaluate parameters of interest for neuroscience from experimental spike train data.

Modulation of Purkinje cell complex spike waveform by synchrony levels in the olivocerebellar system

Purkinje cells (PCs) generate complex spikes (CSs) when activated by the olivocerebellar system. Unlike most spikes, the CS waveform is highly variable, with the number, amplitude, and timing of the spikelets that comprise it varying with each occurrence. This variability suggests that CS waveform could be an important control parameter of olivocerebellar activity. The origin of this variation is not well known. Thus, we obtained extracellular recordings of CSs to investigate the possibility that the electrical coupling state of the inferior olive (IO) affects the CS waveform. Using multielectrode recordings from arrays of PCs we showed that the variance in the recording signal during the period when the spikelets occur is correlated with CS synchrony levels in local groups of PCs. The correlation was demonstrated under both ketamine and urethane, indicating that it is robust. Moreover, climbing fiber reflex evoked CSs showed an analogous positive correlation between spikelet-related variance and the number of cells that responded to a stimulus. Intra-IO injections of GABA-A receptor antagonists or the gap junction blocker carbenoxolone produced correlated changes in the variance and synchrony levels, indicating the presence of a causal relationship. Control experiments showed that changes in variance with synchrony were primarily due to changes in the CS waveform, as opposed to changes in the strength of field potentials from surrounding cells. Direct counts of spikelets showed that their number increased with synchronization of CS activity. In sum, these results provide evidence of a causal link between two of the distinguishing characteristics of the olivocerebellar system, its ability to generate synchronous activity and the waveform of the CS.

Treatment of essential tremor with long-chain alcohols: still experimental or ready for prime time?

AIM

To review current literature on long-chain alcohols and their derivatives as novel pharmacotherapy for the treatment of essential tremor (ET).

BACKGROUND

Currently available and recommended pharmacotherapies for ET are often limited by suboptimal treatment effects, frequent adverse effects, and drug interactions. While ethanol is reported to profoundly decrease tremor severity in the majority of patients with ET, preclinical experience suggests that long-chain alcohols such as 1-octanol might lead to a comparable tremor reduction without ethanol's typical side effects of sedation and intoxication. Here, we review the literature on the first clinical trials on 1-octanol and its metabolite octanoic acid (OA) for the treatment of ET.

METHODS

The literature on preclinical and clinical trials on long-chain alcohols as well as OA was reviewed and summarized, and an outlook given on next phases of development.

DISCUSSION

1-octanol was demonstrated to be safe and effective in a double-blind, placebo-controlled low-dose trial, and open-label data showed excellent tolerability and dose-dependent efficacy up to 128 mg/kg. Despite 1-octanol's efficacy, its future viability as an effective therapy is limited by its pharmacological properties that require large volumes to be orally administered. Pharmacokinetic data indicate that OA is the active metabolite of 1-octanol. Preclinical efficacy data for OA are positive, and human pilot data demonstrated excellent safety as well as efficacy in secondary outcome measures of tremor amplitudes. OA also has more favorable pharmacological properties for drug delivery; hence, OA may be worth developing as a pharmaceutical.

Role of the olivo-cerebellar complex in motor learning and control

How is the cerebellum capable of efficient motor learning and control despite very low firing of the inferior olive (IO) inputs, which are postulated to carry errors needed for learning and contribute to on-line motor control? IO neurons form the largest electrically coupled network in the adult human brain. Here, we discuss how intermediate coupling strengths can lead to chaotic resonance and increase information transmission of the error signal despite the very low IO firing rate. This increased information transmission can then lead to more efficient learning than with weak or strong coupling. In addition, we argue that a dynamic modulation of IO electrical coupling via the Purkinje cell-deep cerebellar neurons – IO triangle could speed up learning and improve on-line control. Initially strong coupling would allow transmission of large errors to multiple functionally related Purkinje cells, resulting in fast but coarse learning as well as significant effects on deep cerebellar nucleus and on-line motor control. In the late phase of learning decreased coupling would allow desynchronized IO firing, allowing high-fidelity transmission of error, resulting in slower but fine learning, and little on-line motor control effects.