Stochastic description of complex and simple spike firing in cerebellar Purkinje cells

Theta-tACS modulates cerebellar-related motor functions and cerebellar-cortical connectivity

OBJECTIVE

To evaluate the effects of cerebellar transcranial alternating current stimulation (tACS) delivered at cerebellar-resonant frequencies, i.e., theta (θ) and gamma (γ), on upper limb motor performance and cerebellum-primary motor cortex (M1) connectivity, as assessed by cerebellar-brain inhibition (CBI), in healthy subjects.

METHODS

Participants underwent cerebellar-tACS while performing three cerebellar-dependent motor tasks: (i) rhythmic finger-tapping, (ii) arm reaching-to-grasp ('grasping') and (iii) arm reaching-to-point ('pointing') an object. Also, we evaluated possible changes in CBI during cerebellar-tACS.

RESULTS

θ-tACS decreased movement regularity during the tapping task and increased the duration of the pointing task compared to sham- and γ-tACS. Additionally, θ-tACS increased the CBI effectiveness (greater inhibition). The effect of θ-tACS on movement rhythm correlated with CBI changes and less tapping regularity corresponded to greater CBI.

CONCLUSIONS

Cerebellar-tACS delivered at the θ frequency modulates cerebellar-related motor behavior and this effect is, at least in part, mediated by changes in the cerebellar inhibitory output onto M1. The effects of θ-tACS may be due to the modulation of cerebellar neurons that resonate to the θ rhythm.

SIGNIFICANCE

These findings contribute to a better understanding of the physiological mechanisms of motor control and provide new evidence on cerebellar non-invasive brain stimulation.

Inferring phenomenological models of first passage processes

Biochemical processes in cells are governed by complex networks of many chemical species interacting stochastically in diverse ways and on different time scales. Constructing microscopically accurate models of such networks is often infeasible. Instead, here we propose a systematic framework for building phenomenological models of such networks from experimental data, focusing on accurately approximating the time it takes to complete the process, the First Passage (FP) time. Our phenomenological models are mixtures of Gamma distributions, which have a natural biophysical interpretation. The complexity of the models is adapted automatically to account for the amount of available data and its temporal resolution. The framework can be used for predicting behavior of FP systems under varying external conditions. To demonstrate the utility of the approach, we build models for the distribution of inter-spike intervals of a morphologically complex neuron, a Purkinje cell, from experimental and simulated data. We demonstrate that the developed models can not only fit the data, but also make nontrivial predictions. We demonstrate that our coarse-grained models provide constraints on more mechanistically accurate models of the involved phenomena.

The dynamic relationship between cerebellar Purkinje cell simple spikes and the spikelet number of complex spikes

Key points

Purkinje cells are the sole output of the cerebellar cortex and fire two distinct types of action potential: simple spikes and complex spikes.

Previous studies have mainly considered complex spikes as unitary events, even though the waveform is composed of varying numbers of spikelets.

The extent to which differences in spikelet number affect simple spike activity (and vice versa) remains unclear.

We found that complex spikes with greater numbers of spikelets are preceded by higher simple spike firing rates but, following the complex spike, simple spikes are reduced in a manner that is graded with spikelet number.

This dynamic interaction has important implications for cerebellar information processing, and suggests that complex spike spikelet number may maintain Purkinje cells within their operational range.

Abstract

Purkinje cells are central to cerebellar function because they form the sole output of the cerebellar cortex. They exhibit two distinct types of action potential: simple spikes and complex spikes. It is widely accepted that interaction between these two types of impulse is central to cerebellar cortical information processing. Previous investigations of the interactions between simple spikes and complex spikes have mainly considered complex spikes as unitary events. However, complex spikes are composed of an initial large spike followed by a number of secondary components, termed spikelets. The number of spikelets within individual complex spikes is highly variable and the extent to which differences in complex spike spikelet number affects simple spike activity (and vice versa) remains poorly understood. In anaesthetized adult rats, we have found that Purkinje cells recorded from the posterior lobe vermis and hemisphere have high simple spike firing frequencies that precede complex spikes with greater numbers of spikelets. This finding was also evident in a small sample of Purkinje cells recorded from the posterior lobe hemisphere in awake cats. In addition, complex spikes with a greater number of spikelets were associated with a subsequent reduction in simple spike firing rate. We therefore suggest that one important function of spikelets is the modulation of Purkinje cell simple spike firing frequency, which has implications for controlling cerebellar cortical output and motor learning.

Purkinje cells are the sole output of the cerebellar cortex and fire two distinct types of action potential: simple spikes and complex spikes.

Previous studies have mainly considered complex spikes as unitary events, even though the waveform is composed of varying numbers of spikelets.

The extent to which differences in spikelet number affect simple spike activity (and vice versa) remains unclear.

We found that complex spikes with greater numbers of spikelets are preceded by higher simple spike firing rates but, following the complex spike, simple spikes are reduced in a manner that is graded with spikelet number.

This dynamic interaction has important implications for cerebellar information processing, and suggests that complex spike spikelet number may maintain Purkinje cells within their operational range.

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

Neurons 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.

Neurons can transmit information by two different coding strategies: Rate coding, where the firing rate of the neuron is vital, and time coding where timing of individual spikes carries relevant information. In this study we analyze the importance of brief cessations in firing of the presynaptic neuron (pauses) on the spiking of the postsynaptic neuron. We perform this analysis on the inhibitory synaptic connection between Purkinje neurons (presynaptic) and nuclear neurons (postsynaptic) of the cerebellum. We employ a computational model of nuclear neurons and “synthetic” Purkinje neuron spike trains to study the effect of synchronous pauses on the spiking responses of nuclear neurons. We find that synchronous pauses can cause both well-timed spikes and increased firing rate in the nuclear neuron. In addition, we characterize the effect of pause length, amount and type of pause synchrony, and spike jitter. As such, we conclude that nuclear cells use both rate and time coding to relay upstream spiking information.

Results on a binding neuron model and their implications for modified hourglass model for neuronal network

The classical models of single neuron like Hodgkin-Huxley point neuron or leaky integrate and fire neuron assume the influence of postsynaptic potentials to last till the neuron fires. Vidybida (2008) in a refreshing departure has proposed models for binding neurons in which the trace of an input is remembered only for a finite fixed period of time after which it is forgotten. The binding neurons conform to the behaviour of real neurons and are applicable in constructing fast recurrent networks for computer modeling. This paper develops explicitly several useful results for a binding neuron like the firing time distribution and other statistical characteristics. We also discuss the applicability of the developed results in constructing a modified hourglass network model in which there are interconnected neurons with excitatory as well as inhibitory inputs. Limited simulation results of the hourglass network are presented.

STD-dependent and independent encoding of input irregularity as spike rate in a computational model of a cerebellar nucleus neuron

Neurons in the cerebellar nuclei (CN) receive inhibitory inputs from Purkinje cells in the cerebellar cortex and provide the major output from the cerebellum, but their computational function is not well understood. It has recently been shown that the spike activity of Purkinje cells is more regular than previously assumed and that this regularity can affect motor behaviour. We use a conductance-based model of a CN neuron to study the effect of the regularity of Purkinje cell spiking on CN neuron activity. We find that increasing the irregularity of Purkinje cell activity accelerates the CN neuron spike rate and that the mechanism of this recoding of input irregularity as output spike rate depends on the number of Purkinje cells converging onto a CN neuron. For high convergence ratios, the irregularity induced spike rate acceleration depends on short-term depression (STD) at the Purkinje cell synapses. At low convergence ratios, or for synchronised Purkinje cell input, the firing rate increase is independent of STD. The transformation of input irregularity into output spike rate occurs in response to artificial input spike trains as well as to spike trains recorded from Purkinje cells in tottering mice, which show highly irregular spiking patterns. Our results suggest that STD may contribute to the accelerated CN spike rate in tottering mice and they raise the possibility that the deficits in motor control in these mutants partly result as a pathological consequence of this natural form of plasticity.

Evaluating the adaptive-filter model of the cerebellum

The adaptive-filter model of the cerebellar microcircuit is in widespread use, combining as it does an explanation of key microcircuit features with well-specified computational power. Here we consider two methods for its evaluation. One is to test its predictions concerning relations between cerebellar inputs and outputs. Where the relevant experimental data are available, e.g. for the floccular role in image stabilization, the predictions appear to be upheld. However, for the majority of cerebellar microzones these data have yet to be obtained. The second method is to test model predictions about details of the microcircuit. We focus on features apparently incompatible with the model, in particular non-linear patterns in Purkinje cell simple-spike firing. Analysis of these patterns suggests the following three conclusions. (i) It is important to establish whether they can be observed during task-related behaviour. (ii) Highly non-linear models based on these patterns are unlikely to be universal, because they would be incompatible with the (approximately) linear nature of floccular function. (iii) The control tasks for which these models are computationally suited need to be identified. At present, therefore, the adaptive filter remains a candidate model of at least some cerebellar microzones, and its evaluation suggests promising lines for future enquiry.

Electrophysiological characterization of the cerebellum in the arterially perfused hindbrain and upper body of the rat

In the present study, a non-pulsatile arterially perfused hindbrain and upper body rat preparation is described which is an extension of the brainstem preparation reported by Potts et al., (Brain Res Bull 53(1):59-67), 1. The modified in situ preparation allows study of cerebellar function whilst preserving the integrity of many of its interconnections with the brainstem, upper spinal cord and the peripheral nervous system of the head and forelimbs. Evoked mossy fibre, climbing fibre and parallel fibre field potentials and EMG activity elicited in forelimb biceps muscle by interpositus stimulation provided evidence that both cerebellar inputs and outputs remain operational in this preparation. Similarly, the spontaneous and evoked single unit activity of Purkinje cells, putative Golgi cells, molecular interneurones and cerebellar nuclear neurones was similar to activity patterns reported in vivo. The advantages of the preparation include the ability to record, without the complications of anaesthesia, stabile single unit activity for extended periods (3 h or more), from regions of the rat cerebellum that are difficult to access in vivo. The preparation should therefore be a useful adjunct to in vitro and in vivo studies of neural circuits underlying cerebellar contributions to movement control and motor learning.

Spatial pattern coding of sensory information by climbing fiber-evoked calcium signals in networks of neighboring cerebellar Purkinje cells

Climbing fiber input produces complex spike synchrony across populations of cerebellar Purkinje cells oriented in the parasagittal axis. Elucidating the fine spatial structure of this synchrony is crucial for understanding its role in the encoding and processing of sensory information within the olivocerebellar cortical circuit. We investigated these issues using in vivo multineuron two-photon calcium imaging in combination with information theoretic analysis. Spontaneous dendritic calcium transients linked to climbing fiber input were observed in multiple neighboring Purkinje cells. Spontaneous synchrony of calcium transients between individual Purkinje cells falls off over approximately 200 microm mediolaterally, consistent with the presence of cerebellar microzones organized by climbing fiber input. Synchrony was increased after administration of harmaline, consistent with an olivary origin. Periodic sensory stimulation also resulted in a transient increase of synchrony after stimulus onset. To examine how synchrony affects the neural population code provided by the spatial pattern of complex spikes, we analyzed its information content. We found that spatial patterns of calcium events from small ensembles of cells provided substantially more stimulus information (59% more for seven-cell ensembles) than available by counting events across the pool without taking into account spatial origin. Information theoretic analysis indicated that, rather than contributing significantly to sensory coding via stimulus dependence, correlational effects on sensory coding are dominated by redundancy attributable to the prevalent spontaneous synchrony. The olivocerebellar circuit thus uses a labeled line code to report sensory signals, leaving open a role for synchrony in flexible selection of signals for output to deep cerebellar nuclei.

Cerebellar LTD and pattern recognition by Purkinje cells

Many theories of cerebellar function assume that long-term depression (LTD) of parallel fiber (PF) synapses enables Purkinje cells to learn to recognize PF activity patterns. We have studied the LTD-based recognition of PF patterns in a biophysically realistic Purkinje-cell model. With simple-spike firing as observed in vivo, the presentation of a pattern resulted in a burst of spikes followed by a pause. Surprisingly, the best criterion to distinguish learned patterns was the duration of this pause. Moreover, our simulations predicted that learned patterns elicited shorter pauses, thus increasing Purkinje-cell output. We tested this prediction in Purkinje-cell recordings both in vitro and in vivo. In vitro, we found a shortening of pauses when decreasing the number of active PFs or after inducing LTD. In vivo, we observed longer pauses in LTD-deficient mice. Our results suggest a novel form of neural coding in the cerebellar cortex.

Regular patterns in cerebellar Purkinje cell simple spike trains

BACKGROUND

Cerebellar Purkinje cells (PC) in vivo are commonly reported to generate irregular spike trains, documented by high coefficients of variation of interspike-intervals (ISI). In strong contrast, they fire very regularly in the in vitro slice preparation. We studied the nature of this difference in firing properties by focusing on short-term variability and its dependence on behavioral state.

METHODOLOGY/PRINCIPAL FINDINGS

Using an analysis based on CV(2) values, we could isolate precise regular spiking patterns, lasting up to hundreds of milliseconds, in PC simple spike trains recorded in both anesthetized and awake rodents. Regular spike patterns, defined by low variability of successive ISIs, comprised over half of the spikes, showed a wide range of mean ISIs, and were affected by behavioral state and tactile stimulation. Interestingly, regular patterns often coincided in nearby Purkinje cells without precise synchronization of individual spikes. Regular patterns exclusively appeared during the up state of the PC membrane potential, while single ISIs occurred both during up and down states. Possible functional consequences of regular spike patterns were investigated by modeling the synaptic conductance in neurons of the deep cerebellar nuclei (DCN). Simulations showed that these regular patterns caused epochs of relatively constant synaptic conductance in DCN neurons.

CONCLUSIONS/SIGNIFICANCE

Our findings indicate that the apparent irregularity in cerebellar PC simple spike trains in vivo is most likely caused by mixing of different regular spike patterns, separated by single long intervals, over time. We propose that PCs may signal information, at least in part, in regular spike patterns to downstream DCN neurons.