Tunable oscillations in the Purkinje neuron

Temporal integration and 1/f power scaling in a circuit model of cerebellar interneurons

Inhibitory interneurons interconnected via electrical and chemical (GABA_A receptor) synapses form extensive circuits in several brain regions. They are thought to be involved in timing and synchronization through fast feedforward control of principal neurons. Theoretical studies have shown, however, that whereas self-inhibition does indeed reduce response duration, lateral inhibition, in contrast, may generate slow response components through a process of gradual disinhibition. Here we simulated a circuit of interneurons (stellate and basket cells) of the molecular layer of the cerebellar cortex and observed circuit time constants that could rise, depending on parameter values, to >1 s. The integration time scaled both with the strength of inhibition, vanishing completely when inhibition was blocked, and with the average connection distance, which determined the balance between lateral and self-inhibition. Electrical synapses could further enhance the integration time by limiting heterogeneity among the interneurons and by introducing a slow capacitive current. The model can explain several observations, such as the slow time course of OFF-beam inhibition, the phase lag of interneurons during vestibular rotation, or the phase lead of Purkinje cells. Interestingly, the interneuron spike trains displayed power that scaled approximately as 1/f at low frequencies. In conclusion, stellate and basket cells in cerebellar cortex, and interneuron circuits in general, may not only provide fast inhibition to principal cells but also act as temporal integrators that build a very short-term memory.NEW & NOTEWORTHY The most common function attributed to inhibitory interneurons is feedforward control of principal neurons. In many brain regions, however, the interneurons are densely interconnected via both chemical and electrical synapses but the function of this coupling is largely unknown. Based on large-scale simulations of an interneuron circuit of cerebellar cortex, we propose that this coupling enhances the integration time constant, and hence the memory trace, of the circuit.

Power Spectral Density Analysis of Purkinje Cell Tonic and Burst Firing Patterns From a Rat Model of Ataxia and Riluzole Treated

Introduction:

Purkinje Cell (PC) output displays a complex firing pattern consisting of high frequency sodium spikes and low frequency calcium spikes, and disruption in this firing behavior may contribute to cerebellar ataxia. Riluzole, neuroprotective agent, has been demonstrated to have neuroprotective effects in cerebellar ataxia. Here, the spectral analysis of PCs firing in control, 3-acetylpyridine (3-AP), neurotoxin agent, treated alone and riluzole plus 3-AP treated were investigated to determine changes in the firing properties. Difference in the power spectra of tonic and burst firing was assessed. Furthermore, the role of calcium-activated potassium channels in the power spectra was evaluated.

Methods:

Analysis was performed using Matlab. Power spectral density (PSD) of PCs output were obtained. Peak frequencies were extracted from the spectrum and statistical comparisons were done. In addition, a multi-compartment computational model of a Purkinje cell was used. This computational stimulation allowed us to study the changes in the power spectral density of the PC output as a result of alteration in ion channels.

Results:

Spectral analysis showed that in the spectrum of tonic and burst firing pattern only high sodium frequency and low calcium frequency was seen, respectively. In addition, there was a significant difference between the frequency components of PCs firing obtained from normal, ataxia and riluzole treated rats. Results indicated that sodium firing frequency of normal, ataxic and treated PCs occurred in approximate frequency of 22.53±5.49, 6.46±0.23, and 31.34±4.07 Hz, respectively; and calcium frequency occurred in frequency of 4.22±2.02, 1.52±1.19, and 3.88±1.37 Hz, respectively. The simulation results demonstrated that blockade of calcium-activated potassium channels in the PC model changed the PSD of the PC model firing activity. This change was similar to PSD changes in ataxia condition.

Conclusion:

These alterations in the spectrum of PC output may be a basis for developing possible new treatment strategies to improve cerebellar ataxia.

θ-Frequency resonance at the cerebellum input stage improves spike timing on the millisecond time-scale

The neuronal circuits of the brain are thought to use resonance and oscillations to improve communication over specific frequency bands (Llinas, 1988; Buzsaki, 2006). However, the properties and mechanism of these phenomena in brain circuits remain largely unknown. Here we show that, at the cerebellum input stage, the granular layer (GRL) generates its maximum response at 5-7 Hz both in vivo following tactile sensory stimulation of the whisker pad and in acute slices following mossy fiber bundle stimulation. The spatial analysis of GRL activity performed using voltage-sensitive dye (VSD) imaging revealed 5-7 Hz resonance covering large GRL areas. In single granule cells, resonance appeared as a reorganization of output spike bursts on the millisecond time-scale, such that the first spike occurred earlier and with higher temporal precision and the probability of spike generation increased. Resonance was independent from circuit inhibition, as it persisted with little variation in the presence of the GABAA receptor blocker, gabazine. However, circuit inhibition reduced the resonance area more markedly at 7 Hz. Simulations with detailed computational models suggested that resonance depended on intrinsic granule cells ionic mechanisms: specifically, K slow (M-like) and KA currents acted as resonators and the persistent Na current and NMDA current acted as amplifiers. This form of resonance may play an important role for enhancing coherent spike emission from the GRL when theta-frequency bursts are transmitted by the cerebral cortex and peripheral sensory structures during sensory-motor processing, cognition, and learning.