Role of cerebellar GABAergic dysfunctions in the origins of essential tremor

Abstract

Essential tremor (ET) is among the most prevalent movement disorders, but its origins are elusive. The inferior olivary nucleus (ION) has been hypothesized as the prime generator of tremor because of the pacemaker properties of ION neurons, but structural and functional changes in ION are unlikely under ET. Abnormalities have instead been reported in the cerebello-thalamo-cortical network, including dysfunctions of the GABAergic projections from the cerebellar cortex to the dentate nucleus. It remains unclear, though, how tremor would relate to a dysfunction of cerebellar connectivity. To address this question, we built a computational model of the cortico-cerebello-thalamo-cortical loop. We simulated the effects of a progressive loss of GABA_A α₁-receptor subunits and up-regulation of α_2/3-receptor subunits in the dentate nucleus, and correspondingly, we studied the evolution of the firing patterns along the loop. The model closely reproduced experimental evidence for each structure in the loop. It showed that an alteration of amplitudes and decay times of the GABAergic currents to the dentate nucleus can facilitate sustained oscillatory activity at tremor frequency throughout the network as well as a robust bursting activity in the thalamus, which is consistent with observations of thalamic tremor cells in ET patients. Tremor-related oscillations initiated in small neural populations and spread to a larger network as the synaptic dysfunction increased, while thalamic high-frequency stimulation suppressed tremor-related activity in thalamus but increased the oscillation frequency in the olivocerebellar loop. These results suggest a mechanism for tremor generation under cerebellar dysfunction, which may explain the origin of ET.

Keywords: GABA; Purkinje cells; dentate nucleus; essential tremor; inferior olivary nucleus.

Fig. 1.

(A) Schematic of the CCTC model. Blue arrows, glutamatergic excitatory connections; red arrows, GABAergic inhibitory connections; PC, Purkinje cells; DCN, deep cerebellar neurons; NO, nucleoolivary neurons; ION, inferior olive nucleus; GrL, granular layer; RN, red nucleus; PN, pontine nucleus; IN, cerebellar interneurons; Vim, ventral intermediate nucleus of the thalamus; MC, motor cortex. (B–E) Response of PC and DCN neurons to a depolarizing stimulus applied in the ION in the proposed network model (B and D) and in rodents in vivo (C and E) in normal, tremor-free conditions. A single suprathreshold (10 pA) current pulse (pulse duration of 20 ms) was applied to all ION neurons in our model (black arrows in B and D) and in the inferior olivary nucleus of the rodent (black arrows in C and E) and resulted in a burst of action potentials with amplitude adaptation (i.e., complex spike) in the PC (B and C) and an after-hyperpolarization rebound burst of action potentials in the DCN (D and E). (B, Inset) Zoom-in of the complex spike. Image in C is reprinted from ref. , which is licensed under CC BY 3.0. Image in E is reprinted from ref. , which is licensed under CC BY 4.0.

Fig. 2.

Single unit activity of neurons in the CCTC model under normal and harmaline-induced tremor conditions. (A–H) Raster plot of ION neurons and PCs under normal condition (A and C) and harmaline-induced tremor condition (B and D), respectively, and correspondent membrane voltage of the DCN and TC neurons (E and G, normal condition; F and H, tremor condition, respectively). Blue bars in E and F report the timing of action potentials fired by the NO neuron. Data in A–H are from one instance of the CCTC model simulated over a 4,000-ms-long period. Time scales in G and H also apply to A, C, and E and B, D, and F, respectively. (I and J) Comparison between the power spectral density (PSD) of the TC neuron in the CCTC model and a tremor cell in the Vim of an ET patient, respectively. PSD in I is reported under normal tremor-free (blue curve) and harmaline-induced tremor conditions (red curve). PSD curves are averaged across three instances of the CCTC model, each one simulated over a 60,000-ms-long period. PSD in J is reported for a single tremor cell in a patient with ET. Image in J is reprinted with permission from ref. .

Fig. 3.

Effects of cerebellar GABAergic dysfunctions on tremor-related neural oscillations in the CCTC model. (A) Two-dimensional map depicting the region of the parameter space (R, τ^PC→DCN) where tremor activity in the Vim is observed along with the tremor peak frequency. The blue mark indicates parameters used to simulate normal, tremor-free conditions. The yellow circle indicates parameters used for the ET-like tremor activity analyzed in B and E, i.e., R = 0.7, τ^PC→DCN = 12 ms. For each combination of parameters (R, τ^PC→DCN), the CCTC model was simulated for 4,000 ms, and the first 1,000 ms were excluded from subsequent analyses. (B–E) Comparison between the bursting activity of DCN under harmaline-induced tremor (HAR; black bars) and GABAergic dysfunctions of the PC-DCN synapses (ET; gray bars). The burst analysis was performed as reported in SI Appendix, Note 2, on data collected over 60,000-ms-long simulations. The average burst period (B), burst duration (C), interburst interval (D), and intraburst discharge rate (E) are reported as mean ± SD across three model instances. Asterisks denote significant difference (Wilcoxon rank-sum test, P < 0.01) between values measured under HAR and ET conditions.

Fig. 4.

Role of the phase of ION subthreshold oscillations in the generation of tremor-related network oscillations. (A) In any ION neuron, the lag between an action potential and the peak of the following subthrehsold oscillation (black asterisk) defines the duration of the oscillation cycle. The onset time T of the depolarizing input current I_STEP is varied between 0 (i.e., at the time of the action potential) and the peak of the subthreshold oscillation. The current is transiently turned off when an action potential is generated (red line). (B) Two-dimensional map depicting the region of the parameter space (I_STEP, T) where ION neurons sustain tonic spiking along with the resultant firing rate. Curves in black, pink, cyan, green, and yellow denote the region where at least 4, 5, 6, 7, or all ION neurons sustain spiking simultaneously, respectively. For each combination (I_STEP, T) in B, three model instances were simulated over a 4,000-ms-long period, and the simulation results from the first 1,000 ms were discarded. The firing rate was measured from any ION neuron that sustained spiking until the end of simulation. (C) The ION firing rate as a function of the duration of the current I_STEP for several values of the current intensity. (D) Role of the dentato-rubro-olivary pathway in propagating tremor-related oscillations through the olivocerebellar loop. A schematic of the interconnections between ION, PC, and DCN cells mediated by disynaptic connections through the red nucleus (RN) is provided (a) along with the simulated spiking activity of an ION neuron (black lines; b and c), PCs (d and e), and the DCN (f and g) under normal, tremor-free condition (b, d, and f) and ET condition (i.e., yellow circle in Fig. 3A) (c, e, and g). Green lines in b and c denote the postsynaptic glutammatergic currents to the ION neuron mediated by the RN. The red vertical lines denote the onset time for the ION neuron’s action potential. This action potential elicits a complex spike in the PCs, which hyperpolarizes the DCN and causes a posthyperpolarization rebound burst (f and g). The lag Δ_{ION→DCN_burst} between the ION neuron’s action potential and the DCN rebound predicts whether the ION neuron will spike again and corresponds to the parameter T in A and B. Time scales in f and g also apply to b and d and to c and e, respectively. (E) Histogram of the values of Δ_{ION→DCN_burst} measured under nontremor (blue bars) and ET conditions (red bars). For each condition, data were obtained from the simulations reported in Fig. 3A.

Fig. 5.

Effect of Vim deep brain stimulation (DBS) under cerebellar GABAergic dysfunctions. (A) Power spectral density (PSD) of Vim under ET condition (i.e., yellow circle in Fig. 3A) with 185-Hz DBS of the Vim (ET + Vim DBS; black line) and without Vim DBS (ET; red line). Note the logarithmic scale on the axes. (B) Two-dimensional map depicting the region of the parameter space (R, τ^PC→DCN) where tonic spiking activity in the ION neurons is observed under 185-Hz DBS of the Vim along with the average ION firing rate. The red dashed lines indicate the boundary of the tremor region when no DBS was applied. The upper right region with no sustained ION firing is due to overly strong DCN rebound firing, which is facilitated as a result of DBS and is not compensated by the postsynaptic inhibitory currents elicited by the PC complex spikes. The PSD curves in A and the 2-D map in B are obtained from 4,000-ms simulations of the CCTC model (first 1,000 ms are discarded to let model instances reach steady-state conditions). (C) Average interburst interval (IBI) for the DCN in response to Vim DBS at different frequencies (black dots) and least-square fourth order polynomial fit (red curve, coefficient of determination for the fitting R²= 0.73). (Inset) Coefficient of variation (CoV) of the IBI values under Vim DBS (black dots) and least-square fourth-order polynomial fit (red curve; R² = 0.41). (D) Average firing rate of the ION neurons under Vim DBS at different frequencies (black dots) and fourth-order polynomial fit (red curve; R² = 0.48). Each data point in C and D is obtained from a 5,000-ms simulation of the CCTC model (first 1,000 ms were discarded for initialization) under ET condition.

Fig. 6.

Scale-up model (i.e., 425- instead of 85-single compartment model) under normal, tremor-free condition (A, C, E, and G) and ET condition (i.e., yellow circle in Fig. 3A) (B, D, F, and H), respectively. (A) A current pulse (duration, 20 ms; amplitude, 10 pA) was applied to all 40 ION neurons simultaneously (red triangle), which led to synchronous firing of ION neurons for 2–3 cycles but no tonic spiking activity. (B) The same current pulse as in A was applied to 16 ION neurons simultaneously under ET condition (red triangle) and caused tonic spiking activities that spread to the entire ION neuron population. (C–F) Spiking pattern of the PC, DCN, and NO neurons in response to the exogenous pulse to the ION neurons in A (C and E) and in B (D and F). (G and H) Power spectrogram of the Vim in response to the pulse to the ION neurons in A (G) and in B (H). Note that under ET condition, a prominent 7–8 Hz oscillation emerged in the spectrogram after the ION neurons were engaged into tonic spiking. Time scales in G and H also apply to A, C, and E and B, D, and F, respectively.