Correlation transfer from basal ganglia to thalamus in Parkinson's disease

Abstract

Spike trains from neurons in the basal ganglia of parkinsonian primates show increased pairwise correlations, oscillatory activity, and burst rate compared to those from neurons recorded during normal brain activity. However, it is not known how these changes affect the behavior of downstream thalamic neurons. To understand how patterns of basal ganglia population activity may affect thalamic spike statistics, we study pairs of model thalamocortical (TC) relay neurons receiving correlated inhibitory input from the internal segment of the globus pallidus (GPi), a primary output nucleus of the basal ganglia. We observe that the strength of correlations of TC neuron spike trains increases with the GPi correlation level, and bursty firing patterns such as those seen in the parkinsonian GPi allow for stronger transfer of correlations than do firing patterns found under normal conditions. We also show that the T-current in the TC neurons does not significantly affect correlation transfer, despite its pronounced effects on spiking. Oscillatory firing patterns in GPi are shown to affect the timescale at which correlations are best transferred through the system. To explain this last result, we analytically compute the spike count correlation coefficient for oscillatory cases in a reduced point process model. Our analysis indicates that the dependence of the timescale of correlation transfer is robust to different levels of input spike and rate correlations and arises due to differences in instantaneous spike correlations, even when the long timescale rhythmic modulations of neurons are identical. Overall, these results show that parkinsonian firing patterns in GPi do affect the transfer of correlations to the thalamus.

Keywords: Parkinson's disease; basal ganglia; bursting; correlation; oscillations; point process; synchrony; thalamus.

Figure 1

Model schematic and basic behavior. (A) Diagram of the connectivity and inputs used for our computational models. Here, λ denotes a time-dependent rate, c a shared spike fraction, and μ a constant rate. (B) Sample response of the conductance-based TC neuron model to the injection of a 5 ms pulse of 3 pA current.

Figure 2

Example model behaviors for each of the four types of GPi input to thalamus: normal, oscillatory, bursty, and oscillatory bursts. (A) Sample GPi firing rates. (B) Corresponding examples of GPi spike trains. (C) T-current inactivation gate, h_T, for the conductance-based thalamic model. (D) Spike train of conductance-based thalamic model neuron in response to Poisson excitatory input at 20 spikes per second in addition to the inhibitory input shown above.

Figure 3

Escape properties of neurons with spike correlation c and escape probability p(t) that depends on well height U(t). (A) Oscillatory well height modulation. (B) Oscillatory bursty well height modulation. (C) Joint escape probabilities of two neurons in the interval (t, t + dt).

Figure 4

Input-output correlation relationships and correlation susceptibility. (A) Output correlation vs. input correlation for T = 95 ms, including zoomed view near the origin (insets). Curves were generated by varying cin steps from 0 to 1 and computing ρ_in and ρ_out for each model, for each c. (B) Correlation susceptibility (S) vs. T. The inset in (B) shows the oscillations in the susceptibility when the thalamic neurons receive oscillatory inputs. The conductance-based model (left), and the IFB model (right) are both shown. The following input conditions are used: normal (blue), oscillatory (green), bursty (red), and oscillatory bursts (black). Error bars in the insets in (A) and confidence bands on the correlation susceptibility in (B) show 98% confidence intervals, calculated using bootstrapping techniques.

Figure 5

Oscillation frequency of S tracks GPi oscillation frequency while oscillation amplitude of S depends non-monotonically on GPi oscillation frequency. (A) Oscillatory bursts in the inputs from GPi to the conductance-based thalamic model. (B) Non-bursty oscillations in GPi inputs to the conductance-based thalamic model. Frequencies are 10 Hz (dark blue), 8 Hz (red), 6 Hz (green), 4 Hz (black), 2 Hz (tan), 1 Hz (light blue), and 0.5 Hz (green). Note that while two of the curves are colored green, the 0.5 Hz green curve is qualitatively similar to the 1 Hz curve and thus can be clearly distinguished from the 6 Hz green curve.

Figure 6

Removing the T-current (dashed lines) affects spike triggered average but not correlation susceptibility. (A) Spike triggered averages. (B) Correlation susceptibility. GPi firing patterns used are: oscillatory (green), bursty (red), and oscillatory bursts (black).

Figure 7

Correlation functions of the conductance-based model spike trains. Autocorrelation (red) and cross-correlation (blue) functions with (A) Normal GPi inputs. (B) Oscillatory GPi inputs. (C) Bursty GPi inputs. (D) Oscillatory bursty GPi inputs.

Figure 8

Oscillations of ρ obtained from calculations on the point process model match those in ρ_out from thalamic model simulations. (A) Comparison of correlation coefficients for the voltage-based thalamic models (conductance-based model, blue; IFB model, red) with input correlation of c = 0and the point process model (black) with c = 0.08. (B) As in (A) with c = 0.2 in the thalamic models. Non-bursty oscillatory inputs from GPi are shown on the left, oscillatory bursty inputs on the right; in both cases, oscillations occur at a frequency of 10 Hz. Parameters for the point process model are D = 0.1, U₀ = 1, and η = 0.4 for oscillatory inputs and D = 0.35, U₀ = 1, and η = 1 for oscillatory bursts.

Figure A1

Thalamic neuron interspike interval (ISI) distributions depend on the pattern of inhibitory inputs from GPi. (A) Conductance-based model. (B) IFB model. Normal (blue), oscillatory (green), bursty (red), and oscillatory bursty (black) patterns of GPi inputs are shown.

Figure A2

Power spectra and cross-spectra of GPi and thalamic spike trains. (A) Spike train power spectra. (B) Spike train cross-spectra. Normal (blue), oscillatory (green), bursty (red), and oscillatory bursty (black) patterns of GPi inputs are shown.