Synchronized Beta-Band Oscillations in a Model of the Globus Pallidus-Subthalamic Nucleus Network under External Input

Abstract

Hypokinetic symptoms of Parkinson's disease are usually associated with excessively strong oscillations and synchrony in the beta frequency band. The origin of this synchronized oscillatory dynamics is being debated. Cortical circuits may be a critical source of excessive beta in Parkinson's disease. However, subthalamo-pallidal circuits were also suggested to be a substantial component in generation and/or maintenance of Parkinsonian beta activity. Here we study how the subthalamo-pallidal circuits interact with input signals in the beta frequency band, representing cortical input. We use conductance-based models of the subthalamo-pallidal network and two types of input signals: artificially-generated inputs and input signals obtained from recordings in Parkinsonian patients. The resulting model network dynamics is compared with the dynamics of the experimental recordings from patient's basal ganglia. Our results indicate that the subthalamo-pallidal model network exhibits multiple resonances in response to inputs in the beta band. For a relatively broad range of network parameters, there is always a certain input strength, which will induce patterns of synchrony similar to the experimentally observed ones. This ability of the subthalamo-pallidal network to exhibit realistic patterns of synchronous oscillatory activity under broad conditions may indicate that these basal ganglia circuits are directly involved in the expression of Parkinsonian synchronized beta oscillations. Thus, Parkinsonian synchronized beta oscillations may be promoted by the simultaneous action of both cortical (or some other) and subthalamo-pallidal network mechanisms. Hence, these mechanisms are not necessarily mutually exclusive.

Keywords: Parkinson's disease; basal ganglia; globus pallidus; oscillations; subthalamic nucleus; synchronization.

Figure 1

Model network. Arrows indicate connection patterns between cells (solid line for excitatory synapses; dashed line for inhibitory synapses). Applied current I_STN(t) is applied to all STN neurons.

Figure 2

Examples of firing activity of an STN neuron, LFP, and the same signals filtered in the beta band for I_app = 7, g_syn = 0.5 with external input ${\mathbf{I}}_{\mathbf{S}\mathbf{T}\mathbf{N}}\left(\mathbf{t}\right)=\mathbf{A}\text{sin}\left(\frac{2\pi {\omega }_0}{1000}\mathbf{t}\right)$, where A = 7 and ω₀ = 13. (A) Presents the stimulation signal. (B) Presents spiking in an STN neuron (black) and spiking signal filtered in the beta band (red). (C) Presents model LFP signal (black) and LFP filtered in the beta band (blue). Arbitrary amplitude units are used.

Figure 3

Effects of periodic sine input ($\mathbf{A}\text{sin}(\frac{2\pi {\omega }_0}{1000}\mathbf{t})$) on STN-GPe network for fixed g_syn = 0.5 and three different values of I_app. The color and size of squares in the amplitude-frequency space characterize the synchronized dynamics in the network. Color indicates the number of principal components in the PCA capturing 80% of variability of the dynamics (see Methods): red is 1–3 components (most synchronous), green is 4–5 components, blue is 6–7 components, black is 8–10 components (least synchronous). The larger squares represent dynamics for which the model phase space is similar to the one reconstructed from the experimental data (see Methods). (A) I_app = 5. (B) I_app = 7. (C) I_app = 9.

Figure 4

The minimal amplitude of the input signal required to have a specific number of principal components in the network's dynamics. (A) Minimal amplitude to get 3 components (red area in Figure 3). (B) Minimal amplitude to get 5 components (green area in Figure 3). Different line types represent different values of I_app: solid is I_app = 5, dashed is I_app = 7, and dotted is I_app = 9.

Figure 5

Effects of periodic input on STN-GPe network for fixed I_app = 5 and different values of g_syn. Color and size of squares in the amplitude-frequency space characterize the synchronized dynamics in the network as in Figure 3. The left plot is the same as the left plot in the Figure 3 because they correspond to the same parameter values. (A) g_syn = 0.5. (B) g_syn = 0.7. (C) g_syn = 0.9.

Figure 6

The minimal amplitude of the input signal required to have a specific number of principal components in the network's dynamics. (A) Minimal amplitude to get 3 components (red area in Figure 5). (B) Minimal amplitude to get 5 components (green area in Figure 5). Different line types represent different values of g_syn: solid is g_syn = 0.5, dashed is g_syn = 0.7, and dotted is g_syn = 0.9.

Figure 7

Effects of noisy periodic input on STN-GPe network for fixed g_syn = 0.5 and different values of I_app. Color and size of squares in the amplitude-frequency space characterize the synchronized dynamics in the network as in Figure 3. (A) I_app = 5. (B) I_app = 7. (C) I_app = 9.

Figure 8

The minimal amplitude of the input signal required to have a specific number of principal components in the network's dynamics for fixed g_syn = 0.5. (A) Minimal amplitude to get 3 components (red area in Figure 7). (B) Minimal amplitude to get 5 components (green area in Figure 7). Different line types represent different values of I_app: solid is I_app = 5, dashed is I_app = 7, and dotted is I_app = 9.

Figure 9

Effects of a noisy periodic input on STN-GPe network for fixed I_app = 5 and different values of g_syn. Color and size of squares in the amplitude-frequency space characterize the synchronized dynamics in the network as in Figure 3. The left plot is the same as the left plot in the Figure 7 because they correspond to the same parameter values. (A) g_syn = 0.5. (B) g_syn = 0.7. (C) g_syn = 0.9.

Figure 10

The minimal amplitude of the input signal required to have a specific number of principal components in the network's dynamics for fixed I_app = 5. (A) minimal amplitude to get 3 components (red area in Figure 9). (B) minimal amplitude to get 5 components (green area in Figure 9). Different line types represent different values of g_syn: solid is g_syn = 0.5, dashed is g_syn = 0.7, and dotted is g_syn = 0.9.

Figure 11

Comparing the effects of sinusoidal input (A) to the model network and input derived from EEG recordings over motor cortex (B). Color and size of squares in the amplitude-frequency space characterize the synchronized dynamics in the network as in Figure 3.