Modulation of high frequency by low-frequency Oscillations in the basal ganglia

Modulation of beta band fioscillatory activity (15-30 Hz) by delta band oscillatory activity (1-3 Hz) in the cortico-basal ganglia loop is important for normal basal ganglia functions. However, the neural mechanisms underlying this modulation are poorly understood. To understand the mechanisms underlying such frequency modulations in the basal ganglia, we use large scale subthalamo-pallidal network model stimulated via a delta-frequency input signal. We show that inhibition of external Globus Pallidus (GPe) and excitation of the Subthalamic nucleus (STN) using the delta-band stimulation leads to the same delta-beta interactions in the network model as the experimental results observed in healthy basal ganglia. In addition, we show that pathological beta oscillations in the network model decorrelates the delta-beta link in the network model. In general, using our simulation results, we propose that striato-pallidal inhibition and cortico-subthalamic excitation are the potential sources of the delta-beta link observed in the intact basal ganglia.


Introduction
Modulated high-frequency oscillations by low-frequency oscillations in the brain continue to provide important clues about healthy and pathological neuronal activities [1]. More specifically, modulation of beta frequency oscillations (i.e. 15-30 Hz) by delta frequency oscillations (1-3 Hz) is an indication of healthy basal ganglia [2, 3, and 4]. It has been shown that beta power of the Local Field Potential (LFP) data recorded from GPe in the basal ganglia is positively correlated with delta power in the healthy state. However, such positive correlation does not exist in Parkinson's disease (PD) state [5]. This is accompanied by reduction in information processing capability of the basal ganglia [6, 7, 8, 9, and 10].
The underlying mechanism of such positive correlation between delta-beta band neuronal activities in the healthy basal ganglia and how it is affected in the pathological state are still unknown. Here we show how delta band oscillations of the STN and GPe can modulate beta oscillations in a subthalamo-pallidal network model. Using our simulation results we also show that pathological PD-like beta oscillations in the network model lead to delta-beta decorrelation in the network model, similar to the experimental LFP data [5] 2  [11]. External input. Excitatory uncorrelated spike trains are used as external input to provide baseline activity of each population in the network model. These inputs were used to obtain realistic baseline firing rates in STN (∼15 Hz) and GPe (∼45 Hz), observed in the healthy state [12,13]. Simulation tools. All network simulations and data analysis were written in Python using PyNN as an interface to the simulation environment NEST [14].

Results
To understand the mechanisms underlying modulation of beta oscillations by delta oscillation in the basal ganglia, we exposed the network model to the delta band frequency stimulation (see Methods for more details). To study how stimulation of the network model in delta frequency band affects the network model dynamics, four different delta stimulation scenarios were considered: 1) excitation of STN, 2) inhibition of STN, 3) excitation of GPe, and 4) inhibition of GPe. Each stimulation scenario was individually investigated in the network model to see which one can lead to the same delta-beta dynamics observed in the experimental data [5].

Interactions between delta and beta band oscillations in the network model
Our simulation results show that excitation of the STN and inhibition of the GPe in delta frequency band can lead to the beta oscillations in the network model. The network beta oscillations emerged at the certain phase of the delta stimulation pattern (e.g. mainly around the peak ; Fig 2A, B). However, when the delta band stimulation was used to excite the GPe or to inhibit the STN, it could not generate beta oscillations in the network model (Fig 2C, D). Therefore, we conclude that the potential mechanism underlying experimentally observed the relationship between delta and beta band LFP oscillations can be delta band excitatory input to STN (i.e. through cortical drive) or inhibitory input to GPe (i.e. through striatal drive).

Fig.2. Response of the network model to the delta band sinusoidal stimulation. (A-D) STN
and GPe population firing rates (blue and red, respectively) in response to the delta band sinusoidal excitatory input to STN (A), inhibitory input to GPe (B), excitatory input to GPe (C), and inhibitory input to STN (D). The delta band stimulation is shown in yellow.
Computing the spectrograms of the GPe and STN population firing rates reveals the interplay between beta-band and delta-band oscillations. It is obvious from this analysis that maximum level of the beta power occurs at the delta peak. (Fig 4A, B, bottom). Such a relationship between delta and beta band oscillation has been reported in experimental studies in the healthy state which is shown in Fig 3 [5, 15].

Delta-beta relationship disappears in pathological state of the network model
The activity of the indirect striatal units pathologically increases in PD which leads to a strong striato-pallidal inhibition in the basal ganglia [16]. To simulate progress of PD in the network model, we increased the strength of the striato-pallidal inhibition from 0 Hz (healthy state) to 500 Hz (pathological state). It has previously been shown that such strong striato-pallidal inhibition leads to beta oscillations in the network model, similar to what has been observed in the basal ganglia of patients with PD [11]. Using our simulation results, we show that as beta power increases (i.e. during the progress of PD) the delta power decreases, consequently. In other words, strengthening the striatal inhibitory input to GPe in the network model leads to increase in pathological beta power and subsequently decrease in delta power (Fig 5). Therefore, in PD state of the network model the delta-beta relationship does not exist anymore, similar to the experimental results [5].

Conclusion
Using our simulation results, we conclude that delta-band excitation of STN (presumably through cortical drive) and inhibition of GPe (presumably through striatal drive) leads to the same relationship between delta and beta band oscillations in the network model as the experimental LFP results. Moreover, similar to the experimental results, we observed in our simulation results that the delta-beta relationship disappears in PD state of the network model.