The emergence of two anti-phase oscillatory neural populations in a computational model of the Parkinsonian globus pallidus - PubMed (original) (raw)
The emergence of two anti-phase oscillatory neural populations in a computational model of the Parkinsonian globus pallidus
Robert Merrison-Hort et al. Front Comput Neurosci. 2013.
Abstract
Experiments in rodent models of Parkinson's disease have demonstrated a prominent increase of oscillatory firing patterns in neurons within the Parkinsonian globus pallidus (GP) which may underlie some of the motor symptoms of the disease. There are two main pathways from the cortex to GP: via the striatum and via the subthalamic nucleus (STN), but it is not known how these inputs sculpt the pathological pallidal firing patterns. To study this we developed a novel neural network model of conductance-based spiking pallidal neurons with cortex-modulated input from STN neurons. Our results support the hypothesis that entrainment occurs primarily via the subthalamic pathway. We find that as a result of the interplay between excitatory input from the STN and mutual inhibitory coupling between GP neurons, a homogeneous population of GP neurons demonstrates a self-organizing dynamical behavior where two groups of neurons emerge: one spiking in-phase with the cortical rhythm and the other in anti-phase. This finding mirrors what is seen in recordings from the GP of rodents that have had Parkinsonism induced via brain lesions. Our model also includes downregulation of Hyperpolarization-activated Cyclic Nucleotide-gated (HCN) channels in response to burst firing of GP neurons, since this has been suggested as a possible mechanism for the emergence of Parkinsonian activity. We found that the downregulation of HCN channels provides even better correspondence with experimental data but that it is not essential in order for the two groups of oscillatory neurons to appear. We discuss how the influence of inhibitory striatal input will strengthen our results.
Keywords: HCN; Parkinson's disease; deep-brain stimulation; downregulation; globus pallidus; oscillation; synchronization.
Figures
Figure 1
An overview of the model. Integrate-and-fire STN neurons, modulated by an approximately 1 Hz rhythm, provide excitatory synaptic input to a population of GP neurons. Inhibitory local synaptic connections between GP neurons have random connectivity.
Figure 2
Properties and spiking activity of STN neurons. (A) Example cross-correlation between two STN neuron spike trains on a short time window (30 bins, 3 ms each) shows independent firing. (B) Longer time window reveals slow (1300 ms) oscillations (400 bins, 20 ms each). (C) Spiking activity of STN neurons under healthy conditions. (D) Increased intensity of active-phase firing under Parkinsonian conditions. In (C,D) the background is shaded to show the active (pink) and inactive (blue) phases of the SWA cycles. (A,B) are normalized using the procedure described in Brillinger (1976): if X i is the unscaled spike count in histogram bin i then the scaled value X'i is given by: X'i = TXi2hNANB, where T is the total simulation time, h is half the width of a cross-correlation bin and N A and N B are the total spike counts for each spike train. A normalized value of 1 indicates that there is no correlation at a particular delay, while deviations from 1 indicate positive or negative correlations. The horizontal bars show the 95% confidence interval for significant correlations (Brillinger, 1976).
Figure 3
Response of a typical isolated model GP neuron to different current injections. (A) Neuron with normal HCN channel density. Depolarizing current causes fast, regular spiking (green trace), while hyperpolarizing current reveals a sag in membrane potential and rebound firing (red, cyan, and purple traces). With no current injection the neuron fires regularly at approximately 22 Hz (blue trace). (B) Neuron with HCN channels removed. Sag in membrane potential is lost and pacemaking is slowed. Note the difference in scale for the injection currents between (A) and (B).
Figure 4
Catergorization and activity of neurons under healthy conditions. (A) The average number of GP neurons in each category across all trials (n = 12), showing that most cells do not display prominent modulation by SWA (error bars show standard deviation). (B) Raster plot showing the spiking activity of TI, TA and NM neurons in one representative trial. The spike trains above the solid gray line are from neurons whose average spike phase is in the active part of the SWA cycle (light pink shaded background), whilst those below the line have average phases in the inactive part of SWA (light blue shaded background). The spike trains are ordered such that those closer to the solid gray line have lower confidence measures than those further away. The dashed gray lines show the confidence measure boundaries that divide neurons classified as NM from those classified as TI or TA (this boundary is set at 0.1).
Figure 5
Catergorization and activity of neurons under Parkinsonian conditions. (A) The average number of GP neurons in each category across all trials (n = 12), showing that most neurons start to display SWA-modulated firing patterns, either in-phase (TA) or anti-phase (TI). (B) Raster plot of Parkinsonian GP neuron activity (description as in Figure 4B).
Figure 6
Average cell properties by categorization across all GP neurons from all trials (n = 1200). (A) Average firing rate is rather variable but is in general slightly lower for TI neurons. (B) Maximum conductance of the persistent sodium channel (NaP) which underlies pacemaking. Quiet neurons can be easily categorized as those with very low NaP conductance. (C) Average total maximum conductance due to excitatory synapses. TA neurons receive more excitation on average, but it is highly variable.
Figure 7
Phase histograms showing the distribution of spikes relative to SWA phase grouped by categorization (Top: TI, Middle: TA, Bottom: NM), demonstrating the effects of HCN downregulation. Numbers indicate the number of spikes in each bin (65 ms bin width). Data are shown from two sets of 12 simulations, one with the HCN downregulation mechanism enabled (left) and one with it disabled (right). The background of each diagram is shaded to illustrate the active (pink, 500 ms) and inactive (blue, 800 ms) parts of the SWA cycle. Downregulation reduces TA neuron firing during the inactive phase (Middle), increases TI firing during the inactive phase (Top) and decreases NM firing (Bottom). Spikes from the latter half of simulations (6.5 s out of 13 s) from all neurons (except those categorized as QU) were used to generate the diagrams. The orientation of the red bars shows the average spike phase and their length shows the phase confidence measure (ω) as a proportion of the total radius.
Figure 8
Spike cross-correlation diagrams showing the relationship between STN and GP neuron firing when STN input is modulated at approximately 14 Hz (70 ms period). (A) Typical average cross-correlation between all STN neurons and a single GP neuron showing synchronized in-phase firing. (B) STN-GP cross-correlation for a (rare) GP neuron that shows firing that is anti-phase to the β rhythm. Normalization is as in Figure 2 (Brillinger, 1976) and the shaded area shows the standard deviation across STN neurons.
References
- Brillinger D. R. (1976). Measuring the association of point processes: a case history. Am. Math. Mon. 83, 16–22 10.2307/2318824 -DOI
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