Cortico-Striatal Cross-Frequency Coupling and Gamma Genesis Disruptions in Huntington’s Disease Mouse and Computational Models

Time series analysis and delta band phase difference during quiet rest. A. Time series analysis. Raw LFP simultaneous recordings from 2 electrodes (X₁, X₂) are processed separately. X₁ is band-pass filtered at 25-50 Hz to extract low-gamma signal γ₁, and gamma events (red circles) are extracted from the envelope of this gamma signal (green trace). X₂ is low-pass filtered at 4 Hz cutoff to extract the delta band activity (δ₂), of which the instantaneous phase is extracted using the angle of the Hilbert transform (H(δ₂)). The phase thetai at which gamma events occur on the delta oscillation is derived from the value of H(δ₂) at the time of the event ti. Traces taken from WT animal #1 for illustrative purpose. B. Example of projections onto the unit circle of all delta phases at which gamma events occur, for one pair of channels. Each red circle indicates the phase of the event. The distribution of phases at which gamma events occur is shown in a polar histogram (orange). The arrow pointing from the origin represents vector strength of phase-locking (length) and mean phase of gamma events (orientation). Left: channel with strong gamma event delta phase-locking. Right: channel without gamma event delta phase-locking. Sample phases from time series in A) are denoted in purple. C. Circular distributions of delta phase difference across channels located in cortex only (Ctx-Ctx, blue), in cortex and striatum (Ctx-Str, green) and in striatum only (Str-Str, red). Animal types are denoted by different line types (legend inset). Delta phase difference between two white noise signals is shown in gray. 0° stands for zero phase difference i.e. synchronization of delta rhythm oscillations across channels.

Delta phase and amplitude modulations are comparable across cortex and striatum. Top: Phase modulation computed as the slope of the unwrapped analytic phase in the delta band, averaged over cortical (blue squares) and striatal (red circles) channels for each animal. Larger symbols on the right indicate the mean slope, corresponding to the mean frequency of the filtered signal (note that 1Hz = 2π rad/s). The degree of phase modulation resides in deviations from the mean, indicated by error bars. Bottom: Amplitude modulation (AM) computed as the standard deviation (SD) of the squared analytic amplitude in the delta band for each cortical (blue squares) and striatal (red circles) channels. Larger symbols on the right indicate the averaged SD across cortical channels per animal (see Methods), a value close to 0 indicates weak AM and deviation from 0 indicates stronger AM signals. Note that some animals do not have channels in every structure (no symbols), or have only one channel per structure (zero SD).

Phase-locking of gamma-events to delta rhythm in WT and R6/2 animals. Mean phase and strength of gamma-event phase-locking to delta oscillations is displayed in a polar plot for each pair of channels (one arrow/pair) across WT (left, 13 animals) and R6/2 (middle, 12 animals), drawn from an average total of 4 channels/animal. The mean vector across animals from the same strain is shown in black, and its norm is magnified by 10 to appear clearly with respect to individual pairs. Polar histograms show the distribution of all gamma events from all channels. Color-coded arrows represent the vector strength and orientation for each pair of channels, with statistically significant vs. insignificant (p < 0.05 vs. p > 0.05) phase-locking indicated by colors blue vs. cyan (Ctx-Ctx), green vs. yellow (Ctx-Str) and red vs. magenta (Str-Str). (Short arrows from insignificant vectors are nearly invisible). Inset histograms on top of each polar plot show (left) statistical tests for unimodality of the distribution (Uni) and the concentration of the distribution (K), and (right) the multimodality of the distribution (Multi) using the Hartigan’s Dip test (see methods).

Phase-locking and inter-gamma events statistics in WT and Q175 animals. Same statistics as Fig. 3 and 4, computed for the Q175 animal strains. Left: Distribution of delta phases at each gamma event occurrence. Total number of gamma events extracted shown above polar plot as n. Histograms on sides of the polar plot indicate p-value of the statistical test for uni-modality (with concentration K) and multi-modality of the distribution, as computed by the Hartigan’s Dip Test (see methods). The mean vector across animals from the same strain is shown in black and its norm is magnified by 5 to appear clearly with respect to individual pairs. Middle: Mean probability distribution function (PDF) of inter-gamma events intervals across all electrodes from all animals. Standard deviation is indicated by error bars and a negative exponential is given as reference in black. Right: Correlation between gamma events for each electrode pairs (black circles) and mean (red circles) for each animal. Mean (open circle) and standard deviation (red bar) across animals from the same lineage are shown on the right-most of the x-axis.

Gamma events have highly variable correlation across channels and brain regions. Left: Pearson correlation coefficients between gamma events from each pair of channels (black) within cortex (squares), between cortex and striatum (triangles), and within striatum (circles). The mean correlation within an animal across channel pairs is color-coded (blue for Ctx-Ctx, green for Ctx-Str, red for Str-Str). Population averages across animals and their standard deviation are denoted by open symbols (right, off-axis) using the same symbols and color code. Mean correlation coefficients of shuffled intervals are filled. Middle: Coherence of signals from each pair of channels during gamma events (same color code as above), averaged over the low gamma frequency band 25-55 Hz and projected in polar coordinates from the complex plane (see Methods). Scattered points showing spread in phase from 0 rule out volume conduction at gamma frequency. Right: Probability density function (pdf) of inter gamma event intervals in a log-log scale for each cortical (blue) and striatal (red) channels are plotted for WT (top), R6/2 (bottom). Black line represent exponential distribution for reference.

Computational model of FSI network and cortical drive. A. Schematic of cortico-striatal FSI network model system. 27 cortical input are set in a 3 x 3 x 3 grid topographically projecting to a 27 x 27 x 27 grid of FSI units. FSI-to-FSI connectivity via gap junctions and GABAergic synapses is distance dependent (inset) and constrained by connection probabilities reported in the literature (Gittis et al. 2010). Extracellular fields are reconstructed by a modeled microelectrode array forming a grid of 64 channels (4x4x4) where each channel is spatially separated by ~750µm. B. Example of single FSI unit membrane potential time series (left), distribution of inhibitory synaptic weights (center) and an exemplar time-series of a single IPSP (right).

Spiking regimes of the modeled FSI network shows gamma-band population spikes embedded in the delta oscillation only when gap junctions are present. A. Power spectra of striatal LFP from experimental data. B. Power spectra of simulated LFP reconstructed from ~20,000 fast-spiking neurons (FSIs) with processed experimental cortical LFP, either without gap junctions (green) or with gap junctions (pink) between neurons. Shading denotes standard deviation. C. Spiking raster plots of neurons in one segment of striatum (receiving drive from one cortical unit) either with (pink) or without (green) gap junctions.

Gamma-band frequency peak shifts depending on the ratio between gap junction and synaptic coupling. A. Example power spectra of simulated LFP reconstructed from ~20,000 fast-spiking neurons (FSIs), displayed for 3 different combinations of gap junctions versus synaptic coupling strengths. The peak in the 2 top yellow spectrum corresponds to power spectrum peak of Q175 animals from Fig. 1B, the blue spectra on bottom corresponds to a combination of parameters that does not produce a significant gamma oscillation. Shading denote standard deviation. The white asterisk (*) denotes the parameter combination used in the remaining of the paper. B. Map of the parameter space exploration of gap junction coupling strength versus inhibitory synaptic strength in the FSI network model, where the color code quantifies the spectral peak frequency (>15 Hz). Blue entries corresponding to “N/A” represent simulations where either no gamma power was detected or the activity of the network was abnormal, e.g. completely silent or tonically firing at >100 Hz. All values are the mean of 10 simulations with random initial conditions. C. Same as A) but the spectrum in pink corresponds to that observed in R6/2 animals (Fig. 1B).

Cortico-FSI coupling strength can transition network from WT to HD gamma phenotype. A. Gamma power (averaged over the 25-55 Hz band of the spectra) of simulated LFP for different cortico-FSI coupling gain levels, with input drive taken from 4 different R6/2 (top) and WT (bottom) animal recordings. Bold traces correspond to spectrum shown in B. B. Power spectrum from simulated FSIs LFP with increasing strengths of cortical drive extracted from R6/2 animal 4 (top) and WT animal 9 (bottom) recordings.

Time-frequency comparison between model and experimental LFP. Wavelet analysis of the LFP from experimental recordings (left) and reconstructed from the model (right), computed between 0 and 100 Hz (step size: 0.5 Hz) for a random epoch of 10s of quiet rest. Wavelet coefficients are normalized to sum at 1. LFP experimental time series taken from R6/2 animal 10 striatal recording, and simulated LFP with scaling factor CtxFSI=1.