External drive to inhibitory cells induces alternating episodes of high- and low-amplitude oscillations

Abstract

Electrical oscillations in neuronal network activity are ubiquitous in the brain and have been associated with cognition and behavior. Intriguingly, the amplitude of ongoing oscillations, such as measured in EEG recordings, fluctuates irregularly, with episodes of high amplitude alternating with episodes of low amplitude. Despite the widespread occurrence of amplitude fluctuations in many frequency bands and brain regions, the mechanisms by which they are generated are poorly understood. Here, we show that irregular transitions between sub-second episodes of high- and low-amplitude oscillations in the alpha/beta frequency band occur in a generic neuronal network model consisting of interconnected inhibitory and excitatory cells that are externally driven by sustained cholinergic input and trains of action potentials that activate excitatory synapses. In the model, we identify the action potential drive onto inhibitory cells, which represents input from other brain areas and is shown to desynchronize network activity, to be crucial for the emergence of amplitude fluctuations. We show that the duration distributions of high-amplitude episodes in the model match those observed in rat prefrontal cortex for oscillations induced by the cholinergic agonist carbachol. Furthermore, the mean duration of high-amplitude episodes varies in a bell-shaped manner with carbachol concentration, just as in mouse hippocampus. Our results suggest that amplitude fluctuations are a general property of oscillatory neuronal networks that can arise through background input from areas external to the network.

Figure 1. Amplitude fluctuations in carbachol-induced oscillations recorded in the infralimbic region of the PFC.

(a) Extracellular field potential (top) at one of the 64 electrodes of a multi-electrode array, and wavelet transform (bottom). Episodes of high power are observed to alternate with episodes of low power. Color indicates power of oscillations. (b) Close up of the activity in (a).

Figure 2. Quantification of high-amplitude episodes (HAEs) and low-amplitude episodes (LAEs) in network oscillations.

(a) Raster diagram showing the firing times (indicated by dots) of the excitatory cells. (b) Corresponding firing-rate histogram. The maximal firing rate (red bar) per oscillation period T is successively determined by using a sliding time window of length T. The time axis is discretized into bins of 6 ms. (c) A spline polynomial is interpolated through the maximal firing rates (red bars) per oscillation period. Time intervals during which the curve exceeds the HAE threshold (dashed line) are considered HAEs, otherwise LAEs. (See further Methods.)

Figure 3. Amplitude fluctuations in oscillations generated in the neuronal network model, with high-amplitude episodes (HAEs) alternating with low-amplitude episodes (LAEs).

The dynamics of alternating HAEs and LAEs occurred in both the excitatory and the inhibitory population. Representative activity is shown separately for the excitatory and the inhibitory population as raster diagrams of cell firing (a, d), firing-rate histograms with interpolated spline polynomials (b, e; red lines on top of histograms), and wavelet transforms of the firing-rate histograms (c, f). The episodes in which the interpolated polynomials (b, e) exceeded the dashed horizontal line (the HAE threshold) are considered HAEs, otherwise LAEs. The excitatory and the inhibitory population exhibited similar dynamics with respect to HAE-LAE alternations. The panels on the right are zoomed-in intervals indicated by the red horizontal lines below the x-axes. The external input to the inhibitory cells consisted of a constant depolarizing current (CDC) and a train of action potentials (AP) activating an excitatory synapse. The excitatory cells received external input only in the form of CDC input.

Figure 4. Alternations between episodes of high- and low-amplitude oscillations occurred only when both the inhibitory (I) and the excitatory (E) cells received an external constant depolarizing current (CDC) and at least the inhibitory cells received a train of external action potentials (AP) activating an excitatory synapse.

Each panel shows the distribution of oscillation amplitudes (in terms of number of spikes per time bin) in the excitatory population for the nine different combinations of external input to the network. Thus, alternations between high-amplitude episodes (HAEs) and low-amplitude episodes (LAEs) occurred only when the distribution contained oscillation amplitudes at both sides of the HAE threshold (the dotted vertical red line; scenarios f and h). The distributions were normalized by dividing the number of time bins by the maximal number of time bins in the distribution.

Figure 5. Alternating episodes of high- and low-amplitude oscillations for two different values of AP randomness.

Raster diagrams of cell firing (a, d), firing-rate histograms with interpolated spline polynomials (b, e) and wavelet transform of the firing-rate histograms (c, f) for the excitatory population for AP randomness 0.7 (a–c) and 0 (d–f) in the minimal stimulation protocol. For rand = 0, APs were simultaneously delivered to all I cells at regular intervals of 90 ms.

Figure 6. The more random the AP train, the shorter the mean HAE duration and the longer the mean LAE duration.

Mean HAE and LAE durations (SEM) in the excitatory population (a, b) and the inhibitory population (c, d) for different values of AP randomness. Red lines, exponential fits.

Figure 7. Alternating episodes of high- and low-amplitude oscillations for two different values of AP frequency.

Raster diagrams of cell firing (a, d), firing-rate histograms with interpolated spline polynomials (b, e), and wavelet transforms of the firing-rate histograms (c, f) for the excitatory population for AP frequency is 20 Hz (a–c) and 7.69 Hz (d–f) in the minimal stimulation protocol. For an AP frequency of 20 Hz, the HAEs were much shorter and had a lower amplitude than for 7.69 Hz. The dashed horizontal line is the HAE threshold.

Figure 8. The higher the AP frequency, the shorter the mean HAE duration and the longer the mean LAE duration.

Mean HAE and LAE durations (SEM) in the excitatory population (a, b) and the inhibitory population (c, d) for different values of AP frequency. Red lines, exponential fits.

Figure 9. During a LAE, for both the excitatory and the inhibitory population, cell firing is less synchronous.

This is revealed by the spread of activity over more time bins and the diminished overlap in membrane potential traces. In addition, fewer cells are firing during a LAE. Shown are the raster diagram of cell firing (a, d), the firing rate histogram with the spline polynomial (b, e), and the cell membrane potentials (c, f) of and interval of activity from Fig. 3. Horizontal dashed line, HAE threshold.

Figure 10. APs can disrupt synchrony among I cells, causing a LAE.

(a) Red, external spikes (AP). Blue, inhibitory spikes. (top) AP frequency was the same as the frequency of the ongoing oscillation (17.63 Hz). If the first AP was delivered (at t_onset = 330 ms) when the membrane potential of the I cells was close to the firing threshold (between 0 and 0.7 mV), I cell firing was slightly advanced, but cells kept firing in synchrony. (middle panel) If the first APs was delivered when the membrane potential of the I cells was further below firing threshold (between 1 and 1.5 mV), I cell firing was reset and temporarily lost synchrony. (bottom) If AP frequency was lower than the frequency of the ongoing oscillation, the likelihood of APs resetting I cell firing increased, generating HAE-to-LAE transitions. (b) The firing pattern of a representative I cell for the different cases in (a). (c) The APs advanced the firing of the I cells compared with the expected firing dictated by the ongoing oscillation. The advancement depended on the cell's membrane potential at the time of AP arrival. The vertical line indicates the firing threshold.

Figure 11. The distributions of HAE duration in the model match those observed for carbachol-induced oscillations in rat prefrontal cortex.

(a) The model distributions (red lines) in the excitatory population and the empirical distributions (histograms) observed in the prelimbic (PrL) and infralimbic (IL) regions of the prefrontal cortex . In each region of the PFC, both fast and slow oscillations occurred, which both exhibited HAE-LAE alternations. The oscillation frequency in the model was adjusted by changing the IPSC decay time τ. The distributions were normalized by dividing the number of HAEs within a given bin by the total number of HAEs in the distribution. (b) The cumulative distributions of the model data (red lines) and the empirical data (black lines). The model distributions are not significantly different (Kolmogorov-Smirnov test) from the empirical distributions. (c) The distributions generated by a Markov process (green line) accurately describe the empirical distributions (histograms). Parameter is the probability that the first oscillation cycle with high amplitude (upstate) in a HAE is followed by an upstate; is the probability that an upstate in the rest of the HAE is followed by an upstate. See further main text.

Figure 12. In the model, as in mouse hippocampus, the mean duration of high-amplitude episodes varies in a bell-shaped manner with CDC input or carbachol concentration.

(a) For different values of the HAE threshold, the mean duration of the HAEs in the model for the excitatory population as a function of CDC input. The CDC input represents cholinergic input. (b) The bell-shaped relationship between cholinergic input and mean HAE duration was confirmed experimentally by using the cholinergic agonist carbachol (CCh) applied to mouse hippocampal slices. A HAE was defined as an episode in which the amplitude envelope of the bandpass-filtered oscillations was above 0.5*the mean oscillation amplitude . For a given HAE threshold, the mean HAE durations were normalized by dividing by the mean HAE duration obtained for the lowest CCh concentration different from zero. Fig. b modified from .