Gap junction plasticity as a mechanism to regulate network-wide oscillations

Abstract

Cortical oscillations are thought to be involved in many cognitive functions and processes. Several mechanisms have been proposed to regulate oscillations. One prominent but understudied mechanism is gap junction coupling. Gap junctions are ubiquitous in cortex between GABAergic interneurons. Moreover, recent experiments indicate their strength can be modified in an activity-dependent manner, similar to chemical synapses. We hypothesized that activity-dependent gap junction plasticity acts as a mechanism to regulate oscillations in the cortex. We developed a computational model of gap junction plasticity in a recurrent cortical network based on recent experimental findings. We showed that gap junction plasticity can serve as a homeostatic mechanism for oscillations by maintaining a tight balance between two network states: asynchronous irregular activity and synchronized oscillations. This homeostatic mechanism allows for robust communication between neuronal assemblies through two different mechanisms: transient oscillations and frequency modulation. This implies a direct functional role for gap junction plasticity in information transmission in cortex.

Fig 1. Network synchrony depends on gap junction strength.

(A) The network consists of excitatory (E) and inhibitory (I) neurons. The neurons are coupled in an all-to-all fashion with chemical synapses. The inhibitory neurons are also connected by gap junctions (jagged green line). (B) Voltage response of one single excitatory (red line) / inhibitory (blue line) neuron to a sub-threshold oscillatory input current (see Methods). Excitatory neurons act as low-pass filters, whereas the inhibitory neurons show a resonance frequency in the gamma range. This resonance is in agreement with the network wide response observed by Cardin et al. 2009, when FS neurons are stimulated in the gamma range (black line, figure redrawn from [32] figure 3d). (C) Simulation of a pair of electrically coupled neurons N1 and N2, where N1 is voltage-clamped (red) such that it is hyperpolarized (light blue) and the potential of N2 is measured for different value of gap junction strength (γ = 3 and γ = 5). (D) Power of the main frequency component in the Fourier domain of the population activity (PA) of inhibitory neurons. The blue area denotes the lack of oscillations AI whereas the red area SR shows periodic oscillations in the spiking activity of inhibitory neurons. (E) Oscillation frequency of the network activity. The white area represents a region where the network is not oscillating and has no oscillation frequency. (F) Histogram of the oscillation frequency of population spiking activity. The values are contained in the γ range, from 30 to 60 Hz. (G) Ratio of bursting A_bursting over spiking A_spiking activity, averaged over 2 seconds. Bursting activity prevails in the light region and sparse firing dominates in the dark region. For the following Figures 1H and 1I, 100 ms of data is represented. (H) Raster plots of 100 FS neurons (blue) and 100 pyramidal neurons (red) for two values of the gap junction coupling, where dots represents spiking times and each line represents a neuron (note that the network E/I proportion is actually 80%/20%). Top raster plot shows asynchronous activity for low gap junction coupling and bottom raster plot shows synchronous activity in inhibitory and excitatory neuron populations, for strong gap junction coupling. (I) Membrane voltage traces of individual inhibitory neurons (dark blue) and population average (light blue, down-shifted) for different values of the gap junction coupling. Bursts appear for strong gap junction coupling on the peaks of the membrane voltage oscillations.

Fig 2. Model of gap junction plasticity: Bursting induces gLTD, spiking gLTP.

(A) Bursting protocol replicated from Haas et al. [16]. A current (red line, top panel) of 300 pA for 50 ms at 2 Hz and of -80 pA otherwise is injected into a pair of coupled neurons induces repeated bursting (blue line, middle panel, voltage trace). To quantify the amount of bursting, we low-pass filtered (b_i) the voltage trace, threshold it at θ_burst = 1.3 (discontinued dark line), and integrate. Light blue areas represent the periods during which bursts are detected and therefore gap junctions are depressed. (B) When neurons N1 and N2 spike sparsely (top panel, dark blue, first part of the stimulus), gap junctions are potentiated (bottom panel, green line, first part of the simulation), whereas when they are bursting, gap junctions are depressed (second part of the simulation). (C) Green dots show steady-state values of the mean gap junction coupling for the gLTP with soft bounds, for different values of the network drive along the y-axis. For slow gLTP, the steady-state can be found in the AI regime, where the power of the oscillations of the population spiking activity is low (blue area). (D) Network architecture: A step excitatory drive is fed to the network of E and I neurons (same network detailed on Fig 1, with plastic gap junctions) inducing gamma oscillations. The activity of the network is read out by a downstream population of 200 regular spiking cells. (E) Top panel, step excitatory drive fed to the networks. Second panel, evolution of the mean gap junction coupling. As the excitatory drive is delivered, a gamma oscillation appears, leading to an increase in bursting activity which is followed by a depression of the gap junctions, until the new fixed point is reached. Bottom panels, raster plots of the inhibitory neurons (blue, I1), excitatory neurons (red, E1) and read-out neurons (red, RON). 6 s of data is represented. (F) Top panel, step excitatory drive. Other panels, population activity of the read-out neurons in red, evolution of the mean gap junction coupling in light blue. Second panel, simulation with plastic gap junctions. The read-out neurons are the most active during the transient oscillations. Third panel, static gap junction coupling. The read-out neurons are active as long as the excitatory drive is high. Bottom panel, no gap junction coupling. The read-out neurons are not active. 10 s of data is represented.

Fig 3. Subnetworks having different frequency preferences can synchronize their activity if they share gap junctions.

(A) Both subnetworks have the same topology with all-to-all connected inhibitory and excitatory neurons. Inhibitory neurons have static gap junctions (GJs). The Gamma Network (GN) is connected to the Slow Network (SN) with a varying number of gap junctions. The time constant of the SN inhibitory neuron membranes is varied. (B) Frequency-transfer characteristics of one single inhibitory neuron to a sub-threshold oscillatory input current (see Methods) for different values of its membrane time constant τ_v. The sub-threshold resonance frequency decreases as τ_v increases. Data of Cardin et al. 2009 is also represented (black line, figure redrawn from [32] figure 3d). (C) Changing the single neuron sub-threshold resonance modifies the network oscillation frequency. Mean inhibitory membrane potential for τ_v = 17 ms (continuous line) and τ_v = 55 ms (dashed line). 100 ms of data is represented. (D) Relationship between single neuron resonance (black line) and network oscillation frequency (gray line). For the following figures E and F, for the tuples (Δf_res; Number of shared GJs), the upper (lower) triangle represents the value in the SN (GN). For panels E, F, H, I, the x-axis represents the number of cross-network gap junctions between the GN and SN. The y-axis represents the difference of resonance frequency between the GN and the SN. (E) Oscillation frequencies. We observe that the GN and the SN adopt the same oscillation frequency for low Δf_res and high number of shared gap junctions. (F) Phase differences between population activities of the GN and the SN, when they share the same frequency. Lighter squares denote parameters for which the phase difference is lower. The GN and the SN are considered in phase when the phase difference is zero. Dark blue squares describe a region that is excluded because the GN and the SN do not oscillate at the same frequency, therefore cannot be in phase. (G) Raster plots, where dots represent spiking times and each line represent a neuron, for small (first column) and large (second column) differences in Δf_res. For all raster plots, from top to bottom are represented excitatory and inhibitory neurons from the SN, then inhibitory and excitatory neurons from the GN. 100 neurons are shown for each population. When no gap junctions are shared (bottom row), both networks do not synchronize and are out-of-phase. With 40 shared gap junctions (top row), the networks synchronize and are in phase for small values of Δf_res. 100 ms of data is represented. (H) Mutual information between the PAs of the GN and SN. The increase in mutual information for the top row, where Δf = 21Hz, can be due to the fact the SN oscillates at half the frequency of the GN (which oscillates around 40Hz). (I) Pearson’s correlation of the PAs of the GN and SN. Comparing with panel H, there is high correlation when the GN and the SN are in phase.

Fig 4. Gap junction plasticity lets networks recover synchronization.

For all panels, the x-axis represents the number of cross-network gap junctions between GN and SN. The y-axis represents the difference of resonance frequency between the GN and the SN. The gap junctions are static from panels A to D and plastic from panels E to H. Values for the Gamma Network (resp. Slow Network) are represented by the lower (upper) triangles. The GN (SN) has weak (strong) initial mean GJ coupling. Shared GJs are initialized with mean coupling strength in the middle between those of the GN and the SN. (A) Oscillation power. The GN, with weak GJ coupling, shows weak or no oscillations. (B) Oscillation frequency. We observe that the GN and the SN oscillate at the same frequency only for high number of shared GJs. (C) Phase differences between PAs of the GN and the SN (as for Fig 3H). The GN and the SN stay mostly out-of-phase. (D) Correlation of the PAs of the GN and the SN. Except for the particular case where Δf_res = 0 and the number of shared GJs is high, the PAs of the GN and the SN show no correlation. (E) Oscillation power. Comparing with panel A, we observe that the oscillation power seems to match in both networks, with mostly the oscillation power of the GN (initially weak) increasing to the SN’s levels (initially strong). (F) Oscillation frequency. Comparing with panel B, we observe an extension of the region where the GN and the SN oscillate at the same frequency. (G) Phase differences between PAs of the GN and the SN. We observe here a large region where the GN and SN are in-phase. (H) Correlation of the PAs of the GN and the SN. Comparing with panel D, we observe a large extension of the region where both networks are synchronized.

Fig 5. Gap junction coupling allows networks to transmit information and gap junction plasticity improves robustness of the transfer.

(A Voltages traces of inhibitory neurons in the input-network (IN) in light blue and in the output-network (ON) in purple, when networks share no GJs (first rows) or 40 GJs (bottom rows). Despite not directly receiving the input signal, the ON synchronizes its activity with the IN. For panels B to I, the networks share 40 GJs. 50 ms of data is represented. For the following figures 5B, 5C and 5H, 1 s of data is represented. (B) Input signal in red, number of spiking events of inhibitory neurons of the IN in light blue and of the ON in purple, for time bins of 0.1 ms. (C) Input signal in red, number of spiking events of inhibitory neurons of the IN in light blue and the ON in purple, for time bins of 25 ms. (D) Input signal amplitude A_i as function of the corresponding PA peak interval T_i for input signals oscillation at 4 Hz with mean varying from 0 to 1000 (See Methods). (E) Input signal in red and decoded input signal in purple. The PA peak interval T_i is used to estimate the input amplitude. (F) Correlation between input signal and decoded input signal. The amplitude of the input is 400 pA, its frequency goes from 0 to 100 Hz. (G) Correlation between input signal and decoded input signal. The amplitude of the input goes from 0 to 10000 pA, its frequency goes from 0 to 100 Hz. (H) Example of 1 s of colored noise input signal (A = 800 pA, mean = 400 pA, τ_filter = 100 ms) in red and decoded input in purple (correlation 0.8). (I) Pearson’s correlation coefficient between input and decoded input for static (plastic) network in black (gray) for different values of the mean initial GJ coupling strength, as function of the number of shared GJs. The simulation is repeated for 10 different inputs. (J) Pearson’s correlation coefficient between input and decoded input for static (resp. plastic) network in black (resp. gray) as function of the proportion of GJs removed. The simulation is repeated for 10 different inputs. (K) Mean gap junction change between the steady-state value obtained with all the gap junctions, and the steady-state value obtained after gap junction removal. The remaining gap junctions compensate for the missing ones as they become stronger in strength.