Heterogeneous mechanisms for synchronization of networks of resonant neurons under different E/I balance regimes

Rhythmic synchronization of neuronal firing patterns is a widely present phenomenon in the brain—one that seems to be essential for many cognitive processes. A variety of mechanisms contribute to generation and synchronization of network oscillations, ranging from intrinsic cellular excitability to network mediated effects. However, it is unclear how these mechanisms interact together. Here, using computational modeling of excitatory-inhibitory neural networks, we show that different synchronization mechanisms dominate network dynamics at different levels of excitation and inhibition (i.e. E/I levels) as synaptic strength is systematically varied. Our results show that with low synaptic strength networks are sensitive to external oscillatory drive as a synchronizing mechanism—a hallmark of resonance. In contrast, in a strongly-connected regime, synchronization is driven by network effects via the direct interaction between excitation and inhibition, and spontaneous oscillations and cross-frequency coupling emerge. Unexpectedly, we find that while excitation dominates network synchrony at low excitatory coupling strengths, inhibition dominates at high excitatory coupling strengths. Together, our results provide novel insights into the oscillatory modulation of firing patterns in different excitation/inhibition regimes.


Supplemental Material
In this Supplemental Material we present results showing how synaptic inhibitory strength qualitatively modulates the results shown in the main text. We track the trajectories of E/I ratio and the difference between E and I currents (total current) as excitatory synaptic strength wE is varied for three different values of inhibitory synaptic strength wI (Fig. S1a). We compare the shape of the trajectory loops for three different values of wI when the network is driven with external oscillatory current input in the resonant frequency range (5Hz) to when it is not driven (0Hz). We observe that increased inhibitory synaptic strength limits the maximum E/I ratio and thus the domain of the trajectory loop, which is further diminished if the resonant drive is present.
The trajectory loops for all three wI values illustrate the two synchronization regimes discussed in the manuscript. In the resonance regime for lower wE values, resonant oscillatory drive constrains the trajectory around E=I balance points with smaller trajectory loop sizes (dashed lines) than when no drive is given (solid lines). In the network-driven PING-like synchronization regime for higher wE values, external oscillatory drive does not have pronounced effects.
At the same time, the trajectories with various wI values show marked differences. First, the size of the trajectory loop in the resonance regime decreases with stronger inhibition. For wI=3mS/cm 2 , the stronger inhibition affects the activity of inhibitory cells diminishing overall inhibitory signaling, so that the network does not exhibit single spike bursting activity even at the strongest wE range. In addition, the network does not enter the inhibition-dominant regime for highest wE values (total current < 0 and E/I ratio <1) even though wI is high. This indicates that the excitatory and inhibitory signals interact in a recurrent, non-linear way.
Figures S2 and S3 depict sample raster plots for higher inhibitory synaptic strength values, wI=1mS/cm 2 and wI=3mS/cm 2 , respectively. In both cases, similarly as for wI=0.3mS/cm 2 in the main text, when wE is weak, the resonant oscillatory drive mediates ordered spiking within synchronous bursts (middle row, left side). For slightly higher wE, resonant oscillatory drive increases the spiking synchrony through phase locking. The colored markers (stars and dots) denote parametric locations from Fig. S1.
However, in the PING-regime, the behavior of the networks for different inhibition wI values diverges. For wI=1mS/cm 2 (Fig. S2, right side), with the increase of wE, the network firing pattern changes from wide (multi-spike) bursts to narrow, often single spike bursts. When wE has medium values (wE=1.5mS/cm 2 , right side, first column), cells fire randomly at a high rate during network bursts rather than synchronously, due to the weakened inhibitory signal. For higher wE (wE=3mS/cm 2 , right side, 2 nd column), inhibitory cells get higher excitatory signaling and generate stronger inhibition, which causes shorter network bursts. For higher inhibitory synaptic strength (wI=3mS/cm 2 , Fig. S3, right side), however, due, to strong inhibitory-to-inhibitory connections, inhibitory signaling is not strong enough to generate single spike bursts, and network bursts are long-lasting. For both levels of inhibitory synaptic strength (wI=1mS/cm 2 and wI=3mS/cm 2 , Figs. S2 and S3, right sides), resonant (5Hz) external oscillatory drive phase-locks the onset of network bursts. Figure S1. Trajectories of E/I ratio and E -I total current as excitatory synaptic strength wE is increased for networks with different inhibitory synaptic strength wI values. In panel (a), trajectories are shown for wI=0.3mS/cm 2 (blue, same curve as Fig.1), wI=1mS/cm 2 (red) and wI=3mS/cm 2 (black) with no external oscillatory drive (solid lines) and with 5Hz drive (dashed lines). The details around E=I balance are displayed in the inset. The magnified curves for wI=1mS/cm 2 and wI=3mS/cm 2 are shown in panel (b) and (c), respectively; markers label the data points for which raster plots are displayed in Figs. S2, S3. Figure S2. Example raster plots for networks with wI=1mS/cm 2 at parameter points marked on the trajectory in Fig S1b. Top row: no external oscillatory drive; middle row: resonant (5Hz) drive; Bottom row: 40Hz (non-resonant) drive (not shown in Fig. S1b).