Interneuronal network model of theta-nested fast oscillations predicts differential effects of heterogeneity, gap junctions and short term depression for hyperpolarizing versus shunting inhibition

Abstract

Theta and gamma oscillations in the hippocampus have been hypothesized to play a role in the encoding and retrieval of memories. Recently, it was shown that an intrinsic fast gamma mechanism in medial entorhinal cortex can be recruited by optogenetic stimulation at theta frequencies, which can persist with fast excitatory synaptic transmission blocked, suggesting a contribution of interneuronal network gamma (ING). We calibrated the passive and active properties of a 100-neuron model network to capture the range of passive properties and frequency/current relationships of experimentally recorded PV+ neurons in the medial entorhinal cortex (mEC). The strength and probabilities of chemical and electrical synapses were also calibrated using paired recordings, as were the kinetics and short-term depression (STD) of the chemical synapses. Gap junctions that contribute a noticeable fraction of the input resistance were required for synchrony with hyperpolarizing inhibition; these networks exhibited theta-nested high frequency oscillations similar to the putative ING observed experimentally in the optogenetically-driven PV-ChR2 mice. With STD included in the model, the network desynchronized at frequencies above ~200 Hz, so for sufficiently strong drive, fast oscillations were only observed before the peak of the theta. Because hyperpolarizing synapses provide a synchronizing drive that contributes to robustness in the presence of heterogeneity, synchronization decreases as the hyperpolarizing inhibition becomes weaker. In contrast, networks with shunting inhibition required non-physiological levels of gap junctions to synchronize using conduction delays within the measured range.

Synchrony in Networks of Type 2 Interneurons is More Robust to Noise with Hyperpolarizing Inhibition Compared to Shunting Inhibition in Both the Stochastic Population Oscillator and the Coupled Oscillator Regimes

“…Figure 6A shows the full 3D parameter space and the region of synchrony and asynchrony for both hyperpolarizing and shunting inhibition. Similar to previous results for the coupled oscillator regime (Via et al 2022), hyperpolarizing synapses are more strongly synchronizing and are thus more robust to noise The red dashed lines in Fig. 6B4 and C4 explain the difference between hyperpolarizing and shunting synapses.…”

“…Here we have introduced temporal heterogeneity in that individual neurons receive distinct current noise. Actual inhibitory interneurons are heterogeneous in the synaptic connectivity, their passive and active properties (Fernandez et al 2022; Via et al 2022) and in their morphologies (Kriener et al 2022). These types of heterogeneity are beyond the scope of this theoretical study.…”

“…We also use a calibrated Hodgkin-Huxley type conductance-based model with Type 2 excitability. The model is described in detail in (Via et al 2022). This single compartment model neurons has five state variables: the membrane potential (V) and four gating variables (m, h, n, and a) that use the same kinetic equations as the original Hodgkin-Huxley model (Baxter et al 2004; Hodgkin and Huxley 1952), but with different parameters tuned to replicate the dynamics of fast spiking neurons in the medial entorhinal cortex.…”

“…We included two delayed rectifier K + currents (I Kv7 and I Kv3 ). K V 7 was mislabeled K V 1 in (Via et al 2022). The differential equation for the membrane potential (V) of each neuron is where C m =81.4 pF is the membrane capacitance, I app is the external current, I Na is the fast sodium current and I L is the passive leak current.…”

“…We modeled the PSC function as a biexponential with latency τ L = 1 ms, rise time constant τ R = 1 ms and decay time constant τ D = 6 ms. The factor ensures that the integral of the PSC (i.e., the total charge received in the postsynaptic neuron due to a presynaptic spike) is one, i.e., ∫ s ( t ) dt=1 . For conductance based synapses the maximum of s(t) is normalized to 1 (Via et al 2022) Prediction of Hopf bifurcation surface using mean field theory .…”