Shunting Inhibition Improves Synchronization in Heterogeneous Inhibitory Interneuronal Networks with Type 1 Excitability Whereas Hyperpolarizing Inhibition Is Better for Type 2 Excitability

Abstract

All-to-all homogeneous networks of inhibitory neurons synchronize completely under the right conditions; however, many modeling studies have shown that biological levels of heterogeneity disrupt synchrony. Our fundamental scientific question is "how can neurons maintain partial synchrony in the presence of heterogeneity and noise?" A particular subset of strongly interconnected interneurons, the PV+ fast spiking basket neurons, are strongly implicated in gamma oscillations and in phase locking of nested gamma oscillations to theta. Their excitability type apparently varies between brain regions: in CA1 and the dentate gyrus they have type 1 excitability, meaning that they can fire arbitrarily slowly, whereas in the striatum and cortex they have type 2 excitability, meaning that there is a frequency threshold below which they cannot sustain repetitive firing. We constrained the models to study the effect of excitability type (more precisely bifurcation type) in isolation from all other factors. We use sparsely connected, heterogeneous, noisy networks with synaptic delays to show that synchronization properties, namely the resistance to suppression and the strength of theta phase to gamma amplitude coupling, are strongly dependent on the pairing of excitability type with the type of inhibition. Shunting inhibition performs better for type 1 and hyperpolarizing inhibition for type 2. Gamma oscillations and their nesting within theta oscillations are thought to subserve cognitive functions like memory encoding and recall; therefore, it is important to understand the contribution of intrinsic properties to these rhythms. Significance Statement The collective, synchronized activity of neurons produces brain rhythms. These rhythms are thought to subserve cognitive functions such as attention and memory encoding and retrieval. We focus on fast spiking basket cells, a subset of inhibitory interneurons. These neurons play an important role in brain rhythms. In some brain regions these neurons can fire arbitrarily slowly (type 1 dynamics) whereas in others they cannot fire below a minimum cutoff frequency (type 2 dynamics). We show that excitability type determines whether shunting or hyperpolarizing inhibition more effectively synchronizes the fast oscillatory activity of networks of these neurons in the presence of heterogeneity and noise, and more effectively drives modulation of fast activity by slower oscillations.

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

“…Although this study focused on interneuronal models with type 1 excitability, they reached similar conclusions using type 2 model neurons [51]. Our previous work on theta-nested gamma oscillations in inhibitory networks [52] also implemented heterogeneity using different levels of bias current; we found tighter phase locking of gamma oscillations to the theta modulation in type 2 models when using hyperpolarizing inhibition, and in type 1 models with shunting inhibition. Whether hyperpolarizing or shunting inhibition is more synchronizing and potentially more robust to heterogeneity will likely to depend on the exact model and synaptic parameters.…”

Kinetics and Connectivity Properties of Parvalbumin- and Somatostatin-Positive Inhibition in Layer 2/3 Medial Entorhinal Cortex

“…In models, the unique kinetics and connectivity properties of fast-firing interneurons can also generate gamma oscillations using solely an inhibitory network (Bartos et al, 2002(Bartos et al, , 2007Tiesinga and Sejnowski, 2009;Tikidji-Hamburyan et al, 2015;Keeley et al, 2017;Tikidji-Hamburyan and Canavier, 2020), with experimental support for this form oscillatory activity noted in the hippocampus and entorhinal cortex (Butler et al, 2016(Butler et al, , 2018. In contrast, neocortical Sst + interneurons in vivo do not correlate with oscillatory network activity (Kwan and Dan, 2012).…”

Parvalbumin interneuron dendrites enhance gamma oscillations

“…Second, PV basket cells in the brain can also be classified as type 1 and type 2 neurons depending on whether they can fire at an arbitrarily low rate (type 1) or they have a threshold frequency below which they cannot sustain firing (type 2) (Hodgkin, 1948;Tikidji-Hamburyan and Canavier, 2020). Previous work and the data presented here show that PV basket cells in the dentate gyrus and area CA1 are type 1 (Ferguson et al, 2013;Tikidji-Hamburyan and Canavier, 2020), while PV basket cells in the neocortex are type 2 (Tateno et al, 2004). So, it remains to be tested whether the mechanisms shown here generalize to multiple types of PV basket cells.…”

“…We varied the maximum conductance of the GABAergic synapses g syn;GABA between 0.5 and 10 nS (z 0.008-0.08 mS/cm 2 ), with a synaptic reversal potential E syn;GABA = À75 mV for hyperpolarizing inhibition, and À60 mV for shunting inhibition. For shunting inhibition, we varied g syn;GABA up to 30 nS, because synchronous states typically require very strong inhibition (Tikidji-Hamburyan and Canavier, 2020;. Synaptic currents are described by IPSCðV; tÞ = g syn;GABA ðtÞðV À E syn;GABA Þ.…”