Model neocortical microcircuit supports beta and gamma rhythms

I. Introduction

Brain rhythms are typically measured using non-invasive scalp and subdural electrodes for humans and implanted multi-electrode arrays for rodents and non-human primates. These electrodes pick up extracellular potentials that reflect cellular electrical activities. Depending on the recording locations, extracellular potentials can be referred into encephalogram (EEG, recorded from the scalp), electrocorticogram (ECoG, recorded on cortical surface), and local field potential (LFP, recorded inside the brain). Among these, LFP has the advantage of exploring localized cellular events at deeper locations, since it is obtained when electrode placed closer to the generating cells. One such event is the rhythmicity in neuronal activity that can typically be detected in LFP signals.

Computational models of brain rhythms are beginning to provide important insights into the underlying microcircuits that might implement these rhythms in neuronal circuits. For instance, the gamma (30–90Hz) rhythm is thought to arise in vivo via feedback interactions between pyramidal cells (PNs) and fast spiking inhibitory (FSI) interneurons (termed pyramidal-interneuron-gamma or PING). The models also suggest conditions for the genesis of the rhythms, e.g., for the PING mechanism, excitatory drive to the interneurons has to largely come from pyramidal cells [1]. On the other hand, beta (15–30Hz) oscillation is thought to arise from either an interaction between pyramidal cells[2] or an interaction between pyramidal and low threshold-spiking (LTS) cells [3]. The long-lasting IPSPs from oriens-lacunosum moleculare (OLM) cells was found to be the critical element supporting another slower oscillation rhythm – theta (4–12Hz) [4].

Computational models thus enable exploration of how the microcircuits underlying different rhythms can give rise to different abilities of a network to form and manipulate cell assemblies [5]. Furthermore, such models can shed light on how the circuits might implement computations, enable information flow across brain regions, and possibly support components of cognition [6].

Recent experimental work has underscored the importance of FSI and LTS neurons in the generation of gamma and beta oscillations, respectively [3]. At the same time, models have emphasized the role of these interneurons in synchronizing activities or selecting ensembles [6]. However, it remains unclear how interneuron networks and their resultant rhythms interact with the patterns of ensemble activity, and how they influence excitatory networks subjected to naturalistic afferent drive.

Rhythms are a critical determining factor in the formation of cell ensemble patterns, and different rhythms are associated with different underlying physiology [6]. The present study uses a computational network model to test whether different patterns of afferent drive representing distinct behavioral states, can engender and shape different ensemble oscillations.

The specific computational example case considered here was motived by recordings from the primary motor cortex M1 that reveals both beta and gamma oscillations during the preparation and execution phases of movement. Beta oscillations dominate during the preparatory phase. It was traditionally thought that these were inherited from the basal ganglia [7], however slices of motor cortex in vitro are capable of generating beta when supplied with tonic excitation pharmacologically [8]. Indeed, biophysical models of M1 circuitry given tonic excitation produce beta oscillations that are consistent with those from human magnetoencephalographic recordings [9]. M1 beta rhythms may co-occur with periods of tonic activity because they are mediated by LTS interneurons [3], which are sensitive to slow changes in local firing rates. This arises because they receive weak, but facilitating, synapses from local principal cells. Facilitating synapses require trains of presynaptic activity – the kind present during tonic firing – to effectively drive spiking. Once excited, LTS interneurons target PN dendritic branches, causing a gradual inhibition [10].

Once movement begins ensemble activity rapidly fluctuates, accompanied by gamma oscillations [11]. Gamma oscillations arise locally from the reciprocal interactions between PNs and FSIs [3], and both in vitro and in vivo experiments have validated this perspective in M1[12]. Since FSIs receive strong, but depressing excitatory synapses from principal cells, have a fast membrane time constant, and deliver robust periosomatic inhibition capable of rapidly cancelling principal cell spiking, they are sensitive to rapid shifts in the pattern of presynaptic activity [13].

Although different populations of interneurons support beta and gamma, they share the same local principal cell network. Principal cells densely project to FSI and LTS interneurons, which in turn promiscuously and indiscriminately reciprocate those connections [14]. Consequently, both interneuron types receive a similar aggregate excitatory signal, and they broadcast their feedback inhibition to all nearby principal cells [15]. This lack of specificity indicates that inhibitory connectivity regulates overall excitability in M1 during different activity modes, but the distinct ensemble patterns therein arise from the excitatory connections amongst principal cells and their extrinsic inputs.

II. Method

Models of single neurons and the network were developed using experimental parameters from our collaborators and the literature, and implemented using the NEURON 7.4 simulator [16], with a fixed time step of 25 μs. We provide a brief overview of the mathematical underpinnings of both single cell and network model development.

Mathematical equations for voltage-dependent ionic currents: The dynamics for each compartment (soma or dendrite) followed the Hodgkin-Huxley formulation as previously described [17] in eqn. 1,

where V_s/V_d are the somatic/dendritic membrane potential (mV), $I_{cur,s}^{int}$ and $I_{cur,s}^{syn}$ are the intrinsic and synaptic currents in the soma, I_ing is the electrode current applied to the soma, C_m is the membrane capacitance, g_L is the conductance of the leak channel, and g_c is the coupling conductance between the soma and the dendrite (similar term added for other dendrites connected to the soma). The intrinsic current $I_{cur,s}^{int}$, was modeled as $I_{cur,s}^{int}=g_{cur}{m}^p{h}^q\left(V_s-E_{cur}\right)$, where g_cur is its maximal conductance, m its activation variable (with exponent p), h its inactivation variable (with exponent q), and E_cur its reversal potential (a similar equation is used for the synaptic current $I_{cur,s}^{syn}$ but without m and h). The kinetic equation for each of the gating variables x (m or h) takes the form but without m and h). The kinetic equation for each of the gating variables x (m or h) takes the form

where x_∞ is the steady state gating voltage- and/or Ca²⁺-dependent gating variable and τ_x is the voltage- and/or Ca²⁺-dependent time constant. The equation for the dendrite follows the same format with ‘s’ and ‘d’ switching positions in eqn. 1. Selection of the channel currents and their model parameters followed an approach we proposed recently that facilitates design while ensuring that the key neurocomputational properties of the cell are preserved [18].

III. Results

To establish the validity of our model neurons, we delivered 300 pA current steps to them and examined their spiking patterns (Fig. 2A). The CP neuron, which is of the regular spiking type, exhibited a low firing frequency during the current pulse without adaptation. On the other hand, both the FSI and LTS interneurons exhibited higher induced firing rates, with the FSI cell exhibiting the fast-spiking phenotype that typifies them. However, the LTS neuron only fired continuously for the highest current level with slight adaptation. We also examined the short-term synaptic plasticity of the connections between these cell types (Fig. 2B). The FSI-to-CP GABAergic synapses showed depression, a weakening of inhibition during repeated spiking. The same was true for the glutamatergic synapse from CP-to-FSI. On the other hand, synapses from CP-to-LTS were facilitating, increasing in strength during trains of spikes.

Having established that our single cell and synapse models match the biological case, we turned our attention to their network effects. Driving the network with short bursts of afferent activity drove relatively stronger gamma centered around 60Hz. Driving with long duration bursts reduced gamma power, but enhanced beta around 20Hz. (Fig. 3A). The average firing rate for each cell type is (Fig. 3C and D): CP,1.37±2.02Hz (hereafter, mean ± std), FSI, 5.75±2.93Hz and LTS, 0.86±0.30Hz, when network was driven with short duration afferents; CP,2.31±4.42Hz, FSI, 5.33±2.97Hz and LTS, 10.78±1.33Hz, when network was driven with long duration afferents. Average firing rate is within the experimental range [26]. Importantly, this phenomenon was not observed when the STP mechanism was removed from the model, suggesting the critical role of STP underlying the collaboration between two oscillations. This further indicates that, beta oscillation is related closely to stable activities like preparation, while gamma is more linked to dynamic activities like movement onset.

IV. Discussion and Conclusion

We have tested the importance of STP in the generation of neural oscillations. Our hypothesis was that because FSI neurons receive depressing synapses, and they are instrumental in producing gamma oscillations, then rapidly fluctuating ensembles would be ideal for gamma genesis. In addition, because LTS neurons receive facilitating synapses from CP neurons, and engender beta oscillations, then tonically active ensembles would induce beta. These dependencies were borne out in our model.

Previous work on gamma and beta oscillations have emphasized the resonant properties of interneuron networks [3, 9] as being instrumental in rhythm generation. Our work indicates that this is only part of the reason for the emergence of brain rhythms. The frequency of the rhythm is largely determined by the resonance of the recurrent principal cells/interneuron network. However, whether that network is activated, and the persistence of that activity, depends upon the slower temporal dynamics of the principal cell ensembles that supply the excitation to fuel the rhythm. This insight opens up new avenues for experimental and theoretical investigations into the function of rhythms in the brain.