Brain rhythms in small and large networks of neurons

I studied two neuronal networks, one small to investigate the interaction of brain rhythms and one large, to investigate the effects of multiple connectivity types on resonance in a target network. Theta (4 − 8 Hz) and gamma (30 − 80 Hz) rhythms are commonly associated with memory and learning. The precision of co-firing between neurons and incoming inputs is critical in these cognitive functions. To understand the interaction of the two rhythms, I considered a single model neuron with an inhibitory autapse and M- current, under forcing from gamma pulses and a sinusoidal current of theta frequency. The M-current has a long time constant (~90 ms) and generates resonance at theta frequencies. I found that this slow M-current contributes to the precise co-firing between the network and fast gamma pulses in the presence of a slow sinusoidal forcing. This current expands the range of phase-locking frequency to the gamma input, counteracts the slow theta forcing, and admits bistability in some parameter range. The effects of the M-current balancing the theta forcing are reduced if the sinusoidal current is faster than the theta frequency band. For these results I used averaging methods, geometric singular perturbation theory, and bifurcation analysis. Beta rhythms (10 − 30 Hz) are associated with motor functions; patients with Parkinson’s Disease display prominent pathological beta rhythms in the basal ganglia. Research has suggested that a sub-circuit of the basal ganglia, subthalamic nucleus- globus pallidus externus (STN-GPe), is a potential generator of beta rhythms. The anatomical structure of STN-GPe also suggests that it may act as an amplifier of incoming rhythms. I considered a model of this sub-circuit based on the work of Kumar et al. (2011) and studied the mechanism of its intrinsic oscillation and how it might amplify inputs from the striatum. Through parameter sweeps, I found that the network manifests a robust intrinsic beta oscillation, not changeable by moderate parameter variation. Surprisingly, this STN-GPe network only amplifies rhythms of or close to the intrinsic oscillatory frequency, regardless of three different connection structures simulated. However, introducing heterogeneity into the network can make the network amplify rhythms of a wide range of frequencies

Prefrontal oscillations modulate the propagation of neuronal activity required for working memory

[EN] Cognition involves using attended information, maintained in working memory (WM), to guide action. During a cognitive task, a correct response requires flexible, selective gating so that only the appropriate information flows from WM to downstream effectors that carry out the response. In this work, we used biophysically-detailed modeling to explore the hypothesis that network oscillations in prefrontal cortex (PFC), leveraging local inhibition, can independently gate responses to items in WM. The key role of local inhibition was to control the period between spike bursts in the outputs, and to produce an oscillatory response no matter whether the WM item was maintained in an asynchronous or oscillatory state. We found that the WM item that induced an oscillatory population response in the PFC output layer with the shortest period between spike bursts was most reliably propagated. The network resonant frequency (i.e., the input frequency that produces the largest response) of the output layer can be flexibly tuned by varying the excitability of deep layer principal cells. Our model suggests that experimentally-observed modulation of PFC beta-frequency (15-30 Hz) and gamma -frequency (30-80 Hz) oscillations could leverage network resonance and local inhibition to govern the flexible routing of signals in service to cognitive processes like gating outputs from working memory and the selection of rule-based actions. Importantly, we show for the first time that nonspecific changes in deep layer excitability can tune the output gate's resonant frequency, enabling the specific selection of signals encoded by populations in asynchronous or fast oscillatory states. More generally, this represents a dynamic mechanism by which adjusting network excitability can govern the propagation of asynchronous and oscillatory signals throughout neocortex.This work was supported by the U.S. Army Research Office under award number ARO W911NF-12-R-0012-02 to N. K., the U.S. Office of Naval Research under award number ONR MURI N00014-16-1-2832 to M. H. and E. M., the National Institute of Mental Health under award number NIMH R37MH087027 to E. M., and The MIT Picower Institute Faculty Innovation Fund to E. M. We would like to acknowledge Joachim Hass and Michelle McCarthy for early discussions of our modeling results, as well as Andre Bastos and Mikael Lundqvist for discussions relating our modeling work to their experiments.Sherfey, J.; Ardid-Ramírez, JS.; Miller, EK.; Hasselmo, ME.; Kopell, NJ. (2020). Prefrontal oscillations modulate the propagation of neuronal activity required for working memory. 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