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Date: 21 September 2018
Neural rhythms: biophysics and dynamics  

Topic Name: Neural rhythms: biophysics and dynamics
Category: Biomedical
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Research persons: Dmitri D. Pervouchine
Theoden I. Netoff
John A. White
Nancy J. Kopell

Location: 111 Cummington Street Boston, MA, United States


Low dimensional maps for gamma and theta oscillations. Postdocs Dmitri Pervouchine, and Tay Netoff , along with J. White and Kopell, finished a paper using 1-D and 2-D maps to describe how 3-cell networks taken from the hippocampus and entorhinal cortex can coordinate. One aim of the paper was to show how phase-response curve methods could be used for multicell networks of heterogeneous cells. Another was to show how the biophysical specifics of the cells affect synchronization in such networks. The paper is in press in Neural ComputationReductions of dimensions.Biophysical models of neurons and neural networks are typically high dimensional, and the variables evolve over many time scales. In some cases, the models are simple enough to be amenable to reduction to lower dimensional systems by making use of the time-scale separation between the different dynamic variables. This is the case for some Hodgkin-Huxley models (four-dimensional) that can be reduced to two dimensional models (Fitzhugh-Nagumo or Morris-Lecar type). By contrast, neural models with more currants can be high dimensional, and have complex dynamics (e.g., mixed mode oscillations, see below.) Research Asst Prof Rotstein, with Clewley and Kopell, showed that the interspike interval can be divided into subintervals inside which a 7-D entorhinal cortex stellate cell model can be reduced to a two- or three-dimensional systems that are amenable to geometric or analytic study. The reduction of dimension process makes use of the different times scales and the fact the some currents are inactive in some ranges of voltage.
Subthreshold oscillations (STOs). It was already known that the interaction between two non-standard intrinsic ionic currents, a persistent sodium and a hyperpolarization-activated (h-) currents, is enough to account for the generation of the STOs in Medial Entorhinal Cortex (MEC) Layer II Stellate Cells (SC). However, the mechanisms by which this phenomenon occurs and the specific role of each of these currents were still open questions. Rotstein, with Tim Oppermann, White, Martin Wechselberger and Kopell used reduction of dimension procedures to study mixed-mode oscillations (i.e., STOs and spikes) in the 7-D stellate cell model. They showed that the STOs and the onset of spikes are generated by a mechanism depending on a dynamic structure they call the “canard structure”. The main ingredients of this structure are the nonlinearities of the reduced model (represented by its nullsurfaces) and the time scale separation between the voltage and the h-current gating variables. This dynamic structure has the potential to produce the canard phenomenon (blowup). Both STOs and MMOs are closely related to the canard phenomenon. These phenomena can be reproduced in models in which the spike is replaced by a threshold and reset. Current work includes the relationship of this dynamical mechanism to other methods of producing STOs and MMOs and the role of each of the ionic currents in producing the resonance. The same group are also working on mathematical aspects of the canard structure that emerges in this regime. Via an appropriate change of variables, they have brought the reduced 3D system to a form (transformed system) suitable for analysis. They have also built and are studying a toy model, consisting of a fast equation with a parabolic nullsurface, and two slow linear equations. It has the same qualitative features of the transformed system.
Subthreshold oscillations and resonance.Last year Rotstein, Kopell, T. Opperman and White submitted a paper on subthreshold oscillation in a kind of cell in the entorhinal cortex, now in press in Journal of Computational Neuroscience. The biophysical model gave rise to a new mechanism for the creation of such low amplitude oscillations, based on “canard” structures. This has been followed up with related work, almost finished, on resonance associated with such oscillators, with Tim Opperman of the lab of Andreas Herz. The work shows the time scales responsible for the resonance are related to the times to traverse the low amplitude oscillations, rather than any associated eigenvalues. More details are in the 2005 report.
Rhythms in entorhinal cortex. Postdoc Jozsi Jalics, PIN grad student Tilman Kispersky, and Kopell are working with Mark Cunningham and Miles Whittington (U. of Newcastle) to investigate the mechanisms underlying various neuronal rhythms and their role in the formation and coordination of neuronal ensembles in superficial layers of the entorhinal cortex, using numerical and analytical techniques. One current project almost completed concerns changes in rhythms in the presence and absence of kainate and NMDA receptor antagonists; modeling has led to an explanation of why NMDAR antagonists can cause a decrease in gamma power in the presence of kainate, but an increase in the absence of kainate. The model, which makes use of a structure involving stellate cells, pyramidal cells and two different kinds of interneurons, makes experimentally testable predictions about anatomy and synaptic kinetics. Jalics et al. have extended the above model to include multiple such modules , and have shown that theta and gamma rhythms can interact with focal inputs to produce ensembles of modules. Also, they have examined the role of inputs from the medial septum, which acts as a theta generator, in the creation of theta-nested gamma rhythms and the formation of ensembles. Some of this work has been presented at the 2004 and 2005 Society for Neuroscience meetings and multiple papers based on this work are in preparation.
Neuronal synchronization and acetylcholine. Following the work of Netoff on neuronal synchronization, described last year, grad student Lisa Giocomo, postdoc Netoff, and BU faculty members Michael Hasselmo (Psychology) and White (BME) have examined the problem of how the neuromodulator acetylcholine changes synchronization properties. They find that the cholinergic agonist carbachol promotes excitation-based synchronization among layer III pyramidal cells in entorhinal cortex, but not among layer II stellate cells. Pharmacological results suggest that carbachol exerts its effects via the non-specific cation current INCM. This effect may be extremely important for ‘mode-switching’ in entorhinal cortex and hippocampus. They plan to submit this work for publication in fall 2006.
Mixed mode oscillations.Postdoc Jalics, Research Asst. Prof. Rotstein and Kopell are analyzing a biophysical model of an entorhinal cortex layer V pyramidal cell that includes a persistent sodium and a slow potassium current, which are active in the intervals between spikes. Using reduction of dimension techniques and bifurcation analysis, they are investigating the mechanisms that generate subthreshold oscillations, mixed mode oscillations, resonance, and rebound firing. Interestingly, they have found that the spiking currents, which are usually neglected, are important in the interspike interval. Also, in the mixed-mode oscillation regime, they play an important role in the analysis of a 3-d canard structure, in which trajectories remain in a neighborhood of an unstable manifold for a significant duration of time, that governs the model's dynamics. To study the mixed-mode regime, the six dimensional model has been reduced to a three dimensional model and transformed into a canonical form that exposes the canard structure and helps reveal a novel mechanism for the generation of mixed-mode oscillations.
Beta and gamma rhythms in the neocortex.M.Whittington, R.Traub and collaborators showed that superficial layers of the neocortex produce gamma rhythms in the presence of kainate. However, some cortical areas produce beta 1 (22-29 Hz) in the deep layers in the same slice. Traub has produced a detailed biophysical model of the deep layer beta, which depends on gap junctional connections among layer V cells. Postdoc Mark Kramer has collaborated with Kopell, Whittington and Traub to produce a reduced model of the beta 2 rhythm, consisting only of three compartments (a soma, axon, and dendrite), which exhibits the bursting activity observed in experimental recordings from deep cortical layers. Kramer and Kopell are now investigating the interaction of the rhythms in the deep and superficial layers.
Gamma and theta rhythms in the hippocampus. In a paper with Kopell, Whittington and other collaborators, T. Gloveli provided anatomical and physiological evidence that the prominent rhythmic network activities of the hippocampus, the behavior-specific gamma and theta oscillations, are seen predominantly along the transverse and longitudinal axes respectively. Modeling showed that this orthogonal relationship is the result of the axonal field trajectories and the differences in the two different kinds of slices in the interaction of the principal cells and major interneuron subtypes involved in generating each rhythm. Thus, the axonal arborization patterns of hippocampal inhibitory cells may represent a structural framework for the spatiotemporal distribution of activity observed within the hippocampus.
Multicompartmental models of hippocampal neurons.Postdoc Adriano Tort is working with Rotstein and Kopell on a more complex model of hippocampal CA1 and CA3 networks; the more complex model has more compartments, allowing one to investigate the role of differences in the h-current along the dendrites when that ionic current is modulated. They plan to collaborate with Gloveli on implications for epilepsy of changes in this current.

Neuronal metabolism and network response state
In a recent PNAS paper, Cunningham et al showed that rhythmic transitions between periods of high activity (up phases) and low activity (down phases) vary between wakefulness and deep sleep/anesthesia. Current opinion about changes in cortical response state between sleep and wakefulness is split between neuronal network-mediated mechanisms and neuronal metabolism-related mechanisms. This paper demonstrates that slow oscillations in network state are a consequence of interactions between both mechanisms: recurrent networks of excitatory neurons, whose membrane potential is partly governed by ATP-modulated potassium (K(ATP)) channels, mediate response-state oscillations via the interaction between excitatory network activity involving slow, kainate receptor-mediated events and the resulting activation of ATP-dependent homeostatic mechanisms. These findings suggest that K(ATP) channels function as an interface between neuronal metabolic state and network responsivity in mammalian cortex. The modeling for that paper was done by postdoc Pervouchine and Kopell.
Axonal plexus activity. Postdoc Stefanos Folias and Kopell are currently developing a project which explores the generation and effects of activity in the plexus of axons of pyramidal cells. Such activity is mediated by both chemical synapses as well as purported electrical gap junctions, and is believed to be centrally important for the creation of gamma oscillations that are induced by kainate. The aim of the project is to produce a model of this activity (less complex than the current model by Traub) and use this to explore the effects of the plexus activity on responses to afferent inputs. Others who have been involved are Roger Traub, Miles Whittington, and Costa Colbert.
Gain modulation in EC stellate cellsPrevious work of Burdakov et al. studied the gain curves (changes in firing rate with input current) starting with different sets of ionic currents starting with the same baseline rate; the gain curves were shown to be different. PIN grad student Shirley Sanchez is carrying out a similar investigation for the EC stellate cells under the direction of Rotstein. They plan to study the consequences of this modulation for synchronization.

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