Amitabha Bose

Dynamics of two mutually coupled slow inhibitory neurons

Abstract Inhibition in oscillatory networks of neurons can have apparently paradoxical effects, sometimes creating dispersion of phases, sometimes fostering synchrony in the network. We analyze a pair of biophysically modeled neurons and show how the rates of onset and decay of inhibition interact with the timescales of the intrinsic oscillators to determine when stable synchrony is possible. We show that there are two different regimes in parameter space in which different combinations of the time constants and other parameters regulate whether the synchronous state is stable. We also discuss the construction and stability of nonsynchronous solutions, and the implications of the analysis for larger networks. The analysis uses geometric techniques of singular perturbation theory that allow one to combine estimates from slow flows and fast jumps.

A Temporal Mechanism for Generating the Phase Precession of Hippocampal Place Cells

The phase relationship between the activity of hippocampal place cells and the hippocampal theta rhythm systematically precesses as the animal runs through the region in an environment called the place field of the cell. We present a minimal biophysical model of the phase precession of place cells in region CA3 of the hippocampus. The model describes the dynamics of two coupled point neurons—namely, a pyramidal cell and an interneuron, the latter of which is driven by a pacemaker input. Outside of the place field, the network displays a stable, background firing pattern that is locked to the theta rhythm. The pacemaker input drives the interneuron, which in turn activates the pyramidal cell. A single stimulus to the pyramidal cell from the dentate gyrus, simulating entrance into the place field, reorganizes the functional roles of the cells in the network for a number of cycles of the theta rhythm. In the reorganized network, the pyramidal cell drives the interneuron at a higher frequency than the theta frequency, thus causing a systematic precession relative to the theta input. The frequency of the pyramidal cell can vary to account for changes in the animals running speed. The transient dynamics end after up to 360 degrees of phase precession when the pacemaker input to the interneuron occurs at a phase to return the network to the stable background firing pattern, thus signaling the end of the place field. Our model, in contrast to others, reports that phase precession is a temporally, and not spatially, controlled process. We also predict that like pyramidal cells, interneurons phase precess. Our model provides a mechanism for shutting off place cell firing after the animal has crossed the place field, and it explains the observed nearly 360 degrees of phase precession. We also describe how this model is consistent with a proposed autoassociative memory role of the CA3 region.

A Mathematical Model towards Understanding the Mechanism of Neuronal Regulation of Wake-NREMS-REMS States

In this study we have constructed a mathematical model of a recently proposed functional model known to be responsible for inducing waking, NREMS and REMS. Simulation studies using this model reproduced sleep-wake patterns as reported in normal animals. The model helps to explain neural mechanism(s) that underlie the transitions between wake, NREMS and REMS as well as how both the homeostatic sleep-drive and the circadian rhythm shape the duration of each of these episodes. In particular, this mathematical model demonstrates and confirms that an underlying mechanism for REMS generation is pre-synaptic inhibition from substantia nigra onto the REM-off terminals that project on REM-on neurons, as has been recently proposed. The importance of orexinergic neurons in stabilizing the wake-sleep cycle is demonstrated by showing how even small changes in inputs to or from those neurons can have a large impact on the ensuing dynamics. The results from this model allow us to make predictions of the neural mechanisms of regulation and patho-physiology of REMS.

BISTABLE OSCILLATIONS ARISING FROM SYNAPTIC DEPRESSION

Synaptic depression is a common form of short-term plasticity in the central and peripheral nervous systems. We show that in a network of two reciprocally connected neurons a single depressing synapse can produce two distinct oscillatory regimes. These distinct periodic behaviors can be studied by varying the maximal conductance,

Almost-synchronous solutions for mutually coupled excitatory neurons

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The activity phase of postsynaptic neurons in a simplified rhythmic network.

, of the depressing synapse. For small

Inhibitory feedback promotes stability in an oscillatory network

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Localized activity patterns in excitatory neuronal networks

, the network has a short-period solution controlled by intrinsic cellular properties. For large

Capturing the bursting dynamics of a two-cell inhibitory network using a one-dimensional map

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Development of new scintillating fiber detectors for high energy physics applications

, the solution has a much longer period and is controlled by properties of the synapse. We show that in an intermediate range of