Slow noise in the period of a biological oscillator underlies gradual trends and abrupt transitions in phasic relationships in hybrid neural networks.

Umeshkanta S Thounaojam,Carmen C Canavier,Robert J Butera,Jianxia Cui,Sharon E Norman

doi:10.1371/journal.pcbi.1003622

Abstract

In order to study the ability of coupled neural oscillators to synchronize in the presence of intrinsic as opposed to synaptic noise, we constructed hybrid circuits consisting of one biological and one computational model neuron with reciprocal synaptic inhibition using the dynamic clamp. Uncoupled, both neurons fired periodic trains of action potentials. Most coupled circuits exhibited qualitative changes between one-to-one phase-locking with fairly constant phasic relationships and phase slipping with a constant progression in the phasic relationships across cycles. The phase resetting curve (PRC) and intrinsic periods were measured for both neurons, and used to construct a map of the firing intervals for both the coupled and externally forced (PRC measurement) conditions. For the coupled network, a stable fixed point of the map predicted phase locking, and its absence produced phase slipping. Repetitive application of the map was used to calibrate different noise models to simultaneously fit the noise level in the measurement of the PRC and the dynamics of the hybrid circuit experiments. Only a noise model that added history-dependent variability to the intrinsic period could fit both data sets with the same parameter values, as well as capture bifurcations in the fixed points of the map that cause switching between slipping and locking. We conclude that the biological neurons in our study have slowly-fluctuating stochastic dynamics that confer history dependence on the period. Theoretical results to date on the behavior of ensembles of noisy biological oscillators may require re-evaluation to account for transitions induced by slow noise dynamics.

Highlights

Synchronized neural firing is a characteristic activity pattern of neural systems
The WB model was used because it produces phase resetting curves (PRCs) that are comprised of only delays in response to an inhibitory input (Figure 1B), and because the WB PRCs resemble those measured in Aplysia neurons [27,28]
The average interspike interval of the biological neuron during coupling, which corresponds to the network period if the system is phase-locked, is different than the uncoupled biological neuron period; this provides evidence that the motifs observed in our hybrid networks result from mutual coupling effects, and do not reflect entrainment of the model neuron by the biological neuron

Summary

Introduction

Synchronized neural firing is a characteristic activity pattern of neural systems. Synchronized neural activity in cortical circuits [1] is thought to underlie many aspects of cognition [2,3], including recognition [4], recall [5], perception [6,7], and attention [8]. The noise takes the form of Gaussian current noise added to the baseline current When this noise is integrated, it is analogous to a trajectory produced by Brownian motion, and produces a one-dimensional random walk in the membrane potential superimposed on the steady upward trend caused by the constant baseline current. In this model, membrane potential is proportional to the phase of the oscillation, so a random walk in the phase occurs.

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