Slow Noise in the Period of a Biological Oscillator Underlies Gradual Trends and Abrupt Transitions in Phasic Relationships in Hybrid Neural Networks

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.

Phase-resetting as a tool of information transmission

“…Moreover, the frequency may also fluctuate due to external input [21,22] or intrinsic noise [23], and the PRC may be frequency dependent [24]. Nevertheless, this conceptual framework for phase resetting is quite generally applicable to nonlinear oscillators.…”

“…The phases of the velocity controlled oscillators (VCOs) will slip with respect to the reference oscillator. Phase resetting theory imposes the constraint that distinct oscillators must be functionally uncoupled to prevent locking [54] or sticking [23]. As they slip, the peak of each VCO will coincide with the reference oscillator each time a characteristic distance has been traversed in its preferred direction.…”

A computational model explains and predicts substantia nigra pars reticulata responses to pallidal and striatal inputs

“…Moreover, based on the shape of the PRC, the magnitude of change in phase is large when phase is away from 0 and 1, such that spiking is asynchronous, and small when the phase of is nearly synchronous. As a result, the network remains close to synchrony most of the time but with approximately periodic asynchronous excursions, a phenomenon referred to as phase slipping ( Thounaojam et al, 2014 ). The frequency of phase slipping is determined by the number of stimulus kicks needed for the phase to progress through one full cycle, which in turn is determined by the shape of the PRC.…”

Optimal entrainment of heterogeneous noisy neurons

“…To reconcile the differences between intracellular vs. intercellular heterogeneity, we postulate that the intrinsic properties of the CA1 hippocampal cells, and hence their PRCs, might be slowly changing throughout each trial. Another recent study (Thounaojam et al, 2014 ) suggested that the natural frequencies of periodically firing neurons can drift over time. A methodology that explicitly accounts for uncertainty in the PRCs across time can help ensure entrainment over the entire duration of the experiment.…”