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

• Type of Material: Article
• Authors: Umeshkanta S. Thounaojam, Louisiana State University; Jianxia Cui, University of California San Diego; Sharon E. Norman, Georgia Institute of Technology; Robert Butera, Emory University; Carmen C. Canavier, Louisiana State University
• Language: English
• Date: 2014-05-15
• Publisher: Public Library of Science
• Publication Version: Final Published Version
• Copyright Statement: © 2014 Thounaojam et al.
• License: Creative Commons Attribution 4.0 International
• Final Published Version (URL): http://dx.doi.org/10.1371/journal.pcbi.1003622
• Title of Journal or Parent Work: PLoS Computational Biology
• ISSN: 1553-734X
• Volume: 10
• Issue: 5
• Start Page: e1003622
• End Page: e1003622
• Grant/Funding Information: This work was supported by NIH grant R01NS054281 to CCC originally awarded under the CRCNS program, and used resources provided in part by the Computational Core of NIH grant P30GM103340.; Experimental work in the lab of RJB was also supported by NIH grant R01EB016407 (subcontract to RJB).
• Keywords: SYNCHRONIZATION; Mathematical & Computational Biology; Life Sciences & Biomedicine; BROWNIAN-MOTION; NEURONS; Biochemical Research Methods; PREDICTION; Biochemistry & Molecular Biology; DYNAMIC CLAMP; MATHEMATICAL & COMPUTATIONAL BIOLOGY; Science & Technology; RESPONSE CURVES; CONDUCTANCES; PRINCIPLES; LOCKING; BIOCHEMICAL RESEARCH METHODS; INHIBITION
• Research Categories: Engineering, Biomedical; Biology, General

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.