Slow noise in the period of a biological oscillator underlies gradual trends and abrupt transitions in phasic relationships in hybrid neural networks.
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.
Department of Cell Biology and Anatomy, Louisiana State University Health Sciences Center New Orleans, Louisiana, United States of America.
Umeshkanta S
US
Thounaojam
BioCircuits Institute, University of California, San Diego, La Jolla, California, United States of America; School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, Georgia, United States of America.
Jianxia
J
Cui
School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, Georgia, United States of America.
Sharon E
SE
Norman
School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, Georgia, United States of America; Department of Biomedical Engineering, Georgia Institute of Technology and Emory University, Atlanta Georgia, United States of America.
Robert J
RJ
Butera
Department of Cell Biology and Anatomy, Louisiana State University Health Sciences Center New Orleans, Louisiana, United States of America; Neuroscience Center of Excellence, Louisiana State University Health Sciences Center, New Orleans, Louisiana, United States of America.
Carmen C
CC
Canavier
D000200:Action Potentials / Q000502:physiology*; D000818:Animals; D001048:Aplysia; D001683:Biological Clocks / Q000502:physiology*; D002478:Cells, Cultured; D003198:Computer Simulation; D025461:Feedback, Physiological / Q000502:physiology*; D008959:Models, Neurological; D015233:Models, Statistical; D009415:Nerve Net / Q000502:physiology*; D009474:Neurons / Q000502:physiology*; D059629:Signal-To-Noise Ratio