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Updated: May 21, 2026

Optogenetic Entrainment of Hippocampal Theta Oscillations in Behaving Mice
Published on: June 29, 2018
Inducing phase-locking and chaos in cellular oscillators by modulating the driving stimuli
Mogens H Jensen1, Sandeep Krishna
1Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, DK-2100 Copenhagen, Denmark. mhjensen@nbi.dk
Abstract:
Inflammatory responses in eucaryotic cells are often associated with oscillations in the nuclear-cytoplasmic translocation of the transcription factor NF-kB. In most laboratory realizations, the oscillations are triggered by a cytokine stimulus. We use a mathematical model to show that an oscillatory external stimulus can synchronize the NF-kB oscillations into states where the ratios of the internal to external frequency are close to rational numbers. We predict a response diagram of the TNF-driven NF-kB system which exhibits bands of synchronization known as "Arnold tongues". We suggest that when the amplitude of the external stimulus exceeds a certain threshold, chaotic dynamics of the nuclear NF-kB concentration may occur. This behavior seems independent of the shape of the external oscillation and the non-linearities transducing this signal.
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