Inducing phase-locking and chaos in cellular oscillators by modulating the driving stimuli

TL;DR

This paper uses a mathematical model to demonstrate how oscillatory stimuli can induce phase-locking and chaos in cellular NF-kB oscillations, revealing potential control mechanisms for immune responses and cell regulation.

Contribution

It introduces a novel model predicting synchronization bands and chaos in NF-kB oscillations under oscillatory stimuli, expanding understanding of cellular response dynamics.

Findings

Oscillatory stimuli can synchronize NF-kB oscillations near rational frequency ratios.

External stimulus amplitude thresholds can lead to multiple synchronized states.

Chaotic dynamics may emerge at high stimulus amplitudes.

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, like the tumor necrosis factor alpha, applied as a step change to a steady level. Here 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 specific response diagram of the TNF-driven NF-kB system which exhibits bands of synchronization known as "Arnold tongues". Our model also suggests that when the amplitude of the external stimulus exceeds a certain threshold there is the possibility of coexistence of multiple different synchronized states and eventually chaotic dynamics of the nuclear NF-kB concentration. This could be used as a way of externally controlling immune response, DNA repair and apoptotic pathways.