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Arnold Tongues and Mode Hopping in Cell Dynamics

Mogens Høgh Jensen

à 14h en salle C. Brot

Oscillating genetic patterns have been observed in networks related to the transcription factors NFkB, p53 and Hes1. We have identified the central feed-back loops leading to oscillations. By applying an external periodic signal, it is possible to lock the internal oscillation to the external signal. For the NF-kB systems in single cells we have observed that the two signals lock when the ration between the two frequencies is close to basic rational numbers [1]. The resulting response of the cell can be mapped out as Arnold tongues. When the tongues start to overlap we may observe a chaotic dynamics of the concentration in NF-kB [1]. The group of Savas Tay (ETH, Zurich) has in single cell dynamics of the NF-kB system observed transitions from one tongue to the other when they overlap. We investigate this effect by Gillespie simulations and observe mode hopping transitions between different tongues in good agreement with the experiments [2]. The distribution of waiting times between subsequent mode hoppings follow a stretched exponential indicating strong correlations. The mode hopping dynamics in the stochastic system resembles very much the chaotic dynamics of the deterministic system [2].

[1] MH Jensen et al, Inducing phase-locking and chaos in cellular oscillators by modulating the driving stimuli, FEBS Lett 586:1664,2012

[2] ML Heltberg et al, Noise-induced NF-kB Mode Hopping Enables Temporal Gene Multiplexing, Cell Systems 3:532, 2016