Epigenetic modifications of histones crucially affect the eukaryotic gene activity. We theoretically analyze the dynamical effects of histone modifications on gene switching by using the Doi-Peliti operator formalism of chemical reaction kinetics. The calculated probability flux in self-regulating genes shows a distinct circular flow around basins in the landscape of the gene state distribution, giving rise to hysteresis in gene switching. In contrast to the general belief that the change in the amount of transcription factor (TF) precedes the histone state change, the flux drives histones to be modified prior to the change in the amount of TF in the self-regulating circuits. The flux-landscape analyses elucidate the nonlinear nonequilibrium mechanism of epigenetic gene switching.
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