(Color) Model of a self-regulating gene. The dimer of the product protein works as a repressor, constituting a negative feedback loop.
(Color) Dependence of static quantities and strength of the fluctuation on adiabaticity and the typical number of protein molecules . From left to right, the probability of the DNA state to be off , the average and variance of the protein number, and the strength of fluctuation are plotted on the plane of and . Results of the mean-field theory (upper figures) and those of the MC calculation (lower figures) are compared.
(Color) Functional form of and examples of , and MC trajectories. In the top two figures, functional form of obtained from the mean-field theory and that of the MC calculation are shown on the plane of and . In the white region, is dominated by a single exponential function and other minor components contribute less than 1% in . In the region shaded with slanting lines, has an oscillatory component and in the cross-hatched region, and is composed of multiple exponential functions. For the points , , , and designated on the plane, and calculated by the mean-field theory (red lines) and those of the MC results (crosses) are compared. Also exemplified are MC trajectories of the protein number and the DNA state shown as functions of time . The horizontal red lines in the figures of and denote their averaged values.
(Color) The relaxation time calculated from and the relaxation time calculated from are plotted with the unit of on the plane of and . The results of the mean-field theory (upper figures) and the MC results (lower figures) are compared.
(Color) Effective temperature defined by Eq. (9) is plotted for and . in the white region. The results of the mean-field theory (upper figures) and the MC results (lower figures) are compared.
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