Fig 2. Equilibrium model predictions for the pattern formation time and readout error.
(A) The early nuclear cycles have a short interphase Tfull and even shorter steady state periods T when the average transcription rate is neither increasing after, nor decreasing before, transcription shut-off during mitosis. The total transcription window Tfull and the time window when the transcription rate is at steady state T of hb transcription in nuclear cycle 10, 11, 12, 13 and early nuclear cycle 14 (before cellularization) at 25°C obtained from 8 MS2-MCP movies [13]. The short periods of transcription inactivity right before and after mitosis are excluded. (B) Steep steady state expression profiles (large H) cannot be reached in short nuclear cycles. Since transcription is shut-off during mitosis, the sigmoidal expression pattern (as in Fig 1D), characterized by the mean promoter activity in nuclei positioned at mid-boundary μP(Tfull, 0) = 0.5, needs to be re-established in each nuclear cycle. We randomize the binding and unbinding rates of the equilibrium model to calculate the upper bound for the mean promoter activity in nuclei positioned at mid-boundary μP(Tfull, 0), and the corresponding Hill coefficient H, for varying OS number N and nuclear cycle duration Tfull. μP(Tfull, 0) < 0.5 indicates the steady state expression profile could not be reached within the nuclear cycle duration. (C) Steep expression profiles (large H) correspond to equilibrium binding models with larger readout errors of the mean activity of the nuclei at the mid-boundary position. The readout error decreases with nc duration. Randomizing parameters of the equilibrium model we plot the lower bound for the readout error of the mean activity of the nuclei, CVP, defined as the standard variation of the readout fP divided by its mean, for varying OS number N and steady state-period T. The bounds in (A-B) are calculated numerically from ∼50000 data points of the solutions of dynamical equations of the equilibrium model (S1D Text) with N OS, each corresponding to a randomized kinetic parameter set.