Precision of Readout at the hunchback Gene: Analyzing Short Transcription Time Traces in Living Fly Embryos
Fig 7
Precision of the hunchback gene transcription readout.
A. Comparison of the relative error in the mRNA produced during the steady state of the interphase estimated empirically from data (abscissa) and from theoretical arguments in Eq 4 for a two state switching promoter (blue symbols) using the inferred parameters in Fig 5C (ordinate), and theoretical arguments in Eq 5 for a Poisson-like static promoter (red symbols) using the inferred parameters in Fig 5A (ordinate), in the anterior (circles and squares) and the boundary (diamonds and triangles) regions. The theoretical prediction for the two state promoter shows very good agreement with the data, whereas the Poisson-like promoter shows poor agreement, especially in the boundary region. B. The relative error in the total mRNA produced in cell cycle 13 directly estimated from the data as the variance over the mean of the steady state mRNA production (red line, same data as in A), sum of the intensity over the whole duration of the interphase (blue line) and the total mRNA produced during cell cycles 11 to 13 (green line) for equal width bins equal to 10% embryo length at different positions along the AP axis. Each line describes an average over four embryos (see S9C Fig for the same data plotted separately for each embryo) and the error bars describe the variance. To calculate the total mRNA produced over the cell cycles, we take all the nuclei within a strip at cell cycle 13 and trace back their lineage through cycle 12 to cycle 11. We then sum the total intensity of each nuclei in cell cycle 13 and half the total intensity of its mother and 1/4 of its grandmother. C. Comparison of the relative error in the mRNA produced during the steady state for a two state, k1/k2 = 0, (solid lines) and three state cycle model, k1/k2 = 1, (dashed lines) with the same , for different values of
and koff, shows that the three state cycles system allows for greater readout precision. D. A comparison of the theoretical prediction of the steady state relative error rate for the Poisson-like and two state promoter as a function of Pon shows that the Poisson-like promoter is always more accurate. Different values of kon are considered for the two state model.