Figure 2

Physical constraints of Bicoid gradient from the ensemble of embryos data. (A) The normalized variance. In the key, "Data" denotes the members of ${\eta }^2({\displaystyle \underset{i}{\cup }{I}_{ij}})$ from the high-variance ensemble of 89 embryos. Lines denote simulation results as shown in the key. [αnβ] denotes the full model ${\eta }^2({\widehat{I}}_j)={\eta }^2([\stackrel{\_}{\alpha n\beta }])$, [α] denotes ${\eta }^2([\widehat{\alpha }])$, [n] denotes ${\eta }^2([\widehat{n}])$, and [β] denotes ${\eta }^2([\widehat{\beta }])$. The parameters used in simulation were σ _α = 0.2, σ _β = 1.7, J = 30 (molecules/s), m = 0.7, D = 17.2 (μ m²/s) and ω = 0.0027 (s^-1). (B) is a scatterplot of Bcd molecular number ${\widehat{n}}_j$, while the inset shows simulated fluorescence intensity for models and parameters used in panel A. (C) shows the residuals (deviations from mean) of panel B. (D), (E) and (F) show the same information as panel A, B, and C respectively, but from the low-variance ensemble of 17 embryos, with parameters used in simulation σ _α = 0.13, σ _β , = 1.0, J = 200 (molecules/s), m = 0.07, D = 17.2 (μ m²/s) and ω = 0.00215 (s^-1). Note that the axes in panel A and D are scaled differently, and the absolute molecule number is shown in the inset to panel E.