Precision in a rush: Trade-offs between reproducibility and steepness of the hunchback expression pattern
Fig 3
The positional resolution of the pattern.
(A) We use the positional resolution ΔX to describe how well nearby nuclei can readout discernible inputs. F+ and F− are the positional readouts in individual nuclei positioned at ±ΔX/2 from the mid-boundary point (X = 0). Positional resolution, ΔX, is the minimal distance between nuclei that make distinct readouts at steady state P(F+ ≤ F−) ≤ 0.05. Positional resolution results from a trade-off between the pattern steepness and the readout error: (i-iii) a cartoon representation of the trade-off for a flat pattern (low H, i), pattern of intermediate steepness (ii) and a steep pattern (high H, iii). Both (i) and (iii) have a large value of positional resolution. At low H (i), the readout errors are low but the mean readout values are very similar. At high H (iii), the mean readout values are different but the readout errors are large. The best positional resolution is reached with an intermediate H (ii). (B) Each nucleus readout is the average of M independent single locus readouts: M can be 1 (there is one copy of the gene as is the case in a heterogeneous gene construct), 2 (there is one gene copy on each chromosome as is the case of the WT embryo) or greater (nuclei at the same position can communicate by diffusion of readout molecules [35, 36] and the readout is the result of spatial averaging). As M increases, the readout error of the nuclei decreases due to spatial averaging.