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Implications of diffusion and time-varying morphogen gradients for the dynamic positioning and precision of bistable gene expression boundaries
Fig 3
(a) Temporal decrease in the morphogen concentration at every point in space can “sweep away” imprecision in the expression boundary. Decrease in morphogen concentration causes the bistable region (solid gray line) to shift anteriorly over time. Thus, cells to the anterior are initially monostable for high 
and remain there as they become bistable, whereas cells in the initially bistable region become monostable for high 
. The initial conditions here are derived from the steady-state solution to a system with a static gradient equivalent to that of the dynamic gradient at t = 0; see Fig 2 with κ = ∞. (b) Slower gradient dynamics are more effective at increasing precision. Lines are mean, error bars are standard deviation across N = 10 simulations with different initial conditions at different values of κ (light to dark red), the ratio between rate of gradient decay and rate of convergence to steady state. R quantifies the maximum width of the imprecise region relative to the width of the bistable region at the time tf by which the boundary has shifted by a fixed amount from its initial location. Lower R corresponds to greater precision (see text). Slower-decaying gradients produce more precise boundaries for the same total shift than do faster-decaying gradients, but take longer to achieve these gains.
doi: https://doi.org/10.1371/journal.pcbi.1008589.g003