Implications of diffusion and time-varying morphogen gradients for the dynamic positioning and precision of bistable gene expression boundaries
Fig 2
The precision of a gene expression boundary forming atop a dynamically growing gradient depends on the relative rates at which the network and the gradient evolve.
The control (static gradient) corresponds to κ = ∞. Top, time lapses illustrating the concentration of u1 across a whole embryo. Assuming the gradient emerges from a uniformly monostable state (here with α(t = 0, x) = 0), then the slower the gradient emerges, the more precise the resulting boundary will be. Boundary formation lags the movement of the bistable region from anterior to posterior. Bottom, the width of the imprecise region can be predicted from the basins of attraction at each coordinate x; see Fig 1. R quantifies the maximum width of the imprecise region (which depends on the initial conditions) relative to the width of the bistable region, with lower R indicating higher precision. That R is higher for κ = 10 relative to κ = ∞ is an artifact of the particular choice of initial conditions, which are shared across all simulations pictured here.