Inference of Morphogen Gradient Precision from Molecular Noise Data

Abstract

During development, morphogen gradients provide spatial information for tissue patterning. Gradients and readout mechanisms are inevitably variable, yet the resulting patterns are strikingly precise. Measurement limitations currently preclude precise detection of morphogen gradients over long distances. Here, we develop a new formalism to estimate gradient precision along the entire patterning axis from measurements close to the source. Using numerical simulations, we infer gradient variability from measured molecular noise levels in morphogen production, decay, and diffusion. The predicted precision is much higher than previously measured—precise enough to allow even single gradients to define the central progenitor boundaries during neural tube development. Finally, we show that the patterning mechanism is optimized for precise progenitor cell numbers, rather than precise boundary positions, as the progenitor domain size is particularly robust to gradient alterations. We conclude that single gradients can yield the observed developmental precision, which provides new prospects for tissue engineering.

Impact of cell size on morphogen gradient precision

“…1D, blue curve). Square-root scaling for the decay length variability (α = 0.5) follows from the law of large numbers and is consistent with the inversesquare-root scaling reported for the dependency of CV λ on the patterning domain length Lp at fixed cell size (Vetter and Iber;2021). Together, this suggests that…”

“…Noisy gradients were obtained by solving a one-dimensional steady-state reaction-diffusion system, as developed by Vetter and Iber (2021), given by the boundary value problem with zero-flux boundary conditions …”

“…Each data point in the figures corresponds to the mean ± SEM of 1000 independent simulations with random parameters. For each generated morphogen gradient, the two coefficients λ and C 0 were extracted by fitting hyperbolic cosines to the logarithmised numerical solution as detailed in Vetter and Iber (2021).…”

“…The Heaviside step function H(−x) ensures that production only occurs in the source, whereas degradation is assumed to take place over the whole domain. The kinetic parameters k = p, d, D were drawn for each cell independently from log-normal distributions with prescribed mean values µ k and respective coefficients of variation CV k (see Vetter and Iber (2021) for details). We fixed molecular variability at the physiological value CV k = 0.3 (Vetter and Iber;2021) here.…”

“…A recently developed numerical framework estimates how much variability in and between morphogen gradients can be accounted for by the molecular noise reported for morphogen production, decay, and diffusion (Vetter and Iber; 2021). The predicted gradient variability is considerably lower than what has been reported.…”