Impact of cell size on morphogen gradient precision

Abstract

Patterning during embryonic development is remarkably precise and reproducible. How high patterning precision is achieved is still largely elusive. Here, we use a novel simulation framework to determine the impact of cell size on the variability of morphogen gradients and the positional information they convey. We find that both variability in the cell diameter and spatial averaging of the local concentration affect the sensed gradient variability only little. In contrast, the mean cell diameter has a profound impact on gradient variability and on the resulting positional accuracy. We reveal the corresponding scaling relationships between positional error, cell diameter and gradient length. Consistent with this observation, apical cell areas are small in tissues that are patterned by morphogen gradients. We conclude that tissues achieve higher patterning precision with small cross-sectional cell areas.

Patterning precision under non-linear morphogen decay and molecular noise

“…We previously showed that in case of linear decay, there is a negligible impact of cell area variability as long as CVA < 1 [19]. We now find that this holds similarly for non-linear decay (Fig.…”

“…No-flux boundary conditions were used at both outer ends of the domain: We generated large numbers of variable morphogen gradients by numerically solving Eq. 9 with kinetic parameters p, d and D , and cell areas A independently drawn from log-normal distributions for each cell in the domain, as described before [2, 19]. The diffusion coefficient, D , and the degradation rate, d , set the steady-state patterning length scale, , and we report positional quantities relative to the average λ or the average cell diameter, which in turn is chosen to be a fixed multiple of the average λ .…”

“…We therefore used CVA = 0.5 in all simulations unless specified otherwise. Random cell areas were drawn from a log-normal distribution with the specified CVA and mean cell area [19] µA = π µ δ 2…”

“…We used a patterning domain length of 200 cells (Lp = 200µ δ ) and a source domain length of 5 cells (Ls = 5µ δ ), unless otherwise stated. Whether cells average the morphogen signal over their entire cell surface, beyond their cell surface via a cilium, or read out the signal at a single point, has little effect on the readout precision [19]. We therefore only analysed the case where cells average the morphogen signal over their cell surface (their diameter in the 1D model here).…”

“…To investigate the physiological relevance of the mode of morphogen degradation, we employ here a recently developed numerical framework that allows us to analyse how physiological molecular noise translates into gradient variability, and thus, patterning precision [2, 19]. For reported molecular noise levels, the simulated gradients have previously been found to be sufficiently precise to yield the observed precision of developmental boundaries in case of linear decay [2].…”