The impact of cell size on morphogen gradient precision

Abstract

Tissue patterning during embryonic development is remarkably precise. In this paper, we numerically determine the impact of the cell diameter, gradient length, and the morphogen source on the variability of morphogen gradients. In this way, we show that the positional error increases with the gradient length relative to the size of the morphogen source, and with the square root of the cell diameter and the readout position. We provide theoretical explanations for these relationships, and show thatthey enable high patterning precision over developmental time for readouts that scale with expanding tissue domains, as observed in the Drosophila wing disc. Our analysis suggests that epithelial tissues generally achieve higher patterning precision with small cross-sectional cell areas. An extensive survey of measured apical cell areas shows that they are indeed small in developing tissues that are patterned by morphogen gradients. Enhanced precision may thus have led to the emergence of pseudostratification in epithelia, a phenomenon for which the evolutionary benefit had so far remained elusive.

2D effects enhance precision of gradient-based tissue patterning

“…We ignore variability in cell areas or diameters here, as physiological levels were previously shown to have negligible impact on gradient precision. 18 The patterning axis of length is further divided into a morphogen source and a patterning domain , such that . The steady-state reaction-diffusion equation from 1D ( Equation 3 ) is extended to 2D by writing …”

“…Indeed, the gradient variability in wider tissues is considerably lower than that predicted in 1D (marked in orange in Figures 2 A–2D). 17 , 18 …”

“…The problem has been studied intensely, both theoretically and experimentally, 3 , 4 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 and recently gained new traction with the realization that morphogen gradients may be considerably more precise than previously measured. 17 , 18 , 19 …”

“…For the reported physiological amount of parameter variability, the resulting 1D gradients differ between separate realizations (i.e., between embryos) ( Figure 1 A), and have a positional error similar to that observed for the readouts in the mouse neural tube. 17 The previous analysis of 1D gradients further revealed that a small average cell diameter along the patterning axis is of key importance, 18 potentially explaining why epithelia that are patterned by gradients, such as the neuroepithelium, are pseudostratified. 27 …”

“…Spatiotemporal averaging over the cell surface has only minor effects on the precision of the gradient readout. 18 As a consequence, cilia and cell surface receptors can be expected to achieve a similar readout precision. Self-enhanced decay has been suggested to increase gradient robustness to noise in the morphogen source, 28 but this effect is negligible when considering the effects of molecular noise more explicitly.…”