Individuals can vary substantially in size, but the proportions of their body plans are often maintained. We generated smaller zebrafish by removing 30% of their cells at the blastula stages and found that these embryos developed into normally patterned individuals. Strikingly, the proportions of all germ layers adjusted to the new embryo size within 2 hours after cell removal. As Nodal-Lefty signalling controls germ-layer patterning, we performed a computational screen for scale-invariant models of this activator-inhibitor system. This analysis predicted that the concentration of the highly diffusive inhibitor Lefty increases in smaller embryos, leading to a decreased Nodal activity range and contracted germ-layer dimensions. In vivo studies confirmed that Lefty concentration increased in smaller embryos, and embryos with reduced Lefty levels or with diffusion-hindered Lefty failed to scale their tissue proportions. These results reveal that size-dependent inhibition of Nodal signalling allows scale-invariant patterning.

Fluorescence Recovery After Photobleaching (FRAP) and inverse FRAP (iFRAP) assays can be used to assess the mobility of fluorescent molecules. These assays measure diffusion by monitoring the return of fluorescence in bleached regions (FRAP), or the dissipation of fluorescence from photoconverted regions (iFRAP). However, current FRAP/iFRAP analysis methods suffer from simplified assumptions about sample geometry, bleaching/photoconversion inhomogeneities, and the underlying reaction-diffusion kinetics. To address these shortcomings, we developed the software PyFRAP, which fits numerical simulations of three-dimensional models to FRAP/iFRAP data and accounts for bleaching/photoconversion inhomogeneities. Using PyFRAP we determined the diffusivities of fluorescent molecules spanning two orders of magnitude in molecular weight. We measured the tortuous effects that cell-like obstacles exert on effective diffusivity and show that reaction kinetics can be accounted for by model selection. These applications demonstrate the utility of PyFRAP, which can be widely adapted as a new extensible standard for FRAP analysis.

The hindered diffusion model postulates that the movement of a signaling molecule through an embryo is affected by tissue geometry and binding-mediated hindrance, but these effects have not been directly demonstrated in vivo. Here, we visualize extracellular movement and binding of individual molecules of the activator-inhibitor signaling pair Nodal and Lefty in live developing zebrafish embryos using reflected light-sheet microscopy. We observe that diffusion coefficients of molecules are high in extracellular cavities, whereas mobility is reduced and bound fractions are high within cell-cell interfaces. Counterintuitively, molecules nevertheless accumulate in cavities, which we attribute to the geometry of the extracellular space by agent-based simulations. We further find that Nodal has a larger bound fraction than Lefty and shows a binding time of tens of seconds. Together, our measurements and simulations provide direct support for the hindered diffusion model and yield insights into the nanometer-to-micrometer-scale mechanisms that lead to macroscopic signal dispersal.