During vertebrate embryogenesis, dorsal-ventral patterning is controlled by the BMP/Chordin activator/inhibitor system. BMP induces ventral fates, whereas Chordin inhibits BMP signaling on the dorsal side. Several theories can explain how the distributions of BMP and Chordin are regulated to achieve patterning, but the assumptions regarding activator/inhibitor diffusion and stability differ between models. Notably, ‘shuttling’ models in which the BMP distribution is modulated by a Chordin-mediated increase in BMP diffusivity have gained recent prominence. Here, we directly test five major models by measuring the biophysical properties of fluorescently tagged BMP2b and Chordin in zebrafish embryos. We found that BMP2b and Chordin diffuse and rapidly form extracellular protein gradients, Chordin does not modulate the diffusivity or distribution of BMP2b, and Chordin is not required to establish peak levels of BMP signaling. Our findings challenge current self-regulating reaction-diffusion and shuttling models and provide support for a graded source-sink mechanism underlying zebrafish dorsal-ventral patterning.

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.