Differential diffusivity of Nodal and Lefty underlies a reaction-diffusion patterning system

Abstract

Biological systems involving short-range activators and long-range inhibitors can generate complex patterns. Reaction-diffusion models postulate that differences in signaling range are caused by differential diffusivity of inhibitor and activator. Other models suggest that differential clearance underlies different signaling ranges. To test these models, we measured the biophysical properties of the Nodal/Lefty activator/inhibitor system during zebrafish embryogenesis. Analysis of Nodal and Lefty gradients revealed that Nodals have a shorter range than Lefty proteins. Pulse-labeling analysis indicated that Nodals and Leftys have similar clearance kinetics, whereas fluorescence recovery assays revealed that Leftys have a higher effective diffusion coefficient than Nodals. These results indicate that differential diffusivity is the major determinant of the differences in Nodal/Lefty range and provide biophysical support for reaction-diffusion models of activator/inhibitor-mediated patterning.

Fig. 1. Model of the Nodal/Lefty activator/inhibitor reaction-diffusion system and regulation of range

(A) In the source, Nodal signals (blue) activate their own expression as well as the expression of Lefty (red), which inhibits Nodal production. Nodal signaling in the responsive field is inhibited by the long-range inhibitor Lefty. (B) Distribution is controlled by both diffusivity, D, and clearance, k₁. Highly mobile molecules that are rapidly cleared from the extracellular space (black circles) can form gradients similar to those formed by poorly diffusive molecules that are slowly cleared (blue). Decreasing the clearance of the more diffusive species results in a long-range gradient (red). Simulations were performed as described in Text S7.

Fig. 2. Measurement of Nodal- and Lefty-GFP distributions

(A) At late blastula stages, approximately 40 cells secreting Nodal- or Lefty-GFP proteins were transplanted from donor embryos into wildtype hosts (Text S4). The gradient profile was determined using a maximum intensity projection of five confocal slices encompassing a depth of 20 μm (about one cell). (B) A representative projection is shown for Squint-GFP. (C–F) Construct schematic, representative maximum intensity projection and distribution profiles 30, 60 and 120 min post transplantation for Cyclops-GFP (C), Squint-GFP (D), Lefty1-GFP (E), and Lefty2-GFP (F). Embryos that did not undergo transplantation were used for background subtraction, and all intensities were normalized to the value most proximal to the source. Error bars indicate standard error. Number of embryos analyzed at 30, 60 and 120 min post transplantation, respectively, for Cyclops-GFP n₃₀=7, n₆₀=7, n₁₂₀=7; for Squint-GFP n₃₀=12, n₆₀=17, n₁₂₀=20; for Lefty1-GFP n₃₀=8, n₆₀=8, n₁₂₀=13; for Lefty2-GFP n₃₀=12, n₆₀=10, n₁₂₀=12.

Fig. 3. Measurement of extracellular clearance rate constants

(A) Uniformly expressed Nodal- or Lefty-Dendra2 fusion proteins were photoconverted using a UV pulse. The average extracellular photoconverted Dendra2 intensity was monitored over time and used to determine the clearance rate constants (k₁) and half-lives (τ = ln(2)/k₁) by fitting exponential functions to data from individual embryos (Text S5). The normalized average intensity from 10 min interval Squint-Dendra2 experiments (black, n = 11) is shown fitted with an exponential function (red). Error bars indicate standard deviation. See fig. S12 for Cyclops-, Lefty1-, and Lefty2-Dendra2 results. (B) Summary of mean extracellular k₁ values. Error bars indicate standard error.

Fig. 4. Measurement of effective diffusion coefficients

(A) Uniformly expressed Nodal- or Lefty-GFP fusion proteins were locally photobleached (yellow box) at blastula stages. Fluorescence recovery was monitored over time, and the effective diffusion coefficient, D, was determined by fitting the resulting recovery profile (black) with simulated recovery curves (red) that were numerically generated using a model that includes diffusion, production and clearance in a three-dimensional embryo-like geometry (Text S6). Results for an individual Squint-GFP embryo are shown. See fig. S18 for Cyclops-, Lefty1-, and Lefty2-GFP results. (B) Summary of mean diffusion coefficients. Error bars indicate standard error.