Quantification of Morphogen Gradients and Patterning Scale Invariance along Dorsal-ventral Embryonic Axis
Morphogen gradients provide positional information to underlying cells that translate the information into differential gene expression and eventually different cell fates. Scale invariance is the property where the gradients of the morphogen adjust proportionately to the size of the domain. Scale invariance of morphogen gradients or patterns of differentiation is a common phenomenon observed between individuals within the same species and between homologous tissues or structures in different species. To determine whether a pattern is scale invariant, we and others developed definitions and measurements of gradient scaling. These include point-wise and global scaling errors as well as global scaling power. Furthermore, there are several mathematical conditions for scale invariance of advection-diffusion-reaction models that inform mechanisms of scaling. Herein we provide a deeper perspective on modeling and measurement of scale-invariance of morphogen gradients. Scale invariance of DV patterning has been investigated in invertebrates but remains poorly-understood in vertebrates. In both vertebrates and invertebrates, spatial patterning progression along Dorsal-ventral (DV) embryonic axis depends on a morphogen gradient of Bone Morphogenetic Protein (BMP) signaling. Here, we introduce a method for studying DV patterning scale invariance by precisely altering the size of zebrafish embryos by reducing vegetal yolk. Use of this method in scaling experiments indicated that the degree of scaling for intraspecies scaling within zebrafish is greater than that between Danioninae species. Specifically, through analysis of experimentally re-sized embryos, we determined that DV patterning and its underlying morphogen gradients are scale invariant within species of zebrafish. We then extended our study to investigate DV patterning between Danioninae species (zebrafish and giant danio) and found that morphogen gradients do not scale between Danioninae species. In the process of developing tools to quantify morphogen gradients from fluorescent images, we created a novel method to match points in two partially overlapping images. Point cloud data sets, or simply point clouds (PCs), originating from a common specimen but containing different measurement parameters (i.e. using different sensors, times, depths, viewpoints, etc.) usually contain both overlapping and non-overlapping points. Registration aligns these distinct PCs into one coordinate system by assigning point-by-point correspondence between PCs and applying a transformation. Registration shows great potential for practical applications, but the effectiveness of current methods is limited in PCs having large differences in relative initial positions, low overlapping ratios, and excessive noise. We introduce a point matching algorithm called Signature that relaxes these constraints. We approach the problem of identifying corresponding points between PCs by assigning and matching point identification (ID), or the distance of a point to a select number of closest points in the same PC. Signature has been tested on both computationally generated images and experimentally generated images from confocal microscopy of biological samples. Signature accurately identifies point correspondence in PCs with any initial angles, with overlapping ratios as low as 15%, and shows some improvement in aligning noisy PCs. Preprocessing with Signature also intelligently relaxes point-wise registration of initial point positions. Furthermore, combining Signature with Anchor Point Alignment allows for robust alignment of noise-free PCs under any initial position.
Umulis, Purdue University.
Bioengineering|Biomedical engineering|Developmental biology
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