Correlations Between the Morphology of Sonic Hedgehog Expression Domains and Embryonic Craniofacial Shape

Quantitative analysis of gene expression domains and investigation of relationships between gene expression and developmental and phenotypic outcomes are central to advancing our understanding of the genotype-phenotype map. Gene expression domains typically have smooth but irregular shapes lacking homologous landmarks, making it difficult to analyze shape variation with the tools of landmark-based geometric morphometrics. In addition, 3D image acquisition and processing introduce many artifacts that further exacerbate the problem. To overcome these difficulties, this paper presents a method that combines optical projection tomography scanning, a shape regularization technique and a landmark-free approach to quantify variation in the morphology of Sonic hedgehog expression domains in the frontonasal ectodermal zone (FEZ) of avians and investigate relationships with embryonic craniofacial shape. The model reveals axes in FEZ and embryonic-head morphospaces along which variation exhibits a sharp linear relationship at high statistical significance. The technique should be applicable to analyses of other 3D biological structures that can be modeled as smooth surfaces and have ill-defined shape.