Computational protocol: Geometric Morphometrics on Gene Expression Patterns Within Phenotypes: A Case Example on Limb Development

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Protocol publication

[…] This set of analyses was performed to assess the dynamic shape changes of the limb bud in association with the Hoxa11 and Hoxa13 gene expression domains over limb development. In this case, we also used a Procrustes-based semilandmark analysis, because it is the only method that allowed us to analyze simultaneously the contours of the limb and the gene expression domains. Furthermore, it allowed us to assess not only the patterns of morphological variation, but also the patterns of covariation between the limb and the gene expression domains at each stage. This provided an extra level of information about the relationship between the gene expression of Hoxa11 and Hoxa13 and the actual morphology of the limb.For each sample, we defined a configuration of 42 equally spaced points: 21 points located along the limb contour and 21 points located along the contour of the gene expression domain. The limb and the gene expression domains were represented by the same number of points to guarantee similar weighting of both features in the shape analysis. The start and end points of the limb bud outline were treated as fixed anatomical landmarks, whereas the remaining 40 points were treated as 2D curve semilandmarks that were slid to minimize the bending energy (; ; ).To assess shape variation in limb and gene expression during the whole sequence of limb development, we performed GPA and PCA using the samples from all four staging groups for Hoxa11 (N=75) and for Hoxa13 (N=130). We also explored the morphological variation within each stage by performing separate GPA and PCAs for each stage.To evaluate the patterns of covariation between the limb and the Hoxa11 and Hoxa13 expression domains, we used partial least squares (PLS) (). This method quantifies the covariation patterns between subsets of landmarks defined within the structure under study. In our study, we defined two different assemblages of the limb/gene configuration of landmarks to explore different scenarios of limb development. First, we separated the landmarks of the limb contour and the landmarks of the contour of the gene expression domains into two different subsets of landmarks to quantify the covariation between the limb and the Hoxa11 and Hoxa13 gene expression domains (c). Second, we divided the limb/gene configuration of landmarks into two subsets of landmarks that represented the anterior and the posterior regions of the limb (d). To have comparable results, the subsets of landmarks systematically had the same number of landmarks (P=21).The Two-Block PLS analysis estimates the covariation between the two blocks of landmarks by performing a singular value decomposition of the covariance matrix between the subsets of landmarks (). As a result, PLS produces orthogonal pairs of new axes derived as linear combinations of the original variables: the first pair of axes has the largest interblock covariance, the second pair the next largest covariance, etc. (). In our analysis, each PLS analysis was applied to the adjusted coordinate data obtained after a joint Procrustes fit of the two configurations of landmarks. The amount of covariation was measured by the RV coefficient, which is a multivariate analog of the squared correlation ().Finally, along with shape analyses, we also performed size analyses. For each sample, we estimated the size of the limb and the size of the high and moderate gene expression domains. Size was computed as the square root of the summed distances between each landmark coordinate and the centroid of the configuration of landmarks defining each structure (i.e., the so-called centroid size) (). We then estimated the average sizes of the limb and the gene expression domains for each staging group, and tested for statistical significant differences between consecutive stages using a Welch Two-Sample t-test.In all limb/gene shape and size analyses, Hoxa11 and Hoxa13 labeled limbs were analyzed separately and for both genes we analyzed high- and moderate gene expression levels and compared the results. All the analyses were performed using R (; http://www.R-project.org, last accessed October 1, 2015); geomorph (), a package available at CRAN (http://cran.r-project.org/web/packages/geomorph, last accessed October 1, 2015), and MorphoJ (). […]

Pipeline specifications

Software tools geomorph, MorphoJ
Application Computerized tomography scan imaging
Organisms Mus musculus, Caenorhabditis elegans