Protein structures as shapes: Analysing protein structure variation using geometric morphometrics

A phenotype is defined as an organism9s physical traits. In the macroscopic world, an animal9s shape is a phenotype. Geometric morphometrics (GM) can be used to analyze its shape. Let9s pose protein structures as microscopic three dimensional shapes, and apply principles of GM to the analysis of macromolecules. In this paper we introduce a way to 1) abstract a structure as a shape; 2) align the shapes; and 3) perform statistical analysis to establish patterns of variation in the datasets. We show that general procrustes super-imposition (GPS) can be replaced by multiple structure alignment without changing the outcome of the test. We also show that estimating the deformation of the shape (structure) can be informative to analyze relative residue variations. Finally, we show an application of GM for two protein structure datasets: 1) in the α-amylase dataset we demonstrate the relationship between structure, function, and how the dependency of chloride has an important effect on the structure; and 2) in the Niemann-Pick disease, type C1 (NPC1) protein9s molecular dynamic simulation dataset, we introduce a simple way to analyze the trajectory of the simulation by means of protein structure variation.