Motivation: Complexome profiling combines native gel electrophoresis with mass spectrometry to obtain the inventory, composition and abundance of multiprotein assemblies in an organelle. Applying complexome profiling to determine the effect of a mutation on protein complexes requires separating technical and biological variations from the variations caused by that mutation. Results: We have developed the COmplexome Profiling ALignment (COPAL) tool that aligns multiple complexome profiles with each other. It includes the abundance profiles of all proteins on two gels, using a multi-dimensional implementation of the dynamic time warping algorithm to align the gels. Subsequent progressive alignment allows us to align multiple profiles with each other. We tested COPAL on complexome profiles from control mitochondria and from Barth syndrome (BTHS) mitochondria, which have a mutation in tafazzin gene that is involved in remodeling the inner mitochondrial membrane phospholipid cardiolipin. By comparing the variation between BTHS mitochondria and controls with the variation among either, we assessed the effects of BTHS on the abundance profiles of individual proteins. Combining those profiles with gene set enrichment analysis allows detecting significantly affected protein complexes. Most of the significantly affected protein complexes are located in the inner mitochondrial membrane (mitochondrial contact site and cristae organizing system, prohibitins), or are attached to it (the large ribosomal subunit).