Further Applications of EDMA - An Invariant Approach to Statistical Analysis of Shapes - page 268

larly in their reactions to other macromolecules in the body, to drugs,
or to pesticides and other toxins. In this section, we show how EDMA
can be applied to the study of molecular structures.
What are the “landmarks” used for molecular comparisons? They
are atoms that are considered “homologous” for all of the molecules
under consideration. To use proteins as an example, these macro-
molecules are made up of amino acids, and each amino acid can
potentially be considered a “landmark” for structural comparisons.
More specifically, we can use the spatial position of a single atom as a
representative of the amino acid as a whole. The choice of this atom is
arbitrary; however, it is usually the C α atom, because all amino acids
have one and only one. Note that we must assume a one-to-one corre-
spondence between amino acids in the proteins we compare. Just as for
morphological comparisons, molecules that are compared using EDMA
must have the same number of labeled landmarks. This requirement
restricts us to comparisons of molecules with similar amino-acid
sequences (as in the example below), where the “homology” between
amino acids can be confidently inferred. The instrumentation and
quantitative methods used for estimating the three-dimensional posi-
tions of the atoms in a molecule are beyond the scope of this discussion.
The reader is referred to Doucet and Weber (1996) for a review.
7.2.1 Studying molecular structure using EDMA
When we use EDMA to compare molecules, we can ask the same gen-
eral questions that are asked in morphological comparisons: What are
Figure 7.4 Schematic diagram of the structure of an insulin molecule (modified from
Ganong, 1985). The two amino-acid chains are held together by disulfide bridges. The
site of the mutation discussed in the example (B24) is indicated.