Further Applications of EDMA - An Invariant Approach to Statistical Analysis of Shapes - page 271

chains. More specifically, we see that the distances between the muta-
tion (B24) and the end of the A chain (A19-A21) are more than twice
the normal values. Therefore, we can conclude that the mutation not
only produces a kink in the B chain but also moves the terminal part
of the B chain further from the A chain.

Table 7.2 Extreme values of a form difference matrix comparing
mutant human insulin in the numerator and normal human insulin
in the denominator.
Mutant << Normal (FDM minima)

Mutant >> Normal (FDM maxima)

B22 — B27 0.224 B1 — B14 1.900

B21 — B26 0.380 A20 — B23 1.916

B21 — B27 0.380 A21 — B22 1.921

B22 — B26 0.398 A1 — B29 1.951

B22 — B28 0.402 A21 — B28 1.962

B23 — B27 0.446 A1 — B30 1.977

B21 — B25 0.456 A1 — B28 2.044

B22 — B29 0.462 A19 — B24 2.263

B21 — B28 0.484 A21 — B24 2.370

A19 — B21 0.514 A20 — B24 2.896

7.2.2 Similarity in shape defined by invariant cliques of landmarks

To study regions of similarity in molecules, we can use a heuristic,
EDMA-based method for finding landmark “cliques.” The method was
originally developed for application to morphological problems, where
“shape-conservative” landmark subsets are identified in a series of
anatomical structures (skulls of different taxa, for example; Cole et al.,
1998, 1999). However, the development of the method was inspired by
algorithms that were developed in the context of molecular biology,
reviewed by Willett (1991) and Doucet and Weber (1996). Those algo-
rithms were designed to find the largest similarly shaped regions in
different molecules. In the molecular biology literature, these are
referred to as “largest common substructures.”
Let us first describe in words what the clique-finding algorithm
does. Suppose we are interested in a case where two landmark config-
urations are compared. Since we need at least three landmarks to
describe shape, we begin by selecting a triangle as the “seed” for the
first clique and then adding landmarks (“growing” the clique) through
an iterative process. The seed triangle is defined as the most similar-