Further Applications of EDMA - An Invariant Approach to Statistical Analysis of Shapes - page 269

the greatest differences in form? What are the greatest similarities in
form? How can these differences and similarities be localized and
summarized? To demonstrate how EDMA methods can be applied to
studies of molecular structure, we examine variations in insulin
molecules, which are small proteins. Insulin is a pancreatic hormone
that is crucial to the maintenance of normal metabolism, so that the
relationship between its structure and function is of great importance
(Hua et al., 1993). The structure of insulin, which is shown schemati-
cally in Figure 7.4 , is very conservative across vertebrates. This
conservatism helps us to feel confident about recognizing atomic
homologies. There are two chains of amino acids (called the A and B
chains), linked by disulfide bridges. The A chain is composed of 21
amino acids, while the B chain is composed of 30.
The data for the following examples are the three-dimensional coor-
dinates of C atoms, available from the Protein Databank at
Brookhaven National Laboratories (Berstein et al., 1977; Abola et al.,
1987). We compare normal human insulin with a mutant form that
substitutes serine (Ser) for phenylalanine (Phe) in the B24 position,
denoting the 24th amino acid of the B chain (Hua et al., 1991, 1993).
The amino-acid sequences are otherwise identical. The clinical conse-
quence of this mutation — diabetes mellitus — is the same as for an
insulin deficiency, even though the molecule is present in normal con-
centrations (Hua et al., 1993). This indicates a reduction in the
bioactivity of the mutant. The amino-acid substitution changes the
three-dimensional structure of the molecule, which causes a change in
its function. The molecules are illustrated in Figure 7.5 . Note that the
atoms that describe amino acid positions are literally surrounded by
empty space. There are no underlying morphological structures (as
with morphological landmarks) to place the molecules in a familiar
visual context for making comparisons. In addition, there is no stan-
dard coordinate system for describing molecules, so that (unlike the
case with many complex organisms) terms like “anterior” and “superi-
or” have no meaning. Finally, the large number of landmarks makes
molecular comparisons even more complex.
We can use a form-difference matrix to localize the structural dif-
ferences that result from the mutation. Table 7.2 s hows the extremes
of a sorted form-difference matrix where the mutant insulin is in the
numerator and the normal insulin is in the denominator. The ten
smallest values indicate distances in the mutant molecule that are
much smaller than normal. Note that these distances are between
amino acids that bracket the site of the mutation on the B chain (B24).