Biology Reference
In-Depth Information
ly-shaped triangle in the two configurations. Because we are interest-
ed in the aspects of shape that change the least, we need to define a
statistic that measures the degree of shape difference. We can then
look at all possible triangles and select the one (not necessarily unique)
where the shape difference is minimum. Once the seed triangle is iden-
tified, we expand the clique by adding a landmark to the seed triangle,
so that the clique has four landmarks. Which landmark should be
added? We search through all possible four-landmark cliques (condi-
tional on the three landmarks already included), and we add the
landmark that creates the four-landmark clique where the shape dif-
ference is again minimal. We then add a fifth landmark using the same
criterion, and so on. When do we stop adding landmarks? The clique
will eventually grow to the size where the addition of any remaining
landmark will result in shapes that will be too different to be consid-
ered shape-conservative. We define “too different” by specifying some a
priori tolerance that the shape-difference statistic cannot exceed. Once
the tolerance is exceeded, the clique has reached its maximum size. We
then begin a search for a new clique, providing there are enough land-
marks left over and that there is some remaining triangle that will
meet the criterion for being shape-conservative. At most, the new
clique can share only one (for two-dimensional data) or two (for three-
dimensional data) landmarks with any preexisting clique. Once the
second clique reaches its maximum size (beyond which the addition of
any new landmark will produce configurations that are too different),
the search for a new clique starts over. The analysis concludes when all
possible cliques (given the tolerance) have been found.
The T statistic, defined by Lele and Richtsmeier (1991; see Chapter
4 ), as a coordinate-system- and scale-invariant measure of shape
difference that can be used for clique formation. Recall that
and that T has a minimum possible value of 1.0, obtained when two
landmark configurations have identical shapes. The a priori choice of
a tolerance value for T is arbitrary, and we can vary the tolerance to
examine its effect on how the cliques form. In many cases, a reasonable
starting tolerance might be 5 to 10% of the T statistic that is observed
in a form comparison that uses all of the landmarks.
To illustrate, we can again compare the structures of the mutant
and normal insulins. The results of the analysis are shown in Figures
7.6 to 7.8 . When all 51 landmarks are included, the T statistic is 11.85,
Search WWH ::

Custom Search