Biomedical Engineering Reference
In-Depth Information
to the others, so this isomer was established as the monomer. After two, three, and
four of these monomers were combined in simple combinations, the cluster energy
decreased monotonically with the number of monomers. However, comparison of
the energies for structures with the most compact morphology at each number
combination showed that the minimum energy was attained with a Ca
9
(PO
4
)
6
trimer.
The structure of Ca
9
(PO
4
)
6
in this case has a
T
h
symmetry, and, when refined to take
up the minimum energy structure on the potential energy surface (PES), it shows an
S
6
symmetry.
Although 24 types of isomers with a local energy minimum appear on the
Ca
9
(PO
4
)
6
PES, among these,
S
6
is a special structure that has nearly the lowest
energy despite its extremely high symmetry. From these results, it was determined
that if clusters are considered as the growth units for HAP,
S
6
is the most appropriate
structure. It has sixfold symmetry, and the crystal structure of HAP cannot be
constructed by aggregating these clusters. However, simply by slightly rotating the
surrounding phosphate ions relative to the calcium ion at the center of the cluster,
the cluster can be changed into a Posner cluster with threefold symmetry. Depending
on whether the direction of rotation is clockwise or counterclockwise, it is possible
to bestow chirality to the cluster as well. The energy required for this rotation is
10 kcal or less and is not a barrier to structural conversion. The above-mentioned
calculation results all presume treatment in vacuum, and no conclusions have yet
been reached on whether or not the
S
6
structure stably exists in actual solutions.
Highly intriguing research results have been reported for the growth units of
biominerals, including HAP [
87
]. In this research, a diluted solution of calcium
chloride was gradually added to a diluted carbonate buffer solution under constant
pH conditions and changes in the solution concentration of calcium ions were
measured using a calcium ion electrode. Even when the solution condition was
undersaturated for calcium carbonate salts (such as calcite), the rate of increase in
free calcium ions was considerably lower than the value calculated from the amount
of calcium ions added (Fig.
3.4
a). In other words, many of the added calcium
ions were in a bound state and were consumed by the formation of some sort of
assembly. A further important point is that the rate of increase in free calcium
ions was nearly constant as the solution transitioned from an undersaturated state
to a supersaturated state as a result of calcium ion addition until immediately
before nucleation occurred. These results indicate that calcium carbonate clusters
in solution are already in the undersaturated state and that their aggregation (or an
increase in their size) causes nucleation. Although the appearance of metastable
clusters during the course of nucleation is also considered in classical nucleation
models, unlike these types, the above-mentioned clusters are energetically stable
(in local energy-minimum state).
In this research, attempts were made to measure the size of the clusters using
analytical ultracentrifugation. This method measures the diffusion coefficients from
the precipitation rate of the clusters formed by centrifugation. Like the dynamic
light-scattering method, the measured diffusion coefficients are converted into
a hydrodynamic radius in accordance with the Stokes-Einstein equation. In an
undersaturated solution, clusters were not detected because of the low concentration;
