Biomedical Engineering Reference
In-Depth Information
R
Figure 6.7
Grid around an atom
For each grid point in turn, we calculate its distance from the centre and determine
whether the grid point lies inside or outside the atom. If
n
is the total number of grid points
and
n
a
the number that lie within the atom whose volume is
V
, we have
V
8
R
3
n
a
n
For a polyatomic, we have to give special consideration to grid points that lie in the
overlap region. Figure 6.8 shows two atoms A and B, with radii
R
A
and
R
B
. The overlap
region is labelled X.
=
X
A
B
Figure 6.8
Atoms A, B and overlap region X
For atomA, we know that the volume is
3
π
R
A
. We now surround atom B with a grid as
described above, and test each grid point in turn. If the grid point lies within sphere B, we
test to see if it lies in region X and so has already been counted as part of the volume of
atomA. The algorithm proceeds until all atoms have been considered in turn. The molecular
volume is found by adding all atomic contributions.
There are similar methods for the estimation of molecular surface area.
