Questions for Morris et al. paper
You can conveniently define the inside and the outside of a molecule
in the following way.
A point X is outside
if there exists a sphere of radius Rw
with center at X that does not intersect any atoms of the molecule.
Rw is taken to be the size of a water molecule,
Rw = 1.4 Angstrom,
although larger or smaller values of Rw may also be useful.
It is assumed that each atom in the molecule is represented
by a sphere of the appropriate radius
(typically in a range of 1.0 to 1.7 Angstroms.)
you may assume that these spheres do not interpenetrate.
You can visualize the boundary between the inside and the outside as follows.
Imagine rolling a sphere of radius Rw around the molecule
(wherever it fits).
The center of the sphere will trace the molecular boundary,
which is often called the solvent accessible surface in this case.
Is it possible that a molecule is "star-like" when one value
of Rw is used,
but not star-like with another?
If Rw is increased,
what happens with the number of spherical harmonics
needed to produce a decent representation of the molecule
(see, e.g., Fig.2)?
Does it increase, decrease, or remain the same?
No rigorous proofs are required, just good logic.
A good description (with pictures!) of spherical harmonics is available
Wolfram's Math World .
You may also work out your answers in 2D.
The principle remains the same,
but recall that in 2D the spherical harmonics simplify
to just cosine and sine functions.
If you want to see what real molecular surfaces look like,
download and install VMD,
then open any protein structure file
from the protein data bank .
You will need to choose an appropriate surface representation in VMD.