I want to calculate the exact surface area of an irregular 3d molecule/cluster using xyz coordinates. Is there a way?

Is there a way calculate the exact surface area of an irregular 3d molecule/cluster using xyz coordinates. I have provided the xyz and the pdb files in text format for the CH cluster/molecule for your reference.

[Walter Roberson]

In my experience, surface area of a molecule is not something that is exactly defined. That and the fact that there are multiple definitions of what surface area might mean.

Mathworks does not provide any functions for this purpose. Perhaps there is something in the file exchange.

[John D'Errico]

Surely not possible, for multiple reasons.

Even at it simplest, what is the exact surface area of an atom? Yes, people like to draw them as little round balls. But that is not the case. In fact, an atom is a fuzzy thing. The electrons do not live in hard immutable shells.

Next, consider even a simple molecule. Again, they are drawn as round little balls packed together. But that is not the truth. Just a nice way to draw them. And the bonds between the atoms? They indicate how electrons are shared between the atoms, making it more clear yet that the atoms invoved are not hard, impenetrable balls.

Next, those little balls do not fill space, at least, not if they were little, impenetrable balls. And that means it will not make sense even to just add up the surface areas of those little pretend balls.

So no, computing an exact surface area is simply not going to make any sense.

Going back to a simple atom, could you compute the surface area of where say, 99.99% of the atom lives? Pick some number of 9's there. But you cannot know where 100% of the atom lives. Heisenberg will probably stick his nose in there to prevent you. Similarly, you might decide to TRY to compute where 99.99% of a molecule lives, shared electrons and all.

So even if you could compute the exact surface area of the little picture you have seen of those balls clustered together, the number you get out would not be meaningfiul in the slightest. Sorry.

Is there some tool in MATLAB that will do this for you? Of course not.

[Walter Roberson]

Some people define surface area in terms of "solvent exclusion area". But that appears to depend upon the decision of which solvent.. and there appears to be multiple ways of calculating it.. and the discussions tend to mention that roughly, "This mostly works, but of course it's only a useful approximation and don't expect it to work too precisely for more complicated molecutes"

Answer 1

[Clay Swackhamer]

This is a really interesting question. Here are my thoughts:

• We need the edge points. I'm assuming that what you have (the x,y,z triplets) are the edge points. If some of your points are in the interior of the shape or structure then they will have to be removed somehow, or else we wouldn't be able to actually define the shape itself, that meaning the shape and thus the surface area would be literally indeterminate until we are sure that the triplets we have are on the edge of the shape.
• We need to decide what our representation actually means in physical terms. If we have the (x,y,z) triplets that define a molecular structure, is that electron cloud (everywhere the density of the cloud exceeds some threshold, for example) or a "ball and stick" model, like one might have in science class. Basically, do our points define the edge of the molecule in some represented space (like the ball and stick) or are they based on calculations of orbitals and electron cloud probability density functions? Also, this will define what unit of measurement our answer will be in.
• We need to decide whether to use a numerical approach or a modeling approach. Say that our edge points for part of this model look like a sphere. Do we numerically calculate the surface of that sphere-ish shape by calculating the area of all of the little polygons made by the edge points (the little "tiles" that tesselate the surface of the structure) and then adding them up, or do we do some kind of curve fitting to get a simple function that represents that sphere-ish shaped part of the molecule, and then calculate the surface area of that sphere using a simple equation (A=4*pi*r^2), calculate all the surface areas of the other parts of the overall structure, and then add them up?
• Slay various details from various devils. If we go with the numerical approach, do we need to do any kind of smoothing or resampling of the points, and then see how our calculated area is influenced by the smoothing/resampling parameters, then only accept our calculated value when it seems to converge? What if it doesn't converge and we have stumbled into a "coastline problem": https://en.wikipedia.org/wiki/Coastline_paradox. If we go with the strateg of discretizing the overall structure into various simpler shapes (cylinders, spheres, whatever) and then add up the areas of those regions, how will we figure out how much area to subtract to account for the parts where they overlap? Lastly, are there any references on this kind of calculation (molecular surface area)? Wouldn't be surprised if there is some research community that deals with this and has already developed methods to do so.

Good luck.

Clay