Given a protein structure from the PDB, I would like to generate NS spheres of radius Rs which cover totally the protein surface. Given RS there, NS is the maximum number of spheres so they do not overlap. I would need the coordinates of the center of each sphere.
Does anybody know if this has been implemented in some method / program? Or how to do it with scripting.
Thanks
I would suggest a lot of Chemists and Material Engeniers would need to do similar tasks. You could try approaching your local/nationl universitys to find out what approach they use.
You could also try breacking this up into a number of much smaller questions on this site.
Step one: Parse(have the computer read and translate) the PDB record.
Step two: construct a 3d shap from the result of step one
Step three: Given an arbitery 3d shape how many sphares of a given size can fit onto the serface without overlapping.
Each of these steps will take a number of hours for someone to do at least the first two steps will have been done lots by people who work with the PDB. I would suggest using chemistry and Material enginering fourms to get at least that part done.
What you are looking for is called Accessible surface area. Take a look at JMol, there's some code that does it.
Edit: sorry, your problem is a bit more complex. You are not looking at the surface. You need to fill the surface with spheres. This is a very interesting problem, and I am not aware of anything specific, but I am sure something exists. You will have, however, to hunt for scientific bibliography to find someone having this kind of code, I guess.
To me this looks like you want to build "sphere trees" but you need to specifiy your problem in more detail. I do no think that it is possible to cover the whole protein in spheres that do not overlap - except for the case that there is only one sphere.
I remember that i did calculations of molecular and solvent accessible surfaces using GEPOL a long while ago, when the FORTRAN sources were available. I did not work on proteins, however, but on much smaller, flexible polyalkenes.
Anyway, the authors of GEPOL, Pascual-Ahuir et al., published two papers in J. Comput. Chem., the DOIs are 10.1002/jcc.540110907 and 10.1002/jcc.540120905, which might be worth a look for further digging. In addition, you might want to look for publications of Michael Conolly.
Hope that helps!