Efficient molecular surface rendering by linear-time pseudo-Gaussian approximation to Lee-Richards surfaces (PGALRS)

The PGALRS (pseudo-Gaussian approximation to Lee-Richards surfaces) algorithm is discussed. By modeling electron density with unphysical pseudo-Gaussian atoms, the Lee-Richards surface can be approximated by a contour level of that density in time approximately linear in the number of atoms. Having that contour level, the atoms and residues closest to that surface can be identified in average time O[n^2/3log(n)] using a NearTree-based nearest neighbor search. If a high-quality Lee-Richards surface is required, then, as a final stage, one of the standard Lee-Richards algorithms can be used but considering only the previously identified surface residues; the typical cost is thereby reduced to O[n^2/3log(n)], making the overall average time for all the steps O(n). For very large macromolecules, such a reduction in computational burden may be essential to being able to render a meaningful molecular surface. This approach extends the feasible range of application for existing molecular surface software, such as MSMS, to larger macromolecules, especially to macromolecules with more than 50 000 atoms, and can be used as a starting point for surface-based (as opposed to backbone-based) motif identification, e.g. using ProMol.