INTRODUCTION:

According to Christopher Bystroff, Dept. of Biology, Rensselaer Polytechnic Institute, MASKER is a modification of an algorithm that computes the solvent accessible molecular surface area (SAS) using Boolean masks (Le Grand, S. M. & Merz, K. M. J. (1993), Journal of Computational Chemistry 14, 349-52). Bystroff modified the original MASKER algorithm to estimate the solvent excluded molecular surface area (SES), which includes contact, toroidal and reentrant surface components. “Numerical estimates of arc lengths of intersecting atomic SAS are used to estimate the toroidal surface, and intersections between those arcs are used to estimate the reentrant surface area.” Bystroff believes that boolean molecular surface areas are continuous and pairwise differentiable, and should be useful for molecular dynamics simulations, especially as the basis for an implicit solvent model.

DESCRIPTION:

A Boolean masks approach for computing SAS was first proposed by LeGrand and

Merz (Le Grand & Merz, 1993). In their approach, a set of points were evenly spaced on the surface of a sphere centered at the origin and having radius 1.0, and each was represented by a single bit in a multi-byte word. A set of ‘masks’ was created by placing a probe sphere of unit radius at all positions around the origin, and all distances from zero to two. Points within the probe radius had their bits set to zero, while the remaining bits were set to one. Therefore, one multi-byte word (mask) corresponded to one probe sphere location. A binary AND operation over any number of masks resulted in another mask whose nonzero bits represent the SAS for one atom. SAS is estimated quickly and accurately by summing the 1-bits and scaling. Bystroff’s improved MASKER takes the method of LeGrand & Merz one step further by using masks to calculate SES. The problem is broken down to its three component parts. The contact surface is a scalar multiple of SAS. The toroidal surface can be estimated based on the length of exposed circular edge at the intersection of two atom surfaces. The reentrant surfaces are calculated by placing a mask at each position where a probe is in contact with exactly three atoms. Intersections and self-burial of toroidal and reentrant surfaces are accounted for by additional masking operations, as are the pairwise partial derivatives.

CODE:

The code for MASKER is written in Portland group Fortran, and is designed to be compiled with a f90 program. MASKER is made capable to calculate the surface from a PDB-formatted input.

RESULT:

Several runs for MASKER were carried out on a terminal with AMD 900 MHz processor with 256 MB memory under RedHat Linux 7.0 platform. A plot of time that MASKER took to compute the molecular surface areas versus the number of atoms in the molecules was created using a program called DataFit by Oakdale Engineering. The plot fits ‘best’ with the graph of a second degree polynomial.

AUTHOR’S RESULT:

Bystroff believes that MASKER is robust, and because of its more brute force approach, it is more likely to be immune to algorithmic bugs that are associated with certain surface singularities (Sanner, 1992). Bystroff comments on the complexity of the computation with the number of atoms. The number of atoms reflected the runtime after initialization of the masks, using a PentiumIII, 750MHz, running RedHat Linux v6.2. According to Bystroff, the runtime was a polynomial with an exponent of approximately 1.42. The slow step in the process was the masking operations which consumed abut 73% of the CPU time.