A FLEXIBLE TRIANGULATION METHOD TO DESCRIBE THE SOLVENT-ACCESSIBLE SURFACE OF BIOPOLYMERS

A relatively simple protein solvent-accessible surface triangulation m ethod for continuum electrostatics applications employing the boundary element method is presented. First. the protein is placed onto a thre e-dimensional lattice with a specified lattice spacing. To each lattic e point, a box is assigned. Boxes located in the solvent region and in the interior of the protein are removed from the set. Improper connec tions between boxes and the possible existence of cavities in the inte rior of the protein which would destroy the proper connectivity of the triangulated surface are taken care of. The remaining set of boxes de fine the outer contour of the protein. Each free face exposed to the s olvent of the remaining set of boxes is triangulated after the surface defined by the free faces has been smoothed to follow the shape of th e macromolecule more accurately. The final step consists of a mapping of triangle vertices onto a set of surface points which define the sol vent-accessible surface. Normal vectors at triangle vertices are obtai ned also from the free faces which define the orientation of the surfa ce. The algorithm was tested for six molecules including four proteins ; a dipeptide, a helical peptide consisting of 25 residues, calbindin, lysozyme, calmodulin and cutinase. For each molecule, total areas hav e been calculated and compared with the result computed from a dotted solvent-accessible surface. Since the boundary element method requires a low number of vertices and triangles to reduce the number of unknow ns for reasons of efficiency, the number of triangles should not be to o high. Nevertheless, credible results are obtained for the total area with relative errors not exceeding 12% for a large lattice spacing (0 .30 nm) while close to zero for a smaller lattice spacing (down to 0.1 6 nm). The output of the triangulation computer program (written in C+) is rather simple so that it can be easily converted to any format a cceptable for any molecular graphics programs.