05 How to Calculate Accessible Surface Area

• Lee & Richards algorithm (first method, 1970)
  • Pick an arbitrary direction from which to view the protein. Slice it into many sections perpendicular to this direction.
  • In each section, cycle over all the atoms. Each atom is represented as a sphere with a radius that is the sum of its VDW radius plus that of a probe solvent -- i.e. 1.4 for water.
  • For each atom determine the circle corresponding to the intersection of this sphere with the sectioning plane. Remove all parts (i.e. arcs) of this circle occluded by the circles of other atoms.
  • Multiply the total amount of non-occluded arc length by the sectioning width to get the surface area for atom. Sum over all atoms and all sections to get total area.
• Shrake & Rupley algorithm (easier)
  • Surround each atom with sphere of uniformly spaced dots (e.g. 92).
  • Remove dots contained in other atoms spheres. Total number of remaining dots is accessible surface.

Talk on Surfaces and Volumes / (C) Mark Gerstein (mbg@hyper.stanford.edu) / May 1996