Patent ID: 8589137

Claim:
A method for performing a molecular dynamics simulation for determining the solvent accessible surface area of a molecule (M) with respect to atomic coordinates, the molecule (M) comprising a plurality of atoms, a sphere (B i ) being assigned to each atom, and each sphere (B i ) comprising a radius (ρ i ) and a center position (r i ) the method comprising: determining, by a computer, for each sphere (B) all neighbouring spheres (B i ) that intersect with the sphere (B); defining, by the computer, a set of one or more contours (C m ), such that all intersecting circles of sphere B with spheres B i intersect on the surface of sphere B; determining, by the computer, for each contour (C m ) an area enclosed by the contour (C m ), wherein the contour (C m ) comprises the area on the surface of said sphere (B) that is enclosed by one or more arcs (a 1 , a 2 , a 3 ) resulting from an intersection of the surface of said sphere (B) with one of the surface of one intersecting sphere (B i ) or the surfaces of a plurality of intersecting spheres (B i ) that have an overlapping intersection area on the surface of said sphere (B); determining, by the computer, the solvent accessible surface (S) of said sphere (B) as the surface of said sphere (B) subtracted by the area comprised by all contours (C m ) on the surface of said sphere (B); determining, by the computer, the solvent accessible surface area of the molecule (M) based on a sum of solvent accessible surface areas (S i ) of the spheres; and determining, by the computer, the derivative ( ⅆ S ⅆ r i ) of the solvent accessible surface area (S) of said sphere (B) with respect to the position (r i ) of the intersecting spheres (B i ) satisfying the formula: ⅆ S ⅆ r i = φ i ⁢ ρ 2 ⁢ ( 1 + ρ 2 - ρ i 2 b i 2 ) ⁢ e i - ρ b i ⁡ [ ( v i + 1 - v i ) × e i ] , wherein S is the solvent accessible surface area of said sphere (B); r i is the center of an intersecting sphere (B i ); ρ is the radius of said sphere (B); ρ i is the radius of the intersecting sphere (B i ); b i =|r−r i | is the distance between the center (r) of said sphere (B) and the center (r i ) of the intersecting (B i ); e i =(r i −r)/b i is the unit vector from the center (r) of said sphere (B) to the center (r i ) of the intersecting sphere B i ; and ν i is the endpoint of an arc (a i ), wherein arc (a i ) is the part of the intersection line (I i ) that contributes to the contour (C m ).