Half sphere exposure Half sphere exposure Half Sphere Exposure (HSE) is a protein solvent exposure measure that was first introduced by . Like all solvent exposure measures it measures how buried amino acid residues are in a protein. It is found by counting the number of amino acid neighbors within two half spheres of chosen radius around the amino acid. The calculation of HSE is found by dividing a contact number (CN) sphere in two halves by the plane perpendicular to the Cβ-Cα vector. This simple division of the CN sphere results in two strikingly different measures, HSE-up and HSE-down. HSE-up is defined
Inversion in a sphere Inversion in a sphere In geometry, inversion in a sphere is a transformation of Euclidean space that fixes the points of a sphere while sending the points inside of the sphere to the outside of the sphere, and vice versa. Intuitively, it "swaps the inside and outside" of the sphere while leaving the points on the sphere unchanged. Inversion is a conformal transformation, and is the basic operation of inversive geometry. Inversion in a sphere is most easily described using polar coordinates. Choose a system of affine coordinates so that the centre of the sphere is at the origin and