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 a powerful transformation. One simple example is in map projection. The usual projection of the North or South Pole is inversion from the Earth to a plane. If instead of making a pole the centre, we chose a city, then Inversion could produce a map where all the shortest routes (great circles) for flying from that city would appear as straight lines, which would simplify the flight path, for passengers at least. Let the reference sphere be Σ, with centre O and radius r denoted by {O, r}. All inverses, in this paper, are in the sphere Σ. The results