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
Quasi-sphere hyperbolic plane, and its conjugate hyperbola, which is its counter-sphere. The "centre" of a quasi-sphere is a point that is equidistant from every point of the quasi-sphere – i.e., the quadratic form applied to the displacement vector (or radius vector) from the centre to a point of the quasi-sphere yields a constant, called the "radius squared", or equivalently, the point at which the pencil of lines normal to the tangent hyperplanes meet. If the quasi-sphere is a hyperplane, the centre is the point at infinity defined by this pencil. When , the displacement vector of the centre from the reference