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
Sphere -sphere of unit radius centered at the origin is denoted and is often referred to as "the" -sphere. Note that the ordinary sphere is a 2-sphere, because it is a 2-dimensional surface (which is embedded in 3-dimensional space). The surface area of the unit ()-sphere is where is Euler's gamma function. Another expression for the surface area is and the volume is the surface area times or General recursive formulas also exist for the volume of an -ball. More generally, in a metric space , the sphere of center and radius is the set of points such that . If