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
N-sphere space and is an example of an -manifold. The volume form of an -sphere of radius is given by where is the Hodge star operator; see for a discussion and proof of this formula in the case . As a result, The space enclosed by an -sphere is called an -ball. An -ball is closed if it includes the -sphere, and it is open if it does not include the -sphere. Specifically: Topologically, an -sphere can be constructed as a one-point compactification of -dimensional Euclidean space. Briefly, the -sphere can be described as , which is -dimensional Euclidean space plus