Half sphere exposure both HSEα and HSEβ based on a big dataset by using multiple-step iterative deep neural-network learning. The predicted HSEa shows a higher correlation coefficient to the stability change by residue mutants than predicted HSEβ and ASA. The results, together with its easy Ca-atom-based calculation, highlight the potential usefulness of predicted HSEa for protein structure prediction and refinement as well as function prediction. 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
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