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
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