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
Sphere -ball; thus, it is homeomorphic to the Euclidean -sphere, but perhaps lacking its metric. The -sphere is denoted . It is an example of a compact topological manifold without boundary. A sphere need not be smooth; if it is smooth, it need not be diffeomorphic to the Euclidean sphere. The Heine–Borel theorem implies that a Euclidean -sphere is compact. The sphere is the inverse image of a one-point set under the continuous function . Therefore, the sphere is closed. is also bounded; therefore it is compact. Remarkably, it is possible to turn an ordinary sphere inside out in a three-dimensional