Half sphere exposure used in predicting discontinuous B-cell epitopes. Song et al. have developed an online webserver termed HSEpred to predict half-sphere exposure from protein primary sequences. HSEpred server can achieve the correlation coefficients of 0.72 and 0.68 between the predicted and observed HSE-up and HSE-down measures, respectively, when evaluated on a well-prepared non-homologous protein structure dataset. Moreover, residue contact number (CN) can also be accurately predicted by HSEpred webserver using the summation of the predicted HSE-up and HSE-down values, which has further enlarged the application of this new solvent exposure measure. Recently, Heffernan et al. has developed the most accurate predictor for
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