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
Circle of a sphere there is exactly one circle that can be drawn through three given points. The proof can be extended to show that the points on a circle are all a common angular distance from one of its poles. To show that a non-trivial intersection of two spheres is a circle, assume (without loss of generality) that one sphere (with radius formula_1) is centered at the origin. Points on this sphere satisfy Also without loss of generality, assume that the second sphere, with radius formula_3, is centered at a point on the positive x-axis, at distance formula_4 from the origin. Its points