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 the minor axis, an oblate spheroid. In three dimensions, the volume inside a sphere (that is, the volume of a ball, but classically referred to as the volume of a sphere) is where is the radius of the sphere. Archimedes first derived this formula, by showing that the volume inside a sphere is twice the volume between the sphere and the circumscribed cylinder of that sphere (having the height and diameter equal to the diameter of the sphere). This assertion can be obtained from Cavalieri's principle. This formula can also be derived using integral calculus, i.e. disk integration to sum