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
3-sphere centered at the origin with radius 1 is called the unit 3-sphere and is usually denoted : It is often convenient to regard as the space with 2 complex dimensions () or the quaternions (). The unit 3-sphere is then given by or This description as the quaternions of norm one identifies the 3-sphere with the versors in the quaternion division ring. Just as the unit circle is important for planar polar coordinates, so the 3-sphere is important in the polar view of 4-space involved in quaternion multiplication. See polar decomposition of a quaternion for details of this development of