To optimize the efficiency, all points in the solvent and solution plateaus are calculated with the trivial analytical expressions (Brown and Schuck 2008) . We note that, for the 10 9 100 grid shown in Fig. 1 , the calculation of the Lamm equation solutions for all 1,000 species with an accuracy of better than 0.001 (maximum error) requires a total of less than 2 s on our PC. Thus, computational expense for achieving high-accuracy Lamm equations should not be limiting the size-and-shape distribution analysis of SV data.