Solubility-Weighted Index: fast and accurate prediction of protein solubility

Bikash K. Bhandari; Paul P. Gardner; Chun Shen Lim

We applied this arithmetic mean approach (i.e., sequence composition scoring) to the PSI:Biology dataset and compared four sets of previously published, normalised B-factors (Bhaskaran and Ponnuswamy 1988; Ragone et al. 1989; M. Vihinen, Torkkila, and Riikonen 1994; Smith et al. 2003 ) Among these sets of B-factors, sequence composition scoring using the most recently published set of normalised B-factors produced the highest AUC score To improve the prediction accuracy of solubility, we iteratively refined the weights of amino acid residues using the Nelder-Mead optimisation algorithm (Nelder and Mead 1965) . To avoid testing and training on similar sequences, we generated 10 cross-validation sets with a maximised heterogeneity between these subsets (i.e. no similar sequences between subsets). We first clustered all 12,216 PSI:Biology protein sequences using a 40% similarity threshold using USEARCH to produce 5,050 clusters with remote similarity (see Methods and Supplementary Fig S4) . The clusters were grouped into 10 cross-validation sets of approximately 1,200 sequences each manually. We did not select a representative sequence for each cluster as about 12% of clusters contain a mix of soluble and insoluble proteins (Supplementary Fig S4C) . More importantly, to address the issues of sequence similarity and imbalanced classes, we performed 1,000 bootstrap resamplings for each cross-validation step (Fig 2A and Supplementary Fig S5) . We calculated the solubility scores using the optimised weights as Equation 1 and the AUC scores for each cross-validation step. Our training and test AUC scores were 0.72 ± 0.00 and 0.71 ± 0.01, respectively, showing an improvement over flexibility in solubility prediction (mean ± standard deviation; Fig 2B and Supplementary Table S3 ).