Table III.

This table lists the average root-mean-squared-error performance results from our 100-fold cross-validation study, ordered by the overall error obtained by the model or method. The table shows performance for BMA, the Null model, as well as performance of categories of pK_a prediction methods. The “Sampled” set contains results from methods which used MD, MC, and Rosetta sampling methods; the “Static” set contains results from methods which did not use conformational sampling. The “Physics” set contains results from meth ods which used GB and PB solvation models; the “Empirical” set includes methods with empirical solvation models. The ensemble of prediction methods is broken into two comparative groups based on conformational sampling strategy (e.g., MD, MC, and Rosetta sampling vs. static) and solvation model (GB and PB solvation methods vs. empirical methods). Additionally, cross-validation results are shown for all amino acids as well as for the individual amino acid types ASP, GLU, and LYS. The statistical significance of BMA’s performance is based on p-values shown in Table VI. Table VI indicates that BMA’s mean RMSE is statistically significant to all other methods. Based on this table’s mean RMSE scores, we see that the BMA-based approach outperforms all other ensemble techniques: BMA-based estimates reduce error by approximately 65% in comparison to methods that use conformational sampling, and by about 73% in comparison to the static-conformation and physics-based solvation methods. In comparison to BMA, empirical solvation methods provide the next-best estimates; these estimates are approximately 45% higher in error than BMA estimates.

Method class	All	ASP	GLU	LYS
BMA	1.155	1.376	0.924	1.023
Empirical solvation	2.031	2.264	1.609	2.280
Physics-based solvation	4.167	4.129	4.051	4.414
Sampled conformations	3.257	3.209	3.034	3.628
Static conformations	4.057	4.061	3.936	4.246
Null	3.420	3.598	3.516	2.861