Bayesian model aggregation for ensemble‐based estimates of protein pK_avalues

Abstract

This paper investigates an ensemble-based technique called Bayesian Model Averaging (BMA) to improve the performance of protein amino acid pKa predictions. Structure-based pKa calculations play an important role in the mechanistic interpretation of protein structure and are also used to determine a wide range of protein properties. A diverse set of methods currently exist for pKa prediction, ranging from empirical statistical models to ab initio quantum mechanical approaches. However, each of these methods are based on a set of conceptual assumptions that can effect a model’s accuracy and generalizability for pKa prediction in complicated biomolecular systems. We use BMA to combine eleven diverse prediction methods that each estimate pKa values of amino acids in staphylococcal nuclease. These methods are based on work conducted for the pKa Cooperative and the pKa measurements are based on experimental work conducted by the García-Moreno lab. Our cross-validation study demonstrates that the aggregated estimate obtained from BMA outperforms all individual prediction methods with improvements ranging from 45-73% over other method classes. This study also compares BMA’s predictive performance to other ensemble-based techniques and demonstrates that BMA can outperform these approaches with improvements ranging from 27-60%. This work illustrates a new possible mechanism for improving the accuracy of pKa prediction and lays the foundation for future work on aggregate models that balance computational cost with prediction accuracy.

Atomistic basis of opening and conduction in mammalian inward rectifier potassium (Kir2.2) channels

“…By contrast, the KW/GD MD simulations predict K + ion occupancy in the open conducting Kir2.2 inner cavity as high as 4.7, with 3.5 K + ions continuously present near E225 in the cytoplasmic cavity. It is conceivable that acidic residues within the channel pore may be protonated due to close apposition(Bradley et al, 2012), and predicted pKa values by PDB2PQR/APBS webserver(Gosink et al, 2014) are indeed close to pH 7.0 for D173 and pH 6.0 for E225 in the closed KW and KW/GD structures (Supplementary Table 3). These values are much higher than the pKa values of these residues in solution (~pH 2.0).…”

Atomistic basis of opening and conduction in mammalian inward rectifier potassium (Kir2.2) channels

“…The calculations were performed using PDB2PQR/APBS webserver (Gosink et al, 2014) for KW (5KUM) and KW/GD (6M84) crystal structures and the open KW/GD and KW/GD(G) MD simulated structures sampled at 1,000 ns. The default options, including PARSE force field, were used for the calculations.…”

Continuum Electrostatics Approaches to Calculating pKas and Ems in Proteins

“…These residues formed the basis of the only blind challenge; i.e., where p K a s were calculated without the experimental value being known (Nielsen et al, 2011). A meta-analysis (Gosink et al, 2014) of the blind predictions found that the RMSD for the null model is ≈3.5, indicating that the p K a s for these residues were very shifted from the model values due to their burial in the protein. Empirical methods such as PROPKA3 (Olsson, 2011) did significantly better than the null model, methods with added conformational sampling did slightly better than the null model, while methods without added sampling did worse.…”

“…The errors for calculations with rigid backbones were smaller when crystal structures of the mutants were used rather then when the mutation was made in silico . Ensemble models which aggregated all of the predictions using Bayesian model averaging gave the best overall results (Gosink et al, 2014). …”

“…Computational methods for modeling these reactions attempt to predict how the energetics of proton (p K a ), electron ( E m ), or ligand ( K a ) change as a function of environment (e.g., protein interior vs. solution). A wide range of experimental data are available for testing the predicted p K a (Stanton & Houk, 2008; Gosink, Hogan, Pulsipher & Baker, 2014), E m (Reedy & Gibney, 2004) and K d (Gilson, Liu, Baitaluk, Nicola, Hwang & Chong, 2016) values. The goal of matching specific numerical values creates a high bar for testing these calculation methodologies.…”