Bayesian model aggregation for ensemble-based estimates of protein pKa values

Comparative Performance of High-Throughput Methods for Protein pKa Predictions

The medically relevant field of protein-based therapeutics has triggered a demand for protein engineering in different pH environments of biological relevance. In silico engineering workflows typically employ high-throughput screening campaigns that require evaluating large sets of protein residues and point mutations by fast yet accurate computational algorithms. While several high-throughput pKa prediction methods exist, their accuracies are unclear due to the lack of a current comprehensive benchmarking. Here, seven fast, efficient, and accessible approaches including PROPKA3, DeepKa, PKAI, PKAI+, DelPhiPKa, MCCE2, and H++ were systematically tested on a nonredundant subset of 408 measured protein residue pKa shifts from the pKa database (PKAD). While no method outperformed the null hypotheses with confidence, as illustrated by statistical bootstrapping, DeepKa, PKAI+, PROPKA3, and H++ had utility. More specifically, DeepKa consistently performed well in tests across multiple and individual amino acid residue types, as reflected by lower errors, higher correlations, and improved classifications. Arithmetic averaging of the best empirical predictors into simple consensuses improved overall transferability and accuracy up to a root-mean-square error of 0.76 pKa units and a correlation coefficient (R2) of 0.45 to experimental pKa shifts. This analysis should provide a basis for further methodological developments and guide future applications, which require embedding of computationally inexpensive pKa prediction methods, such as the optimization of antibodies for pH-dependent antigen binding.

Computing Protein pKas Using the TABI Poisson–Boltzmann Solver

A common approach to computing protein pKas uses a continuum dielectric model in which the protein is a low dielectric medium with embedded atomic point charges, the solvent is a high dielectric medium with a Boltzmann distribution of ionic charges, and the pKa is related to the electrostatic free energy which is obtained by solving the Poisson–Boltzmann equation. Starting from the model pKa for a titrating residue, the method obtains the intrinsic pKa and then computes the protonation probability for a given pH including site–site interactions. This approach assumes that acid dissociation does not affect protein conformation aside from adding or deleting charges at titratable sites. In this work, we demonstrate our treecode-accelerated boundary integral (TABI) solver for the relevant electrostatic calculations. The pKa computing procedure is enclosed in a convenient Python wrapper which is publicly available at the corresponding author’s website. Predicted results are compared with experimental pKas for several proteins. Among ongoing efforts to improve protein pKa calculations, the advantage of TABI is that it reduces the numerical errors in the electrostatic calculations so that attention can be focused on modeling assumptions.

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

This paper presents the crystal structure of a forced open inward rectifier Kir2.2 channel. Molecular dynamics reveals the details of ion permeation through the open channel.

Potassium ion conduction through open potassium channels is essential to control of membrane potentials in all cells. To elucidate the open conformation and hence the mechanism of K⁺ ion conduction in the classic inward rectifier Kir2.2, we introduced a negative charge (G178D) at the crossing point of the inner helix bundle, the location of ligand-dependent gating. This “forced open” mutation generated channels that were active even in the complete absence of phosphatidylinositol-4,5-bisphosphate (PIP₂), an otherwise essential ligand for Kir channel opening. Crystal structures were obtained at a resolution of 3.6 Å without PIP₂ bound, or 2.8 Å in complex with PIP₂. The latter revealed a slight widening at the helix bundle crossing (HBC) through backbone movement. MD simulations showed that subsequent spontaneous wetting of the pore through the HBC gate region allowed K⁺ ion movement across the HBC and conduction through the channel. Further simulations reveal atomistic details of the opening process and highlight the role of pore-lining acidic residues in K⁺ conduction through Kir2 channels.

q-Canonical Monte Carlo Sampling for Modeling the Linkage between Charge Regulation and Conformational Equilibria of Peptides

The overall charge content and the patterning of charged residues have a profound impact on the conformational ensembles adopted by intrinsically disordered proteins. These parameters can be altered by charge regulation, which refers to the effects of post-translational modifications, pH-dependent changes to charge, and conformational fluctuations that modify the pKa values of ionizable residues. Although atomistic simulations have played a prominent role in uncovering the major sequence-ensemble relationships of IDPs, most simulations assume fixed charge states for ionizable residues. This may lead to erroneous estimates for conformational equilibria if they are linked to charge regulation. Here, we report the development of a new method we term q-canonical Monte Carlo sampling for modeling the linkage between charge regulation and conformational equilibria. The method, which is designed to be interoperable with the ABSINTH implicit solvation model, operates as follows: For a protein sequence with n ionizable residues, we start with all 2n charge microstates and use a criterion based on model compound pKa values to prune down to a subset of thermodynamically relevant charge microstates. This subset is then grouped into mesostates, where all microstates that belong to a mesostate have the same net charge. Conformational distributions, drawn from a canonical ensemble, are generated for each of the charge microstates that make up a mesostate using a method we designate as proton walk sampling. This method combines Metropolis Monte Carlo sampling in conformational space with an auxiliary Markov process that enables interconversions between charge microstates along a mesostate. Proton walk sampling helps identify the most likely charge microstate per mesostate. We then use thermodynamic integration aided by the multistate Bennett acceptance ratio method to estimate the free energies for converting between mesostates. These free energies are then combined with the per-microstate weights along each mesostate to estimate standard state free energies and pH-dependent free energies for all thermodynamically relevant charge microstates. The results provide quantitative estimates of the probabilities and preferred conformations associated with every thermodynamically accessible charge microstate. We showcase the application of q-canonical sampling using two model systems. The results establish the soundness of the method and the importance of charge regulation in systems characterized by conformational heterogeneity.

PlayMolecule ProteinPrepare: A Web Application for Protein Preparation for Molecular Dynamics Simulations

Protein preparation is a critical step in molecular simulations that consists of refining a Protein Data Bank (PDB) structure by assigning titration states and optimizing the hydrogen-bonding network. In this application note, we describe ProteinPrepare, a web application designed to interactively support the preparation of protein structures. Users can upload a PDB file, choose the solvent pH value, and inspect the resulting protonated residues and hydrogen-bonding network within a 3D web interface. Protonation states are suggested automatically but can be manually changed using the visual aid of the hydrogen-bonding network. Tables and diagrams provide estimated pK_a values and charge states, with visual indication for cases where review is required. We expect the graphical interface to be a useful instrument to assess the validity of the preparation, but nevertheless, a script to execute the preparation offline with the High-Throughput Molecular Dynamics (HTMD) environment is also provided for noninteractive operations.

Bayesian Model Averaging for Ensemble-Based Estimates of Solvation-Free Energies

This paper applies the Bayesian Model Averaging statistical ensemble technique to estimate small molecule solvation free energies. There is a wide range of methods available for predicting solvation free energies, ranging from empirical statistical models to ab initio quantum mechanical approaches. Each of these methods is based on a set of conceptual assumptions that can affect predictive accuracy and transferability. Using an iterative statistical process, we have selected and combined solvation energy estimates using an ensemble of 17 diverse methods from the fourth Statistical Assessment of Modeling of Proteins and Ligands (SAMPL) blind prediction study to form a single, aggregated solvation energy estimate. Methods that possess minimal or redundant information are pruned from the ensemble and the evaluation process repeats until aggregate predictive performance can no longer be improved. We show that this process results in a final aggregate estimate that outperforms all individual methods by reducing estimate errors by as much as 91% to 1.2 kcal mol^-1 accuracy. This work provides a new approach for accurate solvation free energy prediction and lays the foundation for future work on aggregate models that can balance computational cost with prediction accuracy.

A Soluble, Folded Protein without Charged Amino Acid Residues

Charges are considered an integral part of protein structure and function, enhancing solubility and providing specificity in molecular interactions. We wished to investigate whether charged amino acids are indeed required for protein biogenesis and whether a protein completely free of titratable side chains can maintain solubility, stability, and function. As a model, we used a cellulose-binding domain from Cellulomonas fimi, which, among proteins of more than 100 amino acids, presently is the least charged in the Protein Data Bank, with a total of only four titratable residues. We find that the protein shows a surprising resilience toward extremes of pH, demonstrating stability and function (cellulose binding) in the pH range from 2 to 11. To ask whether the four charged residues present were required for these properties of this protein, we altered them to nontitratable ones. Remarkably, this chargeless protein is produced reasonably well in Escherichia coli, retains its stable three-dimensional structure, and is still capable of strong cellulose binding. To further deprive this protein of charges, we removed the N-terminal charge by acetylation and studied the protein at pH 2, where the C-terminus is effectively protonated. Under these conditions, the protein retains its function and proved to be both soluble and have a reversible folding-unfolding transition. To the best of our knowledge, this is the first time a soluble, functional protein with no titratable side chains has been produced.

Continuum Electrostatics Approaches to Calculating pKas and Ems in Proteins

Proteins change their charge state through protonation and redox reactions as well as through binding charged ligands. The free energy of these reactions is dominated by solvation and electrostatic energies and modulated by protein conformational relaxation in response to the ionization state changes. Although computational methods for calculating these interactions can provide very powerful tools for predicting protein charge states, they include several critical approximations of which users should be aware. This chapter discusses the strengths, weaknesses, and approximations of popular computational methods for predicting charge states and understanding the underlying electrostatic interactions. The goal of this chapter is to inform users about applications and potential caveats of these methods as well as outline directions for future theoretical and computational research.