Constant pH molecular dynamics of proteins in explicit solvent with proton tautomerism

Abstract

pH is a ubiquitous regulator of biological activity, including protein-folding, protein-protein interactions, and enzymatic activity. Existing constant pH molecular dynamics (CPHMD) models that were developed to address questions related to the pH-dependent properties of proteins are largely based on implicit solvent models. However, implicit solvent models are known to underestimate the desolvation energy of buried charged residues, increasing the error associated with predictions that involve internal ionizable residue that are important in processes like hydrogen transport and electron transfer. Furthermore, discrete water and ions cannot be modeled in implicit solvent, which are important in systems like membrane proteins and ion channels. We report on an explicit solvent constant pH molecular dynamics framework based on multi-site λ-dynamics (CPHMD(MSλD)). In the CPHMD(MSλD) framework, we performed seamless alchemical transitions between protonation and tautomeric states using multi-site λ-dynamics, and designed novel biasing potentials to ensure that the physical end-states are predominantly sampled. We show that explicit solvent CPHMD(MSλD) simulations model realistic pH-dependent properties of proteins such as the Hen-Egg White Lysozyme (HEWL), binding domain of 2-oxoglutarate dehydrogenase (BBL) and N-terminal domain of ribosomal protein L9 (NTL9), and the pKa predictions are in excellent agreement with experimental values, with a RMSE ranging from 0.72 to 0.84 pKa units. With the recent development of the explicit solvent CPHMD(MSλD) framework for nucleic acids, accurate modeling of pH-dependent properties of both major class of biomolecules-proteins and nucleic acids is now possible.

Keywords: CPHMD; explicit solvent; molecular dynamics; pH; pKa values; protein dynamics; protein electrostatics; λ-dynamics.

Figure 1

Titration curve of model compounds: (a) aspartic acid, (b) glutamic acid, (c) lysine, (d) (d) histidine-δ and (e) histidine-ε. Calculated pK_a values of model compounds are in excellent agreement with experimental pK_a values. Colors represent the results from the triplicate runs.

Figure 2

Titration coordinate transitions of aspartic acid at pH 4 for (a) unprotonated state, (b) protonated tautomer #1 and (c) protonated tautomer #2 shows that the physical end states are well sampled.

Figure 3

Titration curve of model compounds with proton tautomerism: (a) aspartic acid, (b) glutamic acid and (c) histidine. Calculated pK_a values of model compounds show excellent agreement with experimental pK_a values. Colors represent the results from the triplicate runs.