pH Effects and Cooperativity among Key Titratable Residues for Escherichia coli Glycinamide Ribonucleotide Transformylase

Resolving coupled pH titrations using alchemical free energy calculations

In a protein, nearby titratable sites can be coupled: the (de)protonation of one may affect the other. The degree of this interaction depends on several factors and can influence the measured p K a . Here, we derive a formalism based on double free energy differences ( Δ Δ G ) for quantifying the individual site p K a values of coupled residues. As Δ Δ G values can be obtained by means of alchemical free energy calculations, the presented approach allows for a convenient estimation of coupled residue p K a s in practice. We demonstrate that our approach and a previously proposed microscopic p K a formalism, can be combined with alchemical free energy calculations to resolve pH-dependent protein p K a values. Toy models and both, regular and constant-pH molecular dynamics simulations, alongside experimental data, are used to validate this approach. Our results highlight the insights gleaned when coupling and microstate probabilities are analyzed and suggest extensions to more complex enzymatic contexts. Furthermore, we find that naïvely computed p K a values that ignore coupling, can be significantly improved when coupling is accounted for, in some cases reducing the error by half. In short, alchemical free energy methods can resolve the p K a values of both uncoupled and coupled residues.

Constant pH molecular dynamics simulations: Current status and recent applications

Many important protein functions are carried out through proton-coupled conformational dynamics. Thus, the ability to accurately model protonation states dynamically has wide-ranging implications. Over the past two decades, two main types of constant pH methods (discrete and continuous) have been developed to enable proton-coupled molecular dynamics (MD) simulations. In this short review, we discuss the current status of the development and highlight recent applications that have advanced our understanding of protein structure-function relationships. We conclude the review by outlining the remaining challenges in the method development and projecting important areas for future applications.