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.

Thermostabilizing mechanisms of canonical single amino acid substitutions at a GH1 ß-glucosidase probed by multiple MD and computational approaches.

ß-glucosidases play a pivotal role in second-generation biofuel (2G-biofuel) production. For this application, thermostable enzymes are essential due to the denaturing conditions on the bioreactors. Random amino acid substitutions have originated new thermostable ß-glucosidases, but without a clear understanding of their molecular mechanisms. Here, we probe by different molecular dynamics simulation approaches with distinct force fields and submitting the results to various computational analyses, the molecular bases of the thermostabilization of the Paenibacillus polymyxa GH1 ß-glucosidase by two-point mutations E96K (TR1) and M416I (TR2). Equilibrium molecular dynamic simulations (eMD) at different temperatures, principal component analysis (PCA), virtual docking, metadynamics (MetaDy), accelerated molecular dynamics (aMD), Poisson-Boltzmann surface analysis, grid inhomogeneous solvation theory and colony method estimation of conformational entropy allow to converge to the idea that the stabilization carried by both substitutions depend on different contributions of three classic mechanisms: (i) electrostatic surface stabilization; (ii) efficient isolation of the hydrophobic core from the solvent, with energetic advantages at the solvation cap; (iii) higher distribution of the protein dynamics at the mobile active site loops than at the protein core, with functional and entropic advantages. Mechanisms i and ii predominate for TR1, while in TR2, mechanism iii is dominant. Loop A integrity and loops A, C, D, and E dynamics play critical roles in such mechanisms. Comparison of the dynamic and topological changes observed between the thermostable mutants and the wildtype protein with amino acid co-evolutive networks and thermostabilizing hotspots from the literature allow inferring that the mechanisms here recovered can be related to the thermostability obtained by different substitutions along the whole family GH1. We hope the results and insights discussed here can be helpful for future rational approaches to the engineering of optimized ß-glucosidases for 2G-biofuel production for industry, biotechnology, and science.