pK(A) in proteins solving the Poisson-Boltzmann equation with finite elements

Correlations between the 1H NMR chemical shieldings and the pKa values of organic acids and amines

The acid dissociation constants and ¹H NMR chemical shieldings of organic compounds are important properties that have attracted much research interest. However, few studies have explored the relationship between these two properties. In this work, we theoretically studied the NMR chemical shifts of a series of carboxylic acids and amines in the gas phase and in aqueous solution. It was found that the negative logarithms of the experimental acid dissociation constants (i.e., the pK_a values) of the organic acids and amines in aqueous solution correlate almost linearly with the corresponding calculated NMR chemical shieldings. Key factors that affect the theoretically predicted pK_a values are discussed in this paper. The present work provides a new way to predict the pK_a values of organic/biochemical compounds. Graphical abstract The chemical shielding values of organic acids and amines correlate near linearly with their corresponding pK_a values.

Empirical Conversion of pK a Values between Different Solvents and Interpretation of the Parameters: Application to Water, Acetonitrile, Dimethyl Sulfoxide, and Methanol

An empirical conversion method (ECM) that transforms pK _a values of arbitrary organic compounds from one solvent to the other is introduced. We demonstrate the method's usefulness and performance on pK _a conversions involving water and organic solvents acetonitrile (MeCN), dimethyl sulfoxide (Me₂SO), and methanol (MeOH). We focus on the pK _a conversion from the known reference value in water to the other three organic solvents, although such a conversion can also be performed between any pair of the considered solvents. The ECM works with an additive parameter that is specific to a solvent and a molecular family (essentially characterized by a functional group that is titrated). We formally show that the method can be formulated with a single additive parameter, and that the extra multiplicative parameter used in other works is not required. The values of the additive parameter are determined from known pK _a data, and their interpretation is provided on the basis of physicochemical concepts. The data set of known pK _a values is augmented with pK _a values computed with the recently introduced electrostatic transform method, whose validity is demonstrated. For a validation of our method, we consider pK _a conversions for two data sets of titratable compounds. The first data set involves 81 relatively small molecules belonging to 19 different molecular families, with the pK _a data available in all four considered solvents. The second data set involves 76 titratable molecules from 5 additional molecular families. These molecules are typically larger, and their experimental pK _a values are available only in Me₂SO and water. The validation tests show that the agreement between the experimental pK _a data and the ECM predictions is generally good, with absolute errors often on the order of 0.5 pH units. The presence of a few outliers is rationalized, and observed trends with respect to molecular families are discussed.

Development of constant-pH simulation methods in implicit solvent and applications in biomolecular systems

pH is a critical parameter for biological and technological systems directly related with electrical charges. It can give rise to peculiar electrostatic phenomena, which also makes them more challenging. Due to the quantum nature of the process, involving the forming and breaking of chemical bonds, quantum methods should ideally by employed. Nevertheless, due to the very large number of ionizable sites, different macromolecular conformations, salt conditions, and all other charged species, the CPU time cost simply becomes prohibitive for computer simulations, making this a quite complex problem. Simplified methods based on Monte Carlo sampling have been devised and will be reviewed here, highlighting the updated state-of-the-art of this field, advantages, and limitations of different theoretical protocols for biomolecular systems (proteins and nucleic acids). Following a historical perspective, the discussion will be associated with the applications to protein interactions with other proteins, polyelectrolytes, and nanoparticles.