Computing pK_a Shifts Using Traditional Molecular Dynamics: Example of Acid-Base Indicator Dyes in Organized Solutions

A compound's acidity constant (K_a) in a given medium determines its protonation state and, thus, its behavior and physicochemical properties. Therefore, it is among the key characteristics considered during the design of new compounds for the needs of advanced technology, medicine, and biological research, a notable example being pH sensors. The computational prediction of K_a for weak acids and bases in homogeneous solvents is presently rather well developed. However, it is not the case for more complex media, such as microheterogeneous solutions. The constant-pH molecular dynamics (MD) method is a notable contribution to the solution of the problem, but it is not commonly used. Here, we develop an approach for predicting K_a changes of weak small-molecule acids upon transfer from water to colloid solutions by means of traditional classical molecular dynamics. The approach is based on free energy (ΔG) computations and requires limited experiment data input during calibration. It was successfully tested on a series of pH-sensitive acid-base indicator dyes in micellar solutions of surfactants. The difficulty of finite-size effects affecting ΔG computation between states with different total charges is taken into account by evaluating relevant corrections; their impact on the results is discussed, and it is found non-negligible (0.1-0.4 pK_a units). A marked bias is found in the ΔG values of acid deprotonation, as computed from MD, which is apparently caused by force-field issues. It is hypothesized to affect the constant-pH MD and reaction ensemble MD methods as well. Consequently, for these methods, a preliminary calibration is suggested.