Dynamic protonation equilibrium of solvated acetic acid.

The biological functions of many proteins are crucially coupled to protonation equilibria, for instance, in the enzymatic reactions of serine proteases and carbonic anhydrase, and in integral membrane proton pumps such as bacteriorhodopsin, cytochrome c oxidase (COX), and FOF1-ATP synthase. [8] Proton-transfer (PT) reactions are also crucial in many other areas of chemistry, such as membrane permeation in hydrogen fuel cells and in polymers. Despite their tremendous importance, many aspects of PTreactions in biomolecules remain poorly understood. As the direct observation of PT reactions by experimental techniques faces fundamental and/or technical difficulties, it is highly desirable to use computational methods as a complement. In the past decades, various efficient computational methods have been developed to calculate the pKa values of amino acid side chains as well as to perform simulations of proteins at constant pH, using, for example, fractional charges and implicit solvent models. However, these methods do not model explicit proton-exchange reactions between the titratable sites and the surrounding aqueous solution or the exchange between different titratable sites; this makes it difficult to identify PT pathways and to characterize the mechanisms of PT reactions. This is the area where dynamic simulations of explicit proton-transfer reactions come into play. Tuckerman et al. studied the shared proton in hydrogen bonds and a hydrated excess proton in water using the Car–Parrinello molecular dynamics (CPMD) method. Lobaugh and Voth investigated proton transport in water by simulating an excess proton in a box of water molecules within the centroid molecular dynamics framework and by using a multistate empirical valence bond (MS-EVB) model for proton transfer. A recent study also presented the dynamic simulation of pKa values for amino acid side-chain analogues using the MS-EVB model and the umbrella sampling technique. 29] The deviation between their computed value and the experimental pKa was 1–2 pKa units. CPMD combined with metadynamics and transition-path sampling was employed to compute free-energy profiles for the deprotonation of acetic acid in water. Several further applications showed the importance and success of studying PT in protein systems by theoretical approaches, for instance, PT in bacteriorhodopsin, PT in gramicidin A, PTalong a water chain in the D-pathway of COX, and proton translocation in carbonic anhydrase. A simulation model of intermediate accuracy, the Q-HOP MDmethod, was introduced by our research group in 2001 to study dynamic proton transport between general titratable sites in biomolecular systems. In the Q-HOP scheme, the PT probabilities for each proton-donor and -acceptor pair are calculated using a semiempirical approach during the MD simulation (see the Supporting Information for details). Depending on whether PT occurs (by comparing the PT probability to a random number), the topology of the system is modified or kept unchanged before the next step of MD simulation. The transfer probabilities depend on the momentary donor–acceptor distance (RDA) and the energy difference between the minima at the donor and acceptor (E12). This method has been applied successfully to study the proton shuttle in green-fluorescent protein and to understand the mechanism of proton blockage in aquaporin. Herein we present the application of Q-HOP-MD to study the explicit protonation equilibrium of solvated acetic acid on a time scale of tens of nanoseconds&German: 50 nm & and at a reasonable pH (pH 1). The pKa of acetic acid is calculated based on the relative populations of protonated and deprotonated states observed during a 50-ns-long QHOP MD simulation. By analyzing the unbiased MD simulation, we can also identify the proton-hopping mechanism and the driving force of the activated processes of proton transfer. This study thus serves as a proof of principle of the method, and it provides detailed mechanistic insight into atomistic protonation equilibria on two separate time scales, femtoseconds and nanoseconds. During the Q-HOP MD simulation, two types of protonation equilibria were observed. Figure 1a,b show the position of the “free” proton and the distance between the hydronium ion and the deprotonated acetic acid (when the proton stays on hydronium ion) during the first 10 ns. (The results for the full length of the simulation are presented in Figure 5 of the Supporting Information.) Two different situations can be distinguished. The first type of protonation equilibrium, “proton swapping”, involves only the acetic acid and a nearby H2O/H3O + molecule, which forms a hydrogen