Theoretical Calculations of Heteroconjugation Equilibrium Constants in Systems Modeling Acid−Base Interactions in Side Chains of Biomolecules Using the Potential of Mean Force

Abstract

The potentials of mean force (PMFs) were determined for systems forming molecular and ionic heterocomplexes (in which the proton is transferred from a neutral acid to a neutral base molecule) composed of acetic acid and phenol with amines in three solvents with different polarities and hydrogen-bonding propensities: acetonitrile (AN), dimethyl sulfoxide (DMSO), and water. For each pair and each solvent, a series of umbrella-sampling molecular dynamics simulations with the AMBER force field and explicit solvent molecules were carried out and the PMF was calculated by using the weighted histogram analysis method (WHAM). Subsequently, heteroconjugation equilibrium constants were calculated by numerical integration of the respective PMF profiles. All complexes except those involving acetic acid as a proton donor in water were found to form in solution, which was manifested by the presence of contact minima corresponding to hydrogen-bonded species in the PMF curves. The calculated heteroconjugation constants were found to be greater for complexes with proton transfer than for those without proton transfer for the acetic acid-n-butylamine system in all solvents and for the phenol-imidazole and phenol-n-butylamine systems in DMSO when the same reference state (molecular acid and molecular base) was considered. For the acetic acid-n-butylamine system in acetonitrile and dimethyl sulfoxide, the calculated constants of ionic heterocomplex formation are greater than the values determined by potentiometric titration, while the calculated constants of molecular heterocomplex formation, as well as the calculated constants of heterocomplex formation from acetic acid and 4(5)-methylimidazole, are in good agreement with the experimental data, which suggests that the force field applied overestimates the energy of the interactions of oppositely charged ions or the energy of the interactions of hydrogen-bonding species with solvent molecules. The constants were found to decrease with an increasing polarity and hydrogen-bonding propensity of the solvent (i.e., in the series AN > DMSO > H 2 O), this being in agreement with the available experimental data.