Theoretical pK_a calculations with continuum model solvents, alternative protocols to thermodynamic cycles

Abstract

This article reviews different formulations of the thermodynamic cycles used for the prediction of pK a values, their advantages, and disadvantages with special emphasis on the limitations resulting from the necessity of gas-phase calculations, which allow introducing some difficult cases that motivated alternative strategies. Before introducing the protocols that do not consider gas-phase calculations, the two current opinions available in the literature on the debate about the correct formalism for the calculation of free energies in solution are briefly introduced. Then, the isodesmic proton exchange reaction in solution is reviewed by analyzing its performance on difficult cases for thermodynamic cycles such as carbon acids and amino acids. The pK a values predicted by the isodesmic reaction for common acid species are also reviewed to compare their accuracy results in relation with those of thermodynamic cycles. Linear regressions between experimental pK a values and the calculated free energies obtained with the isodesmic reaction provide expressions for the dependence of the error in the calculated pK a s on the pK a difference between the studied acid and the reference species. Finally, it is shown that linear regressions correct the calculated free energies of the isodesmic reaction, when high constant precision is required in a large pK a range. The deviations from the expected behavior are equivalent to those reported previously for different pK a calculation protocols and are determined by the inaccuracies of continuum solvent models on the interactions with ionic species.

Communication: Accurate hydration free energies at a wide range of temperatures from 3D-RISM

“…It provides information about the partitioning of a solute between gas and solution phases and is used in calculating solubility, 1-3 acid-base dissociation constant, 4 octanol-water partition coefficient, 5 and protein-ligand binding free energy, 6 amongst other properties. The hydration free energies of non-ionic organic solutes can be computed using molecular dynamics (MD) simulations with an accuracy approaching that of experiments.…”

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

“…Thus, the reacting system can be described by a high-level ab initio are gas-phase acidity, Gibbs free energy of deprotonation in solution, Gibbs free energy of solvation for AH, A − and proton species, respectively method and the environment is represented by sites interacting following molecular mechanics force fields, (Kamerlin et al 2009) or even simplified as a dielectric medium (Li et al 2002;Freitas et al 2007;Ho and Coote 2009b;Casasnovas et al 2014). Such calculations are all performed on thermodynamic cycles and, although the free-energy difference between initial and final states is not path dependent, the chosen cycle can determine the predicted pK a accuracy (the physical meaning of this quantity and other thermodynamical ones are described in detail in the next section).…”

“…Different thermodynamic cycles can also be derived by inclusion of solvent molecules, (Ho and Coote 2009b;Casasnovas et al 2014) but they do not eliminate the sources of uncertainties. These uncertainties on the solvation-free energies are higher for ionic species when compared with neutral molecules (Ho and Ertem 2016).…”

Competition reaction-based prediction of polyamines’ stepwise protonation constants: a case study involving 1,4,7,10-tetraazadecane (2,2,2-tet)

“…Proton transfer is one of the most important processes in chemical and biochemical systems [8][9][10][11][12][13]. Consequently, the ability of a molecule to accept or donate a proton is crucial and fundamental to our understanding of the pathways/mechanisms for several important reactions in living systems [9,12].…”

“…Consequently, the ability of a molecule to accept or donate a proton is crucial and fundamental to our understanding of the pathways/mechanisms for several important reactions in living systems [9,12]. Several experimental techniques, such as mass spectrometry and ioncyclotron resonance techniques in the gas phase as well as UV-visible spectroscopy, potentiometry, and NMR titration procedures in the solvent phase, have been used to obtain protonation constants [8,10,12]. Using most accurate experimental technique, glass electrode potentiometry, it is possible to obtain protonation constants with typical uncertainty on the second decimal place of the log unit.…”