The Choice of Dielectric Constant Proton Binding as a Paradigm

4 The Choice of Dielectric Constant Proton Binding as a Paradigm 

The most important model parameter in PBFE and MM/PBSA is the dielectric constant used for the solutes. Most studies have taken an empirical approach, viewing the dielectric constant as an adjustable parameter. While this seems plausible, it is prudent to analyze the physical problem in more detail, because, in some cases, the experimental data can be fit by models that are distinctly unphysical, despite some plausible features. We therefore come back to the simplest possible PBFE calculation the important problem of proton binding, or pKa shifts. We discuss a nonem-pirical model that attempts to avoid parameter fitting and that gives insights into the limitations of simplified continuum electrostatic free energy methods. 

A larger protein dielectric constant of four was used by Eberini et al. [124] to fit the experimental pKa, in a case where the protein structural relaxation upon protonation was especially large. The need for a larger protein dielectric suggests a breakdown of the linear response assumption for this system. It may be preferable in such a case to simulate an additional point along the reaction pathway, such as the midpoint, rather than shifting to what is effectively a parameter-fitting approach. 

Relaxation Free Energy and Internal Consistency of the Model 

Importantly, another expression also exists for AArtx, (12.32). This expression makes explicit use of both the reactant and product structures, and so contains an explicit representation of the structural relaxation. The implicit (12.31) and explicit (12.32) representations of the relaxation are equivalent 

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