Nonlocal continuum electrostatic theory predicts surprisingly small energetic penalties for charge burial in proteins

Abstract

We study the energetics of burying charges, ion pairs, and ionizable groups in a simple protein model using nonlocal continuum electrostatics. Our primary finding is that the nonlocal response leads to markedly reduced solvent screening, comparable to the use of application-specific protein dielectric constants. Employing the same parameters as used in other nonlocal studies, we find that for a sphere of radius 13.4 Å containing a single +1e charge, the nonlocal solvation free energy varies less than 18 kcal/mol as the charge moves from the surface to the center, whereas the difference in the local Poisson model is ∼35 kcal/mol. Because an ion pair (salt bridge) generates a comparatively more rapidly varying Coulomb potential, energetics for salt bridges are even more significantly reduced in the nonlocal model. By varying the central parameter in nonlocal theory, which is an effective length scale associated with correlations between solvent molecules, nonlocal-model energetics can be varied from the standard local results to essentially zero; however, the existence of the reduction in charge-burial penalties is quite robust to variations in the protein dielectric constant and the correlation length. Finally, as a simple exploratory test of the implications of nonlocal response, we calculate glutamate pK(a) shifts and find that using standard protein parameters (ε(protein) = 2-4), nonlocal results match local-model predictions with much higher dielectric constants. Nonlocality may, therefore, be one factor in resolving discrepancies between measured protein dielectric constants and the model parameters often used to match titration experiments. Nonlocal models may hold significant promise to deepen our understanding of macromolecular electrostatics without substantially increasing computational complexity.

Gradient models in molecular biophysics: progress, challenges, opportunities

“…In addition, calculations of protein electrostatics in solutions of changing pH (i.e. as happens in biological signaling and disease [101]) require very large dielectric constants for the protein, much larger than are measured (see discussion in [10, 102]). It is true that ε P is often a semi-empirical parameter [103], but there exists a rigorous, formal statistical mechanical definition of this model that leads to an unambiguous continuum model in which ε P = 1 by construction.…”

Nonlocal Electrostatics in Spherical Geometries Using Eigenfunction Expansions of Boundary-Integral Operators

“…To accelerate studies of the promising Lorentz nonlocal model 17,26,27,65 , we have derived the exact analytical solution for a spherical solute containing an arbitrary charge distribution. Our approach uses Hildebrandt’s boundary-integral equation (BIE) formulation 26 and the analytically known eigendecompositions of the associated boundary-integral operators.…”

The role of spatial dispersion of the dielectric constant of spherical water cavity in the lowering of the free energy of ion transfer to the cavity

“…In what follows we show that in the Hildebrandt method [11] the quantity λ H is an adjustable parameter. The Hildebrandt method [11] was used [13] in the calculations of the energy of ion located in a spherical water cavity surrounded by proteins. However, the using of formula (5) for ε(r, r') did not allow obtaining a coincidence between the cal culated solvation energy and experimental data at λ H ≈ 0.3-0.5 nm.…”

“…By substituting equations (11) and (12) to equation (13) and proceeding to the limit, we obtained the sought for formula (14) for the energy W NE of ion resolvation upon its transfer from water bulk to spherical water cavity:…”