Between Algorithm and Model: Different Molecular Surface Definitions for the Poisson-Boltzmann Based Electrostatic Characterization of Biomolecules in Solution

Abstract

The definition of a molecular surface which is physically sound and computationally efficient is a very interesting and long standing problem in the implicit solvent continuum modeling of biomolecular systems as well as in the molecular graphics field. In this work, two molecular surfaces are evaluated with respect to their suitability for electrostatic computation as alternatives to the widely used Connolly-Richards surface: the blobby surface, an implicit Gaussian atom centered surface, and the skin surface. As figures of merit, we considered surface differentiability and surface area continuity with respect to atom positions, and the agreement with explicit solvent simulations. Geometric analysis seems to privilege the skin to the blobby surface, and points to an unexpected relationship between the non connectedness of the surface, caused by interstices in the solute volume, and the surface area dependence on atomic centers. In order to assess the ability to reproduce explicit solvent results, specific software tools have been developed to enable the use of the skin surface in Poisson-Boltzmann calculations with the DelPhi solver. Results indicate that the skin and Connolly surfaces have a comparable performance from this last point of view.

Implicit solvent methods for free energy estimation

“…The choice and definition of the molecular surface was [28] and still is [33] a matter that deserves a deep attention from several viewpoints.…”

“…More recently, the Solvent Excluded Surface, or Connolly surface has been widely used as a reference surface together with Boundary Element and Finite Element methods [34–41]. Despite the physical soundness and the widespread utilization of the Connolly surface, the latter however present some limitations [33] and alternative approaches have been investigated [33][41,42]. Finite difference PB solvers map fixed charges on point of a grid and use molecular surface information to assign a dielectric value to each grid midpoint (middle point between two grid points) and, indirectly, to map also the ionic accessibility function.…”

“…AGBNP2 was successfully applied in molecular dynamics simulations: among other results it was shown, rather impressively, that this model was able to recover both the solvation barrier at 5 Å and the “second minimum” of the PMF simulation of propyl guanidinium and ethyl acetate in a bidentate coplanar formation where classical continuum models fail [51][33]. …”

Progress in developing Poisson-Boltzmann equation solvers

“…The most commonly used definitions of boundary macromolecule-water are the solvent accessible surface (ASA) definition [102] and the solvent excluded surface [50] definition, which is also well known as molecular surface (MS surface). Other definitions were also used including van der Waals surface [131] , Gaussian surface [71] , spline surface [90] , geometric flow surface [46] , blobby and skin surfaces [59] . Depending on the task and the problem studied, different surface definitions are preferred.…”

Accuracy of continuum electrostatic calculations based on three common dielectric boundary definitions

“…Still, the Lee-Richards molecular surface is not the only type of DB proposed for use in the PB 14,48–51 and the GB models. 52–55 Other recent examples of DB definitions include Gaussian boundary in which a transition between the low and high dielectric regions is smooth, 48 and the skin surface 50,56 which has a similar appearance to the Lee-Richards surface, but avoids singularities associated with the latter.…”