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.

Keywords: Blobby Surface; Connolly Surface; Molecular Surface; Poisson-Boltzmann; Skin Surface.

Figure 1

Self-intersection induced singularities of the Lee and Richards molecular surface; projected points computed from DelPhi surface algorithm

Figure 2

Thermal motion grid for three atoms; 0.5 level set surface

Figure 3

Skin Surface and mixed complex (transparent) in 2D and 3D. In 3D a simple case where 8 equal atoms are put on the vertices of a cube. Surfaces of the following mixed complexes ${\mu }_{0,3}^s,{\mu }_{3,0}^s,{\mu }_{2,1}^s$, and ${\mu }_{1,2}^s$ are represented in red, green, yellow and magenta, respectively.

Figure 4

Blobby surface of a dialanine for respectively B = −0.5, −1.0, −1.5, −2.0, −2.5, −3.0, the Skin surface for s =0.5 and the Connolly surface with 1.4Å probe radius.

Figure 5

Hausdorff distance and Surface Area discrepancy for dialanine: blobby and skin VS Connolly

Figure 6

Comparison of surface area of skin and blobby surfaces versus Connolly MS for a dialanine trajectory: percentage difference is reported

Figure 7

Pathological configurations for skin and blobby surface

Figure 8

Skin internal void (atoms patches were removed) and blobby internal void

Figure 9

Surface Opening for the Connolly, skin and blobby

Figure 10

Surface Areas for the Connolly, skin and blobby vs position

Figure 11

Energy profiles for Arg-Glu pair, OPLS2001 and CHARMM22 force fields.

Figure 12

Energy profile for the Lys-Glu pair in two different mutual orientations, OPLS2001 and CHARMM22 force fields

Figure 13

Electrostatic potential for His-Glu pair, OPLS2001 and CHARMM22 force fields

Figure 14

Energy profile for the His-His pair, OPLS2001 and CHARMM22 force fields

Figure 15

Energy profile for the Lys-Lys pair, OPLS2001 and CHARMM22 force fields

Figure 16

Energy profile for Arg-Arg pair, OPLS2001 and CHARMM22 force fields