To illustrate the improvements in the visualization of channels surfaces with HOLLOW, we use the example of the ammonia channel Rh50 of Nitrosomonas europaea
(PDB ID 3BHS) [6
]. One commonly available method is to generate a channel trajectory with the program MOLE [3
]. The MOLE-generated surface corresponds to a spherical volume from the center of the channel at each point along the path and illustrates the two most likely average paths of ammonia conduction (Figure ). However, the MOLE-generated surface lacks atomic details: the surface does not suggest a mechanism for "gating" (dashed box), nor identify vestibules for the substrate (dotted box), nor illustrate the entire apertures to the channel (solid boxes).
Figure 1 Representations of channel surfaces. Comparison of (A) MOLE tunnel, (B) selected molecular surface, (C) and HOLLOW surface. The periplasmic opening (black box) and the cytoplasmic opening (grey box) regions show a clear loss of detail in the MOLE tunnel (more ...)
By running HOLLOW on Rh50, dummy atoms (defined on a 0.5 Å grid) are generated to fill the channel volume. The channel residues are easily selected by proximity to the dummy atoms. The display of the molecular surface can be restricted to the surface of the channel residues, which produces a highly detailed visualization of the channel surface in atomic detail (Figure ). Nevertheless, there are unnecessary additional surfaces in this display (Figure – left side and lower right of black solid box, lower right of dotted box, and grey box), which arise from the display of other surfaces associated with the atoms in the channel residues. In comparison, the molecular surface of the HOLLOW-generated dummy atoms is shown (Figure ), which clearly shows the channel lumen in atomic detail without gratuitous surfaces. Comparison to the molecular surface of the channel (atoms selected by proximity to the HOLLOW-generated dummy atoms – Figure ) reveals a very similar surface with only minor differences.
The use of HOLLOW-generated dummy atoms also permits control over other aspects of surface visualization. The displayed surface can be customized by the selection of a subset of dummy atoms. It is important to note that only part of the molecular surface of a group of dummy atoms is complementary to the protein surface. However, the selective display of the complementary surface can be easily controlled using HOLLOW in the manual mode with constraints. For example when a cylindrical constraint is used to generate a "casting" of the protein channel, dummy atoms found on the surface of the cylindrical constraint are tagged with occupancy = 0 while those inside are tagged with occupancy = 1 (Figure ). By restricting the surface to dummy atoms with occupancy = 1, a channel surface is displayed where the opening is defined by the intersection of the cylindrical constraint to the molecular surface of the protein (Figure ). As HOLLOW stores the average B-factor of nearby protein atoms to the B-factor of a dummy atom, the accuracy of the channel surface can be illustrated by coloring the HOLLOW-generated surface to this B-factor (Figure ). Similarly, the electrostatic potential of the heavy atoms near each dummy atom can be assigned to the surface resulting in an electrostatic potential map of the channel surface (Figure ).
Figure 2 Surface properties on HOLLOW surface. (A) The opening of a surface channel can be specified in terms of a cylindrical constraint by displaying the surface of the dummy atoms found wholly inside the constraint (white) while hiding the surface of dummy (more ...)
Compared to other surface generation programs, HOLLOW focuses on customization of surface rendering. VOIDOO [7
] and SURFNET [8
] generate polygon surfaces, which cannot be easily edited in molecular viewers. Instead, HOLLOW generates dummy atoms, which not only provides a convenient tool for selecting residues that line cavities by proximity to the dummy atoms, but also permits control over the rendering of partial surfaces leading to significantly clearer visualizations of channel surfaces. Indeed, the origin of HOLLOW arose from the difficulty that the authors found in generating detailed channel surfaces using standard existing programs.
The van der Waals (vdW) surface of the HOLLOW-generated dummy atoms at an infinitely-small grid-spacing can be shown to be an exact representation of the molecular surface of the protein. The molecular surface of the protein is commonly defined in terms of the Connolly surface [9
], which is a smoothly differentiable surface defined over the surface of the protein. As the vdW surface of the protein contains abrupt cusps between overlapping atoms, the Connolly surface defines reentrant surfaces over the cusps (Figure ). The reentrant surface is defined as the surface traced out by a probe sphere rolling over the protein. The vdW surface of the dummy atoms, as the grid-spacing approaches zero, approaches the surface of a probe sphere rolling over the protein surface, which is the Connolly surface (Figure ).
Figure 3 Molecular surface grid-approximation. (A) The molecular surface (black) is defined by the atomic contact of a rolling sphere and the reentrants (dashed) resulting at the sphere contacts of multiple atoms. (B) The finite-grid approximation in HOLLOW results (more ...)
To determine the accuracy of the HOLLOW-generated spheres as a function of grid spacing, one could measure surface area or volume of a set of dummy atoms. Though a good measure for the representation of a surface, closely overlapping spheres using the Shrake-Rupley dot-density method require an unreasonably high number of dots for an accurate surface area. In contrast, a grid-based volume approximation of the overlapping spheres generates an accurate value for the volume with a reasonably coarse grid spacing. As an example, interior volumes of myoglobin [10
] (PDB ID 1J52) (Figure ), which form a fully-contained network of interior pathways (Figure ), can be used to assess the accuracy of the HOLLOW sphere approximation (Figure ) (details available on the website). As the grid spacing decreases, the volume of the dummy atoms increases linearly to an asymptotic value of ~720 Å3
, corresponding to the ideal volume as defined by the Connolly surface. At a grid-spacing of 0.5 Å, the volume of the dummy atoms constitutes 70% of the ideal volume, providing a reasonable approximation to the ideal volume. For higher accuracy, a grid-spacing of 0.1 Å results in dummy atoms that constitute 93% of the ideal volume. The calculation time increases exponentially with grid-spacing and grid volume, however even at grid spacing of 0.2 Å and a 27000 Å3
grid, results can be obtained in minutes on most desktop computers.
Figure 4 The interior volume of myoglobin. (A) The voids (green) identified in myoglobin using a grid-spacing of 0.2 Å. (B) With the volume-filling spheres, it is easy to select the residues (stick display) that define the interior volume by proximity (more ...)