Unfortunately, in standard molecular viewers, extraneous pieces of surfaces are a persistent problem in the selective representation of molecular surfaces. The reason is that partial surfaces are, by convention, encoded as a property of an atom. Certain atoms in a protein structure may contribute to more than one surface where for example, an atom lining a channel may also form part of a void. If the surface of this atom is selected to be displayed, then both the channel and void surfaces will be displayed, where the partial surface of the void is an artifact if the area of interest is the channel.

Another common problem is the selection of channel residues. As the exterior part of the molecular surface obscures the channel surface, the exterior surface must also be removed. Typically, the viewing plane is clipped and the surface representation is restricted to the display of channel-lining residues. Unfortunately, there is no simple way to select channel residues and the channel residues must be selected manually, which is a tedious and error-prone process for the user.

In order to identify pockets and tunnels, an exterior envelope needs to be defined. As channels open from multiple positions of the protein, the exterior envelope is used to demarcate the end of the channel. Dummy atoms found above the envelope are eliminated. The dummy atoms below the envelope and above the protein surface correspond to the volume of pockets. In HOLLOW, the exterior envelope is defined by rolling a large 8.0 Šsphere over the surface atoms. Surface atoms are defined by the solvent-accessible surface area (SASA) by SASA > 9 Ų. Both the SASA and exterior envelope elimination are calculated using the Shrake-Rupley dot-density method [5].

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 ​(Figure1B).1B). Nevertheless, there are unnecessary additional surfaces in this display (Figure ​(Figure1B1B – 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 ​(Figure1C),1C), 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 ​Figure1B)1B) 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 ​(Figure2A).2A). 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 ​(Figure2B).2B). 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 ​(Figure2B).2B). 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 ​(Figure2C2C).

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 ​(Figure3A).3A). 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 ​(Figure3B3B).

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 ​(Figure4A),4A), which form a fully-contained network of interior pathways (Figure ​(Figure4B),4B), can be used to assess the accuracy of the HOLLOW sphere approximation (Figure ​(Figure4C)4C) (details available on the website). As the grid spacing decreases, the volume of the dummy atoms increases linearly to an asymptotic value of ~720 ų, 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 ų grid, results can be obtained in minutes on most desktop computers.

• Project home page: http://hollow.sourceforge.net

• Operating system(s): Platform independent

• Programming language: Python