Interactive Analysis of Connolly Surfaces for Various Probes

Abstract

The Connolly surface defines the boundary between a molecular structure and its environment. Its shape depends on the radius of the probe used to inspect the structure. The exploration of surface features is of great interest among chemists because it helps them to better understand and describe processes in the molecular structure. To help chemists better explore these features, we have combined two things together: a fast extraction of Connolly surfaces from a Voronoi diagram of atoms and a fast visualization based on GPU ray casting. Not only the surface but also the volume description is provided by the diagram. This enables to distinguish surface cavities one from another and compute their properties, e.g. the approximate volume, the maximal filling sphere or the maximal probe that can escape from the cavity to the outer environment. Cavities can be filtered out by applying restrictions to these properties. Views behind the surface and surface clipping improve the perception of the complex internal structure. The surface is quickly recomputed for any probe radius, so interactive changes of the probe radius show the development of cavities, especially how and where they merge together or with the outer environment.The contour-buildup algorithm was parallelized for both CPU [LBPH10] and GPU [KGE11]. The CPU variant runs in

Voronoi‐based detection of pockets in proteins defined by large and small probes

“…To overcome disconnected cases, the points of local maxima are connected to Voronoi vertices or to other extreme points by segments along which d aw is nondecreasing. These segments are called bridges and lie on Voronoi faces . Bridges for the situation in Figure c are depicted in Figure 4d.…”

“…A simple solution is to find all probes that intersect the sphere of the triangle via spatial hashing. For visualization, we do not need to prepare a triangular mesh if we use ray‐casting and perform trimming on GPU …”

“…Probe regions are represented as parts of the Voronoi 1‐skeleton and Connolly surfaces are used for visualization. CAVER Analyst (a software tool for the analysis and visualization of molecular structures) can display these surfaces in high quality thanks to GPU‐based ray‐casting . We will need to estimate the volume of probe regions and compare them with other methods.…”

Exploration of Empty Space among Spherical Obstacles via Additively Weighted Voronoi Diagram

“…The aw‐Voronoi diagram has also been used for the detection of tunnels and cavities in proteins [KCKS13], for the computation, visualization and analysis of Connolly surfaces [RKC*05, RPK07, MJK16] and molecular paths [LBH11]. The method [RKC*05] also navigates a shrinking probe along diagram edges, but it does not handle disconnected cases.…”

“…The method [RKC * 05] also navigates a shrinking probe along diagram edges, but it does not handle disconnected cases. The method [MJK16] extracts Connolly surface elements from the aw-Voronoi diagram. The analytical description of these elements is then uploaded to GPU and efficiently rendered via ray-casting.…”