Extension of the edge tracing algorithm to disconnected Voronoi skeletons

2019

J Comput Chem

Self Cite

The function of enzymatic proteins is given by their ability to bind specific small molecules into their active sites. These sites can often be found in pockets on a hypothetical boundary between the protein and its environment. Detection, analysis, and visualization of pockets find its use in protein engineering and drug discovery. Many definitions of pockets and algorithms for their computation have been proposed. Kawabata and Go defined them as the regions of empty space into which a small spherical probe can enter but a large probe cannot and developed programs that can compute their approximate shape. In this article, this definition was slightly modified in order to capture the existence of large internal holes, and a Voronoi‐based method for the computation of the exact shape of these modified regions is introduced. The method first puts a finite number of large probes on the protein exterior surface and then, considering both large probes and atomic balls as obstacles for the small probe, the method computes the exact shape of the regions for the small probe. This is all achieved with Voronoi diagrams, which help with the safe navigation of spherical probes among spherical obstacles. Detected regions are internally represented as graphs of vertices and edges describing possible movements of the center of the small probe on Voronoi edges. The surface bounding each region is obtained from this representation and used for visualization, volume estimation, and comparison with other approaches. © 2019 Wiley Periodicals, Inc.

Section: Voronoi Diagrams and Related Conceptsmentioning

confidence: 99%

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

2019

J Comput Chem

Self Cite

“…The diagram can be constructed by the edge‐tracing algorithm [KCK05, MVLG06, MK16]. Implementations are available [AWV16, VDR16].…”

Section: Related Workmentioning

confidence: 99%

Interactive Analysis of Connolly Surfaces for Various Probes

Computer Graphics Forum

Jirkovsky

Kolingerová

2016

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

“…Furthermore, the Voronoi 1-skeleton (the union of edges) can have several components. Disconnected cases were solved recently [MK16].…”

Section: Related Workmentioning

confidence: 99%

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

Computer Graphics Forum

2016

Properties of granular materials or molecular structures are often studied on a simple geometric model – a set of 3D balls. If the balls simultaneously change in size by a constant speed, topological properties of the empty space outside all these balls may also change. Capturing the changes and their subsequent classification may reveal useful information about the model. This has already been solved for balls of the same size, but only an approximate solution has been reported for balls of different sizes. These solutions work on simplicial complexes derived from the dual structure of the ordinary Voronoi diagram of ball centers and use the mathematical concept of simplicial homology groups. If the balls have different radii, it is more appropriate to use the additively weighted Voronoi diagram (also known as the Apollonius diagram) instead of the ordinary diagram, but the dual structure is no longer a simplicial complex, so the previous approaches cannot be used directly. In this paper, a method is proposed to overcome this problem. The method works with Voronoi edges and vertices instead of the dual structure. Additional bridge edges are introduced to overcome disconnected cases. The output is a tree graph of events where cavities are created or merged during a simulated shrinking of the balls. This graph is then reorganized and filtered according to some criteria to get a more concise information about the development of the empty space in the model.