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

Narrow Passage Problem Solution for Motion Planning

The paper introduces a new randomized sampling-based method of motion planning suitable for the problem of narrow passages. The proposed method was inspired by the method of exit points for cavities in protein models and is based on the Rapidly Exploring Random Tree (RRT). Unlike other methods, it can also provide locations of the exact positions of narrow passages. This information is extremely important as it helps to solve this part of space in more detail and even to decide whether a path through this bottleneck exists or not. For data with narrow passages, the proposed method finds more paths in a shorter time, for data without narrow passages, the proposed method is slower but still provides correct paths.

Detection of cave pockets in large molecules: Spaces into which internal probes can enter, but external probes from outside cannot

Geometric features of macromolecular shapes are important for binding with other molecules. Kawabata, T. and Go, N. (2007) defined a pocket as a space into which a small probe can enter, but a large probe cannot. In 2010, mathematical morphology (MM) was introduced to provide a more rigorous definition, and the program GHECOM was developed using the grid-based representation of molecules. This method was simple, but effective in finding the binding sites of small compounds on protein surfaces. Recently, many 3D structures of large macromolecules have been determined to contain large internal hollow spaces. Identification and size estimation of these spaces is important for characterizing their function and stability. Therefore, we employ the MM definition of pocket proposed by Manak, M. (2019)—a space into which an internal probe can enter, but an external probe cannot enter from outside of the macromolecules. This type of space is called a “cave pocket”, and is identified through molecular grid-representation. We define a “cavity” as a space into which a probe can enter, but cannot escape to the outside. Three types of spaces: cavity, pocket, and cave pocket were compared both theoretically and numerically. We proved that a cave pocket includes a pocket, and it is equal to a pocket if no cavity is found. We compared the three types of spaces for a variety of molecules with different-sized spherical probes; cave pockets were more sensitive than pockets for finding almost closed internal holes, allowing for more detailed representations of internal surfaces than cavities provide.