Title: Vertex-transitive Haar graphs that are not Cayley graphs
Other Titles: Vrcholovo tranzitivní Haarovi grafy kterí nejsou Cayleyho
Authors: Conder, Marston
Estélyi, István
Pisanski, Tomaž
Citation: MAŇÁK, M. Voronoi-Based Detection of Pockets in Proteins Defined by Large and Small Probes. Journal of Computational Chemistry, 2019, roč. 40, č. 19, s. 1758-1771. ISSN 0192-8651.
Issue Date: 2018
Publisher: Wiley
Document type: článek
URI: 2-s2.0-85063670773
ISSN: 2194-1009
Keywords: Haarův graf, Cayleyho graf, vrcholovo tranzitivní graf
Keywords in different language: Haar graph, Cayley graph, vertex-transitive graph
Abstract: V nedávním článku Electron. J. Combin. 23 (2016) Estélyi a Pisanski se ptali, jestli existují vrcholovo tranzitivní Haarovi grafy kterí nejsou Cayleyho. V tomhle článku se konštruuje nekoneční třída kubických Haarových grafů, které jsou vrcholovo tranzitivní, avšak nejsou Cayleyho. Nejmenší takový graf má 40 vrcholů a je známy jako Kroneckerove nakrytí dodekaedra G(10,2), a ve Fosterověm cenzusu je uveden jako graf "40".
Abstract in different language: 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.
Rights: Plný text je přístupný v rámci univerzity přihlášeným uživatelům.
© Wiley
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