Journal of Molecular Graphics and Modelling 66 (2016) 108–114 Contents lists available at ScienceDirect Journal of Molecular Graphics and Modelling j ourna l h om epa ge: www.elsevier.com/locate/JMGM Investigating the importance of Delaunay-based definition of atomic interactions in scoring of protein–protein docking results Rahim Jafari a,* , Mehdi Sadeghi b,c , Mehdi Mirzaie d a Department of Nanobiotechnology, Faculty of Biological Sciences, Tarbiat Modares University, Tehran, Iran b National Institute of Genetic Engineering and Biotechnology, Tehran, Iran c School of Biological Sciences, Institute for Research in Fundamental Sciences (IPM), Tehran, Iran d Department of Applied Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, Jalal Ale Ahmad Highway, P.O. Box 14115-134, Tehran, Iran a r t i c l e i n f o Article history: Received 27 October 2015 Received in revised form 8 March 2016 Accepted 1 April 2016 Available online 4 April 2016 Keywords: Delaunay tessellation Interaction Protein–protein docking Scoring Potential function a b s t r a c t The approaches taken to represent and describe structural features of the macromolecules are of major importance when developing computational methods for studying and predicting their structures and interactions. This study attempts to explore the significance of Delaunay tessellation for the definition of atomic interactions by evaluating its impact on the performance of scoring protein–protein docking pre- diction. Two sets of knowledge-based scoring potentials are extracted from a training dataset of native protein–protein complexes. The potential of the first set is derived using atomic interactions extracted from Delaunay tessellated structures. The potential of the second set is calculated conventionally, that is, using atom pairs whose interactions were determined by their separation distances. The scoring poten- tials were tested against two different docking decoy sets and their performances were compared. The results show that, if properly optimized, the Delaunay-based scoring potentials can achieve higher suc- cess rate than the usual scoring potentials. These results and the results of a previous study on the use of Delaunay-based potentials in protein fold recognition, all point to the fact that Delaunay tessella- tion of protein structure can provide a more realistic definition of atomic interaction, and therefore, if appropriately utilized, may be able to improve the accuracy of pair potentials. © 2016 Elsevier Inc. All rights reserved. 1. Introduction Protein-protein interactions are involved in many biological processes. Owing to inherent difficulties in studying them exper- imentally, computational methods for the structural prediction of protein–protein complexes from their constituent components, referred to as protein–protein docking, are of great value. These methods typically include two steps: exploring a large number of possible protein–protein configurations in computa- tionally reasonable time to identify a set of structures that contain near-native solutions, followed by refinement step with the aim of improving the rank of the near-native poses. Refining the structures generated in the first step can be performed using combination of several procedures, including: clustering and filtering [1–3], re- * Corresponding author at: Department of Nanobiotechnology, Faculty of Biolog- ical Sciences, Tarbiat Modares University, Jalal Ale Ahmad Highway, Tehran, Iran. E-mail address: rjafari57@yahoo.com (R. Jafari). ranking with scoring functions [4,5] and structural refinements (energy minimization) [6–8]. There are several classes of scoring functions that have been successfully utilized for docking purpose: Physics-based or force- field-based [9,10], empirical [4,6,11,12] and knowledge-based [4,5,13–17] scoring functions. The functions from the last class are obtained by statistical analysis of structural and physico-chemical features taken from a set of known protein structures. The approach is to convert the observed frequency of features to a set of averaged energy parameters by using the inverse Boltzmann equation. They were originally developed for single protein structure pre- diction [18], and over the past years have gained attention in the field of protein docking for their ease of use and computational efficiency. Regardless of their actual application domain, generally there are several factors that can contribute to the effectiveness of the statistical potentials. One is the method by which the “reference state” is modeled, the state at which the features occur purely by chance. It is used for estimation and removal of random part of the observed frequencies. The next factor is the type of feature(s) cho- http://dx.doi.org/10.1016/j.jmgm.2016.04.001 1093-3263/© 2016 Elsevier Inc. All rights reserved.