Doing a Good Turn: The Use of Quaternions for Rotation in Molecular Docking

Abstract

Much work has been done on algorithms for structure-based drug modeling in silico, and almost all these systems have a core need for three-dimensional geometric models. The manipulation of these models, particularly their transformation from one position to another, is a substantial computational task with design questions of its own. Solid body rotation is an important part of these transformations, and we present here a careful comparison of two established techniques: Euler angles and quaternions. The relative superiority of the quaternion method when applied to molecular docking is demonstrated by practical experiment, as is the crucial importance of proper adjustment calculations in search methods.

A two-layer mono-objective algorithm based on guided optimization to reduce the computational cost in virtual screening

“…Concerning the projection operator, we must highlight another important innovative feature of GO-Pharm related to the problem knowledge: the circular limits. The main idea of the circular limits is to give search continuity to those angular variables whose search domain is (see 26 ). In this regard, if any of these variables takes a value above 2 or below 0, then it is translated to an angle in the interval [0, 2 ] by computing its 2 module.…”

Quantitative Characterization of Domain Motions in Molecular Machines

“…In this approach, a closed-form solution to the least-squares problem of absolute orientation is determined using unit quaternions. Quaternions have been previously used in biomolecular research and structural biophysics for molecular modeling. − The basics of quaternions and the least-squares problem of absolute orientation using unit quaternion are briefly outlined in the Supporting Information (Text S3 and S4, respectively). Here we merely present the implementation steps, in Section below.…”