Description of protein secondary structure using dual quaternions

The main aim of this paper is to introduce the application of dual quaternions in one interesting problem in structural biology, i.e., the description of protein structure. The secondary protein structure is a specific geometric shape and the description uses Chasles theorem which states that any rigid body displacement can be described by a screw motion. We will briefly introduce the theory of dual quaternions in connection with the screw motion. Consequently, it is shown that modeling based on dual quaternions is an elegant mathematical method and a compact formula for the description of secondary protein structure is derived using the dual quaternion calculus.