Structural Compliance Analysis and Internal Motion Properties of Proteins From a Robot Kinematics Perspective: Formulation of Basic Equations

Abstract

From a perspective of robot kinematics, we develop a method for predicting internal motion properties and understanding the functions of proteins from their threedimensional (3D) structural data (protein data bank (PDB) data). The key ideas are based on the structural compliance analysis of proteins. In this paper, we mainly discuss the basic equations for the analysis. First, a kinematic model of a protein is introduced. Proteins are simply modeled as serial manipulators constrained by linear springs, where the dihedral angles on the main chains correspond to the joint angles of manipulators. Then, the kinematic equations of the protein model are derived. In particular, the forced response or the deformation caused by the forces in static equilibrium forms the basis for the structural compliance analysis. In the formulations, the protein models are regarded as manipulators that control the positions in the model or the distances between them, by the dihedral angles on the main chains. Next, the structural compliance of the protein model is defined, and a method for extracting the information about the internal motion properties from the structural compliance is shown. In general, the structural compliance refers to the relationship between the applied forces and the deformation of the parts surrounded by the application points. We define it in a more general form by separating the parts whose deformations are evaluated from those where forces are applied. When decomposing motion according to the magnitude of the structural compliance, we can infer that the lower compliance motion will easily occur. Finally, we show two application examples using PDB data of lactoferrin and hemoglobin. Despite using an approximate protein model, the predicted internal motion properties agree with the measured ones.