Kinematic Modeling and Internal Motion Analysis of Proteins From a Robot Kinematics Viewpoint

This paper discusses the kinematic modeling of proteins and the analysis of their internal motion from the viewpoint of robot kinematics. First, a kinematic model of a protein is introduced. This model consists of multiple serial link mechanisms and interaction lines (lines between alpha carbons). The protein model is regarded as a type of a robot manipulator that uses joint angles to control the lengths of the interaction lines, and the Jacobian matrix of the manipulator is derived. On the basis of this Jacobian matrix, the basic equations for calculating the deformation caused by external forces and evaluating the structural compliance of specified parts are derived. Finally, by combining the derived basic equations, we analyze the internal motions of lactoferrin and hemoglobin and compare the results with the reported measured characteristics of their internal motions. Despite the approximations by the model, the results obtained by the proposed method agree with the measured internal motion.