Residue Level Three-dimensional Workspace Maps for Conformational Trajectory Planning of Proteins

The function of a protein macromolecule often requires conformational transitions between two native conformations. Understanding these transitions is essential to the understanding of how proteins function, as well as to the ability to design and manipulate protein-based nanomechanical systems. In this paper we propose a set of 3D Cartesian workspace maps for exploring protein pathways. These 3D maps are constructed in the Euclidean space for triads of chain segments of protein molecules that have been shown to have a high probability of occurrence in naturally observed proteins based on data obtained from more than 38,600 proteins from the Protein Data Bank (PDB). We show that the proposed 3D propensity maps are more effective navigation tools than the propensity maps constructed in the angle space. We argue that the main reason for this improved efficiency is the fact that, although there is a one-to-one mapping between the 2D dihedral angle maps and the 3D Cartesian maps, the propensity distributions are significantly different in the two spaces. Hence, the 3D maps allow the pathway planning to be performed directly in the 3D Euclidean space based on propensities computed in the same space, which is where protein molecules change their conformations.