Kinematic mobility analysis of peptide based nano-linkages

Given that proteins are the nano devices of choice for evolution, it is increasingly believed by scientists that the practical and viable approach to the design and fabrication of artificial nano devices and machines is to use polypeptide chains, protein building blocks found in nature. A peptide chain (building block of proteins) is an open loop serial linkage that in the process of folding is turned into a complex network of closed and open loops by hydrogen and disulphide bonds. Over-constrained closed loops form rigid structural domains in the proteins and therefore reduce the movement flexibility (mobility) of the protein molecules. The objective of this work is to identify the rigid domains and flexible regions in a peptide chain using only one of its native conformations. Protein molecules that exhibit conformation changes upon stimuli consist of rigid domains connected by flexible links. In order be able to design nano devices that will exhibit similar behavior, we need to predict the internal mobility of the molecules. To identify the rigid domains of the peptide chain, we use the Grübler–Kutzbach (GK) criterion to predict the mobility and degrees of freedom of the chain. The majority of the existing methods in the literature for identifying rigid domains involve the comparison of two conformations of a protein in order to identify the rigid domains in the molecule and, therefore, require atom coordinates in these configurations. These methods cannot be effective in the design process where predictive ability based on the structural characteristics of the chain, rather than experimental observations, is the aim.To be able to apply GK criterion, the following procedure is proposed. For any conformation of the peptide chain, hydrogen and disulphide bonds will be established based on the geometric and energy criteria reported in the literature; develop the connectivity matrix for all of the bond and atom connections; based on a search of the connectivity matrix, identify all of the independent loops of the chain; apply GK criterion to independent loops in order to identify the rigid regions as well as to identify the mobility (degrees of freedom) of the flexible regions.This procedure also identifies the flexible domains as well as their degree of flexibility. Identification of rigid domains significantly simplifies the motion modeling procedures that use dihedral angles of the protein chain as variables. The developed methodology is applied to two protein molecules and the results are presented.