Stability of Ramachandran Plots under Small Perturbations of Bond and Dihedral Angles of a Backbone Protein Structure

Abstract

The existence of Amide Planes of Protein Structures has been confirmed recently by a Mathematical Programming Approach [1]. The proposed cost function is the expression of a dihedral angle in terms of three variables: two bond angles, and the angle corresponding to alpha-carbon geometry. The average value of this dihedral angle is calculated to be 180 degrees by exhaustive statistical analysis of dipeptide structures [2] and this was the first indirect confirmation of Pauling’s insight on the existence of amide planes of Protein Structure [3]. In this work we show how the methods of Mathematical Programing can be applied to derive the same average value which we believe to be the first of a series of introductory results belonging to a new modelling process of biomolecular structure. We then consider the small perturbation of the three variables above and we introduce the expressions of the two remaining dihedral angles.

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