The existence of Amide Planes of Protein Structures has been confirmed recently by a Mathematical Programming Approach . 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  and this was the first indirect confirmation of Pauling’s insight on the existence of amide planes of Protein Structure . 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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