Modelling the optimal simulation path in the peptide chain folding--studies based on geometry of alanine heptapeptide

The theoretical background of a simple model of polypeptide chain structure using two parameters: R (A)--the radius of curvature for each pentapeptide chain fragment in the protein, and V (deg)--the dihedral angle between two consecutive peptide bond planes, is presented. The mathematical relationship between these two geometrical parameters leads to the optimal searching path for low-energy peptide conformations. This R versus V relation, corresponding to low-energy structures in Ramachandran plot, appeared to fit the square function well. Here, the minimum of this function is taken as the optimal starting point for the minimization of all second-order conformations in the peptide chain. The extension, including all structures that satisfy the square function between V and R, showed the Phi, Psi angles that are optimal in searching for the path to low-energy structures. The path is an ellipse connecting the alpha R-, beta- and alpha L-structures, indicating the possible transitions from one to the next.