Secondary-structure design of proteins by a backbone torsion energy

We propose a new backbone-torsion-energy term in the force field for protein systems. This torsion-energy term is represented by a double Fourier series in two variables, the backbone dihedral angles 0 and psi. It gives a natural representation of the torsion energy in the Ramachandran space in the sense that any two-dimensional energy surface periodic in both phi and psi can be expanded by the double Fourier series. We can then easily control secondary-structure-forming tendencies by modifying the torsion-energy surface. For instance, we can increase/decrease the alpha-helix-forming tendencies by lowering/raising the torsion-energy surface in the alpha-helix region and likewise increase/decrease the beta-sheet-forming tendencies by lowering/raising the surface in the beta-sheet region in the Ramachandran space. We applied our approach to AMBER parm94 and AMBER parm96 force fields and demonstrated that our modifications of the torsion-energy terms resulted in the expected changes of secondary- structure-forming tendencies by performing folding simulations of alpha-helical and beta-hairpin peptides.