  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 phi 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.
