Atomic torsional modal analysis for high-resolution proteins

We introduce a formulation for normal mode analyses of globular proteins that significantly improves on an earlier one-parameter formulation [M. M. Tirion, Phys. Rev. Lett. 77, 1905 (1996)] that characterized the slow modes associated with protein data bank structures. Here we develop that empirical potential function that is minimized at the outset to include two features essential to reproduce the eigenspectra and associated density of states in the 0 to 300cm-1 frequency range, not merely the slow modes. First, introduction of preferred dihedral-angle configurations via use of torsional stiffness constants eliminates anomalous dispersion characteristics due to insufficiently bound surface side chains and helps fix the spectrum thin tail frequencies (100-300cm-1). Second, we take into account the atomic identities and the distance of separation of all pairwise interactions, improving the spectrum distribution in the 20 to 300cm-1 range. With these modifications, not only does the spectrum reproduce that of full atomic potentials, but we obtain stable reliable eigenmodes for the slow modes and over a wide range of frequencies.