Langevin dynamics of molecules with internal rigid fragments in the harmonic regime

An approximation scheme is developed to compute Brownian motion according to the Langevin equation for a molecular system moving in a harmonic force field (corresponding to a quadratic potential energy surface) and characterized by one or more rigid internal fragments. This scheme, which relies on elements of the rotation translation block (RTB) method for computing vibrational normal modes of large molecules developed by Sanejouand and co-workers [Biopolymers 34, 759 (1994); Proteins: Struct., Funct., Genet. 41, 1 (2000)], provides a natural and efficient way to freeze out the small amplitude, high frequency motions within each rigid fragment. The number of dynamical degrees of freedom in the problem is thereby reduced, often dramatically. To illustrate the method, the relaxation kinetics of the small membrane-bound ion channel protein gramicidin-A, subjected to an externally imposed impulse, is computed. The results obtained from all-atom dynamics are compared to those obtained using the RTB-Langevin dynamics approximation (treating eight indole moieties as internal rigid fragments): good agreement between the two treatments is found.