A rigid-body Newtonian propagation scheme based on instantaneous decomposition into rotation and translation blocks

The rotation and translation block (RTB) method of Durand et al. [Biopolymers 34, 759 (1994)] and Tama et al. [Proteins 41, 1 (2000)] provides an appealing way to calculate low-frequency normal modes of large biomolecules by restricting the space of motions to exclude internal motions of preselected rigid fragments within the molecule. These fragments are modeled essentially as rigid bodies and the need to calculate high-frequency relative motions of the atoms that form them is obviated in a natural way. Here we extend the RTB approach into a method for computing the classical (Newtonian) dynamics of a biomolecule, or any large molecule, with effective rigid-body constraints applied to a prechosen set of internal molecular fragments. This method, to be termed RTB dynamics, is easy to implement, conserves the total energy of the system, does not require the construction of the matrix of second spatial derivatives of the potential-energy function (Hessian matrix), and can be used to compute the classical dynamics of a system moving in an arbitrary anharmonic force field. An elementary numerical application to signal propagation in the small membrane-bound polypeptide gramicidin-A is presented for illustration purposes.