Equilibrium states of rigid bodies with multiple interaction sites: Application to protein helices

Equilibrium configurations of rigid building blocks with multiple embedded interaction sites are investigated, as a coarse-grained approach for conformational sampling of protein structures with known secondary structure. First, hypothetical structures of asymmetric shapes, and pairs of rods composed of multiple interaction sites are considered. The rods are either disconnected or joined by a flexible loop. The sites are assumed to interact with a classical 6-12 Lennard-Jones potential. Subsequently, the investigation is extended to the study of two disconnected α helices composed of homogeneous interaction sites and to the ROP monomer, a small protein consisting of two heterogeneous α helices connected by a loop. Residue-specific long-range and short-range potentials extracted from a protein database are used. A Monte Carlo procedure combined with an energy minimization algorithm, originally developed by Li and Scheraga [Proc. Natl. Acad. Sci. USA 84, 6611 (1987)] is used to generate a set of low energy conformations over the full conformational space. Results show that: (i) The potential of mean force between two rods as a whole exhibits an inverse linear dependence on the separation between rods despite the individual sites interacting via a 6-12 Lennard-Jones potential. (ii) As the length of the rods (or helices) increases, they tend to align parallel to one other. (iii) This tendency to become parallel is enhanced when the density of interaction sites is higher. (iv) The angle between the principal axes of the rods is found to scale as $n^{\text{−5/3}}$ with the number $n$ of sites. (v) The native conformation of the ROP monomer, including the detailed rotational states of the virtual bonds located in the loop connecting the α helices is correctly predicted. This lends support to the adoption of such a coarse-grained model and its parameters for future simulations.