Macromolecular flexibility

We explore the conformational space of a macromolecule that has interlocking flexible rings. The model molecule has two internal degrees of freedom. Four interconnected ten-fold rings in the molecule are closed at every step in a random-walk procedure. Rings are closed by following the trajectory of solutions to the set of simultaneous ring closure equations. We show there are three useful hierarchies in the conformational space. The first is the space sampled when only bond length and angle constraints are imposed, which almost covers the whole allowed two-dimensional conformational space. The conformational space is reduced significantly when van der Waals constraints are imposed. Finally, the conformational space shrinks further to a few discrete states when conformations are optimized using the MM3 force field. These results validate the fact that this approach, which involves searching conformations with only bond length, bond angle and van der Waals constraints followed by a minimization with a full force field, is effective in exploring the low-energy conformations of macromolecules.