A Rational Approach to Ring Flexibility in Internal Coordinate Dynamics

Internal coordinate molecular dynamics (ICMD) is an efficient method for studying biopolymers, but it is readily applicable only to molecules with tree topologies, that is with no internal flexible rings. Common examples violating this condition are prolines and loops closed by S-S bridges in proteins. The most important such case, however, is nucleic acids because the flexibility of the furanose rings always plays an essential role in conformational transitions both in DNA and RNA. There are a few long-known theoretical approaches to this problem, but, in practice, rings with fixed bond lengths are closed by adding appropriate harmonic distance restraints, which is not always acceptable especially in dynamics. This paper tries to overcome this handicap of ICMD and proposes a rational strategy which results in practical numerical algorithms. It gives a unified analytical treatment which shows that this problem is very close to the difficulties encountered by the method of constraints in Cartesian coordinate dynamics, and certain ideas of the latter appear helpful in the context of ICMD. The method is affordable for large molecules and generally applicable to all kinds of rings. A specific implementation for five-membered rings is described and tested for a proline-rich polypeptide and a decamer DNA duplex. In both cases conditions are found which make possible time steps around 10 fsec in ICMD calculations.