  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.
