Motifs in nucleic acids: molecular mechanics restraints for base pairing and base stacking

In building and refining nucleic acid structures, it is often desirable to enforce particular base pairing and/or base stacking interactions. Energy-based modeling programs with classical molecular mechanics force fields do not lend themselves to the easy imposition of penalty terms corresponding to such restraints, because the requirement that two bases lie in or near the same plane (pairing) or that they lie in parallel planes (stacking) cannot be easily expressed in terms of traditional interactions involving two atoms (bonds), three atoms (angles), or four atoms (torsions). Here we derive expressions that define a collection of pseudobonds and pseudoangles through which molecular mechanics restraints for base pairing and stacking can be imposed. We have implemented these restraints into the JUMNA package for modeling DNA and RNA structures. JUMNA scripts can specify base pairing with a variety of standard geometries (Watson-Crick, Hoogsteen, wobble, etc.), or with user-defined geometries; they can also specify stacking arrangements. We have also implemented "soft-core" functions to modify van der Waals and electrostatic interactions to avoid steric conflicts in particularly difficult refinements where two backbones need to pass through one another. Test cases are presented to show the utility of the method. The restraints could be adapted for implementation in other molecular mechanics packages.