Using internal and collective variables in Monte Carlo simulations of nucleic acid structures: chain breakage/closure algorithm and associated Jacobians

This article describes a method for solving the geometric closure problem for simplified models of nucleic acid structures by using the constant bond lengths approximation. The resulting chain breakage/closure equations, formulated in the space of variable torsion and bond angles, are easy to solve, and have only two solutions. The analytical simplicity is in contrast with the high complexity of the closure problem in the torsion angle space with at most 16 solutions, which has been dealt with by several authors and was solved analytically by Wu and Deem (J. Chem. Phys. 1999, 111, 6625). The discussion on the choice of variables and associated Jacobians is focussed on the question of how conformational equilibration is affected in Monte Carlo simulations of molecular systems. In addition to the closure of the phosphate backbone, it is necessary to also solve the closure problem for the five-membered flexible furanose sugar ring. Explicit closure equations and the resulting Jacobians are given both for the complete four-variable model of the furanose ring and simulations in the phase-amplitude space of the five-membered ring, which are based on the approximate two-variable model of furanose introduced by Gabb et al. (J. Comput. Chem. 1995, 16, 667). The suggested closure algorithm can be combined with collective variables defined by translations and rotations of the monomeric nucleotide units. In comparison with simple internal coordinate moves, the resulting concerted moves describe local structural changes that have high acceptance rates and enable fast conformational equilibration. Appropriate molecular models are put forward for prospective Monte Carlo simulations of nucleic acids, but can be easily adapted to other biomolecular systems, such as proteins and lipid structures in biological membranes.