Theory for the force-stretched double-stranded chain molecule

Abstract

We modify and extend the recently developed statistical mechanical theory of chain molecules having noncovalent double-stranded conformations, as in RNA or single-stranded DNA, and β sheets in protein, to the force-stretched case as in a typical single-molecule experiment. The conformations of double-stranded regions of the molecules are calculated based on polymer graph-theoretic approach [S.-J. Chen and K. A. Dill, J. Chem. Phys. 109, 4602 (1998)], while the unpaired single-stranded regions are treated as self-avoiding walks. Two classes of conformations—the hairpin conformations and RNA secondary structures—are explored. For the hairpin conformations, all possible end-to-end distances corresponding to the different types of double-stranded regions are enumerated exactly. For the RNA secondary structures, a recursive formula incorporating the secondary structure and end-to-end distribution has been derived. The sequence dependence and excluded volume interaction are taken into account explicitly. Using the extended theory, we investigate the extension-force and force-extension curves, distribution of the extensions at fixed forces, and reentering phenomenon, respectively. We find that the mechanical behaviors of homogeneous chains of hairpin conformations and secondary structures are quite different: the unfolding of the hairpin case is two state, while the unfolding of the latter is one state. In addition, a reentering transition is observed in hairpin conformations.