We modify and extend the recently developed statistical mechanical model forpredicting the thermodynamic properties of chain molecules having noncovalentdouble-stranded conformations, as in RNA or ssDNA, and $\beta-$sheets inprotein, by including the constant force stretching at one end of molecules asin a typical single-molecule experiment. The conformations of double-strandedregions of the chain are calculated based on polymer graph-theoretic approach[S-J. Chen and K. A. Dill, J. Chem. Phys. {\bf109}, 4602(1998)], while theunpaired single-stranded regions are treated as self-avoiding walks. Sequencedependence and excluded volume interaction are taken into account explicitly.Two classes of conformations, hairpin and RNA secondary structure are explored.For the hairpin conformations, all possible end-to-end distances correspondingto the different types of double-stranded regions are enumerated exactly. Forthe RNA secondary structure conformations, a new recursive formulaincorporating the secondary structure and end-to-end distribution has beenderived. Using the model, we investigate the extension-force curves, contactand population distributions and re-entering phenomena, respectively. we findthat the force stretching homogeneous chains of hairpin and secondary structureconformations are very different: the unfolding of hairpins is two-state, whileunfolding the latter is one-state. In addition, re-entering transitions onlypresent in hairpin conformations, but are not observed in secondary structureconformations.
展开▼
