Theory for the conformational changes of double-stranded chain molecules

We develop statistical mechanical theory to predict the thermodynamic properties of chain molecules having noncovalent double-stranded conformations, as in RNA molecules and β-sheets in proteins. Sequence dependence and excluded volume interactions are explicitly taken into account. We classify conformations by their polymer graphs and enumerate all the conformations corresponding to each graph by a recently developed matrix method [S-J. Chen and K. A. Dill, J. Chem. Phys. 103, 5802 (1995)]. All such graphs are summed by a recursive method. Tests against exact computer enumeration for short chains on a 2D lattice show that the density of states and partition function are given quite accurately. So far, we have explored two classes of conformations; hairpins, which model small β-sheets, and RNA secondary structures. The main folding transition is predicted to be quite different for these two conformational classes: the hairpin transition is two-state while the RNA secondary structure transition is one-state for homopolymeric chains.