Single-molecule pulling and the folding of donor-acceptor oligorotaxanes: phenomenology and interpretation.

The thermodynamic driving force in the folding of a class of oligorotaxanes is elucidated by means of molecular dynamics simulations of equilibrium isometric single-molecule force spectroscopy by atomic force microscopy experiments. The oligorotaxanes consist of cyclobis(paraquat-p-phenylene) rings threaded onto an oligomer of 1,5-dioxynaphthalenes linked by polyethers. The simulations are performed in a high dielectric medium using MM3 as the force field. The resulting force versus extension isotherms show a mechanically unstable region in which the molecule unfolds and, for selected extensions, blinks in the force measurements between a high-force and a low-force regime. From the force versus extension data the molecular potential of mean force is reconstructed using the weighted histogram analysis method and decomposed into energetic and entropic contributions. The simulations indicate that the folding of the oligorotaxanes is energetically favored but entropically penalized, with the energetic contributions overcoming the entropy penalty and effectively driving the folding. In addition, an analogy between the single-molecule folding/unfolding events driven by the atomic force microscope (AFM) tip and the thermodynamic theory of first-order phase transitions is discussed. General conditions (on the molecule and the AFM cantilever) for the emergence of mechanical instabilities and blinks in the force measurements in equilibrium isometric pulling experiments are also presented. In particular, it is shown that the mechanical stability properties observed during the extension are intimately related to the fluctuations in the force measurements.