Dynamic force spectroscopy of synthetic oligorotaxane foldamers

Abstract

Wholly synthetic molecules involving both mechanical bonds and a folded secondary structure are one of the most promising architectures for the design of functional molecular machines with unprecedented properties. Here, we report dynamic single-molecule force spectroscopy experiments that explore the energetic details of donor-acceptor oligorotaxane foldamers, a class of molecular switches. The mechanical breaking of the donor-acceptor interactions responsible for the folded structure shows a high constant rupture force over a broad range of loading rates, covering three orders of magnitude. In comparison with dynamic force spectroscopy performed during the past 20 y on various (bio)molecules, the near-equilibrium regime of oligorotaxanes persists at much higher loading rates, at which biomolecules have reached their kinetic regime, illustrating the very fast dynamics and remarkable rebinding capabilities of the intramolecular donor-acceptor interactions. We focused on one single interaction at a time and probed the stochastic rupture and rebinding paths. Using the Crooks fluctuation theorem, we measured the mechanical work produced during the breaking and rebinding to determine a free-energy difference, ΔG, of 6 kcal·mol^-1 between the two local conformations around a single bond.

Keywords: AFM; equilibrium dynamics; foldamers; molecular machines; single-molecule force spectroscopy.

Fig. 1.

Structural formulas of the oligorotaxanes and schematic description of the AFM-based single-molecule force spectroscopy experiment. (A and B) Structure formulas and coconformations of the [4]rotaxane (A) and [7]rotaxane (B) of the [0.5(n − 1) + 2] family. The terms in square brackets denote the total number of interlocked components and n is the number of DNP units present in the backbone components. In this coconformation, half of the DNP units (in red) are encircled by CBPQT⁴⁺ rings (in blue). Noncovalent intramolecular interactions such as π-interactions linking DNP units and Blue Boxes, hydrogen bonds linking α-hydrogen atoms of the Blue Boxes with tetra(ethylene oxide) chains in the backbones, and Coulombic interactions between the molecular rings and PF₆⁻ counterions stabilize the folded conformation. PF₆⁻ counterions are not shown. (C) Mechanical unfolding of individual oligorotaxanes, leading to the breaking of the intramolecular interactions maintaining the folded conformation.

Fig. 2.

Characteristic force-extension curves of a [4]- (A) and [7]rotaxane (B) mechanically stretched at 7.5 × 10⁴ pN·s⁻¹ in DMF, showing equally spaced force peaks, each separated by 2.4 nm. Each peak corresponds to the breaking of intramolecular interactions on both sides of the ring and the maximum peak value corresponds to the rupture force. The red dotted lines are worm-like chain fits. See Supporting Information for details. Distribution of the rupture force for the pulling of the [4]- (C) and [7]rotaxane (D) in DMF at 7.5 × 10⁴ pN·s⁻¹. The most probable values were obtained by log-normal fits and peak at 101.2 ± 1.2 pN (n = 3,338) (C) and 104 ± 4.5 pN (n = 362) (D).

Fig. 3.

Dynamic force spectrum of the mechanical unfolding of the [4]rotaxane in DMF at 11 loading rates (from 6 × 10² to 4 × 10⁵ pN·s⁻¹). Each datum (n ≥ 150) is associated with its effective loading rate and its most probable rupture force (Fig. S1). As shown by the horizontal red line (F_eq = 108.1 ± 1.2 pN), the rupture force does not increase with the loading rate, establishing the near-equilibrium regime of the experiment.

Fig. 4.

Force spectrum of the mechanical unfolding of the [4]rotaxane in DMF (in red) superimposed with force spectra of 10 data sets (in gray scale) taken from the literature and fit to the Friddle–Noy–De Yoreo model (adapted from ref. 23). The kinetic regime of the oligorotaxane is not reached yet at the highest loading rates, and the equilibrium force (F_eq = 108.1 ± 1.2 pN) is high compared with the one observed for the various molecules measured previously.

Fig. 5.

Stochastic behavior of a single [7]rotaxane during pulling(blue)–relaxing(red) experiments in DMF (the pulling traces A–E and G are shown with a 30-pN offset for more clarity). These curves exhibit the recovery of the characteristic sawtooth pattern during the relaxation step (A–C), the reversible breaking of a single interaction without (D) and with (E) hysteresis, the simultaneous breaking of two interactions and their subsequent reforming (F), and the presence of fluctuations between folded and unfolded states during the pulling and the relaxing curves (G–I).

Fig. 6.

Distributions of forward (pulling step, Lower) and reverse (relaxing step, Upper) works corresponding, respectively, to the breaking and the reforming of a single interaction within the folded [4]rotaxane in DMF (n = 96). These distributions were obtained from pulling–relaxing experiments in the near-equilibrium regime (loading rate of 10³ pN·s⁻¹). Gaussian fits of the raw data are superimposed with the histograms (bin size = 0.5 k_BT). The forward and reverse works have the same value (red line) at W = 10 ± 2 k_BT or 6 ± 1 kcal·mol⁻¹.