Fig. 2

Chaperone binding accelerates hairpin folding. a Representative donor (green) and acceptor (magenta) fluorescence time traces depicting unassisted folding of the surface-immobilized 5′-3′ FRET-labeled hairpin. The uncorrected transfer efficiency, \(\hat E\), (black) and the most likely state trajectory (gray) based on the Viterbi algorithm are shown below. b Analogous to a, but depicting chaperone-assisted hairpin folding with saturating concentrations of NCD (150 nM) to ensure that hairpin molecules are almost always chaperone-associated. c Survival probability plots of folded- (upper left) and unfolded-state (lower left) dwell times in the absence of chaperone, fit with single-exponential decays to determine the unfolding and folding rate constants, k_U and k_F, respectively; 〈k_U〉 and 〈k_F〉 represent mean values obtained from 54 single-molecule measurements. The donor-acceptor fluorescence cross-correlation function (right) decorrelates with a rate constant that is consistent with the sum of k_U and k_F from the dwell-time analysis. d Analogous to c, but for chaperone-assisted folding; 〈k_U〉 and 〈k_F〉 represent mean values obtained from 26 single-molecule measurements. The black lines in c and d are fits with single exponentials with 99% confidence bands shown in gray. e Representative fluorescence time trace measured at a chaperone concentration near ^appK_d. Transitions between chaperone-bound (cyan shading) and chaperone-free (red shading) kinetic regimes arise from binding and dissociation of NCD. f Kinetic 4-state model for chaperone-assisted folding. The folded, F, and unfolded, U, conformations of the hairpin freely interconvert in the absence of chaperone, C, with an equilibrium constant that favors U. When the chaperone is bound, the unfolded, UC, and folded, FC, conformations of the hairpin still interconvert, but with an equilibrium constant that favors F. g Trajectory from coarse-grained molecular dynamics simulation showing binding (cyan shading) and dissociation (red shading) of the chaperone to the hairpin concomitant with the formation of intermolecular contacts (gray). The folding and unfolding of the hairpin, monitored via native contacts (black), is shifted to favor hairpin formation when the chaperone is bound. Structural representations are taken from the simulations (see Supplementary Movies 1 and 2). Source data for mean values in c and d are provided as a Source Data File