Figure 4.

BVA of a dynamic DNA hairpin reveals FRET dynamics. (A) Structure and kinetics of a DNA hairpin. The hairpin is a stem-loop structure, where the stem contains a 31-nucleotide (nt) double-stranded region and the loop contains a stretch of 30 adenines followed by a 5-nt region complementary to a single-stranded portion of the stem. The stem and loop are labeled with donor and acceptor fluorophores (green and red, respectively); in its closed conformation (left; 5-nt region is annealed), the hairpin exhibits high FRET; in its open conformation (right; 5-nt region is melted), it exhibits low FRET. We model the transition between these two states as a simple two-state kinetic system, with first-order kinetic rates $k_{open}$ and $k_{close}$. (B) PDA and BVA of a mixture of two static controls, each of which is designed to mimic either the open or closed conformation of the hairpin. Both distributions show broadening beyond shot noise (Fig. S6) but could be well-fit assuming a Gaussian distribution of FRET efficiencies, with $\langle E_{open}^{\ast }\rangle =0.285\pm 0.002$, ${\sigma }_{open}^r=0.18\pm 0.01\text{nm}$, $\langle E_{closed}^{\ast }\rangle =0.905\pm 0.001$ and ${\sigma }_{closed}^r=0.28\pm 0.02\text{nm}$ (${\chi }_r^2=1.76$, upper). BVA suggests that this heterogeneity is static (lower), or else due to dynamics several orders of magnitude slower than the diffusion timescale (Fig. 3, D and E). (C) PDA and BVA of the dynamic FRET hairpin. The E^∗ histogram could be fit to a two-state dynamic model in which the hairpin fluctuates between the FRET values of the controls at rates $k_{open}=641\pm 9{\text{s}}^{-1}$ and $k_{close}=463\pm 14{\text{s}}^{-1}$ (${\chi }_r^2=1.53$; upper); consistent with this model, BVA shows a dramatic increase in $s_{E^{\ast }}$ at intermediate E^∗ for the experimental data (lower). Furthermore, BVA of the PDA prediction generated an $s_{E^{\ast }}$ profile (green triangles) similar to that of the experimental data (black and red triangles). In contrast, simulations of several static species could accurately reproduce the E^∗ histogram of the dynamic hairpin (upper, blue line,${\chi }_r^2=1.47$); however, BVA analysis of these simulations (blue triangles) produced s_E^∗ values that were clearly static and diverged strongly from the experimental data.