Measuring the folding transition time of single RNA molecules

Abstract

We describe a new, time-apertured photon correlation method for resolving the transition time between two states of RNA in folding--i.e., the time of the transition between states rather than the time spent in each state. Single molecule fluorescence resonance energy transfer and fluorescence correlation spectroscopy are used to obtain these measurements. Individual RNA molecules are labeled with fluorophores such as Cy3 and Cy5. Those molecules are then immobilized on a surface and observed for many seconds during which time the molecules spontaneously switch between two conformational states with different levels of flourescence resonance energy transfer efficiency. Single photons are counted from each fluorophore and cross correlated in a small window around a transition. The average of over 1000 cross correlations can be fit to a polynomial, which can determine transition times as short as the average photon emission interval. We applied the method to the P4-P6 domain of the Tetrahymena group I self-splicing intron to yield the folding transition time of 240 micros. The unfolding time is found to be too short to measure with this method.

FIGURE 1

(a) Structure of the P4–P6 molecule labeled with Cy3 (light gray) and Cy5 (dark gray). At the conditions of these experiments the molecule spends about half the time in the folded and unfolded states corresponding to high FRET and low FRET, respectively. (b) Typical time trace of single molecule FRET. The light gray line is the number of photons detected (per 10 ms) in the Cy3 channel and the dark gray line is the number of photons detected in the Cy5 channel. (c) Fluorescence resonance energy transfer efficiency (FRET) given by Eq. 1 of the data in panel b. (d) Histogram of FRET efficiency from 15 representative molecules. The two Gaussian peaks yield a low FRET state, A′ = 0.344, and a high FRET state, B′ = 0.747 (ΔFRET = 0.403). (e) Averaged cross correlation from 1133 folding transitions.

FIGURE 2

A model of SM FRET in RNA folding and photon correlations from simulated folding events. (a) A model of SM FRET signal changes during RNA folding. The FRET pair is assumed to be attached to an RNA molecule such that FRET efficiency increases as it folds; a, b, c, and d = fluorescence intensities, t = folding time, T = data window size for correlation. (b) An averaged cross correlation of simulated photons from 10 folding transitions. Fluorescence photons from donor within a time window T were generated in 100-ns resolution to follow the Poisson statistics using a random number generator. According to the FRET efficiency defined as in panel a, donor photons are transferred to the acceptor. Single photons from donor and acceptor were correlated as explained in the text. Individual correlation curves from individual traces were then averaged. Simulation conditions are 500 kHz photon emission rate, A = 0.1, B = 0.9, t = 400 μs, and T = 5 ms, where A and B are the FRET efficiencies before and after the folding transition. Solid line is a third-order polynomial fit to the correlation (with the fixed first order coefficient). Equation 5 was used to determine the folding transition time, t. The folding transition time was measured to be 370 μs from the intercept of Eq. 5. (c) An averaged cross correlation of simulated photons from 1000 folding transitions. Simulation conditions are 50 kHz photon emission rate, A = 0.2, B = 0.8, t = 200 μs, and T = 10 ms. Solid line is a third-order polynomial fit to the correlation (with the fixed first order coefficient). The folding transition time t was measured to be 180 μs from the intercept of Eq. 5. Fitted t estimates the simulated t reproducibly within 20% error for 200, 400, 600, and 800 μs from the averaged 1000 transitions per each case with 50 kHz photon emission rate to confirm the validity of the simulation.

FIGURE 3

Simulated cross correlations based on the model in Fig. 2, fitting errors, and calibration curves. (a) Averaged cross correlations with single exponentially distributed transition times with t_TRUE = 200, 400, and 600 μs. Three-thousand transitions are averaged per each case with 5 kHz photon emission rate, A = 0.2, B = 0.8, and T = 10 ms. As t_TRUE increases, the intercept of the cross-correlation curve becomes more positive (i.e., the triangular points are above the squares and the circles in the small τ region). (b) Error between t_FIT and t_TRUE with respect to the number of simulated transitions averaged. Each data point is averaged from four to 10 cases. (c) A calibration curve to correct the error in t when correlations from 3000 transitions are averaged. Points were averaged from four to 10 cases. Standard deviation at each point is also shown in the chart. In the range of 200–800 μs, the t_FIT estimates t_TRUE reasonably well (within an average error of 30%). (d) A calibration curve in the case of 1000 transitions averaged.

FIGURE 4

Noise in the cross correlation. (a) Reciprocal probability of detecting multiple photons within τ ∼ τ + Δτ as in Eq. 10, i.e., the Poissonian noise in the correlation. (b) Noise of experimental data fitted to Eq. 11. Experimental conditions are A = 0.344, B = 0.747, T = 10 ms, and N = 1133. Least square fit estimates 6.6 kHz as the average photon emission rate including background.

FIGURE 5

Averaged cross correlations of photons from folding and unfolding events. (a) An average cross correlation from 1133 folding events with the 10-ms data window around the folding. Average photon emission rate from the dye is ∼5 kHz. FRET efficiencies before and after the transitions from Fig. 1 d were shifted to correct the background. To correct the background, data in the range from 400 μs to 1 ms are fit to a line, giving an intercept of −0.245, thereby A′ − n/I_tot and B′ − n/I_tot are found to be 0.205 and 0.608, respectively. The data were fitted to a third-order polynomial to yield folding time of 310 μs from Eq. 9 and calibration curve in Fig. 3 d. Accounting the difference in total number of photons before and after the transition, the folding time is further corrected to 240 μs. (b) Comparison between the cross correlation of folding transitions in panel a and the averaged cross correlation from 1202 unfolding transitions with T = 10 ms. Cross correlation from unfolding transition is shifted upward to cancel out the effect of different background level by matching the two correlation curves in the region from 400 μs to 1 ms. The unfolding transition time is found to be too short to measure with the proposed method. The two correlations show apparent difference in their short time regime (<400 μs), with more positive correlation values for the folding transition. The solid and dashed lines are linear fits to the correlations for unfolding and folding, respectively, to clearly show the difference in the early time region correlation. The intercept of the correlation from the unfolding transition is significantly different from the folding transition and yields a transition time too short to measure with the current method. Therefore, this unfolding transition time can serve as an experimental control.