Force unfolding kinetics of RNA using optical tweezers. II. Modeling experiments - PubMed (original) (raw)

Force unfolding kinetics of RNA using optical tweezers. II. Modeling experiments

M Manosas et al. Biophys J. 2007.

Abstract

By exerting mechanical force, it is possible to unfold/refold RNA molecules one at a time. In a small range of forces, an RNA molecule can hop between the folded and the unfolded state with force-dependent kinetic rates. Here, we introduce a mesoscopic model to analyze the hopping kinetics of RNA hairpins in an optical tweezers setup. The model includes different elements of the experimental setup (beads, handles, and RNA sequence) and limitations of the instrument (time lag of the force-feedback mechanism and finite bandwidth of data acquisition). We investigated the influence of the instrument on the measured hopping rates. Results from the model are in good agreement with the experiments reported in the companion article. The comparison between theory and experiments allowed us to infer the values of the intrinsic molecular rates of the RNA hairpin alone and to search for the optimal experimental conditions to do the measurements. We conclude that the longest handles and softest traps that allow detection of the folding/unfolding signal (handles approximately 5-10 Kbp and traps approximately 0.03 pN/nm) represent the best conditions to obtain the intrinsic molecular rates. The methodology and rationale presented here can be applied to other experimental setups and other molecules.

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Figures

FIGURE 1

FIGURE 1

Schematic picture of the model for the experimental setup used in the manipulation of RNA molecules. We show the configurational variables of the system _x_b, i.e., _x_r, _x_h1, and _x_h2, which are the extensions of each element (trapped bead, RNA molecule, and handles, respectively) along the reaction coordinate axis (i.e., the axis along which the force is applied). _X_T is the end-to-end distance of the whole system, i.e., the distance between the center of the optical trap and the tip of the micropipette. The optical potential is well described by a harmonic potential of a one-dimensional spring of stiffness _ɛ_b and equilibrium position at _x_b = 0.

FIGURE 2

FIGURE 2

Schematic representation of the kinetic model for the RNA hairpin. The model assumes that the dynamics of the folding and unfolding of the hairpin is sequential. Therefore, each intermediate configuration n is only connected to its first neighbors n+1 and _n_−1, where n represents the number of sequential bps unpaired from the opening of the helix. The kinetic rates to go from n to _n−_1 or n+1 govern the F-U dynamical process.

FIGURE 3

FIGURE 3

Extension traces for P5ab hairpin with 3.2 Kbp handles in CFM from the simulations for two different trap stiffnesses _ɛ_b ≈ 0.1 pN/nm (upper panel) and _ɛ_b ≈ 0.035 pN/nm (lower panel). The bandwidth used is 200 Hz.

FIGURE 4

FIGURE 4

Force traces for P5ab hairpin with 3.2 Kbp handles in PM from the simulations for two different trap stiffnesses _ɛ_b ≈ 0.1 pN/nm (upper panel) and _ɛ_b ≈ 0.035 pN/nm (lower panel). The bandwidth used is 1 KHz. We show the mean forces, _f_F and _f_U, in the upper and lower parts of the square-like-sign force traces, corresponding to the forces at the folded and unfolded states, respectively. Note that the value of such forces, _f_F and _f_U, is higher than the ones measured in experiments (1) by ∼1–1.5 pN. This discrepancy is consistent with the fact that the free energy parameters for P5ab used in simulations (–34) corresponds to higher salt concentrations than the experimental ones.

FIGURE 5

FIGURE 5

CFM critical rates as a function of the length of the handles from the experiments (open symbols connected by lines) and simulations (solid symbols) for two different values of the trap stiffness _ɛ_b = 0.1 pN/nm (upper panel) and 0.035 pN/nm (lower panel). Results obtained by using different bandwidth B = 10, 50, and 200 Hz (circles, squares, and triangles, respectively) are shown. The molecular rate formula image (dotted line) is also shown in the bottom panel for comparison. Better results are obtained for the softest trap _ɛ_b = 0.035 pN/nm where distortion effects are less important.

FIGURE 6

FIGURE 6

The logarithm of the PM folding (in blue) and unfolding (in red) rates as a function of force from experiments (open circles) and simulations (solid circles). The folding and unfolding lines from simulations have been shifted by 1.5 pN to account for the experimental salt conditions. Straight lines are the linear fits to the data from the simulation. The intersection point between the folding and unfolding lines gives the value of the PM critical rate.

FIGURE 7

FIGURE 7

PM critical rates as a function of the length of the handles measured in PM from experiments (open circles connected by lines) and simulations (solid symbols) for two different values of the trap stiffness _ɛ_b = 0.1 pN/nm (squares) and 0.035 pN/nm (circles). The bandwidth (1 KHz) is much larger than the characteristic frequency of the F-U reaction. The intrinsic molecular rate formula image (dotted line) is shown for reference. The PM rates show a tendency to approach the value of formula image for long handles as the analysis done in Instrumental Effects predicts. Better results are also obtained for the softest trap _ɛ_b = 0.035 pN/nm. The agreement among the experiments, simulations, and theory is good.

FIGURE 8

FIGURE 8

We compare the experimental CFM critical rates (open symbols connected by lines) with the experimental PM critical rates (solid diamonds connected by lines) for two different trap stiffnesses _ɛ_b = 0.1 pN/nm (upper panel) and _ɛ_b = 0.035 pN/nm (lower panel). CFM results with bandwidths of 10 Hz, 50 Hz, and 200 Hz are shown in triangles, squares, and circles, respectively.

FIGURE 9

FIGURE 9

We show the quality factor Q (defined as the closeness between the measured rate and the intrinsic molecular rate) obtained from different measured critical rates in experiments as a function of the length of the handles and the trap stiffness. For the CFM experimental results we show the Q corresponding to the CFM critical rates at two different values of the bandwidth, B = 200 Hz (red) and B = 10 Hz (black). The Q for the PM critical rates extracted from PM experiments is also shown (blue). Generally, better measurements (higher _Q_-values) are obtained from softer traps and longer handles.

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References

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