Unfolding single RNA molecules by mechanical force: A stochastic kinetic method

Using simple polymer elastic theory and known RNA free energies, we study the single RNA folding and unfolding on the secondary structure level under mechanical constant force by stochastic kinetic simulation. As a primary application, this method is used to simulate the experiment performed by Liphardt et al. [Science 292, 733 (2001)]. The extension-force curves in equilibrium and kinetic reaction rate constants for folding and unfolding are calculated. Our results show that the agreement between simulation and experimental measurements is satisfactory.

Figure 1

Theoretical model and RNA sequences and their native structures studied in the present work. The structures are folded by the VIENNA RNA package 1.4. The equilibrium and kinetic behaviors of these three RNAs, p5ab, $\mathrm{p}5\mathrm{abc}\Delta A$, and p5abc, have been studied in detail [6].

Figure 2

The extension-force curves for the three RNA molecules. Our simulations show that the folding and unfoldings for p5ab and $\mathrm{p}5\mathrm{abc}\Delta A$ under constant force are all or none around the transitions $13.3\mathrm{pN}$ and $11.3\mathrm{pN}$, respectively, while the extension-force curve for p5abc has an intermediate phase between 8.0 and $11.0\mathrm{pN}$.

Figure 3

Simulation for RNA p5ab kinetics. (a) The extension versus time traces of the molecule at different forces in equilibrium; here the unit of time is ${\tau }_o$. (b) The frequency distributions of the lifetimes of the single stranded and hairpin states at the transition force $12.90\mathrm{pN}$. The average lifetimes of these two states in this simulation can be obtained by fitting to exponential functions.

Figure 4

Logarithm of the average lifetimes of single stranded and hairpin states for the p5ab molecule at difference forces around the transition $12.9\mathrm{pN}$. The time is in unit ${\tau }_o$, which can be obtained by fitting to experimental data. Note the slopes of $\ln ⟨{\tau }_f⟩$ and $\ln ⟨{\tau }_u⟩$ are independent of the fitting value ${\tau }_o$.