Coupled Dynamics of RNA Folding and Nanopore Translocation

The translocation of structured RNA or DNA molecules through narrow pores necessitates the opening of all base pairs. Here, we study the interplay between the dynamics of translocation and base pairing theoretically, using kinetic Monte Carlo simulations and analytical methods. We find that the transient formation of base pairs that do not occur in the ground state can significantly speed up translocation.

Figure 1

Translocation of a structured RNA molecule through a narrow pore, which allows single but not double strands to pass. The driving force is an applied voltage, which acts on the negatively charged backbone of the RNA. An appropriate reaction coordinate is the number of bases $m(t)$ that have reached the trans side. The dynamics of $m(t)$ is coupled to the dynamics of the base-pairing patterns ${\mathcal{S}}_{cis}(t)$ and ${\mathcal{S}}_{trans}(t)$ on the cis and trans sides.

Figure 2

Mean translocation time $⟨\tau ⟩$ for RNAs with the same length $N=50$, but different structures [we plot $⟨\tau ⟩$ in units of $k_0^{-1}$, which is $O(\mu \mathrm{s})$ in typical experiments [2] ]. Symbols represent simulation data, while dashed lines show the adiabatic limit (2) and solid lines the expression (3) for the two random walker model. (a) Crossover from slow to fast translocation at a fixed bias $\Delta U=0.5k_{B}T$. Typical base-pairing rates are $k_{\mathrm{bp}}\sim 1\mu {\mathrm{s}}^{-1}$ [17], so that typical experiments would fall into the crossover region. (b) Dependence on the bias at a fixed ratio $k_0/k_{\mathrm{bp}}=1$.

Figure 3

Translocation time distributions for (a) the RNA hairpin and (b) the random sequence at $\Delta U=0.5$ and $k_0=k_{\mathrm{bp}}$. The histograms show simulation data, whereas the solid line in (a) is an exponential fit and in (b) is a fit to the drift-diffusion form [4]. The insets show the free energy landscapes ${\mathcal{F}}_1(m)$ of the adiabatic limit (2); see main text for details.