Translocation of “Rod-Coil” Polymers: Probing the Structure of Single Molecules within Nanopores

Using simulation and analytical techniques, we demonstrate that it is possible to extract structural information about biological molecules by monitoring the dynamics as they translocate through nanopores. From Langevin dynamics simulations of polymers exhibiting discrete changes in flexibility (rod-coil polymers), distinct plateaus are observed in the progression towards complete translocation. Characterizing these dynamics via an incremental mean first passage approach, the large steps are shown to correspond to local barriers preventing the passage of the coils while the rods translocate relatively easily. Analytical replication of the results provides insight into the corrugated nature of the free energy landscape as well as the dependence of the effective barrier heights on the length of the coil sections. Narrowing the width of the pore or decreasing the charge on either the rod or the coil segments are both shown to enhance the resolution of structural details. The special case of a single rod confined within a nanopore is also studied. Here, sufficiently long flexible sections attached to either end are demonstrated to act as entropic anchors which can effectively trap the rod within the pore for an extended period of time. Both sets of results suggest new experimental approaches for the control and study of biological molecules within nanopores.

Figure 1

Simulation model and biologically relevant examples of rod-coil polymers.

Figure 2

IMFPT data for rod-coil polymers. (a)–(f) display the $\tilde{\eta }=0.1$, $\tilde{F}=0.5$ simulation (red) and analytic (blue) results along with the free energy profile in units of $kT$ (green, axis on the right) for $N_{\mathrm{rod}}=1$, 2, 3, 5, 10, 20, respectively. In (g) the net translocation time $\tau$ is plotted against $N_{\mathrm{rod}}$ for $\tilde{F}=0.5$. The inset shows the scaling of the barrier height $h$ with the number of rods $N_{\mathrm{rod}}$ in units of $kT$. (h) displays the results for differing $q_{\mathrm{coil}}$ and $q_{\mathrm{rod}}$ as well as the case when all monomers carry charge $q=1$ (red) at $\tilde{F}=2$. (i) displays the simulation results for all $N_{\mathrm{rod}}$ cases at $\tilde{\eta }=1$ at $\tilde{F}=0.5$. The $N_{\mathrm{rod}}=1$, 2, 3, 5 cases are shown in (j) for both a wide pore (upper line in each pair) and tight pore (lower line). The $N_{\mathrm{rod}}=1$, 2, 3 cases have been shifted vertically by $7.5\times {10}^4$, $5\times {10}^4$, and $2.5\times {10}^4$ respectively and the wide pore results have been normalized to match the end points of the tight pore results.

Figure 3

IMFPT results for a single rod within a pore for increasing coils lengths: $M_{\mathrm{coil}}=1$ (red), 5 (blue), 10 (green), 15 (brown), 20 (grey), 25 (orange), 30 (purple) in the absence of a driving force. The locations where either coil is half-way through the pore are marked by circles. The inset shows the estimated barrier height in units of $kT$ for different coil lengths.