Schematic of simulation model. The impermeable membrane, shown in black, separates the cis (donor) side from the trans (recipient) side. A fluid of dielectric constant fills the cis chamber, the trans chamber, and the pore providing a means of passage through the membrane. On the cis side, a spherical container of radius prevents the diffusion of the polymer away from the channel opening, which provides the only means of escape. The applied potential drop is assumed to occur entirely across the length of the membrane. Thus the electric field is constant within the channel.
Simulation preparation procedure. For each , a free solution is determined and used as the radius of the confining sphere to be used in subsequent steps (a)–(d). (a) A single free solution configuration, selected so as not to extend beyond the walls of the confining sphere, is placed inside the confining sphere. This configuration then serves as the template configuration for all simulations with chains of length . (b) Clones of the template configuration are generated and equilibrated with a unique random seed (no field), generating (c) a large number of uncorrelated initial configurations. (d) Simulation runs: The electric potentials are applied to each of the initial configurations and data are collected.
Sample translocation snapshots. The emphasis is on the ds-DNA configurations. The pore is outlined by the black wire frame. The membrane is not shown. (a) Single-file-initiated translocation attempt. (b) Hairpin translocation attempt. The position of the hairpin vertex is illustrated with a circle.
Snapshot of hairpin initiation. A cis-side view of a “hairpin” event. (a) The chain gyrates near the entrance of the channel; (b) a non-chain-end bead is presented at the opening and is drawn in, forcing the formation of a hairpin; (c) the vertex of the hairpin pushes trans ward into the channel, with two strands trailing behind. While such a configuration should lead to measurable drop in current flux through the channel, we have found that the chain may still ultimately be rejected by the channel. Such rejection is more prominent at lower potential differences and when -like charge distributions are included in the channel.
Translocation time as a function of vertex position for larger pore. Translocation time data for chains of length through the diameter channel is plotted. Curves for five different potential differences are given. Larger potential differences lead to shorter translocation times. For all potential differences, the minimum in translocation time is found when the hairpin vertex is located directly in the middle of the chain.
Comparison of larger and smaller channels—translocation time as a function of vertex position. Translocation time data for chains of length through both (a) and (b) diameter channels are plotted. Curves for two different potential differences are given. In both cases, larger potential differences lead to shorter translocation times. However, translocation times are longer through the channel. In addition, the vertex position dependence of the translocation time is not evident in the smaller.
Success ratio. Success ratio is plotted for each chain length and potential difference. For all chain lengths, success ratio increases monotonically with increasing applied potential differences. At all potential differences, success ratio increases with decreasing chain length. This increase follows from the increasing fraction of free ends with decreasing molecular weight: More free ends means more single file attempts, which in turn are more likely to succeed.
Fraction of single file events. For each chain length and potential difference (0.15–2.4) considered in this study, the fraction of total events in which chain penetration occurred in a single file fashion is plotted. Dashed lines are exponential fits. All events, regardless of whether they lead to successful translocation, were considered. At all potential differences, single file events are more prevalent for shorter chain lengths, due to the increased fraction of free ends for shorter chains. As has been reported experimentally, larger potential differences lead to higher probabilities of single file events.
Fraction of single file translocations. This figure is as Fig. 8, except that failed translocation events are excluded from consideration. The fraction of single-file successful translocations can be seen to decrease at higher potential differences, as the energetic barrier to hairpin formation becomes less significant at higher potentials.
Histogram of index of initiating bead N=40. Histograms are plotted for all events (dashed line) and translocations only (solid line). For each type, the histogram is normalized by the number of attempts for that type (i.e., the total area under each curve is 1). The bead index of the initiating bead identifies an event as being either single file (indices 1–5 and 36–40) or hairpin (indices 6–35). (a) . As can be seen from the dotted curve, a reasonable fraction of all attempts are initiated by hairpins. However, successful translocations (solid curve) are dominated by single file configurations (see solid curve). Therefore, at this low driving potential difference, the population of failed attempts must be dominated by hairpin configurations. (b) . Histograms are similar for all events and translocations only.
Failed event depth histogram N=40, ΔV=0.15. The abscissa is the maximum distance of penetration attained during a failed translocation attempt; the ordinate is the relative number of occurrences. The failed attempts quantified in this figure occurred in the course of what eventually became 3000 successful translocations. Two features of this graph are particularly significant: Firstly, hairpin attempts can be seen to comprise the majority of failed attempts at this low potential. Secondly, hairpins penetrate on average more deeply into the channel before being rejected than do chain ends. As potential difference is increased, these features become progressively indiscernible.
Translocation time as a function of chain length . A linear relationship is found for translocation time as a function of chain length. Five different voltages are shown: Circles ; squares ; diamonds ; up triangles ; sideway triangles . Solid lines are linear fits. Inset: translocation time as a function of for and .
Event Diagram: Nanopore. Data points correspond to individual events (see text). Data are plotted for chain length and two potential differences, 0.3 and 0.9. The penetration depth refers to the position of maximum penetration attained by the leading bead of the polymer chain during an event. The pore spans from (cis end) to (trans end). Successful translocation penetration depths are found in the region of . Translocation times decrease with an increase in potential difference. Short-time data points form a shoulder-shaped region, also seen in experimental translocation data. The banding phenomenon prevalent in experiments is not present.
Event diagram for N=40, ΔV=0.6 with modified nanochannel. The data for the event diagram were obtained using a modified nanochannel meant to mimic the channel through the inclusion of two key features: A narrower channel and the presence of a ringlike distribution of negative charges along the channel wall near the trans opening (see text). The small diameter allows only single file access to the channel, whereas the charges act as an additional barrier, temporarily “stalling” the chain within the channel. The stalling yields long-time events of intermediate penetration depth, which are visible as the “band” overlying the translocation events.
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