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Translocation of Rigid Rod-Shaped Virus through Various Solid-State

Jan 21, 2016 - Nanopores have been used as a high throughput tool for characterizing individual biomolecules and nanoparticles. Here, we present the t...
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Translocation of Rigid Rod-Shaped Virus through Various Solid-State Nanopores Hongwen Wu,† Yuhao Chen,‡ Qizhao Zhou,§ Rongliang Wang,† Baicheng Xia,‡ Dejun Ma,∥ Kaifu Luo,‡ and Quanjun Liu*,† †

State Key Laboratory of Bioelectronics, Southeast University, Nanjing, Jiangsu 210096, China CAS Key Laboratory of Soft Matter Chemistry and Department of Polymer Science and Engineering, University of Science and Technology of China, Hefei, Anhui 230026, China § The Third Affiliated Hospital of Southern Medical University, Guangzhou, Guangdong 510000, China ∥ State Key Laboratory of Elemento-Organic Chemistry and Department of Chemical Biology, National Pesticide Engineering Research Center (Tianjin), Nankai University, Tianjin, 300071, China ‡

W Web-Enhanced Feature * S Supporting Information *

ABSTRACT: Nanopores have been used as a high throughput tool for characterizing individual biomolecules and nanoparticles. Here, we present the translocation of rigid rod-shaped tobacco mosaic virus (TMV) through solid-state nanopores. Interestingly, due to the high rigidity of TMV, three types of events with distinctive characteristics at the capture process and a strong current fluctuation during the translocation of TMV are observed. A kinetic model is then proposed to address the dynamics of the translocation, followed by corresponding dynamics simulations. The results reveal that TMV has to rotate to fit and pass the pore when it is captured by a nanopore with an angle larger than the maximum angle that allows it to pass through. Then, we investigate the dependence of the rotation of TMV on the conductance fluctuations at the blockade stage. The results show that the rotation of TMV during the passage through the pore affects the current signal significantly. This study gives a fundamental understanding of the dynamics of rod-shaped particles translocating through the nanopore and how the current responds to it. It opens a new possible way to characterize the rigidity of analytes by nanopores.

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translocating,16,23 interactions with the pore wall,24 stochastic thermal motion, and so on,25 it still remains challenging to reveal the microscopy dynamics of the translocation from the outcome complex current signals. An alternative approach is to study the translocation of rigid rod-shaped particles without folding and coil configurations,26 which can address the drag effect due to various configurations of biopolymers, opening a simpler way to study the physics of nanopore translocation. Additionally, the expanding applications of nanopores for measuring the size and surface charge of individual nanoparticles27−30 and characterizing various-shaped virus26,31,32 led us to study the translocations of rigid particles rather than flexible biopolymers. McMullen et al. performed and simulated the translocation of semiflexible filamentous bacteriophage fd virus which is 880 nm long and 6.6 nm in diameter with a persistence length P ≈ 2.4 μm,26 while Ling’s group reported a nonlinear electro-

anopores have been used as high throughput singlemolecule sensors for characterizing individual unlabeled biomolecules,1−7 as well as DNA/protein,8,9 DNA/ligand,10−12 and RNA/ligand complexes.13 Due to the potential for distinguishing four kinds of nucleic acids, one promising application of nanopores is high-throughput label-free DNA sequencing,14 which may cut down the cost of sequencing to a very low price. One of the major challenges of this technique is understanding the dynamical processes of biopolymer translocation through nanopores,15,16 which is crucial for the development of nanopore techniques to DNA sequencing. In a typical nanopore measurement, each translocation event involves two steps: capture and translocation.17 Previous theoretical and experimental studies were mainly focused on how DNA is captured and translocated through nanopores and developments to control the motion of DNA by salt gradients,17 surface modification,18,19 low-power visible light,20 pressure,21 gate electrodes,22 and so on. However, in the translocation of flexible biopolymers (e.g., DNA), due to the various folding configurations,1 the random coil outside the pore while © 2016 American Chemical Society

Received: December 29, 2015 Accepted: January 21, 2016 Published: January 21, 2016 2502

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Figure 1. Characteristics of the events of TMV translocation through the 30 nm nanopore. (a) Schematic of the detection of TMV translocation through a nanopore. (b) TEM image of a typical 30 nm solid-state nanopore. (c) TEM image of a single TMV particle. (d) Typical current trace of TMV translocation through the 30 nm nanopore at 100 mV in 1 M NaCl solution (pH 7.0). (e) A close-up view of the current trace from 42.95 to 44.2 s, showing 22 events numbered by the colors according to the type of event: type A (green), type B (blue), type C (red), and type D (black). (f) The close-up view of the representive events of each type, and the colors are same as in (e). (g) Plot of three types of events on top of each other with the alignment at the end of the event. (h) A representive type B event with a type A and D event appear at its fluctuation period.

phoresis in the translocation of the same virus.32 In addition, Venta et al. found an unclear fluctuation in the translocation of gold nanorods.30 Even the DNA molecule, when its length was shorter than its persistence length (50 nm) behaving like a rigid rod, produced unexpected levels of current blockage at the beginning of the translocation.33 These results show that the rigidity of a polymer or particle would influence its dynamics of the translocation and affect the current signals which are still not well understood. Therefore, we are motivated to find a new way to study the dynamics of nanopore translocation using a rigid rod, tobacco mosaic virus (TMV). TMV is one of the most investigated and well-known viruses.34,35 It is a plant virus that infects a wide range of plants on the earth, causing mosaic disease of the hosts. TMV appears as a rigid rod 300 nm in length and 18 nm in diameter. Each TMV particle contains 2130 identical coat proteins and a single strand RNA forming a right-hand helix.36 It is a polyelectrolyte with a high uniform negative linear charge density of 10−20 e/nm at pH 7.37 The persistence length of TMV exceeds 10-fold of its length,37 which is larger than that of DNA and fd, indicating a high rigidity of TMV.38,39 Therefore, TMV could serve as an ideal candidate for the translocation of a rigid rod through a nanopore. In this study, we investigate the dynamics of TMV translocation through 25, 30, and 50 nm nanopores. To our knowledge, this is the first translocation experiment of TMV through solid-state nanopores. Interestingly, due to the high

rigidity of TMV, three types of events with distinctive characteristics at the capture process are observed. In addition, we also find a strong current fluctuation during the translocation of TMV. A kinetic model is then proposed to account for the dynamics of TMV translocation, which is consistent with the dynamics simulations. On the basis of the model, we are able to reveal the behaviors of TMV during its translocation through the nanopore by the characteristics of the event. This study gives a fundamental understanding of the dynamics of rod-shaped particles translocating through nanopores. It suggests that the influence of the random rotation of the analytes to the ionic current should be considered in the measurements of rigid rod-like particles.

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EXPERIMENTAL SECTION Materials. NaCl and phosphotungstic acid hydrate were purchased from Sigma. Milli-Q water with resistance >18 MΩ/ cm was used throughout the experiments. Prior to use, all the solutions were filtered with 0.02 μm Anotop filter (Whatman Co.). TMV was extracted and purified according to the literature method,40 and the details can be found in the Supporting Information. The DLS measurement was performed using Zetasizer Nano ZS90 (Malvern). Methods. The silicon chips supporting 30 nm thick freestanding SiN membranes (DTF-030523, DuraSiN) were purchased from Protochips, Inc. A FEI Titan 80-300 TEM was used to fabricate and image the nanopores according to the 2503

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Analytical Chemistry previous report.41 Nanopores with diameter larger than 30 nm were drilled by a Helium Ion Microscopy (HIM) system, and the diameters of the pores were determined by the open-pore conductance.29,42 After the treatment with piranha solution at 80 °C for 30 min, the chip was then assembled in a custombuilt Teflon cell and connected to the current amplifier (Axopatch 200B, Molecular Devices) by two Ag/AgCl electrodes. (CAUTION: “Piranha” solution reacts violently with organic materials; it must be handled with extreme care.) The corresponding current was filtered at 10 kHz by a low-pass filter embedded in the amplifier and digitized at 100 kHz or higher (Axon 1440A digitizer, Molecular Devices). More details of the nanopore experiment can be found in Figure S1.

polymer,1 attachment of ligand,8,10−12,46 distinct regions,16,47 duplex unzipping/unraveling,48−50 interactions of proteins/ particles with the nanopore,51−53 various positions in the nanopore,54,55 and asymmetric pore geometry45,56 were reported in previous studies. However, in our case, as TMV is a rigid rod with uniform size and charge, it is hard to bend39 or fold like DNA molecules in solution. In addition, the pore with a 30 nm diameter can not allow the passage of two TMV at the same time, and the DLS measurement shows no aggregation (Figure S2). Therefore, the current fluctuations at the blockade stage and the beginning of type B and C events can not be attributed to the variations of TMV conformation or the passage of multiple TMV. For the fluctuations at the beginning of type B events, the similar pretranslocation fluctuations were found in the fd experiment by Ling and coworkers32 and in some reports of DNA translocation under certain conditions,24,33,57,58 which demonstrated that the trapping of analytes near the pore entrance before translocation led to a shallow blockade at the beginning of the event, and the following translocation produced a deep tail in the current− time of the event. For a better comparison, Figure 1g plots three representive events of each type on top of each other with the alignment at the end of the events. Interestingly, one can find that the three types of events share the same signatures at the blocked stage and the end. It indicates that the blocked stage of type B and C event is due to a full translocation, and the only difference between these two types of events and type A events appears at the beginning of the event, in other words, the capture process. In addition, Figure 1h shows that events can occur at the fluctuating period of a type B event, indicating TMV has not occupied the pore entrance at the time of the fluctuations of the type B event. Therefore, we address the current fluctuations of type B events by TMV trapping near the nanopore and trying to get one end of it in the pore, which blocks the access conductance of the pore and gives the fluctuations at the beginning of the event.24,33,57,58 However, for type C events, the fluctuations could occur at the levels lower than the maximum blockage of the access conductance (ΔGacc) which is about −10 nS (blue dashed line in Figure 1f) in our condition,58 even at the level of blockade stage (event 9). It indicates that one end of TMV is in the pore but has not approached the back side, and the pore is partially occupied. Kinetic Model of TMV Translocation through SolidState Nanopore. Similar to the explanation made by Rosenstein et al.,33 all these observations suggest a kinetic model of TMV translocation through the nanopore, as the example shows in Figure 2a. First, TMV randomly diffuses in the bulk (step (i)), and the ionic current would not change until it approaches the capture radius of the pore (black trace). Once it diffuses to the capture radius, the electric field dominates the motion of TMV and drives it toward to the pore (step (ii)). However, as it may come from any position with various angles (θ), the time it takes to get one end of TMV to the pore mouth can spread to a wide range. In this step, the access conductance of the pore is blocked, and the trapping of TMV near the pore entrance varies the ionic current (blue trace). When one end of TMV approaches to the pore mouth, as TMV can not be bent, the angle of TMV to the pore central axis (θ) must be smaller than the maximum angle (θmax) that allows passing through. If not (θ > θmax), TMV has to rotate to fit the pore geometry to pass through (step (iii)), which costs energy and time (red trace). Otherwise, it will go back to the

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RESULTS AND DISCUSSION Classify the Events of TMV Translocation. TMV was first translocated through the 30 nm nanopore at 1 M NaCl solution with pH 7.0. Figure 1a shows the crossover view of our experimental setup. TMV was added in the negative side; after applying a bias voltage, TMV was driven through the pore by the corresponding electric field. The details of the experimental section can be found in Supporting Information. Figure 1b shows a 30 nm nanopore drilled by TEM, and Figure 1c is a TEM image of a single TMV which is about 300 nm long and 18 nm wide. The dynamic light scattering (DLS) measurement of TMV in the same solution of the translocation experiment shows no aggregation, as shown in Figure S2. Figure 1d shows a typical current trace of TMV translocation at 100 mV. Each transit downward pulse represents a TMV translocation event. A close-up view of the current trace from 42.95 to 44.2 s is shown in Figure 1e. As we go through all the events, four kinds of events can be isolated, and the representive events are shown in Figure 1f. Type A (green) is the typical square-shaped event with extremely steep leading edge and trailing edge, which is related to a head-to-tail translocation of TMV. The slope of the current−time trace at the beginning (or end) of the blockade is larger than 50 nA/ms. Type B (blue) is the event with unusual current fluctuations beyond the level of −10 nA (marked as blue dash line) at the beginning and a steep end as that of type A. Type C (red) events are similar to type B, but the fluctuations appear at a level lower than −10 nA. The fourth type (type D, black) is the event with small amplitude and short dwell time, which is related to a collision of TMV with the nanopore and not a translocation.26,29 In a typical nanopore measurement, without various configurations, the translocation of individual rod-shaped polymers/particles through thin nanopores (≤30 nm) usually leads to a flat blocked level (blockade stage).1,9,32,43,44 However, in our observations, for all the events as shown in Figure 1f, the current at the blockade stage is not always flat, challenging the evaluation of the current blockage. Mostly, there are three possible states, flat (events 6, 17, and 19), sloped (the current first goes down to a relatively low level and then rises to a relatively high level before the steep end; see events 3, 4, 13, and 18), and random fluctuations (event 9) the scale of which is larger than that of open pore current. Although the basic application of the nanopore is measuring the size and charge of analytes by the amplitude and dwell time of translocation events,45 it is generally acknowledged that the dynamics of the current−time in a translocation event can reveal the local structure and position of the analyte. Events with multiple current levels due to the folding configurations of 2504

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blocked. The current fluctuations due to the attempt of TMV to rotate to fit in the pore should be at a level lower than that of TMV being trapped near the pore. After that, TMV will move across the pore until the other end of it gets out of pore mouth at the back side (step (iv)). During the passage, the conductance of the pore and the access regions of the two sides are blocked because TMV occupies the whole pore, and the random rotation and thermal motion of TMV fluctuates the current at the blocked stage (green trace),59,60 as we will discuss later. To support this model, the dynamics simulations of TMV translocation through nanopores were performed using coarsegrained Langevin Dynamics.26,61−63 TMV was modeled as a coarse-grained bead−spring chain consisting of 17 monomers, giving the correct aspect ratio. The persistent length was set to be ten times of the contour length of TMV.37 The details of the simulations can be found in the Supporting Information. Figure 2b presents three representive simulated TMV translocations through the 30 nm nanopore, which are in good agreement with the kinetic model. See the corresponding Movies 1, 2, and 3. To examine the experimental events with the dynamics simulations, Figure 2c plots the representive events with all possible signatures that we recorded. Considering three relevant sensing regions of nanopore, the pore itself and two access regions,58 the correspondence of the current signatures of event and the dynamics of translocation can be found. If TMV finds the pore entrance immediately after it diffuses into the capture radius, with a suitable angle θ < θmax, then it will go as a traditional head-to-tail passage (left panel), which leads a type A event (green, Figure 2c). However, if it takes a long enough time to get one end of TMV to the pore entrance, a fluctuation beyond the level of ΔGacc is expected at the beginning of event, and the angle θ at the time it approaches the pore entrance dominates the next motion of TMV and, thus, the event’s type. At this time, if θ < θmax (middle panel), the following translocation is the same as that of the type A event, leading a type B event (blue, Figure 2c). Otherwise (right panel), it will lead a type C event (red, Figure 2c). However, we did observe the events with the fluctuations only at a low level ( θmax at the time of one end of it arriving at the pore entrance. The time scale of t is 7.98 ns. (c) The representive events with all possible signatures that we recorded, and the color of events is the same as in Figure 1.

bulk (type D event, Figure 1f) or be stuck into the pore; see Figure S3. In this step, as one end of TMV is in the pore, the access conductance and part of the pore conductance are

Figure 3. The angle of TMV to the pore central axis (θ) as a function of time after it approaches the pore entrance. In the simulations, the translocation of TMV was modeled to start at three positions which are indicated by θp as shown in the inset schematics of each figure. (a) θp = 90°, (b) θp = 45°, and (c) θp = 20°. Each figure includes 6 translocations, and the time scale is 7.98 ns. 2505

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Analytical Chemistry approached the back side of the pore. The observation of three possible states at the blockade stage (flat, sloped, and random fluctuations) can be attributed to the rotation of TMV during the translocation.59,60 When θ = 0, a vertical translocation gives a typical square-shape event with a flat blockade stage; see the first and third events in Figure 2c. When θ > 0, in other words TMV is not vertical, an oblique insertion of TMV into the pore will lead to a deeper current blockage at first because more ions are excluded out of the pore, and then, the current rises to the blockage level of a vertical translocation; see the other four events in Figure 2c. This indicates that TMV has rotated to a vertical form at the final part of the translocation, which is coincident with the previous simulation results of the cylindrical particle translocation through a nanopore.64 To examine the rotation of TMV during the translocation, dynamics simulations of TMV translocation starting at three different positions were performed, and θ was tracked as a function of time after it approaches the pore entrance, as shown in Figure 3. We find that no matter what θ is at the beginning of the insertion of TMV into the pore, it reduces to the same value range of the vertical translocation at the end of the passage. Besides these two situations, the random rotation and thermal motion of TMV during the translocation account for the current fluctuations at the blockade stage. Comparing the signatures of TMV translocation events with that of fd virus32 and DNA,33,58 two major differences can be found. First, the fluctuations at the beginning of type C events can occur at a relatively low level, even at the level of blockage stage, and it is hard to find the demarcation between steps (iii) and (iv) in the current−time trace, e.g., event 9 in Figure 1f. Second, the multiple states at blockade stage of TMV translocation were absent in the translocations of fd virus and DNA which led to flat blockade stages. A reasonable explanation is the high rigidity of TMV particles. When one end of a rod-like particle approaches the pore entrance with θ > θmax, there is an electric force acting on the end driving it toward the pore center. Besides the motion toward the pore center, there is a bending tendency at the end of the particle because most of it is still far from the pore where the electric field is weak.65 At this time, the configuration of the particle depends on the competition of the electric force and the rigidity of the particle. For the flexible polymers like DNA, the electric force dominates, and it bends toward the pore center when one end of it approaches the pore entrance. In contrast, for the rigid rods like TMV, due to a strong connection of its coat proteins, it rotates or gets stuck in the pore rather than bends. To prove our interpretation, we performed two additional dynamics simulations to investigate the influence of the rigidity of rod-shaped particle on the dynamics of its translocation through the nanopore. The geometries of the particles and nanopores were the same as the previous simulations (Figure 2b), and the only alternating quantity was the rigidity of the particle. Figure 4 presents the translocations of two rod-shaped particles with persistence lengths (P) of 21.6 nm (a) and 156.4 nm (b) through 30 nm nanopores; see the corresponding Movies 4 and 5. Compared to the translocation dynamics of TMV with a persistence of 3000 nm, the flexible rods show strong bending configurations during the translocations. It suggests that the appearance of the current fluctuations at the level lower than the maximum access current blockage in the translocation of TMV is dominated by the high rigidity of TMV.

Figure 4. Dynamics simulations of the translocations of rod-shaped particles with various rigidities. The persistent length of (a) is 21.6 nm (Movie 4) and (b) is 156.4 nm (Movie 5). The time scale is 7.98 ns.

Amplitude of the Current Blockage. To give a rigorous and coherent analysis, an equation with two sigmoid functions was used to fit each event and obtain the corresponding current blockage (ΔI) and translocation time (Δt), which can be written as I = I0 − ΔI +

ΔI ΔI + 1 + exp((t − t1)k1) 1 + exp((t 2 − t )k 2)

where I0 is open pore current and ΔI is the current blockage. t1 and t2 are the start and end of the event, leading to Δt = t2 − t1. k1 and k2 are the slope factors that describe the steepness of the leading edge and trailing edge, respectively. Figure 5a shows the representive events of each type fitted by the equation where the fitting parameters ΔI and Δt are indicated accordingly. Figure 5b shows the scatter plots of ΔI and Δt of all types of events of the 30 nm nanopore at 100 mV (N = 814). Twentyone type C events can not be fitted, and their ΔI and Δt values were obtained by full width of half-maximum.52 We can find that ΔI and Δt of type A and B events show similar distributions, while that of type C events are larger and longer. This is because the only difference between types A and B is at the capture process, while for type C events, the rerotation of TMV to fit in the pore and a larger θ lead to a longer dwell time and larger blockage.66,67 It indicates that the rotation of TMV influences the ionic current of the nanopore. Additionally, Figure 6 shows the gallery plots of the representive events of TMV translocation though 25, 30, and 50 nm nanopores. The blue dashed line marks ΔGacc, and the red dashed line and the green dashed line mark the range of the conductance fluctuations during TMV translocation. We find that ΔGacc and the conductance change of the vertical translocation (ΔG0) decrease with the pore diameter, as a detailed study of ΔGacc and ΔG0 as a function of the pore diameter shows in the Supporting Information,58 indicating a pore-size dependent ΔGacc and ΔG0. Dependence of Pore Size on the Conductance Fluctuations. From Figure 6, one can also find that the range of the conductance fluctuations at the blockade stage increases with the pore diameter. A qualitative interpretation would be as follows: the larger the pore, the more space there is that allows the random rotation of TMV in the pore. As a result, the possible conductance blockage spreads to a wider range. As we described above, the conductance fluctuations at the blockade stage is mainly attributed to the random rotation of TMV during its translocation. However, we can not give an analytical expression of the conductance fluctuations. To give a numerical study of the dependence of the angle of TMV to the pore central axes (θ) on the conductance fluctuations at the blockade stage, a 2D finite element simulation was performed using a PNP model by Comsol Multiphysics 3.5a,64,68 where 2506

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Figure 5. Comparison of distributions of the current blockage (ΔI) and translocation time (Δt) of the three types of events. (a) The illustrations of fitting each type of event in a 30 nm nanopore by the sigmoid model; the solid lines are the resulting curves. The fitting parameters, ΔI and Δt, are indicated accordingly. (b) The scatter plots of ΔI vs Δt of each type of event; the accompanying histograms are put on the right and the top. The histograms of ΔI are fitted by Gaussian. The applied voltage is 100 mV.

Figure 6. Gallery plots of aligned representive events of TMV translocation through 25 nm (top), 30 nm (middle), and 50 nm (bottom) nanopores. The traces were recorded at 450, 100, and 300 mV, respectively. The color coding is as in Figure 1f. The black dashed line marked the open pore conductance which is centered at 0 nS. The blue dashed line marks the maximum blockage of the access conductance (ΔGacc); the red dashed line marks the conductance blockage of the vertical translocation (ΔG0), and the green dashed line is the maximum conductance blockage (ΔGmax).

the contribution of electro-osmosis flow (EOF) and the diffusion of ions to the ionic current were considered. The model and simulated distribution of EOF at the y direction in a 40 nm nanopore are shown in Figure S10. Figure 7a shows the simulated results of the conductance change (ΔG) as a function of θ in five nanopores. For a better comparison, the conductance change was normalized by (ΔG − ΔG0)/G0, where G0 is the open-pore conductance. The simulated ΔG0/ G0 as a function of pore diameter can be found in Figure S11. From Figure 7a, we can find that, for a given pore, ΔG increases as θ becomes larger. This is because more ions are excluded by the presence of TMV when it leans more. The range of the conductance fluctuations at the blockade stage can be defined as range = ΔGmax − ΔG0. The inset of Figure 7a shows the range normalized by G0 as a function of pore diameter. Interestingly, we find an excellent fit to (ΔGmax − ΔG0)/G0 as a function of dpore by the function y = A × dpore. It indicates that the range of the conductance fluctuations at the blockade stage is proportional to G0 × dpore. However, in our observation as shown in Figure 6, the conductance fluctuation range of the 50 nm nanopore is a little smaller than that of the 30 nm pore. The possible reason is the hourglass shape of the 25 and 30 nm nanopores with a reduced effective length and bigger openings at both sides of the pore, which enables larger maximum angles that allow TMV to pass through. This is proven by the additional simulation of the conductance change

of an hourglass shaped nanopore with 30 nm in diameter, as the black square line shown in Figure 7a. Rotation Frequency of TMV during the Translocation through Nanopore. Next, we examine the frequency of TMV rotation using the method of Golibersuch.59,60 Due to the space limitation for the rotation of TMV in the nanopore, the ratio (K) of the maximum current blockage (ΔImax) to the minimum current blockage (ΔImin) at the same applied voltage can be described by59 f⊥ + (f − f⊥ )cos2 θmax ΔImax K= ≈ ΔImin f⊥ + (f − f⊥ )cos2 0°

(1)

where f⊥ and f∥ are the electrical shape factors of TMV for the cases of it parallel to and perpendicular to the electric field. Because the aspect ratio of TMV is larger than 10, we assume f⊥ = 2 and f∥ = 1. Thus, the ratio of ΔImax to ΔImin can be rewritten as ΔImax/ΔImin ≈ 2 − cos2θmax and so the ΔGmax/ΔGmin. For a given pore geometry, θmax can be calculated using the following expression θmax =

⎛ ⎞ d pore d TMV 180° ⎜ ⎟ − arcsin arcsin 2 2 2 2 ⎟ π ⎜ + + d l d l pore pore pore pore ⎝ ⎠

(2)

The derivation of eq 2 can be found in Figure S12. Substituting θmax of each pore size leads to K = 1.05 for the 25 nm 2507

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Figure 7. Study of conductance change due to the rotation of TMV as a function of pore diameter. (a) Finite element simulations of (ΔG − ΔG0)/ G0 as a function of θ in various nanopores. The black square line is the (ΔG − ΔG0)/G0 of an hourglass shaped nanopore with 30 nm in diameter (solid arrow). The inset is the normalized range of the conductance fluctuations (ΔGmax − ΔG0)/G0 at the blockage stage as a function of dpore, which is fitted by a line with fixed intercept at 0, yielding a slope of 0.012 nm−1. (b) The scatter plots of ΔGmax vs ΔGend of the three nanopores. The applied voltage of the 25 and 50 nm pore is 450 mV and that of the 30 nm pore is 100 mV. (c) The distributions of ΔGend and ΔGmax in the translocation of TMV through the 30 nm pore. The inset is the typical A event showing the level of ΔGend, ΔG0, and ΔGmax. The violet dashed line at 35.8 nS is ΔG0 of the 30 nm nanopore.

nanopore, K = 1.12 for the 30 nm nanopore, and K = 1.43 for the 50 nm nanopore. Because the current fluctuations at the beginning of the event can occur at the level of blockade stage, we take the current blockage at the end of the event for the minimum current blockage (ΔIend). Figure S13 shows the scatter plots of ΔImax vs ΔIend of the three nanopores at all voltages. For a better comparison, the scatter plots of corresponding conductance change at the end of the event (ΔGend) and the maximum conductance change (ΔGmax) is shown in Figure 7b. We find that the data points of the three nanopores fall between two lines,59,60 one is the line for ΔGmax = ΔGend (lower), and the other is the line ΔGmax = KΔGend (upper), where K = 1.25 for the 25 nm nanopore, K = 1.5 for the 30 nm nanopore, and K = 2 for the 50 nm nanopore; see Figure S13 as well. One can find that K increases with respect to the pore size, demonstrating the range of the current fluctuations at the blockade stage increases with pore size, which is consistent with the experimental data and numerical simulation. However, we find that all the K values are larger than the theoretical ones. Besides the geometry of the pore as we discussed above, several other reasons may account for the larger K. First, unlike the experiment carried by Golibersuch using a pore with diameter and length far larger than that of the translocating particle, in our case, the pore length is much shorter than the TMV length; the change of access conductance due to the rotation of TMV while translocating through the pore contributes to the whole conductance change. Second, the use of eq 1 is based on the approximation that rod-shaped TMV can be treated as a prolate ellipsoid, which leads to a deviation. Figure 7c plots the distributions of ΔGend and ΔGmax in the translocation of TMV through the 30 nm pore. One can find that ΔGend at all the voltages show similar distributions, and the Gaussian fits yield a mean conductance change of ∼34 nS which is ∼1.8 nS smaller than ΔG0. The small difference could be attributed to the current fluctuations and sloped states at the blockade stage, as a representive type A event shown in the inset of the upper panel with ΔGend, ΔG0, and ΔGmax being pointed out. However, if we look at the distribution of ΔGmax, we can find the maximum conductance changes of more than 50% of the events at each voltage are at least 4 nS larger than ΔG0. It shows that TMV is commonly captured by nanopore with an oblique form and then rotates to a vertical form during

the translocation through the pore, which is consistent with the dynamics simulations shown in Figure 3.

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CONCLUSION We present the experimental results of rigid rod-shaped TMV translocation through solid-state nanopores, and three types of events with distinctive characteristics at the beginning were observed. The kinetic model and the dynamics simulations demonstrate that there are two independent steps ((ii) and (iii)) dominating the behaviors of TMV in the capture process. After one end of the TMV approaches the back side of the pore, the random rotation of TMV gives the conductance fluctuations at the blockage stage, the range of which is mainly dependent on the pore geometry. At the end, we investigate the rotation frequency of TMV during the translocation, and the results indicate that TMV orientation tends to be parallel to the electric field during the translocation. The results show that the rotation of TMV would significantly influence the recorded current signal, which suggests one should consider this effect in the measurements of rod-shaped particles. This study will shed light on the physics studies of the dynamics of nanopore translocation. As the event shape depends on the shape and aspect ratio of the particle, it provides a possible method to distinguish particles with various shapes,67 aspect ratios,69 and aggregations66 by examination of the current dynamics of the events. Compared to the results of flexible biopolymers and semiflexible fd virus, it opens a new possible way to characterize the rigidity of the analytes by nanopore measurements.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.analchem.5b04905. Detailed experimental section, Langevin dynamics simulation of TMV translocations, DLS measurement of TMV, current trace of TMV getting stuck in the pore, the study of ΔG0 and ΔGmax as a function of dpore, the current traces of TMV translocation through 25 and 50 nm nanopore at various voltages, the model and simulated distribution of EOF in a 40 nm nanopore, the simulated ΔG0/G0 as a function of dpore, the 2508

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Analytical Chemistry derivation of the eq 2, and scatter plots of ΔImax vs ΔIend. (PDF)

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W Web-Enhanced Features *

Movies of the trajectories of the simulated TMV translocations in AVI format are available in the online version of the paper.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank X. S. Ling for the useful discussions. This work was funded by National Basic Research Program of China (2011CB707600), the National Natural Science Foundation of China (61071050, 61372031).

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