Entropic cages for trapping DNA near a nanopore

Nanopores can probe the structure of biopolymers in solution; however, diffusion makes it difficult to study the same molecule for extended periods. Here we report devices that entropically trap single DNA molecules in a 6.2-femtolitre cage near a solid-state nanopore. We electrophoretically inject DNA molecules into the cage through the nanopore, pause for preset times and then drive the DNA back out through the nanopore. The saturating recapture time and high recapture probability after long pauses, their agreement with a convection–diffusion model and the observation of trapped DNA under fluorescence microscopy all confirm that the cage stably traps DNA. Meanwhile, the cages have 200 nm openings that make them permeable to small molecules, like the restriction endonuclease we use to sequence-specifically cut trapped DNA into fragments whose number and sizes are analysed upon exiting through the nanopore. Entropic cages thus serve as reactors for chemically modifying single DNA molecules. Nanopore sensors provide a useful way of analysing single molecules, such as DNA. Here, the authors present a nanopore-based single-molecule reactor, into which DNA can be fed and removed, and which also acts as an entropic cage allowing for DNA chemical modifications.

A nanometre-scale pore in a thin membrane can be used to detect a single molecule and sense its physical structure as it passes through the pore while in solution 1,2 . Nanopore sensors have enabled fundamental studies on single biopolymers [3][4][5][6][7][8][9] and show promise for use in a variety of biosensing applications [10][11][12][13][14][15][16][17][18][19] . Nanopores are particularly well suited for probing chemical interactions between DNA and other molecules [20][21][22] , because these interactions often substantially modify the structure of a DNA molecule. For example, oligonucleotide hybridization probes 23 bind to specific DNA target sequences and create bulges that are easy to detect when they pass through a nanopore. Applying this principle, Singer et al. 14 mapped the locations of target sequences on long, doublestranded DNA molecules, and Wanunu et al. 12 identified different microRNAs. To correctly infer that the structure of a DNA molecule has changed, however, it is crucial to know what was the structure of that molecule before the chemical interaction occurred. This presents a serious epistemic challenge, as nanopore sensors should ideally discover the characteristics of a molecule without prior knowledge.
A solution is to use a nanopore to characterize the same DNA molecule before and after a chemical interaction; For that, we require what amount to single-molecule test tubes in which DNA can interact with other molecules without diffusing away. Rant et al. 24 took an important step towards that goal when they developed devices comprising two pores and a microscale cavity. They demonstrated that the diffusion of particles and DNA can be significantly slowed inside the cavity 25 . Those devices held DNA molecules in the cavity for only a few seconds, however, which is too short to be practical for studying chemical interactions. (In a separate set of experiments, similar devices were used to measure the transit time of DNA molecules moving between two opposing nanopores by electrophoresis 26 ).
Here we report the fabrication and use of devices that juxtapose a solid-state nanopore with a cage that can trap a single DNA molecule for many minutes. The cage is a disc-shaped, micrometre-scale cavity with a few-hundred-nanometre-wide opening in one face and a nanopore in the other. DNA is driven into and out of the cage by electrophoresis through the nanopore. The cage traps DNA entropically 27 , which means that DNA is prevented from diffusing away by the reduction in configurational entropy that would be required for the polymer coil to squeeze through an opening smaller than its radius of gyration 28 . Small molecules like hybridization probes and restriction enzymes can nevertheless diffuse through the opening without difficulty. We experimentally demonstrate that single DNA molecules can be stably trapped in a cage for several minutes and recovered with nearly perfect efficiency. We then demonstrate how our devices can analyse DNA before and after a chemical reaction using a restriction endonuclease to cut DNA held in the cage and detecting the resulting fragments with the nanopore. Entropic cages are useful as single-molecule chemical reactors for nanopore biosensing with a variety of chemical probes 29,30 , and for studying biologically significant interactions between DNA and other molecules.

Results
Nanopore cage structures and experiments. Figure 1a illustrates the nanopore cage structure, and Fig. 1b shows transmission electron microscope (TEM) images of a typical one. The structure is similar to the pore-cavity-pore device developed by Pedone et al. 24 , but it features a cylindrical cavity as opposed to a pyramidal one. Furthermore, we judge our fabrication method to be simpler while granting us better control over the device dimensions. Each structure was made in a freestanding membrane on a silicon chip. The membrane comprised a threelayer stack of materials. The outermost layer, made of low-stress silicon nitride, was 20 nm thick. The middle layer was 1.5 mm thick and made of silicon dioxide. The layer closest to the silicon chip was 400 nm thick and made of low-stress silicon nitride. To create the nanopore cage structures, we first used a focused ion beam machine (FEI Helios) to mill a 200-nm-diameter opening through the innermost layer of silicon nitride. A buffered hydrofluoric acid etch then selectively removed SiO 2 from the middle layer, creating a 1.5-mm-high cavity whose diameter was selected by controlling the duration of the etch. A diameter of 2.3 mm was obtained after 10 min of etching. The cavity was large enough to accomodate a l DNA molecule, which is 16.5 mm long and has a radius of gyration that is R g ¼ 730 nm in equilibrium 31 . Finally, we focused the beam of a TEM (JEOL 2100F) onto the 20-nm-thick silicon nitride layer to mill a E10-nm-diameter nanopore through it. Figure 1c shows a TEM image of a nanopore. Table 1 summarizes the dimensions of every device used to generate data presented here.
In our DNA-sensing experiments, the chip separated two reservoirs of buffered ionic solution, one contacting the opening of the cavity (the 'opening side') and the other contacting the nanopore and containing l DNA (the 'nanopore side'). The only fluidic path between the two reservoirs passed through the  nanopore, the cavity and the opening. An electrometer biased the opening side to a voltage V relative to the nanopore side and measured the resulting ionic current through the nanopore, I, by means of Ag/AgCl electrodes immersed in the reservoirs. The opening, while small enough to confine l DNA, was too big to significantly affect the ionic resistance of the device, which was governed by the nanopore. I is the basis of the sensing mechanism: DNA molecules pass through the nanopore due to electrophoresis, and the presence of a molecule inside the nanopore causes a measurable change in I 8 . The time course of I reflects the structure of the molecule 14,15,22,32 . A field-programmable gate array (FPGA) digitized I and enabled real-time control over V in response to changes in I or pre-programmed delays 7 .
Dynamics of DNA in entropic cages. We investigated the dynamics of l DNA molecules in the entropic cage with 'pingpause-pong' experiments, illustrated in Fig. 2a. A current trace from a typical experiment is shown in Fig. 2b. The application of V ¼ 100 mV resulted in a current of 9.73 nA through the 8.5-nmdiameter nanopore. When a DNA molecule translocated the nanopore into the cage, it caused a transient decrease in I. We call this first translocation signal the 'ping'. We maintained the positive voltage bias for 2 ms following the ping. The voltage bias was then removed for a pause time, t p , during which the molecule could relax and diffuse within the cavity. We varied t p in experiments between 2 ms and 50 s. Following the pause, we flipped the voltage to V ¼ À 100 mV for 5 s. We usually observed another transient conductance drop, which we call the 'pong', and attribute to the same DNA molecule returning through the nanopore. The interval of time between the voltage reversal and the pong is t r , the recapture time. In these experiments, the ionic current approached a new open-pore value gradually and reproducibly following a change in voltage, whether or not a molecule had translocated the nanopore. The slow change in the baseline current is therefore related to the instrumentation and the nanopore rather than the DNA 7 . Figure 3 shows examples of ping and pong translocation events for delay times ranging from 10 ms to 10 s. Interestingly, the course of the current baseline could be extrapolated continuously across ping and pong events, without any shift resulting from the translocation of a molecule into or out of the cage. The presence of a DNA molecule inside the cage therefore had no observable effect on the access resistance of the device.  ARTICLE For each DNA translocation, we computed the event charge deficit (ECD), which is the induced current change integrated over the duration of the event. Previous studies showed that ECD is primarily related to the length of a DNA molecule and not the folding configuration in which it translocates 5,9 . Since l DNA is very long, it is an excellent candidate for entropic trapping, but is also relatively easy to break and difficult to purify. Consequently, nanopore studies of l DNA typically reveal a subpopulation of much shorter molecules 9,33-35 (presumably fragments) that could respond differently to an entropic cage, especially if their radius of gyration is smaller than the opening. We have used ECD to identify and remove short fragments of DNA from our data. Figure 4a shows a scatter plot indicating the ECD of each ping and the corresponding t r for t p ¼ 30 ms. Most of the data clustered in a major group centred around ECD ¼ 0.4 pC and t r ¼ 20 ms. A small numer of molecules with low ECD (B0.1 pC) were more broadly distributed in t r , and a few of them exhibited extremely long return times (41 s). Figure 4b shows the distribution of ping ECD values, which has a major peak near 0.4 pC and a minor tail that is most prominent around 0.1 pC. We attribute the pings in the major group to translocations of intact l DNA molecules, and those in the minor tail to shorter fragments 9 . We used the threshold ECD ¼ 0.2 pC to distinguish between intact molecules and fragments. Figure 4c-f shows ECD distributions from experiments with different t p , while distinguishing between intact molecules and fragments. The distributions of ping ECDs were all similar, showing a main group of translocations that was unaffected by the threshold. Furthermore, molecules identified as fragments based on the ping ECD resulted in low pong ECDs, as expected. Fragments comprised less than 20% of the translocations in every experiment. For the analysis that follows, we only considered the intact molecules. Figure 5a shows the dependence of the mean return time ht r i on t p . ht r i increased with t p until t p E700 ms, where it saturated at ht r iE250 ms (blue data). We determined that the saturation in ht r i was due to the presence of the cage by performing the following control experiments. We applied the same ping-pausepong procedure, only this time we used a device whose cavity and opening diameters (7.32 and 5.32 mm, respectively) were so much larger than the equilibrium coil size of l DNA that the cavity could not possibly impede the molecule's motion. Because of this, the device behaved as if there was no cage at all. The results of these control experiments are shown in Fig. 5a (red squares). ht r i increased with t p over the full range of pause times tested. The longest pause, t p ¼ 50 s, gave t r ¼ 2 s, which was nearly an order of magnitude longer than the t r plateau value observed in experiments with a cage. Similar results were obtained using a second device with a large 6.12-mm-diameter cavity and a 1.56mm-diameter opening. Those results are also shown in Fig. 5a (red circles).
The cage also significantly enhanced the probability of recapturing a molecule, defined as the fraction of ping-pausepong cycles where the ping was followed by a pong. Figure 5b plots the dependence of the recapture probability on t p for translocations into a cage and for translocations across a device with no cage. In the absence of a cage, the recapture probability decreased precipitously with t p for t p 4200 ms. The longest pause in the cage-free experiments was 5 s because beyond that, pongs were very rarely detected. By contrast, the recapture probability remained high in devices with a cage, even for t p ¼ 50 s (100% for two devices and 480% for a third device).
Finally, Fig. 6 plots normalized distributions of 4-ms-long samples of the current blockage caused by translocations, DI, for different t p . As has been found previously 36 , translocations produced bimodal distributions of current blockage amplitudes, with a major peak near DI ¼ 0.13 nA caused by the presence of an unfolded DNA molecule inside the nanopore, and minor peaks at about double the DI, corresponding to the presence of a DNA molecule in a folded configuration inside the nanopore. The amplitude of the minor peak relative to the major peak was higher for pongs than for pings, especially for short t p , indicating that folded configurations occurred with greater frequency during the pong. This can be explained by DNA forming a compact coil close to the nanopore immediately after the ping, which increases the frequency of folded configurations during the pong 37 . The peaks in the current blockage distribution of the pongs tended to shift modestly (B10%) towards higher values relative to the pings. We have not determined the reason for this shift. The difference in current blockage distributions was not accompanied by a clear difference in translocation durations between pings and pongs (see Supplementary Fig. 1).
Dynamical modelling. To guide our interpretations, we modelled the dynamics of DNA in a ping-pause-pong cycle theoretically, and compared the predictions with our experimental results. Our approach was similar to the one used by Gershow and Golovchenko 7 to model the capture and recapture of DNA without a pause step or a cage. We treated l DNA as a charged particle drifting due to the electric fields outside the nanopore and diffusing at the same time. When a voltage was applied, it induced hemispherically symmetric electric fields that decayed as the inverse square of the distance from the nanopore, as one would expect from a point source of current injected into fluid with a uniform conductivity. Our model used no free parameters; we set the diffusivity of the particle equal to that of l DNA in a bulk electrolyte 31 , and we took the value of mobility to be m ¼ 2.2 Â 10 À 4 cm 2 V À 1 s À 1 in 1 M KCl based on the theoretical estimate by Grosberg 38 . That estimate is consistent with mobility measurements by Stellwagen and Stellwagen 39 if those measurements are extrapolated to a salinity of 1 M. The particle was located 100 nm away from the nanopore at the start of a ping-pause-pong cycle. The evolution of its probability distribution was obtained by numerically solving the convectiondiffusion equation in spherical coordinates in the ping and pause phases. To model a DNA trapped in the cage, we imposed an additional, no-flux boundary condition at a radial distance of 1.5 mm away from the nanopore. The pause phase leaves the probability distribution finite at the boundary of the nanopore. If the pong phase was modelled with the convection-diffusion equation by making the nanopore a sink for particles, the probability distribution would be discontinuous there, leading to a singular recapture rate. This creates a computational problem that does not occur in the absence of a pause 7 . We circumvented this problem by ignoring diffusion in the pong phase and instead computing the deterministic drift times of particles back to the nanopore. (See Supplementary Note 1 and Supplementary Fig. 2 for details of this theoretical modelling.) Figure 5a,b shows that the theoretical model is in excellent agreement with the experimental results. Without a cage, ht r i increased monotonically with t p because DNA could diffuse away from the nanopore without bound. The saturation in ht r i obtained from devices with a cage is a clear signature of DNA becoming trapped and returning to the nanopore from a short distance within the cage. The model also provides two explanations for the missing pongs in the experiments with no cage. First, a molecule can diffuse far from the nanopore into the diffusion-dominated region where the electrophoretic force is too weak to drive the molecule back to the nanopore 7,38 . Second, it is likely that in some cases we did not wait long enough for the molecule to return to the nanopore. This also explains why ht r i rises slowly with t p after long pauses in experiments with no cage, as these missing pongs would have shown a longer t r than 5 s and they occur more frequently with increasing t p .
The model disagrees most with the experimental results in relative terms at short pause times, where t r is predicted to be longer than observed. This error likely stems from treating DNA as a point particle. Since a DNA molecule remains close to the nanopore when t p is short, the distance from the nanopore to the nearest DNA segment can be significantly smaller than the distance to the molecular centre of mass. Therefore, the molecule should be recaptured well before its centre of mass arrives at the nanopore.
Visualizing an entropically trapped DNA molecule. We visually confirmed that the entropic cage stably trapped l DNA in a seperate series of experiments. We applied a voltage to pull a DNA molecule into an entropic cage and left it trapped there. We then transferred that chip to an optical microscope, with the opening side facing up, and placed a drop of solution containing the fluorescent dye YOYO-1 onto the chip, as illustrated in Fig. 7a. The YOYO-1 could diffuse through the opening of the cage and stain the DNA molecule inside while we observed the process optically. We located the cavity in white-light mode (Fig. 7b) and then monitored that region in flourescence mode for about 25 min, recording an image every 10 s. A bright spot appeared in the location of the cavity (Fig. 7c), showing that a DNA molecule was trapped inside. This experiment was repeated on two more nanopore devices and the same result was obtained. Figure 7d shows the results of a control experiment where we used the ping-pause-pong procedure to pull the DNA molecule into the cavity, pause for 5 s and then remove it before transferring the device to the microscope. As expected, no flourescence was visible since no molecule was in the cage. The result of this control experiment was reproduced on a second nanopore device.
Cutting trapped DNA molecules with a restriction endonuclease. We used an entropic cage to subject trapped DNA molecules to a sequence-specific biochemical reaction, as illustrated in Fig. 8a. Buffer containing the SmaI restriction endonuclease was added to the reservoir on the opening side, while the reservoir on the nanopore side was filled with a similar buffer that contained l DNA instead of the enzyme. We used the pingpause-pong technique to draw a DNA molecule into the cage, where it could interact with SmaI during the pause, and then reverse the voltage so that the nanopore would interrogate the products of the reaction. SmaI cuts double-stranded DNA at a particular recognition sequence found at three sites along l DNA. We therefore expected a l DNA molecule entering the cage to be cut into as many as four pieces, with the number of pieces increasing as the reaction progresses to completion. Figure 8b shows a typical current trace obtained with t p ¼ 5 s. Applying V ¼ 200 mV drew a DNA molecule into the cage through the nanopore, in this case causing an increase in I because the DNA is highly charged and therefore entrains enough counterions into the nanopore to increase its conductance in lowsalinity enzyme buffer 40 . After the pause, the voltage was flipped to V ¼ À 200 mV and maintained for 5 s. From the single ping, we obtained two pong signals in this case, indicating that a molecule was trapped inside the cavity, cut and pulled back through in pieces. We varied t p in our experiments between t p ¼ 1, 5 and 20 s to probe the restriction reaction after different incubation times. At each t p , we repeated the experiment at least 60 times. We also performed control experiments with no SmaI present and t p ¼ 5 s. Figure 8c shows the distribution of the number of pongs observed per ping-pause-pong cycle (N pong ) for the different incubation times and for the experiment with no enzyme. Between one and four molecules were recaptured per cycle. Without SmaI, 98.6% of the experimental cycles returned only one pong. With SmaI present, the probability of detecting multiple pongs in a cycle increased with t p , from 17.3% at t p ¼ 1 s to 50.0% at t p ¼ 20 s.
To confirm that multiple pong signals were caused by fragments of the original molecule, we verified that the fragments were smaller than the original molecule and compared the total size of the recaptured fragments in a cycle with the size of the original molecule, using ECD as a measure of size. Figure 8d shows the distributions of ECD pong ECD ping , the ECD values of the pongs relative to the corresponding ping, grouped by N pong (white bars). That figure also plots the distributions of AEECD pong ECD ping , the total ECD of all the pongs in a cycle relative to the corresponding ping (grey bars). When N pong ¼ 1, the distribution of ECD pong ECD ping was centred around 1, indicating that the molecule was not cut because its size did not change. As more pongs were detected per cycle, the distribution of ECD pong ECD ping shifted to lower values, indicating that the recaptured molecules were becoming smaller than the original one. The peak of the AEECD pong ECD ping distribution remained near 1 for all N pong , however, indicating that the total size of the recaptured molecules was the same as the original.
Finally, Fig. 9 is a scatter plot of pong events from the enzymatic cutting experiments indicating t r and ECD. Molecules that had not been cut gave pongs in the high ECD, short t r region of the data, while the fragments produced by the restriction digest gave pongs in the low ECD, long t r region. These results reflect the fact that short DNA fragments, which give low ECD, have a relatively high diffusivity 31 , so they can more easily diffuse away from the nanopore. We note that these results are also consistent with Grosberg's model of the DNA capture rate in the regime, where the rate is limited by an entropic barrier 38 ; within that model, the low effective charge of short polymer fragments can more easily resist the weakened pull of the electrophoretic force. Fragments consequently exhibited longer recapture times than intact l DNA molecules. This also explains the data in Fig. 4a,b, which show that short DNA fragments, as measured by ECD, resulted in the longest t r .

Discussion
We have demonstrated that entropic cages can capture single DNA molecules next to a nanopore. We have confirmed this by observing plateauing recapture time and high recapture probability in devices with cages, and by directly imaging trapped molecules using fluorescence microscopy. The ability to capture and constrain a single molecule allows us to study the physics of a molecule's translocation of a nanopore in general, since it affords us some control over the state of the molecule before reverse translocation 7,[41][42][43] . Entropic traps also enhance solid-state nanopore technology by serving as single-molecule test tubes in which a molecule, interrogated by the nanopore on the way in, can react and then be probed again on the way out. As an ARTICLE example, we demonstrated the cutting of a trapped DNA molecule in the cavity, which can provide a way to simulate the restriction modification systems of bacteriophage resistance mechanisms 44 in vitro. In addition, compared with the widely used genomic analysis method of optical mapping [45][46][47] , which uses a microscope to observe the results of cutting long, single DNA molecules with restriction enzymes, our device provided a fast and label-free way to study the enzymatic cutting of DNA in real time. Given careful choice of enzyme and more thorough study of the reaction conditions, one could use the device to study genetic variations using restriction fragment length polymorphisms 48 .

Methods
Nanopore devices. Silicon chips with freestanding membranes suspended over 50-mm-wide square openings were microfabricated by standard procedures described in detail elsewhere 49 . We fabricated nanopore cage structures following the procedure described in the nanopore cage structure and experiments subsection of the Results. Prior to a DNA-sensing experiment, each device was cleaned in Nanostrip (Cytantek corporation) at 75°C for 2 h, and its ionic conductance was tested in the presence of 1 M KCl buffer to ensure that the s.d. of the baseline current in a 1-min recording was no greater than 0.01 nA with V ¼ 100 mV. Electrical control and signal processing. I was monitored by an electrometer (Axon Axopatch 200B), whose output was conditioned by an analogue, eight-pole, low-pass Bessel filter with a 10-kHz cutoff (Stanford Research Systems), and digitally sampled at 250 kHz. The filtered output of the current amplifier was simultaneously monitored by a FPGA (NI PCI-7830R) running a custom LabView program, which executed ping-pause-pong cycles. The FPGA controlled V by means of an analogue voltage command line to the electrometer. A ping-pausepong cycle was triggered in experiments performed in 1 M KCl solution by a decrease in the current from the baseline that exceeded 0.1 nA and that lasted longer than 200 ms. In the enzymatic DNA-cutting experiments, which were performed in a lower ionic strength solution, a ping-pause-pong cycle was triggered by an enhancement of the current above the baseline of 0.04 nA or more and lasting 100 ms or longer.
Experimental controls. We ensured that our measurements of t r and the recapture probability were not confounded by molecules that were left over on the opening side of the device from an earlier ping-pause-pong cycle, where, for example, a captured molecule failed to trigger a ping or was not recaptured within the 5 s allotted. Between sets of experiment with different t p , we checked that the opening side was clean by applying V ¼ À 100 mV for 1 min. We usually detected no translocations during this time. Only in a few experiments was a single event observed during 1 min, which indicated that molecules left over from previous ping-pause-pong cycles had negligible influence on subsequent experiments. Similarly, we confirmed that the multiple pongs observed in the enzymatic DNAcutting experiments were not caused by enzyme molecules translocating the nanopore. We applied V ¼ À 200 mV for 1 min between sets of experiments using a different t p . No translocation signals were detected, which indicated the SmaI molecule is too large to translocate the nanopore or its translocation signal is too short to be detected.
Fluorescence imaging. After a DNA-trapping experiment, we removed the nanopore chip from its fluidic chuck, rinsed it in distilled, deionized water to wash away any DNA stuck to the membrane, placed the chip on a microscope cover glass with the opening side facing up, added a small drop of YOYO-1 solution to the opening side and then placed another cover glass on top to prevent evaporation. We mounted the chip sandwiched between cover glasses on an inverted microscope (Nikon, ECLIPSE TE2000-U) equipped with a Â 100, oil-immersion objective lens (Nikon, CFI Apo TIRF), an ultraviolet light source (EXFO X-Cite 120), a fluorescence imaging filter set (C125492, Chroma Technology Corp.) and an EMCCD camera (Andor, iXon). Fluorescence images were recorded every 10 s using a 50-ms exposure time and a mechanical shutter that minimized photobleaching.
Baseline subtraction from pong events. We fit and subtracted the baseline beneath pong events when that baseline was recovering from a sudden change in voltage, as can be seen in Figs 2b, 3a,b and 8b. We fit a 4th-order polynomial to a section of I(t) containing the pong event using an asymmetric Huber cost function 50 . Specifically, the best fit, 4th-order polynomial, f(t), is the one that minimizes the cost function where j x ð Þ is the asymmetric Huber function We used the threshold s ¼ 10 pA. f x ð Þ increases slowly when x4s, which limits the influence of the pong event on the fit to the baseline. The MatLab software we used is available online at (http://www.mathworks.com/matlabcentral/fileexchange/ 27429-background-correction).