LETTER pubs.acs.org/NanoLett
A Pore-Cavity-Pore Device to Trap and Investigate Single Nanoparticles and DNA Molecules in a Femtoliter Compartment: Confined Diffusion and Narrow Escape Daniel Pedone,† Martin Langecker,† Gerhard Abstreiter,†,‡ and Ulrich Rant*,†,‡ † ‡
Walter Schottky Institut, Technische Universit€at M€unchen, Am Coulombwall 3, 85748 Garching, Germany Institute for Advanced Study, Technische Universit€at M€unchen, Lichtenbergstrasse 2a, 85748 Garching, Germany
bS Supporting Information ABSTRACT: Spatial confinement from the nano- to the microscale is ubiquitous in nature. Striving to understand the behavior of nanoscale objects in confined domains we present a nanofluidic silicon device which consists of two stacked nanopores forming the in/outlets to a pyramidal cavity of micrometer dimensions (10 fL volume). Being electrically addressable, charged objects can be actively loaded into, trapped inside, and unloaded from the “pore-cavity-pore” (PCP) device. When operated passively, confined Brownian motion and the entropy barriers of the nanopores govern the behavior of nano-objects within the PCP device. We present measurements with single fluorescent nanoparticles as well as particle-ensembles and analyze their trajectories and residence times. Experimental data are compared to random walk simulations and analytical theories on confined diffusion and the Brownian escape of nanoobjects across entropy barriers. Single particle data corroborate analytical solutions of the narrow escape problem, but ensemble measurements indicate crowding effects even at low particle concentrations. The utilization of the device to trap biomolecules is demonstrated for single λ-DNA molecules. KEYWORDS: Nanopore, narrow escape, confinement, trapping, diffusion
B
ecause most of molecular biology operates inside cellular compartments or involves the trafficking of molecules across domain boundaries, confined diffusion1-6 and methods to study suppressed Brownian motion7,8 have received substantial attention. A fundamental problem in that context is the escape of nano-objects from a microdomain through a small opening. The “narrow escape problem” has numerous analogues in cell biology, e.g., the transport of molecules through protein pores in cell membranes9 or the binding of a diffusing molecule to a reaction partner localized on a wall,10,11 and thus has been studied extensively from a theoretical point of view.12-18 Here, we introduce the pore-cavity-pore (PCP) structure as a novel device for single molecule investigations19-21 combining a microscale fluidic compartment22,23 with solid-state nanopores.24 It allows us to obtain experimental narrow escape time and diffusion data for single nano-objects under well-defined geometrical conditions. Because the device as a whole is pervious to ions, electrical currents can be driven across the PCP structure; this adds the element of electrical addressability and permits electrical amplification or canceling out the entropy barrier effect of the narrow apertures. Furthermore, the PCP structure is scalable and thus can be adapted to a versatile storage, investigation, and reaction chamber which resembles an artificial cell. Results and Discussion. Pore-Cavity-Pore (PCP) Device. The PCP device as depicted in Figure 1 is fabricated from a silicon wafer which is coated on both sides with 50 nm thick r 2011 American Chemical Society
silicon nitride (SiN) layers. The fabrication process involves four steps (see Methods and Supporting Information for details):25 first, the “SiN” nanopore is created by electron beam lithography and reactive ion etching (RIE) in the bottom SiN layer.26 Second, a large square window is opened by optical lithography and RIE in the top SiN layer. Third, the pyramidal cavity above the SiN pore is created by wet chemical etching. In the final step, the Si chip is being etched from the top side in a feedback controlled manner,27 until the pyramid apex opposite from the SiN pore is truncated. This way, the second nanopore, the “Si-pore”, is formed. During the fabrication process the desired dimensions of the SiN-pore and the Si-pore can be controlled well by the e-beam exposure dose (d g 10 nm) and to a lesser extent by adjusting the termination set point (i.e., current threshold) of the feedback etching process, respectively. The cavity size can be tuned with ca. 0.1 μm accuracy by adjusting the etch time. Panels c and d of Figure 1 show scanning (SEM) and transmission (TEM) electron micrographs of the pyramidal cavity and the nanopores, respectively. Figure 1e shows the measurement setup. The cavity is electrically addressed by applying potentials across the PCP structure using Ag/AgCl electrodes. This way, charged objects can be driven into and out of the device. For this Received: December 14, 2010 Revised: February 16, 2011 Published: March 09, 2011 1561
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Figure 1. The pore-cavity-pore (PCP) device. (a) Schematic depiction of the fabrication steps after e-beam and optical lithography, the cavity etching step, and the second feedback controlled etching step (from left to right, not drawn to scale). (b) 3D representation of the PCP device showing the pyramidal cavity in the silicon chip, the SiN-pore in the base center (bottom side), and the rectangular Si-pore on the top side. (c) Scanning electron micrograph of the cavity imaged from bottom through the SiN membrane. (d) In the transmission electron micrograph a slightly oval SiN-pore (d1 = 45 nm; d2 = 51 nm) can be seen through a larger Si-pore, the latter featuring a rectangular shape which results from the truncation of the cavity pyramid tip (side lengths: 148 and 166 nm). Alternating bright and dark regions around the pore originate from Bragg reflections at the inclined side walls. (e) Measurement setup. The chip separates two electrolyte compartments with Ag/AgCl electrodes. The optical detection volume encompasses the cavity lumen, but not the upper fluidic compartment, which is blocked by the opaque silicon.
Figure 2. Confined single particle diffusion. (a) Single particle trajectory of a fluorescent 74 nm particle confined to the cavity of the PCP device recorded for 13 s with a sampling rate of 80 Hz and (b) time-integrated fluorescence intensity emitted by the particle diffusing inside the cavity. (c) Mean square displacement (MSD) evaluated for particles confined in three different PCP devices with varying cavity volumes (red, V1 = 18.7 μm3; black, V2 = 11.7 μm3; blue, V3 = 8.4 μm3). Solid lines are fits with eq 3. (d) MSD from a 3D random-walk simulation of a 74 nm particle in a V (=V3) = 8.4 μm3 cavity (without escape from cavity). Simulation results have been fitted with eq 3, yielding a confinement box length l 3 sim = 2.3 μm, which agrees well with the experimentally obtained value l 3 = 2.4 μm. The inset shows a simulated random walk trajectory within the cavity until the particle escapes eventually.
work, the Si-pore size was chosen larger than the size of fluorescent nanoparticles (34 or 74 nm in diameter), while the SiN-pore was too small to let a particle pass through. Thus, the particles may enter and exit the cavity only through the Si-pore, but ionic currents can be applied and sustained across the whole device. In the “injection” mode, a positive voltage of typically 100 mV is applied to the bottom electrode (Figure 1e) so that the negatively charged particles are drawn from the upper reservoir through the Si-pore into the cavity. After the cavity is loaded to a desired fill state (one to hundreds of particles), the potential of the bottom electrode is adjusted to a slightly positive, zero, or negative bias which sets the device to “trapping”, “passive”, or “ejection” mode. The fluorescence intensity emitted by the nanoparticles is observed over time to monitor the cavity’s fill state and to follow the trace of a particle within the cavity. Confined Diffusion of Single Particles. After a single particle is electrically injected into the cavity, the potential is turned off (i.e., adjusted so that the ionic current across the device is 100 particles simultaneously and observing the efflux of fluorescent particles after switching the PCP device to “passive mode”. Table 1 lists the experimentally determined mean narrow escape times together with theoretical predictions according to eq 4 and simulation results obtained by computing 600 particle trajectories. Single particle measurements are in very good agreement with analytical solutions and simulation results (cf. Table 1). In order to compare the theoretical predictions—valid for pointlike Brownian objects—with the experiments, a reduced effective window diameter aeff = dSi-pore - dparticle was used to account for the finite dimensions of the particles. Not unexpectedly, the experiments show that 34nm particles escape from the cavity 34nm significantly faster than 74nm particles, i.e., τh74nm escape ≈ 5 τhescape. In part, this is a consequence of the faster diffusive motion of the 2 -1 2 -1 74nm smaller particles (D34nm DLS = 14.6μm s , DDLS = 6.5μm s ), which—according to eq 4—should contribute a factor of 2 to the difference in escape times. In addition to that, the invariant Sipore (dSi-pore ≈ 157nm) represents a window of varying effective ≈ 123nm diameter aeff for the differently sized particles: a34nm eff ≈ 83 nm. However, we note that an estimation of aeff and a74nm eff based solely on geometric reasoning may oversimplify the situation: although the diameter of the “small” SiN-pore (slightly oval, d = 45 nm by 51 nm) was nominally larger than the 34 nm particles, we never observed particles escaping through the SiN-pore. If this was only due to the higher entropy barrier of the SiN-pore, or whether other interactions, e.g., electrostatic repulsion between the likewise negatively charged particles and inner pore surfaces, further reduced the effective pore diameters cannot be determined from the present data set. Ensemble measurements (Figure 4d,e) reveal that when the cavity is loaded with multiple particles, the escape time is substantially longer than the mean single particle escape time. This is most likely caused by particle-particle interactions (collisions) or a congestion effect (short-lived blockages of the Si-pore due to the transitory adsorption of particles onto pore walls). Crowding-induced changes of the particles’ diffusion can 1563
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Figure 4. Escape time τescape analysis of single particles (left) and multiple particles (right) loaded in a Vcavity = 8.4 μm3 cavity. (a, b) Histograms of escape times measured for individual 34 nm particles (black) and 74 nm particles (blue). (c) Population probability derived from the histograms shown in (a) and (b). (d) Epi-fluorescence images of an ensemble of nanoparticles confined to a cavity. The intensity at each x,y point corresponds to the cavity height above that point; thus, the profile resembles the pyramidal cavity shape. (e) Time-dependent cavity fill-state as followed by the fluorescence intensity. The cavity was loaded with approximately 500 small (34 nm) or 130 large (74 nm) particles. Solid lines in (c) and (e) are single exponential fits, from which the mean escape times of the single and multiple particle measurements are derived.
Table 1. Comparison of Experimental and Theoretical Mean Escape Times τhescape and Effective Window Diameters aeff for 34 and 74 nm Particles τhescape (s) simulation
a
a
dparticle (nm)
aeff (nm)
34
123
2.5 ( 0.3
74
83
7.1 ( 0.7
single particle
τhescape (s) theoryb single particle
τhescape (s) experiment single particle
multiple particles
2.3 ( 0.3
1.5 ( 0.5
4.5 ( 2.5
7.8 ( 1.2
8.1 ( 0.5
14 ( 4.0
aeff = dSi-pore - dparticle. b Equation 4 with D experimentally determined by DLS and a = aeff.
be excluded, because DLS measurements were carried out at similar particle concentrations, i.e., σ(10 nM). Active Particle Trapping and Ejection. In contrast to the Brownian motion driven escape discussed so far, Figure 5 demonstrates how particles can be actively retained inside—or ejected from—the cavity by the application of external bias potentials. Forward potentials of 2.5mV are high enough to prolong the residence time of single 74nm particles in the cavity five times from 2.5mV τh0mV escape = 8.1 s to τhescape = 37.1 s (Figure 5a). With the microfluidic setup used in this work, higher forward potentials led to the loading of the cavity with additional particles; by improving the setup so that the solution above the upper reservoir can be exchanged rapidly after a single particle has been captured, it will be possible to apply higher forward potentials during trapping and hence to store single particles much longer. The opposite effect, that is the bias triggered ejection of particles from the cavity, is shown in panels b-d of Figure 5. Here, more than a hundred 74 nm particles were loaded into the cavity by applying a forward bias (Figure 5b); subsequently, reverse potentials ranging from -20 to -180 mV were applied while the diminishing fill-state was monitored over time (Figure 5c). Notably, the particle concentration inside the cavity, Ccav, increases linearly with time during the injection phase but decreases exponentially during the ejection phase. This results from the fact that during injection particles are transported from an inexhaustible outside reservoir of constant particle
concentration into the cavity Cres ¼ constant
dCcav =dt ¼ kin Cres sf Ccav kin t while during ejection the particle transport per time decreases with the continuously decreasing particle concentration inside the cavity Ccav ¼ Ccav ðtÞ
dCcav =dt ¼ - kout Ccav sf Ccav expð - kout tÞ
Given that the particles are transported by electrophoresis, the applied voltage U must appear as a scaling factor in the effective injection and ejection rates, k U. In fact we find a linear relationship between the ejection rate (kout = 1/τhescape) and the applied voltage, as shown in Figure 5d, corroborating the notion of electrophoretic transport. DNA Trapping. The successful trapping of biological macromolecules with the PCP device is demonstrated for single λDNA molecules in Figure 6. In contrast to the particle trapping procedure applied above, where one nanopore was chosen small enough to act as an impenetrable barrier for the particle, a different trapping procedure was devised because λ-DNA is a flexible biopolymer that can, when electrically facilitated, thread through even the smallest pores produced here. After λ-DNA was added to the top reservoir (above the Si pore), the application of a forward potential of 100 mV (cf. Figure 6a) led to the translocation of individual λ-DNA through the PCP device. 1564
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Figure 6. Trapping of single λ-DNA molecules. (a) Potential sequence: DNA molecules are electrophoretically translocated (top to bottom in schematic inset) through the PCP device at þ100 mV; after passing through the SiN pore, individual molecules are recaptured into the cavity by applying a -30 mV reverse potential pulse. (b) Exemplary current trace: The current spike at t = 162ms indicates the translocation of a DNA molecule through the SiN pore and is used as a trigger to reverse the potential. (c) Fluorescence microscopy images of a single PicoGreen labeled λ-DNA molecule in the cavity which escaped through the large Si pore (d = 700 nm) after 6 s.
Figure 5. Single particle trapping and multiple particle injection and ejection. (a) Population probability of a single particle in a Vcav = 8.4 μm3 cavity, in the unbiased “passive” state (blue) and when a trapping potential of 2.5 mV is applied (red). (b) Roughly 130 particles (d = 74 nm) are injected into a Vcav = 8.4 μm3 cavity at a forward bias of 120 mV (green) and subsequently ejected at -120 mV (blue). (c) Ejection of multiple particles at different ejection potentials (black squares, -120 mV; red triangles, -40 mV; green circles, -80 mV; blue diamonds, -160 mV). Solid lines are single exponential fits yielding the ejection rates kout = 1/τhescape which are plotted as a function of the applied ejection potential in panel d; the red line is a linear fit to the data.
When a molecule passed the SiN-pore (d = 30 nm), a current spike was detected in the measured ionic trans-PCP current (t = 162 ms in Figure 6b), which was used as a trigger to apply a -30 mV reverse potential pulse for 5 ms before setting the voltage to zero (cf. Figure 6a). Due to the reverse voltage pulse, molecules which had just exited through the SiN-pore were sucked back into the cavity. The fluorescently labeled DNA was then observed within the cavity until it escaped through the large Si-pore (d = 700 nm) within typically ∼10 s (Figure 6c). This work demonstrates that the PCP device is well suited to controllably trap and investigate nano-objects on the single particle/molecule level. The device dimensions are scalable in a straightforward way so that pores with diameters
