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Moving-Wall-Driven Flows in Nanofluidic Systems Roger Karlsson,†,# Mattias Karlsson,‡,# Anders Karlsson,†,# Ann-Sofie Cans,† Johan Bergenholtz,† Bjo¨rn Åkerman,‡ Andrew G. Ewing,§ Marina Voinova,| and Owe Orwar*,‡,⊥ Department of Physical Chemistry, and Microtechnology Centre at Chalmers, Chalmers University of Technology, SE-41296 Go¨ teborg, Sweden, Department of Chemistry, Go¨ teborg University, SE-41296 Go¨ teborg, Sweden, Department of Chemistry, Pennsylvania State University, State College, Pennsylvania 16802, and Department of Applied Physics, Go¨ teborg University, SE-41296 Go¨ teborg, Sweden Received January 15, 2002. In Final Form: March 21, 2002 We describe fluidic control in lipid nanotubes 50-150 nm in radius, conjugated with surface-immobilized unilamellar lipid bilayer vesicles (∼5-25 µm in diameter). Transport in nanotubes was induced by continuously increasing the surface tension of one of the conjugated vesicles, for example, by ellipsoidal shape deformation using a pair of carbon microfibers controlled by micromanipulators as tweezers. The shape deformation resulted in a flow of membrane lipids toward the vesicle with the higher membrane tension; this lipid flow in turn moved the liquid column inside the nanotube through viscous coupling. Thus, micrometer-sized vesicles are used as a handle for controlling fluid flow inside nanometer-sized channels. We show transport and trapping of a single 30-nm-diameter carboxylate-modified latex particle inside a ∼100-nm-radius nanotube. Fluidic control in nanometer-sized channels using a moving wall provides pluglike liquid flows, offers a means for efficient routing and trapping of small molecules, polymers, and colloids, and offers new opportunities to study chemistry in confined spaces. Networks of nanotubes and vesicles might serve as a platform to build nanofluidic devices operating with single molecules and nanoparticles.
Introduction Control of fluid delivery inside small-dimension channels is of paramount importance in microfluidic devices. Such devices are emerging as important tools with applications in, for example, chip-based chemical analysis,1 drug screening,2 computations,3 and chemical kinetics.4 In these systems, materials dissolved or dispersed in a fluid matrix are directed to specific compartments where a given chemical or physical operation is made on the contents. Techniques used for fluid delivery in micrometersized channels include electroosmotic flow,5 electrochemistry,6 electrowetting,7 electrocapillary pressure,8 mechanical pumping,9 and thermocapillary coupling.10 When using smaller channel dimensions (low nanoscale), it becomes difficult not only to fabricate the channels using traditional micro- and nanofabrication techniques but also * To whom correspondence should be addressed. E-mail: orwar@ amc.chalmers.se. † Department of Chemistry, Go ¨ teborg University. ‡ Department of Physical Chemistry, Chalmers University of Technology. § Department of Chemistry, Pennsylvania State University. | Department of Applied Physics, Go ¨ teborg University. ⊥ Microtechnology Centre at Chalmers, Chalmers University of Technology. # These three authors contributed equally to this publication. (1) Culbertson, C. T.; Jacobson, S. C.; Ramsey, J. M. Anal. Chem. 2000, 72, 5814. (2) Dove, A. Nat. Biotechnol. 1999, 17, 859. (3) Chiu, D. T.; Pezzoli, E.; Wu, H.; Stroock, A. D.; Whitesides, G. M. Proc. Natl. Acad. Sci. U.S.A. 2001, 98, 2961. (4) Service, R. F. Science 1994, 265, 316. (5) Jorgenson, J. W.; Lukacs, K. D. Anal. Chem. 1981, 53, 1298. (6) Gallardo, B. S.; Gupta, V. K.; Eagerton, F. D.; Jong, L. I.; Craig, V. S.; Shah, R. R.; Abbott, N. L. Science 1999, 283, 57. (7) Beni, G.; Tenan, M. A. J. Appl. Phys. 1981, 52, 6011. (8) Prins, M. W.; Welters, W. J. J.; Weekamp, J. W. Science 2001, 291, 277. (9) Unger, M. A.; Chou, H. P.; Thorsen, T.; Scherer, A.; Quake, S. R. Science 2000, 288, 113. (10) Burns, M. A., et al. Proc. Natl. Acad. Sci. U.S.A. 1996, 93, 5556.
to handle and manipulate the flow of fluid inside the channels. For these decreasing scales, where channel dimensions are approaching the size of a single large protein, fluidic devices capable of handling single molecules might be realized. To achieve this, new materials, new principles of fluid delivery, and new fabrication techniques might be necessary to develop. Inspiration to build such nanofluidic devices may come from biology where fluidic systems of extremely small physical dimension are controlling the localization and fate of single molecules. Some transport between major organelle systems such as the endoplasmic reticulum (ER) and Golgi is stipulated to occur through flow of twodimensional membrane fluid over nanotube-connected compartments.11,12 Theoretical studies have supported the feasibility of such transport by showing that tension differences in connected membranes can pull lipids to the point of highest membrane tension.13 We here present control of fluid transport in biomimetic lipid bilayer systems that are composed of micrometersized containers connected by lipid nanochannels having a radius of 50-150 nm. These systems can be viewed as simplistic single-tube analogues to the ER-Golgi networks mentioned above. By control of the membrane tension difference between interconnected vesicle containers, fast and reversible membrane flow (moving walls) with coupled liquid flow in the connecting lipid nanotubes was achieved. We suggest that these systems might serve as a platform for building a new type of nanofluidic device, capable of controlling flows of extremely small volumes of fluid and even transport of single molecules. (11) Sciaky, N.; Presley, J.; Smith, C.; Zaal, K. J.; Cole, N.; Moreira, J. E.; Terasaki, M.; Siggia, E.; Lippincott-Schwartz, J. J. Cell Biol. 1997, 139, 1137. (12) Lippincott-Schwartz, J.; Yuan, L. C.; Bonifacio, J. S.; Klausner, R. D. Cell 1989, 56, 801. (13) Chizmadzhev, Y. A.; Kumenko, D. A.; Kuzmin, P. I.; Chernomordik, L. V.; Zimmerberg, J.; Cohen, F. S. Biophys. J. 1999, 76, 2951.
10.1021/la025533v CCC: $22.00 © 2002 American Chemical Society Published on Web 05/03/2002
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Materials and Methods Vesicle Preparations. Vesicles were prepared from soybean lecithin (SBL), dissolved in chloroform, typically 100 mg/mL, as a stock solution. The SBL lipids used consisted of a mixture of phosphatidylcholine (45.7%), phosphatidylethanolamine (22.1%), phosphatidylinositol (18.4%), phosphatidic acid (6.9%), and others (6.9%) (Polar lipid extract composition from Avanti Polar Lipids, Inc.). To make unilamellar vesicles, a dehydration/rehydration technique described by Criado and Keller14 was used with modifications.15 Briefly, 5 µL of a lipid dispersion (1 mg/mL buffer) was placed on a cover slip glass, and the solution was then dehydrated in a vacuum desiccator. When the lipid film was completely dry, it was carefully rehydrated with buffer (Trizma base 5 mM, K3PO4 30 mM, KH2PO4 30 mM, MgSO4 1 mM, EDTA 0.5 mM, pH 7.8) to swell the lipid film. After a few minutes, giant unilamellar vesicles were formed.15 Formation of Nanotube-Conjugated Vesicles. A carbon fiber microelectrode (5 µm diameter, Dagan Corp., Minneapolis, MN) and a tapered micropipet, controlled by high-graduation micromanipulators (Narishige MWH-3, Tokyo; coarse manipulator: Narishige MC-35A, Tokyo), were used to create the unilamellar nanotube-interconnected vesicles, using a microelectroinjection technique.16 Briefly, the unilamellar vesicle was penetrated by the micropipet through a combination of a mechanical force and an electric field. After the membrane had resealed around the micropipet, a nanotube was created by pulling the micropipet away from the vesicle. By injecting buffer into the nanotube, a new vesicle was created at the tip of the micropipet. This vesicle was then placed at the surface at a target site near the original vesicle. The tapered injection micropipets were made from borosilicate capillaries (GC100TF-10, Clark Electromedical Instruments, Reading, U.K.) that were pulled on a CO2 laser puller instrument (model P-2000, Sutter Instrument Co., Novato, CA). A microinjection system (Eppendorf Transjector 5246, Hamburg, Germany) and a pulse generator (Digitimer Stimulator DS9A, Welwyn Garden City, U.K.) were used to control the electroinjections. Nanotube diameters were estimated by inflating daughter vesicles with buffer solution using an electroinjection technique15 and simultaneously measuring the lipid transport velocity in the nanotube. From the increase in membrane area per second in the inflated vesicle, which equals πdtvl, that is, the circumference of the tube times the lipid velocity, it was estimated that the nanotubes had a diameter of 100-300 nm. For the transport experiments, only one of the two vesicles contained transport markers (30-nm-diameter latex particles or small liposomes) that were introduced either during formation of the system16 or after the system was formed using electroinjection.15 Microscopy, Fluorescence, and Bright-Field Imaging. Rectangular cover slip glasses (no. 1) with vesicle suspension were placed directly on the microscope stage of an inverted microscope (Leica DM IRB, Wetzlar, Germany) equipped with a Leica PL Fluotar 40× and PL APO 100× objective. The 488 nm line of an Ar+ laser (2025-05, Spectra-Physics Lasers Inc., Mountain View, CA) was used in the fluorescence experiments. To break the coherence and scatter the laser light, a transparent spinning disk was placed in the light path. The light was sent through a polychroic mirror (Leica) and an objective to excite the fluorophores. The same objective collected the fluorescence, and a VIM camera system (VIM C2400-41H, Hamamatsu Photonics K.K., Japan) controlled by an Argus-20 image processor (Hamamatsu Photonics Norden AB, Solna, Sweden) was used to capture the images. Recordings were made in a 16-frame averaging mode using a Super VHS (Panasonic S-VHS AG-5700, Stockholm, Sweden, 25 Hz frame collection rate). Bright-field images were captured by a CCD camera (Hamamatsu Photonics Norden AB), and the Argus-20 image processor was used as a real-time image enhancer. Chemicals and Materials. Trizma base and potassium phosphate were from Sigma-Aldrich Sweden AB. Soybean lecithin (14) Criado, M.; Keller, B. U. FEBS Lett. 1987, 224, 172. (15) Karlsson, M.; Nolkrantz, K.; Davidson, M. J.; Stromberg, A.; Ryttsen, F.; Akerman, B.; Orwar, O. Anal. Chem. 2000, 72, 5857. (16) Karlsson, M.; Sott, K.; Cans, A.-S.; Karlsson, A.; Karlsson, R.; Orwar, O. Langmuir 2001, 17, 6754.
Figure 1. Schematic showing two surface-immobilized unilamellar vesicles, with radius Ra and Rb, connected by a nanotube of radius rt and length Lt. The size of the vesicles was typically 5-25 µm in diameter, and the diameter of the nanotube was in the range of 100-300 nm. (a) Axial view and sideview (inset), where the surface tension σ in both vesicles is the same and no net lipid flow occurs. (b) Lipid flow induced through a continuous ellipsoidal deformation of a vesicle (axial view). By applying a force, F, using two carbon fibers, the surface-to-volume ratio increases and the membrane in the deformed vesicle is stretched, resulting in an increased surface tension. To eliminate this tension gradient, lipid flows from regions of lower tension, σa, to regions of higher tension, σb, with velocity vl. Since the fluid and the particles are dragged along the lipid flow, the lipid velocity in practice sets an upper limit for the velocity of the particles, vp, and the fluid, va. Zero or small pressure differences result in flat (pluglike) flow profiles. (polar lipid extract) was from Avanti Polar Lipids, Inc. (Alabaster, AL). Chloroform, EDTA (titriplex III), magnesium sulfate, potassium dihydrogen phosphate, potassium chloride, sodium chloride, and magnesium chloride were from Merck (Darmstadt, Germany). Glycerol was from J. T. Baker, and deionized water from a Milli-Q system (Millipore Corp., Bedford, MA) was used. Green-fluorescent carboxylate-modified latex beads (30 nm in diameter) were from Molecular Probes (Leiden, The Netherlands).
Results and Discussion Surface-Tension-Controlled Lipid Flow in Nanotubes. We have previously described a micromanipulation method to produce networks of unilamellar nanotubes and containers.16 This technique enables the construction of complex networks that have controlled connectivity and are well-defined with regard to container-size, angle between nanotube extensions, and nanotube length. By selection of the solution contained in the micropipet, the internal fluid composition of individual vesicles can be set during formation of the network. To demonstrate the concept of transport in these networks, a simple system was used, as schematically shown in Figure 1. The geometry of the experimental system can be described as two surface-immobilized vesicles with near-spherical geometry of equatorial plane radius Ra and Rb (Ra ∼ Rb), conjugated by a cylindrical tube of radius rt and length Lt. It is important to realize (i) that the nanofluidic systems we are considering are in a fluid state consisting of a single, continuous lipid membrane bilayer, that is, they are spheres from a topological point of view, and (ii) that the
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terminal vesicles in these systems are anchored to the surface. In Figure 1a, the system is unperturbed and the surface free energy in the two nanotube-interconnected containers is the same. Therefore, there is no lipid flow between the containers in this instance, other than diffusion-driven movement. Figure 1b illustrates how lipid flow can be driven by a difference in membrane tension across a nanotube by increasing the surface-to-volume ratio using ellipsoidal deformation of one of the vesicles. The rapid membrane dynamics is well below the time resolution of our experimental setup;17 however, at these short time scales the deformations made in our experiments are continuous over time and will therefore maintain a tension difference, ∆σ, across the nanotube. This is reflected in a continuous flow of lipids from a source (vesicle at lower membrane tension) to a drain (vesicle at higher membrane tension). The flow of the lipid membrane can be represented by a lateral translation of the cylindrical wall structure with velocity vl, which can be measured. This velocity depends on the balance of the tension forces work per unit time and viscous dissipation due to the shear deformation of the lipid flow: vl ∝ ∆σ/2η, where η is a coefficient of the viscous resistance of the system. The viscous resistance in a nanotube-vesicle system18 is much higher compared to the surface viscosity measured in solitary vesicles.19 This higher resistance to lipid flow from the spherical vesicle surface to the nanotube region might come from the fact that the curvature of the lipid membrane is increased by 1000-fold in the junction between the nanotube and the vesicle. Besides giving rise to a geometrical funnel-like junction, the change in curvature also leads to a difference in the velocity of the two leaflets of the bilayer. An interlayer frictional drag can therefore contribute to the viscous resistance of the vesicle-nanotube system.18 Intratubular Liquid Flow Created by a Moving Lipid Wall. The fluid contained in the nanotube is dragged along with the lipid membrane flow due to the fluid’s viscosity. Molecules or particles contained in the fluid are therefore transported through the tube toward the deformed vesicle. The undisturbed fluid velocity, va, assumes the following profile:
va ) vl - v0(1 - (r/rt)2)
(1)
vl - v0 ) vl - (∆p/Lt)(rt2/4ηw)
(2)
where
is the fluid velocity on the centerline of the cylinder, vl is the lipid velocity, v0 is the backflow arising from a difference in hydrostatic pressure, r is the radial distance from the centerline, rt is the tube radius, Lt is the tube length, ηw is the viscosity of water, and ∆p is the pressure difference between the cylinder exit and entrance. For uniaxial liquid flow in a cylinder of uniform cross-sectional area, inertia forces vanish. As the system responds to the deformation by changing the surface area at constant volume, there will not be any substantial pressure buildup across the nanotube. The dominant driving force for moving fluid inside the nanotube will therefore be the moving lipid wall. Even for small pressure differences, created by any relative motion between the boundary and internal fluid, this situation corresponds to a “solid body”, lateral translation of the (17) Evans, E.; Needham, D. J. Phys. Chem. 1987, 91, 4219. (18) Evans, E.; Yeung, A. Chem. Phys. Lipids 1994, 73, 39. (19) Waugh, R. E. Biophys. J. 1982, 38, 19.
Figure 2. (Left) Time series of micrographs showing forward and reverse transport and trapping of a small liposome inside a nanotube. (Right) Corresponding graphs showing the coordinate along the tube axis versus time. As the vesicle to the right is deformed (shown by the arrows at the carbon fibers), a membrane tension difference is established inducing lipid flow and liposome movement toward the mechanically deformed vesicle (a-c). When translation of the microfibers is stopped, the system rapidly equilibrates resulting in a trapping of the liposome inside the nanotube (d, e). As the vesicle is further deformed, the liposome again moves toward the deformed vesicle (f, g). When the carbon fibers are pulled away from the vesicle, it regains its spherical shape resulting in a reversal of the lipid flow and transport of the liposome in the opposite direction (h-j).
cylinder with the entrapped fluid. This results in extremely flat flow profiles that are essentially pluglike (Figure 1b). Another factor that might affect the hydrostatic pressure in the system is the amount of fluid that is cotransported with the lipid flow during transport. From pure geometrical considerations, it can be seen that the net volume of fluid transported across the nanotube is extremely small compared to the relative amount of membrane material that drives the flow. Transport of Particles in Lipid Nanotubes. In Figure 2, transport of a ∼400-nm-radius liposome by lipid flow and coupled intratubular fluid flow between conju-
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gated vesicles is demonstrated. The shape deformation of one vesicle in the system was created by using two highgraduation micromanipulator-controlled 30-µm-long, 5-µmdiameter carbon fibers as mechanical tweezers. By simply compressing one of the vesicles in the system with the carbon fibers, membrane tension was locally increased and transport was initiated. It can easily be calculated that very small perturbations in the surface area to volume ratio are sufficient to result in membrane flow across nanotubes. We considered two 10-µm-diameter spherical vesicles, connected by a 200nm-diameter perfectly cylindrical nanotube. To move a particle a length of 30 µm in the tube, an area displacement of 19 µm2 is required (corresponding to the surface area of the 30-µm-long tube segment). This means that the vesicle surface area has to increase by 4.7%. To be able to assimilate this increase in area and at the same time maintain a constant volume, the degree of ellipsoidal (oblate) deformation has to be a ) 5.2 µm and b ) 4.7 µm (with an ellipsoidal eccentricity (a2 - b2)1/2/a ) 0.43). Of course, this applies only if the starting vesicle is perfectly spherical. In our case, the vesicles were attached to a surface, thereby making them somewhat hemispherical. Since the adhesion contributes with energy to the system, the extent of adhesion introduces limits to the degree of deformation of the vesicle. A too high surface adhesion will lead to unstable systems and possibly to membrane rupture.20 The rate of transport was controlled by the rate and extent of shape deformation applied and was usually in the range of 20-30 µm/s, although velocities up to ∼60 µm/s were sometimes achieved. The duration of perturbation we used (subsecond) was fast enough to assume that the vesicle maintains a constant inner volume. Very slow changes, however, would give the vesicle a chance to relax by allowing water to pass through the membrane, thereby reducing the inner volume.19,21 Figure 2 shows that this transport is reversible. Removal of the induced tension drove the flow in the opposite direction as the system relaxed. If the applied tension instead was locked after an initial perturbation by stopping the translation of carbon fibers, the system rapidly equilibrated and a particle could be trapped and held at a given coordinate inside the nanotube with very little lateral displacement. The particle transported in this experiment had a diameter larger than the nanotube. During transport of such a particle, the nanotube was deformed into a bulbous structure to accommodate the particle, which moved with the lipid flow. After transport in a nanotube, it was possible to inject a particle into any of the two connecting vesicles (not shown). Single-Particle Diffusion and Trapping in Lipid Nanotubes. To demonstrate transport of nanoparticles smaller than the nanotube radius, we used 30-nmdiameter green-fluorescent carboxylate-modified latex particles as transport markers. Since these particles have a negative surface potential, as does the SBL nanotube membrane, we do not expect any significant adsorption of particles to the nanotube walls. Figure 3a shows a schematic drawing of the system. Transport and trapping were controlled by ellipsoidal deformation of the vesicle to the left using carbon microfibers as described above. Figure 3b shows unidirectional transport of a single nanoparticle inside a ∼200-nm-diameter nanotube connected to two vesicles. The particle moved at a near(20) Sandre, O.; Moreaux, L.; Brochard-Wyart, F. Proc. Natl. Acad. Sci. U.S.A. 1999, 96, 10591. (21) Olbrich, K.; Rawicz, W.; Needham, D.; Evans, E. Biophys. J. 2000, 79, 321.
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Figure 3. Single-particle trapping and transport. (a) Schematic drawing of the system with a box around the nanotube and the nanotube-vesicle junction areas. The boxed area represents the full view of the time-lapse videomicrographs (b-d). (a) also shows the false color coding used to identify, at different time points, a single particle inside the tube in (b-d). (b) Unidirectional transport of a single particle induced by a membrane tension gradient caused by an ellipsoidal deformation of the vesicle to the left. (c) Stochastic motion of a single particle inside a tube. (d) Trapping of a single particle by balancing the stochastic motion through adjustment of the membrane tension. The scalebar in (d) represents 1 µm and is the same for (b) and (c). (e, f) 3-D false-colored fluorescence intensity plots of a single particle trapped in a nanotube and two single particles and a cluster immobilized on a cover slip, respectively. In (b-d), images were sampled over sixteen 40-ms frames at each time point using a VIM camera. The images were then false-colorcoded and overlayed to create the resulting time-lapse images. Images in (e) and (f) were sampled over sixteen 40-ms frames and then false-color-coded. Latex beads were introduced into vesicles using the electroinjection technique (ref 15). Experimental conditions were otherwise the same as in Figure 2.
constant rate, and its position is shown at five different time points which are indicated by false color coding according to the key in Figure 3a. The image was captured in a 16-frame-averaging mode, thereby giving rise to several fluorescence spots in a single time frame. In the unperturbed system, single nanoparticles exhibited stochastic motion inside a nanotube. This movement is due to Brownian motion and possibly random membrane tension differences elicited by convection in the external medium or vesicle-surface adsorption/ desorption processes. The stochastic motion of a 30-nmdiameter particle inside a 100-nm-radius nanotube is largely one-dimensional. The theoretical diffusion coefficient22 for a 30-nm-diameter particle at 298 K in a 100(22) Brenner, H.; Gados, L. J. Colloid Interface Sci. 1977, 58, 312.
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nm-radius tube is 9.05 µm2 s-1, and the corresponding root-mean-square displacement of such a particle during a 2.56-s time interval is 6.81 µm. Figure 3c shows how a particle spontaneously occupied a ∼6-µm-long segment of a 12.5-µm-long nanotube in a random fashion during a 2.56-s observation time (sampled at five different time points), which is in good agreement with the theoretical value. We were also able to trap single free-floating particles inside a nanotube. This was achieved by rapidly counteracting any positive or negative particle movement along the tube long axis from an arbitrary starting coordinate by adjusting the membrane tension in small increments or decrements using micromanipulator-controlled carbon microfibers. Figure 3d shows an image of single-particle trapping which maps the position of a particle at five discrete time points over a total observation time of 2.56 s. During the majority of this time, the particle could be trapped within a 1-µm-long tube segment, thus residing in a volume element of only ∼300 aL (0.3 × 10-15 L). We compared the fluorescence intensity of a single particle immobilized on a microscope cover slip (Figure 3e) with that of a particle resident inside a nanotube (Figure 3f) to ascertain that we transported single particles rather than clusters. Conclusion We describe novel wall-driven fluid transport in cylindrical lipid channels ∼50-150 nm in radius. These types of lipid channels can be made with a radius down to ∼10 nm.23 In combination with the possibility to create complex networks of nanotubes and containers,16,24 interesting possibilities emerge to develop nanofluidic systems that (23) Waugh, R. E.; Song, J.; Svetina, S.; Zeks, B. Biophys. J. 1992, 61, 974. (24) Karlsson, A.; Karlsson, R.; Karlsson, M.; Cans, A.-S.; Stromberg, A.; Ryttsen, F.; Orwar, O. Nature 2001, 409, 150.
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can work with single molecules, a capability that is unique to biological systems. Several applications utilizing controlled transport in nanotube networks can be envisioned. For example, such networks could allow the construction of microscopic models of biological Hopfield type neural networks,25 optimized architectures for DNA-based chemical computations,26 and miniature chemical laboratories for synthesis and analysis. In such applications, the interior contents of the containers within a network can be differentiated to provide a unique reaction environment for a transported molecule or particle.16,24 Also, in simple systems, the transport described here could be used for trapping and manipulation of individual molecular species inside the extremely small confines of a nanotube to examine, for example, single-molecule reaction dynamics,27 single-file diffusion,28 and chemical and physical processes in confined systems.29,30 Acknowledgment. R. N. Zare, D.T. Chiu, C. Wilson, R. Kjellander, and D. Biddle gave helpful comments on the manuscript. This work was supported by the Swedish Natural Science Research Council (NFR), the Swedish Foundation for Strategic Research (SSF), and the Royal Swedish Academy of Sciences through a donation by the Wallenberg foundation. LA025533V (25) Hjelmfelt, A.; Weinberger, E. D.; Ross, J. Proc. Natl. Acad. Sci. U.S.A. 1991, 88, 10983. (26) Kurtz, A.; Mahaney, S. R.; Royer, J. S.; Simon, J. DNA Based Computers II: DIMACS Workshop June 10-12, 1996; DIMACS Series in Discrete Mathematics and Theoretical Computer Science Vol. 44; American Mathematical Society: Providence, RI, 1999; p 171. (27) Nie, S.; Zare, R. N. Annu. Rev. Biophys. Biomol. Struct. 1997, 26, 567. (28) Wei, Q.-H.; Bechinger, C.; Leiderer, P. Science 2000, 287, 625. (29) Heuberger, M.; Za¨ch, M.; Spencer, N. D. Science 2001, 292, 905. (30) Chiu, D. T.; Wilson, C. F.; Karlsson, A.; Danielsson, A.; Lundqvist, A.; Stro¨mberg, A.; Ryttse´n, F.; Davidson, M.; Nordholm, S.; Orwar, O.; Zare, R. N. Chem. Phys. 1999, 247, 133.
