Diffusive Transport of Molecular Cargo Tethered to a DNA Origami

Mar 5, 2015 - For distances on the scale of the origami platform itself, however, cargo transfer mediated .... Current Opinion in Biotechnology 2017 4...
0 downloads 0 Views 4MB Size
Download PDF
Letter pubs.acs.org/NanoLett

Diffusive Transport of Molecular Cargo Tethered to a DNA Origami Platform Enzo Kopperger, Tobias Pirzer, and Friedrich C. Simmel* Lehrstuhl für SystembiophysikE14, Physik Department and ZNN/WSI, Technische Universität München, Garching 85748, Germany S Supporting Information *

ABSTRACT: Fast and efficient transport of molecular cargoes along tracks or on supramolecular platforms is an important prerequisite for the development of future nanorobotic systems and assembly lines. Here, we study the diffusive transport of DNA cargo strands bound to a supramolecular DNA origami structure via an extended tether arm. For short distances (on the order of a few nanometers), transport from a start to a target site is found to be less efficient than for direct transfer without tether. For distances on the scale of the origami platform itself, however, cargo transfer mediated by a rigid tether arm occurs very fast and robust, whereas a more flexible, hinged tether is found to be considerably less efficient. Our results suggest diffusive motion on a molecular tether as a highly efficient mechanism for fast transfer of cargoes over long distances. KEYWORDS: DNA nanotechnology, molecular transport, diffusion, nanomachines, nanorobotics

B

only made a few steps on short, linear DNA scaffolds,16−21 recently molecular walking was demonstrated over 10−100 nm length scales using tracks made from DNA origami structures.12,13,22−24 Moreover, DNA-based transporter systems were utilized to support nanoassembly tasks. For instance, Seeman and co-workers demonstrated the first working molecular assembly line made from DNA, in which a molecular walker programmably collected nanoparticles from a series of loading stations to form small nanoparticle assemblies.11 In a similar spirit, Liu and co-workers demonstrated a system which combined molecular walking with DNA-templated synthesis.25 For some applications it is desirable to precisely control the motion of molecules along well-defined paths. This can be accomplished by tightly binding molecular transporters (or “walkers”) to tracks with finely spaced binding sites with spacing xstep. This, however, inevitably results in relatively slow motion, as the velocity v of the molecular transporters is given by v = xstep/τ, where τ is the typical time it takes for a single step. Depending on the mechanism, τ = (kon + koff)−1 will be approximately determined by the time scale of binding to the track or unbinding from it. Correspondingly, previous realizations of DNA based walkers, typically involving slow hybridization or cleavage reactions and nanometer step lengths, have shown only comparatively moderate velocities. For instance, hybridization-based walkers displayed an average velocity of ≈0.01 nm s−1,19 whereas walkers based on deoxyribozymes12 or nicking enzyme action13 moved with ≈0.05 nm s−1 and ≈0.1 nm s−1,

iological cells are highly organized chemical systems that utilize various mechanisms to control the localization and transport of molecules. Such control can improve the efficiency of chemical processes and provides the basis of many biological phenomena such as motility, growth, or cell division. Depending on task, length and time scale, passive or active transport mechanisms are employed. Passive mechanisms rely on random thermal motion, which can be utilized by suitably controlling the spatial organization of molecular components. For example, intracellular compartmentalization can help to separate competing reaction pathways from each other, suppress leak reactions, or enhance local concentrations of compounds. Co-localization of reactants on scaffold structures is presumed to play a similar role.1 Also the control of dimensionality can be used to alter the dynamics of molecular processes, as the properties of diffusion processes differ in one, two, three, or even fractal dimensions.2,3 In cases where diffusive transport is not effective enough, in biology molecules are transported over a longer range using active processes. For instance, dedicated molecular machines and motors such as kinesin or myosin actively carry molecules along long cytoskeletal filaments, consuming chemical energy to achieve directed motion and to actively create forces. Nanotechnologists seek to imitate biology in order to realize artificial chemical systems with similar power and capabilities as living cells. In this spirit, initial efforts have been made to realize artificial molecular motors and transporters, and even to combine them into molecular robotic systems and assembly lines. In particular, using the powerful methodology of DNA nanotechnology,4−9 various components of nanoscale robotic systems have been already established.10−15 Following the development of a series of prototypic molecular walkers that © XXXX American Chemical Society

Received: January 28, 2015 Revised: March 3, 2015

A

DOI: 10.1021/acs.nanolett.5b00351 Nano Lett. XXXX, XXX, XXX−XXX

Letter

Nano Letters

Figure 1. (A) Schematic side view of a DNA origami platform with a rigid tether fixed in the center. The cargo (domains b, c, d, e, f) can hybridize to sequence domains at the start (e*, f*) and a target (d*, e*) position, as well as to a single stranded extension (b*, c*) of the rigid tether. The inset shows an alternative binding orientation, which results in a more flexible, “hinged” structure. Complementary sequences are indicated by matching colors as well. All sequence domains have a length of 8 nt except for a/a*(88 nt) and z/z*(21 nt). (B) Typical AFM image of the DNA origami rectangle, on which the start position (blue) and three different target positions are indicated. The position of two dumbbell hairpin loops (light gray) is also shown, which are placed asymmetrically to create height contrast for AFM imaging. (C) Mechanism of cargo transport and fluorescent labeling. The cargo DNA is functionalized with a Black Hole Quencher I molecule. Duplex formation with start or target strand reduces the fluorescence intensity of the Atto 488 dye (blue) and Atto 532 dye (green), respectively. An additional Atto 655 dye (red) used as a marker for gel electrophoresis experiments (cf. Supporting Information Figure S2) is permanently attached to the tether and is not affected by quenching. Upon addition of starter strand (domains g, f, e), the beam and cargo are released from the start site, unquenching the blue dye. Upon binding to the target site, the green dye is quenched.

molecular tether attached to a flexible hinge in the center of the rectangle (Figure 1). The tip of the arm can be fixed to an initial position or one of several target positions on the platform, and thus facilitate local transport of molecular cargoes attached to the arm. The role of the tether is to prevent diffusive loss of the cargo, whereas transport itself is driven by thermal motion. In a typical experiment, the tether is released from its initial position by the addition of a trigger oligonucleotide. The tether then diffusively searches for an alternative binding position on the platform and, finally, attaches to the desired target site. Our kinetic studies indicate that this mechanism provides fast transport over distances of up to 52 nm with ef fective velocities of at least several nanometers per second and, thus, is much faster than transport with DNA walkers. For very short distances between start and end positions, we find effective transport also in the absence of a tether. This can be explained with a direct physical overlap between the sites, which allows a direct “handing over” of the cargo, which effectively never detaches from the platform.28 We also find differences in transport efficiency between a rigid, beam-like tether and a more flexible transport arm with two hinges. The general phenomenology observed in the experiments can be rationalized using reaction-diffusion modeling accompanied by Monte Carlo simulations of random walkers restricted to a spherical volume. Assembly and Operation of the System. Assembly of the molecular platform and tether arm is performed in several annealing and purification steps.29 First, an origami platform is formed which contains staple extensions that define start and target positions of the tip of the tether and its central pivot. Then a DNA construct composed of a double-stranded tether arm (with a length of 88 base pairs) and a cargo strand is

respectively. The longest trajectories recorded so far were on the order of ≈100 nm, essentially determined by the length of the origami-based tracks. By contrast, biological motors are much faster (on the order of ≈10 nm s−1), and often processively walk over tracks with a length of several micrometers.26 In this context, it is interesting to note that biological linear molecular motors are only found in the eukaryotes. In fact, in prokaryotes, diffusion is already an extremely effective transport mechanism on the scale of the cells (which is ≈1 μm). The time required for a molecule to diffuse over a distance L is given by its diffusion time tD ≈ L2/D, which is on the order of just 1− 100 ms for L = 1 μm and typical diffusion coefficients D in the range 10−1000 μm2/s. L2/D also corresponds to the “mixing time” tmix,27 which is defined as the time it takes for the molecule to be found at any location of a compartment of linear size L with equal probability. We may further relate tD to an effective diffusive transport “velocity” vD = L/tD = D/L, which obviously is several orders of magnitude larger than that of current DNA-based walkers. Thus, if a precise control of the path of a molecule to be transported from a starting position to a target position is not required, diffusive transport is the preferable transport mechanism for short distances within a small volume. If the process of interest takes place in a large volume, however, the diffusing molecules can get lost and never reach their target. Based on these considerations, we here explore a simple strategy to achieve effective transport of molecules on an intermediate, 10−100 nm length scale, which utilizes localization and restricted diffusive transport on a DNA-based supramolecular platform. Using the scaffolded DNA origami technique,4 we created a rectangular platform with dimensions 90 nm × 60 nm, which was equipped with a 30 nm long B

DOI: 10.1021/acs.nanolett.5b00351 Nano Lett. XXXX, XXX, XXX−XXX

Letter

Nano Letters

of the system the blue start dye is quenched, whereas the green target dye is bright. In the course of the cargo transfer reaction, the blue dye is unquenched, whereas the fluorescence of the green dye is reduced. In the following, we utilized the fraction Q′ of quenched target fluorophores as a proxy for reaction progress (i.e., cargo transfer). In order to obtain Q′, raw fluorescence data was processed to account for the spectral overlap of the dyes, different quenching efficiencies, and also interorigami crosstalk (cf. Supporting Information section “Fluorescence Spectroscopy”, Figure S3 to S5). These processed data typically varied in the range from 0 to ≈0.35, which corresponds to the maximum fraction ξ of correctly assembled platforms. Thus, we can identify Q′ = ξQ, where Q ∈ [0, 1] is the reaction progress of the f unctional fraction of the platforms. We measured the kinetics of cargo transfer for two different tether geometries - a more flexible tether with two hinges, and a rigid, singly hinged tether (cf. Figure 1) and also in the absence of such a tether. Each configuration was studied for the three start-target site distances d1 = 9 nm, d2 = 31 nm, and d3 = 52 nm (Figure 3). For the 9 nm cases (blue traces), we found a very fast transfer in all three configurations, with the largest signal change occurring in the first 20 s after cargo release. Surprisingly, with Q′ ≈ 33% (i.e., Q ≈ 1) the initial signal change is largest for the freely diffusing cargo strand (Figure 3A). For the two longer distances, tether-free cargo transfer occurs much more slowly and less efficient (Q′ ≈ 5%/Q ≈ 15%) than for all other cases, and presumably mainly involves interorigami transfer, that is, not on the same platform. As can be seen in Figure 3 B, C, tethering considerably improves the cargo transfer for the longer distances. The improvement appears to be more drastic for the rigid than for the more flexible tether. With a transfer fraction of Q′ ≈ 30% (i.e., Q ≈ 90%) the transfer efficiency increases by a factor of ≈6, both for the intermediate and long distances d2 and d3. The kinetics of rigid tether cargo transfer consists of a fast initial phase and a much slower second phase. The largest fraction of the cargo is transferred in the fast phase within the first 20 s, whereas a smaller fraction slowly follows with a half-time of about 500 s (Figure 3). Although the fast phase most probably represents the desired on-platform cargo transfer, the time-scale of the slow phase indicates that it is caused by a slower interorigami strand exchange process. As expected, the kinetics of cargo release from the start position, which can be derived from the Atto 488 fluorescence signal, is independent of the distance (with characteristic halftimes τrelease ≈ 1 s) and also seems not to be affected by tethering (Supporting Information, Figure S5). Competition Experiments. Competition experiments provide an alternative method to determine the efficiency of the cargo transfer process and also to assess its robustness with respect to external disturbances. We therefore also performed kinetics measurements in the presence of the freely floating competitor strands L, which could bind to and block the binding domain of the cargo strands. The rationale behind the experiments is that cargo transfer is expected to be suppressed when the transfer rate becomes much smaller than that for hybridization with a competitor. In Figure 4A, fluorescence traces from a competition assay are shown for the case of rigid tether transport over d3 = 52 nm. As expected, the transfer fraction Q′ decreases with increasing [L], while the kinetics of the initial signal increase appears to sharpen. This sharpening is caused by the disappearance of the “slow phase” of the kinetics

attached to both pivot and start position as indicated in Figure 1A, which defines the starting state of the system. Since the cargo strand necessarily is partly complementary to the start and target strands (sequence domains e and f, and d and e, respectively), a series of protection and deprotection reactions are required to ensure correct assembly (cf. Supporting Information section “Sample Preparation”, Figure S1 and S2). Overall, a fraction of ξ ≈ 30%−35% of all origami platforms finally contain all components required for the operation of the tether system. This relatively low yield is caused by the accumulation of assembly errors at various stages of the fabrication process (Supporting Information section “Sample Preparation”). A high resolution AFM image of an origami platform without tether arm is shown in Figure 1B, where also the pivot, the starting position and the alternative target positions are indicated. The fully assembled tether arm is actuated as depicted in Figure 1C. Addition of a trigger strand displaces the cargo from the start position.30 The tether arm then randomly searches for the target position until it is finally fixed by hybridization between cargo and target sequence. For Figure 2, we directly visualized the rigid tether at the starting position (Figure 2A) and two alternative end positions

Figure 2. AFM images of origami platforms before and after transport. The rigid tether is visible as height contrast in (A) starting position, (B) 31 nm distant end position, and (C) 52 nm distant end position. Dumbbell hairpins are placed onto the platform to create a left/right asymmetry.

(the “intermediate” 31 nm distance position, Figure 2B, and the “remote” 52 nm distance position, Figure 2C) by AFM imaging. For these images, the structures were prepared and operated in solution, and the reaction end points were documented by AFM. The double-stranded DNA beams turned out to be exquisitely sensitive to the AFM imaging process. Using typical imaging parameters, the DNA arms were quickly disrupted or torn out of the origami platform, which prevented observation of the same structure over longer periods of time. Direct in situ imaging of the switching process by AFM on mica, thus, could not be achieved. The images in Figure 2 were obtained using adjusted “gentle” imaging parameters, which reduced their overall quality (compare to Figure 1B). Reaction Kinetics. We studied the kinetics of cargo transfer using fluorescence time course experiments. To this end, the start and target positions were labeled with two spectrally distinct dyes (Atto 488 and Atto 532), whereas the cargo strand was modified with a quencher molecule capable of quenching both of these marker dyes. The experiments were performed at high monovalent salt concentrations ([NaCl] = 1 M), and at origami platform concentrations of 0.5 nM. Cargo transfer was triggered by the addition of a 200-fold excess of the starter strands. As schematically depicted in Figure 1, in the initial state C

DOI: 10.1021/acs.nanolett.5b00351 Nano Lett. XXXX, XXX, XXX−XXX

Letter

Nano Letters

Figure 3. Fraction Q′ of quenched target fluorophores as a function of time for varying distances for (A) untethered motion, (B) transfer on a hinged tether, and (C) transfer on a more rigid tether (the schematic images exemplarily depict the large start-end distance only). In each trace, the cargo is released from the start site at t = 0. The color of the traces encodes the distance between start and end position: blue traces are for d1 = 9 nm, green traces for d2 = 31 nm, and red traces for d3 = 52 nm. Dots represent actual data points of three superimposed traces recorded for each case, whereas continuous lines represent their mean smoothed with a gliding average. Graphs at the bottom show the time of the experiment from 0 to 3500 s, whereas the top graphs show only the first 600 s.

Figure 4. (A) Competition assay for the 52 nm transport case with rigid tethering. Competitor strands are added simultaneously with the starter solution at varying concentrations [L]. The competitor strands can bind to the cargo and prevent binding to the on-platform target. The disappearance of the “slow phase” of the kinetics is indicated by the colored area. (B) Comparison of the residual transport for all start-target distances and tether geometries at a constant competitor concentration [L] = 50 nM.

in the presence of competitor strands, which can interfere with the interorigami transfer processes more effectively than with the fast on-platform transfer. A comparison between the different tether geometries in terms of competition experiments is made in Figure 4B. For each geometry, transfer kinetics for the three start-target distances are shown for a competitor concentration of [L] = 50 nM. Whereas cargo transfer over the smallest distance d1 = 9 nm occurs for all three cases, transport over the longer distances is entirely suppressed for all but the rigidly tethered geometries. The negative slope apparent in the fluorescence traces in Figure 4B originates from slow strand displacement

reactions, in which the highly concentrated competitor strands displace the cargo from the target after binding. Theoretical Considerations and Modeling. Overall, the fluorescence kinetics experiments presented in the previous sections demonstrate that for the small d1 = 9 nm distance diffusive transfer of cargo without tether surprisingly is the most effective transfer mode, even so in the presence of competitor strands. For the larger distances, however, diffusive transfer is ineffective, whereas tethering with a rigid tether improves speed and robustness of cargo transfer. In the following, we attempt to rationalize these observations using simple theoretical considerations and modeling of the D

DOI: 10.1021/acs.nanolett.5b00351 Nano Lett. XXXX, XXX, XXX−XXX

Letter

Nano Letters dynamics of the cargo transfer process. For the small distance the size of the start site, the length of the cargo strand and the target site are comparable to the start-target distance itself. This allows the start-cargo complex and the target strand to physically overlap, which probably enables a direct cargo transfer from start to target site via a bridging mechanism (through sequence domains d and e).28 Attachment of the cargo to a tether in this case actually reduces the transfer efficiency, potentially caused by a lower diffusivity and due to sterical and mechanical constraints. For the large distances, transport via a flexible tether presumably is less efficient than for a rigid arm, as after cargo release, the flexible tether can explore a larger volume, and thus, the cargo is considerably less likely to meet the target site. We tried to capture the basic features of the different tether geometries in a highly simplified model of a diffusing reactive particle in a hemispherical volume and used it to study the reaction-diffusion dynamics of the system at long time scales as well as their Brownian dynamics at very short time scales. In this model, the rigidly tethered cargo was approximated by a diffusing particle confined to the shell of a hemisphere, whereas the flexibly attached cargo was allowed to also explore the hemisphere’s interior. Free diffusion was modeled with the only constraint that the DNA origami plate was reflecting, whereas the cargo could freely move through the hemisphere’s boundary. Reaction-Diffusion Dynamics. We first formulated the transfer process in terms of a reaction-diffusion (RD) problem, in which the cargo was initially localized at a high concentration at the start position. After release of the cargo, it was allowed to diffuse in a hemispherical volume (cf. Supporting Information section, Figures S6 and S7) and react with the target site, which was modeled as a disk on the hemisphere with radius 10 nm (roughly corresponding to the extension of the target staple). The corresponding RD equation was solved numerically using COMSOL Multiphysics for various settings for the reaction rate constant k and the diffusion coefficient D. Translational diffusion coefficients have typical values in the range 10−100 μm2/s, as well as the rotational diffusion constant of our tether.31 For the hybridization reaction at the target site a second-order process with typical rates for DNA duplex formation in the range k ≈ 105−107 M−1 s−1 was assumed (as described in detail in the Supporting Information section “COMSOL simulations”). For the free diffusion case, our RD model did not result in any successful cargo transfer for any of the combinations of k and D, as with these parameter settings the cargo escapes before it can bind to the target. This is remedied by confining (“tethering”) the cargo to the platform. In Figure 5, simulation results for the fraction of successfully transferred cargo Q as a function of time are shown for cargo diffusion confined to a hemispherical shell and to a hemispherical volume. In contrast to the freely diffusing case, Q(t) is nonzero and quickly converges to 1 due to the confinement. Immediately after its release, the cargo starts to diffusively explore its neighborhood. After a time much shorter than the typical reaction time-scale, corresponding well with the expected mixing time L2/D ≈ 30 μs, the probability to find the cargo at a specific point (i.e., its effective concentration) is roughly the same everywhere in the volume it is allowed to explore. Cargo is then absorbed at the target site at a rate determined by the hybridization reaction. In this model, cargo transfer is only slightly dependent on the start-to-target

Figure 5. Occupation probability Q of target volume by diffusing particles in (A) a hemispherical shell and (B) a hemispherical volume for D = 100 μm2/s and three reaction rates k. In a first approximation, Q is basically only affected by the used k and not by the used distances. If the accessible volume is increased the processes slow down.

distance, and it is independent of D within a physically realistic range. The temporal progress of Q(t) is essentially determined by the reaction rate k, and as a result can be treated by an ordinary rate equation that simply describes the hybridization of the tether’s cargo to the target. Only at very high reaction rates (k = 108 M−1 s−1) distance and diffusivity have a considerable effect on cargo transfer efficiency (cf. Supporting Information, Table S1 and Figures S8 and S9). We can rationalize the results of the numerical RD simulations by comparing the typical time-scales involved. The time for diffusion from start to target site is given by tD ≈ d2/D, which for the distances d1, d2, d3, is tD ≈ 1, 10, and 30 μs, assuming a diffusion coefficient of D = 100 μm2/s. The time for diffusive exploration of the spherical volume defined by the tether arm of length L (tmix = (2L)2/D ≈ 30 μs), necessarily is of the same order. We can further estimate the typical reaction time-scale for delivery of the cargo to the target site, by calculating an “effective concentration” of the cargo, which is given by ceff = 1/(NA2πL2ΔL) if we assume confinement to a shell of thickness ΔL ≈ 1−10 nm, and ceff = 3/(NA2πL3) for confinement to a half sphere. Here, NA is Avogadro’s constant. The reaction time-scale is then given by tR = 1/(k·ceff), which amounts to tR ≈ 3−30 ms for the shell, and tR ≈ 30 ms for the sphere, if we assume a typical hybridization rate of k = 1 × 106 M−1 s−1. The tR obtained from these simple estimates thus correspond well to the time scales observed in the simulations. Brownian Dynamics. In order to study the initial phase of diffusive exploration of the reaction volume in more detail, we also performed Brownian dynamics simulations of the motion of the cargo and calculated the first passage time (FPT), after which the target site is reached for the first time (which typically occurs without a successful binding reaction). For each geometry, we simulated 103 particles taking 107 steps of size 0.1 nm in randomly chosen directions. Time steps were chosen to match a diffusion coefficient of 100 μm2/s. The target area was represented by an absorbing sphere of radius a = 3 nm at an appropriate distance from the start position, while the origami platform was modeled by a reflecting box as in the RD simulations (cf. Supporting Information section “Monte Carlo Simulations”). E

DOI: 10.1021/acs.nanolett.5b00351 Nano Lett. XXXX, XXX, XXX−XXX

Letter

Nano Letters

probability of encountering the target region than the hinged tether, which diffusively explores a much larger volume. As the rate of tethered cargo delivery is reaction-limited, there is no distance dependence for the kinetics of on-platform delivery. Our simulations indicate that the delivery kinetics would become distance-dependent only for much larger reaction rates (not attainable with DNA hybridization, but potentially for other reactions) or for much lower diffusion coefficients (which could play a role for more bulky cargoes or in crowded environments). Judging from our experiments, the effective speed of rigidly tethered cargo transport for the largest distance (d3 = 52 nm) is at least 2.5 nm/s; this lower bound is obtained from the limited time-resolution of the experiments and our finding that the onplatform transport process is completed within the first 20 s of the experiment. Our simulations indicate, however, that the reaction should in fact be much faster (on the order of 30 ms), resulting in an effective velocity of 2 μm/s (!). To determine the actual speed of the transport process, however, our system would have to be studied at a much higher time-resolution using, for example, single-molecule fluorescence techniques. Given the distance-independence of cargo transport kinetics, the best strategy to achieve fast transport over a long distance is to simply take a single, long step. In our experiment, the stepsize is determined by the size of the origami platform, but one could construct much larger systems with much longer tether arms, resulting in even higher effective transport speeds. What is the limit for this approach? Increasing the length of a rigid tether L would increase the reaction time scale as tR = (k· ceff)−1 ∼ L2, again assuming that the cargo is restricted to a spherical shell. On the other hand, the typical time for diffusion would be tD = L2/D ∼ L3, where we have to consider that the diffusion coefficient of the tether arm itself would scale as D ∼ 1/L. This shows that for long tethers, there will be a crossover to diffusion-limited cargo transport, which we estimate to occur at around L ≈ 1.2 μm (Supporting Information, Figure S10). In summary, we have studied the diffusive transport of DNA cargo molecules attached to a DNA origami platform via a long molecular tether arm. Although for short distances, transport from a start to a target site was less efficient than for direct (untethered) transfer, for long distances cargo transfer occurred fast and efficient, with a speed independent of the actual transport distance. The effective transport velocity is found to be at least 2.5 nm/s, much larger than for typical DNA walker devices, and theoretical considerations even indicate actual velocities on the order of 1 μm/s. Our results show that tethered, diffusive transport along DNA-based nanotracks could be a highly efficient transport mechanism, which could find application in the context of larger scale nanorobotic systems12,22 and assembly lines11 or for the implementation of active self-assembly schemes such as signaling tile assembly.33

In Figure 6, the fraction of absorbed particles over time (corresponding to the integrated first passage time density) is

Figure 6. (A) Typical random walk traces for unrestrained diffusion (left), diffusion confined to a hemispherical volume (top right) and diffusion confined to a hemispherical shell (bottom right). The absorbing boundary is indicated in green. The surface of the confining hemisphere is drawn in red. A reflecting box is placed below the release point, to mimic the origami platform. (B) Absorption kinetics for N = 1000 particles, which were released at d = 9 nm (blue), 31 nm (green), and 52 nm (red) from the center of an absorbing sphere with radius 3 nm.

shown for different geometries and for varying distance between start and absorber. For free diffusion, this fraction converges to the value a/d, which is the expected probability of capture for a particle released close to an absorbing sphere32 (Supporting Information, Figure S11). As is also apparent from the simulations, first passage to the target on a shell (which is effectively 2D) is much faster than when the cargo is allowed to explore all of the hemispherical volume. In both cases, diffusion to the “close” target site at d = 9 nm is faster than to the remote sites, which are roughly equal in terms of FPT. Discussion and Conclusion. The main results of our experiments on Brownian transport of DNA cargo molecules on a supramolecular platform can be summarized as follows. For very short distances, when start and target positions on the platform can be physically bridged by a cargo molecule, untethered transport is the fastest and most robust process. For larger distances, however, untethered cargo strands diffuse away without ever reacting with the target strand, a consequence of the fact that hybridization reactions occur on a much slower time-scale than diffusive processes. In these cases, simple tethering of the cargo to the platform prevents diffusive loss and, therefore, enforces cargo delivery to the target. In our experimental system, transport occurs much more efficiently for a rigidly tethered cargo than for a tether containing a hinge. For the rigid tether, the cargo is effectively confined to a hemispherical shell and thus has a higher

■

ASSOCIATED CONTENT

S Supporting Information *

Additional information on sample preparation, fluorescence spectroscopy experiments, AFM imaging, Monte Carlo simulations, COMSOL simulations, additional data, and DNA sequences are given. This material is available free of charge via the Internet at http://pubs.acs.org/. F

DOI: 10.1021/acs.nanolett.5b00351 Nano Lett. XXXX, XXX, XXX−XXX

Letter

Nano Letters

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +49 (0)89 289 11611. Fax: +49 (0)89 289 11612. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS We gratefully acknowledge financial support by the DFG through the SFB 1032 Nanoagents (TP A2) and the Cluster of Excellence Nanosystems Initiative Munich (NIM). We would like to thank Korbinian Kapsner for computational advice and support, and Florian Praetorius for kindly providing the M13mp18 scaffold.

■

REFERENCES

(1) Conrado, R. J.; Varner, J. D.; et al. Curr. Opin. Biotechnol. 2008, 19, 492−499. (2) Havlin, S.; Ben-Avraham, D. Adv. Phys. 1987, 36, 695−798. (3) Tejedor, V.; Benichou, O.; et al. Biophys. J. 2010, 98, 1364−1372. (4) Rothemund, P. W. K. Nature 2006, 440, 297−302. (5) Zheng, J.; Birktoft, J. J.; et al. Nature 2009, 461, 74−77. (6) He, Y.; Ye, T. Nature 2008, 452, 198−201. (7) Douglas, S. M.; Dietz, H.; et al. Nature 2009, 459, 414−8. (8) Dietz, H.; Douglas, S. M.; et al. Science 2009, 325, 725−730. (9) Krishnan, Y.; Simmel, F. C. Angew. Chem., Int. Ed. 2011, 50, 3124−3156. (10) Ding, B. Q.; Seeman, N. C. Science 2006, 314, 1583−5. (11) Gu, H.; Chao, J.; et al. Nature 2010, 465, 202−205. (12) Lund, K.; Manzo, A. J.; et al. Nature 2010, 465, 206−210. (13) Wickham, S. F. J.; Endo, M.; et al. Nat. Nanotechnol. 2011, 6, 166−169. (14) Wang, Z.-G.; Elbaz, J.; et al. Angew. Chem., Int. Ed. 2012, 51, 4322−4326. (15) Fu, J.; Yang, Y.; et al. Nat. Nanotechnol. 2014, 9, 531−536. (16) Shin, J. S.; Pierce, N. A. J. Am. Chem. Soc. 2004, 126, 10834− 10835. (17) Yin, P.; Choi, H. M.; et al. Nature 2008, 451, 318−322. (18) Green, S., Bath, J. et al. Phys. Rev. Lett.. 2008101art. no. 238101. (19) Omabegho, T.; Sha, R.; et al. Science 2009, 324, 67−71. (20) Cheng, J.; Sreelatha, S.; et al. Phys. Rev. Lett. 2012, 109, 238104. (21) Masoud, R.; Tsukanov, R.; et al. ACS Nano 2012, 6, 6272− 6283. (22) Wickham, S. F. J.; Bath, J.; et al. Nat. Nanotechnol. 2012, 1−5. (23) Tomov, T. E.; Tsukanov, R.; et al. J. Am. Chem. Soc. 2013, 135, 11935−11941. (24) Liber, M.; Tomov, T. E. Small 2014, 11, 568−575. (25) He, Y.; Liu, D. R. Nat. Nanotechnol. 2010, 5, 778−782. (26) Howard, J. Mechanics of Motor Proteins and the Cytoskeleton, 1st ed.; Sinauer: Sunderland, 2001. (27) Hess, B.; Mikhailov, A. J. Theor. Biol. 1995, 176, 181−4. (28) Teichmann, M.; Kopperger, E.; et al. ACS Nano 2014, 8, 8487− 96. (29) Stahl, E.; Martin, T. G.; et al. Angew. Chem., Int. Ed. 2014, 53, 12735−12740. (30) Zhang, D. Y.; Winfree, E. J. Am. Chem. Soc. 2009, 131, 17303− 17314. (31) Zero, K. M.; Pecora, R. Macromolecules 1982, 15, 87−93. (32) Berg, H. Random Walks in Biology; Princeton University Press: Princeton, NJ, 1993. (33) Padilla, J., Patitz, M.; et al. In Unconventional Computing and Natural Computing 2013. Lecture Notes in Computer Science; Springer: New York, 2013; 174−185.

G

DOI: 10.1021/acs.nanolett.5b00351 Nano Lett. XXXX, XXX, XXX−XXX