Direct Mechanical Measurements Reveal the Material Properties of

LETTER pubs.acs.org/NanoLett

Direct Mechanical Measurements Reveal the Material Properties of Three-Dimensional DNA Origami Dominik J. Kauert,† Thomas Kurth,‡ Tim Liedl,*,§ and Ralf Seidel*,† †

Biotechnology Center and ‡DFG-Center for Regenerative Therapies Dresden, Technische Universit€at Dresden, Dresden, 01062, Germany § Center for Nanoscience and Department of Physics, Ludwig-Maximilians-Universit€at M€unchen, Geschwister-Scholl-Platz 1, 80539 M€unchen, Germany

bS Supporting Information ABSTRACT: The application of three-dimensional DNA origami objects as rigid mechanical mediators or force sensing elements requires detailed knowledge about their complex mechanical properties. Using magnetic tweezers, we directly measure the bending and torsional rigidities of four- and six-helix bundles assembled by this technique. Compared to duplex DNA, we find the bending rigidities to be greatly increased while the torsional rigidities are only moderately augmented. We present a mechanical model explicitly including the crossovers between the individual helices in the origami structure that reproduces the experimentally observed behavior. Our results provide an important basis for the future application of 3D DNA origami in nanomechanics. KEYWORDS: 3D DNA origami, single-molecule mechanics, bending rigidity, torsional rigidity, finite element modeling

T

he recent development of the origami technique has revolutionized DNA-based assembly1 by allowing the synthesis of arbitrarily shaped and submicrometer sized two-dimensional2 (2D) and three-dimensional3 (3D) architectures with atomic precision. The establishment of robust, efficient, and simple protocols has driven the field from the pure exploration of self-assembly principles toward rapidly emerging applications of DNA structures in very distant areas of research, such as NMR spectroscopy,4 crystallography,5 protein cryo-electron microscopy,6 site-specific chemistry,7 and nanooptics.8,9 The most commonly used design principle for higher-order DNA structures is the parallel arrangement of multiple DNA double strands (dsDNA) which results in multihelix bundles or sheets. DNA bundles can be assembled from oligonucleotides only10,11 or using the DNA origami concept with the help of a long single-stranded scaffold.4,12,13 More complex structures are obtained by arranging the DNA strands into large periodic lattices with a bundle geometry forming the unit cell. Lattices with a honeycomb-like unit cell, based on six-helix bundles (6HBs),3 and a tetragonal unit cell, based on four-helix bundles (4HBs),14 have been employed. The bundling of multiple helices allows the creation of very stiff structures.15 This has stimulated great interest to use DNA nanostructures as rigid mechanical scaffolds and for the construction of mechanoresponsive structures and sensors, e.g., in single-molecule and cellular biophysics.15
19 The development of nanoscaled architectures with designed stabilities and responsiveness, however, requires detailed knowledge about the currently inadequately characterized complex material properties of multihelix DNA nanostructures. Previous studies that investigated equilibrium fluctuations10,15,20 provided bending rigidities for multihelix bundles that agreed within error with a r 2011 American Chemical Society

simple mechanical model in which the helices of a bundle can be approximated by homogeneous, rigidly connected cylinders, each of which having the same bending rigidity as dsDNA. It is unclear however, whether such a simple model can account for all mechanical parameters of such complex DNA structures. In particular, the Holliday-like connections between as well as the relative positions of nicks along the individual helices are expected to provide behaviors different from those predicted. In order to obtain a more comprehensive understanding of the mechanical properties of 3D DNA origami structures, we set up direct mechanical measurements using magnetic tweezers. We designed and fabricated 6HBs and 4HBs consisting of a 7560 nucleotide long single-stranded “scaffold strand” and hundreds of DNA oligomer “staple strands”. To support mechanical measurements, the DNA origami bundles were attached at one end through incorporated digoxigenin modifications to the antidigoxigenin coated surface of the flow cell in which the measurements are carried out and on the other end through incorporated biotin modifications to the streptavidin coated magnetic bead, which is used to exert mechanical stress. In an initial attempt we prepared 428 nm long 6HBs, which carried a single biotin or digoxigenin anchor at one of the helices of each end (Figure 1). However, such a flexible attachment that allows the bundle to swivel around its attachment point does not support the application of torsional stress. Therefore, we designed a 6HB with 18-helix bases of 371 nm in length carrying nine attachment anchors at each end as well as a 4HB with 20-helix bases of 478 nm in length and Received: October 6, 2011 Revised: October 29, 2011 Published: November 02, 2011 5558

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Figure 1. Characterized DNA-origami structures. (a) Six-helix bundle with a single biotin at one and a digoxigenin anchor at the other end. (b) Six-helix bundle with 14 nm long 18-helix ends each comprising nine anchors. (c) Four-helix bundle with 22 nm long 20-helix ends each comprising 10 anchors. Shown are a 3D schematics of the origami structures together with schematic cross sections of the bundle (upper) and of its ends (lower). Dark gray circles indicate helices with anchors and light gray circles helices without anchors. TEM images of the assembled structures are shown below. The length of the scale bars is 200 nm in the main images and 40 nm in the insets that depict an enlarged view on the bundle ends.

10 attachment anchors at each end (Figure 1 and Methods). These solid foundations should provide a rigid perpendicular attachment of the bundle at the corresponding surface. The DNA origami objects were assembled in a one-pot reaction in which the scaffold strand and staple strands are heated to 80 °C and then cooled down over the course of 15 h to room temperature. Transmission electron microscopy (TEM) imaging confirmed the correct assembly of the bundles and their expanded ends (Figure 1). For the mechanical measurements the origami structures were bound at one end to 1 μm magnetic beads and flushed into the flow cell in which the second end was allowed to attach. In order to verify the tethering of a single DNA origami structure and its correct, i.e., flexible or rigid, attachment, we recorded for each bundle type long time trajectories (273 s) at a fixed force in which the 3D position of the bead was tracked (Figure 2). For comparison we performed the same experiments using a dsDNA molecule of 428 nm length. Depending on the stretching force significant differences between all four tested constructs were observed. Compared to dsDNA the 3D fluctuations obtained for any of the tested origami structures appear considerably more expanded in particular at lower forces (Figure 2c). Also, the maximum distance from the surface adopted by the bead is force-invariant for the origami structures but not for dsDNA (Supporting Information, Figure S1) as expected for a rigid rod compared to a random coil that is attached to the bead. Further remarkable differences can be observed between the individual origami structures from the bead fluctuations in the xy plane (Figure 2). These fluctuations are asymmetric due to the external magnetic field that pins the anisotropy axis of the bead along the direction of the field lines oriented along the y axis (Figure 2a,b). While the bead is free to rotate around this axis (Figure 2a,b, right), rotations around the perpendicularly oriented x axis are suppressed (Figure 2a,b, left). Therefore lateral

Figure 2. Behavior of the DNA-origami structures in magnetic tweezers measurements at low force. Bead movements for (a) flexibly and (b) rigidly attached bundles. Shown are views parallel and perpendicular to the magnetic field lines. The maximum lateral excursion of the bead for the given field orientation and attachment are illustrated by the second lighter gray bead. Projections of (c) measured and (d) simulated bead positions in the xy and the xz planes at an applied magnetic force of 0.02 pN for a 428 nm dsDNA molecule (gray) and the origami structures depicted in Figure 1. For each projection, 20000 data points are shown.

fluctuations along the y axis are more suppressed compared to the x axis. Strikingly, at low external force the degree of this suppression becomes dependent on the attachment of the origami structure at its ends. Fluctuations along y are for the 6HB with single anchors much more pronounced than for the two structures with multiple anchors (Figure 2c). For the latter this causes the bead to fluctuate along a semicircle, clearly visible as an arc in the xz projections. This is anticipated when assuming a rigid perpendicular attachment of these structures to bead and surface, since in this case displacements along the y direction are counteracted by the necessary bending of the bundles (Figure 2b, left). In order to understand this behavior more rigorously, we carried out coarse-grained Monte Carlo (MC) simulations of our bead-origami system.21 The DNA structures are considered to be wormlike chains with bending rigidities pbend  kBT, where pbend is the persistence length of the chain. We assumed values for pbend of 50, 2000, and 750 nm for dsDNA, 6HBs and 4HBs, respectively. In addition, we implemented flexible end attachments for dsDNA and 6HBs with single anchors but rigid perpendicular attachments for 6HBs and 4HBs with multiple anchors. For these conditions, the simulations reproduced the 3D fluctuations for the different constructs at low (Figure 2c,d) and at elevated external force (Supporting Information, Figure S1) remarkably well. 5559

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Figure 3. Force
extension behavior of the DNA-origami structures. Measured force
extension data of a 428 nm dsDNA molecule (gray dots) and the DNA origami structures (blue, green and red dots, colors as indicated by the sketches on the right side). Extensions are normalized by their contour length. The prediction for an infinitely long wormlike chain22 with pbend = 50 nm is shown as a dashed gray line. Individual graphs for each construct on the right show in addition to the experimental data (solid dots) predictions for three different persistence lengths from MC simulations that take the particular attachment geometries into account (solid lines that form the shaded areas). In the simulations persistence lengths of 1000, 2000, and 3000 nm and of 500, 750, and 1000 nm were employed for 6HBs and 4HBs, respectively.

This provides evidence for a controlled attachment of DNA origami structures with defined boundary conditions in singlemolecule mechanical measurements as well as for a considerably increased bending rigidity of 4HBs and 6HBs compared to dsDNA. In order to quantitatively evaluate the bending rigidity of the multihelix bundles, we extracted from our measurements the characteristic force
extension behavior for each investigated structure, where the extension is the mean elevation of the fluctuating bead from the surface (Figure 3, left). The force
extension behavior appears to be influenced by the rigidity of the attachment (compare both 6HB constructs) as well as the bending rigidity of the bundle itself (compare 4HB and 6HB constructs with rigid attachments, see also Supporting Information, Figure S2). For molecule lengths in the order of the bending persistence length, the bending rigidity cannot be obtained by fitting the force
extension data with the usually applied expression for an infinite wormlike chain molecule22 due to finite length effects.23 Therefore, we carried out a set of MC simulations for each structure, in which we varied the bending rigidity over a certain range and compared the simulated force
extension behavior with the experimental results (Figure 3, right). The simulated force
extension behavior for the 6HBs with flexible attachments agreed with the experimental data but was found to be insensitive to a particular value of pbend that is larger than the molecule length (Figure 3, right). In contrast, the simulated force
extension behavior of the multihelix bundles with rigid attachments was much more dependent on pbend which allowed the quantitative evaluation of the measurements (Figure 3, right). Using a simple fit routine (see Methods) and evaluating several molecules, we obtain pbend = 740 ( 140 nm (N = 5) and 1880 ( 270 nm (N = 4) for 4HBs and 6HBs with rigid attachments. Compared to dsDNA (pbend = 50 nm) this corresponds to an increase in bending rigidity of 15- and 38-fold. As a successful consistency check, we

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Figure 4. Direct torsional measurements of DNA-origami structures. (a) Schematics of the magnet configuration consisting of cylindrical rings partially stacked in opposite magnetization direction (indicated by arrows) to each other. Field gradient as well as the field lines are oriented in the vertical direction. Small field asymmetries cause a minor horizontal field component that is strong enough to pin the angular orientation of the magnetic bead around the z axis but weak enough to allow detectable angular displacements of the bead due to external torque within the attached DNA structures. (b) Mean extension and torque upon twisting a 9 kbp dsDNA molecule. The molecule shows the characteristic behavior expected at the applied force of 0.8 pN and 20 mM monovalent ions in solution. A linear fit (solid black line) of the torque data between
5 and 20 turns provides an apparent torsional persistence length for DNA of 80 ( 4 nm in agreement with published values at the given force.31,30 (c) Direct torsion measurements on 6HBs at 2.0 pN (red circles) and 3.7 pN (red triangles) and on 4HBs at 9 pN (green circles) and 6 pN (green triangles). Linear fits to the data (black solid lines) provide torsional persistence lengths of 530 ( 20 and 390 ( 30 nm for the 6HBs and 4HBs, respectively.

also evaluated the mean-square fluctuations along the y direction (Supporting Information, Figure S3). In addition to bending we characterized the torsional properties of multihelix bundles. The twisting of attached molecules is readily supported in magnetic tweezers due to the significant magnetization anisotropy of the available magnetic beads.24,25 Very recently, direct torque measurements became available.26
28 These measurements are, however, currently restricted to low forces or low time resolution and require complicated modifications of the magnetic beads (see Discussion in Supporting Information). To enable such measurements on the short origami constructs, we improved the existing measurement schemes. We designed a magnet configuration consisting of cylindrical magnets that are partially stacked on top of each other in opposite orientation (Figure 4a and Supporting Information, Figure S4) which supports high forces at small bead sizes. In addition we developed an angular tracking routine that is applicable for standard magnetic beads (Supporting Information, Figure S5). 5560

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Nano Letters To validate our measurement scheme, we reproduced the results of previous torque measurements on single DNA molecules (Figure 4b). Upon overtwisting dsDNA under tension, the torque initially builds up proportionally to the applied turns. This is detected in our setup by an angular displacement of the magnetic bead from its equilibrium position in the absence of twist, since the cylindrical magnets act as a soft torsional spring for the bead (Figure 4b and Supporting Information, Figure S5). Once a critical torque is reached, the DNA abruptly buckles29,30 and subsequently shortens in a linear fashion with applied turns, due to the extrusion of a plectonemic superhelix. In this phase the torque remains at a constant level. Both, the force-dependent slopes in the linear phase of the torque increase and the torque plateaus (Figure 4b and Supporting Information, Figure S6) correspond within errors to literature values27,30,31 given a concentration of 20 mM monovalent ions in solution. From the force dependence of the slope, we extrapolated a torsional persistence length for dsDNA of 97 ( 4 nm (Supporting Information, Figure S6). We then carried out supercoiling experiments on the two multihelix bundles with rigid attachments. Upon strong supertwisting both constructs show similar to dsDNA reversible twistinduced buckling albeit at a much larger extent (Supporting Information, Figure S7). This shows that the multiple attachment anchors of the bundles indeed support twist generation. To avoid that strong supertwisting affects the bundle structure, we restricted the direct torsion measurements to a few applied turns. Similar to dsDNA, the torque increases linearly with the applied turns for both 4HBs and 6HBs (Figure 4). From linear fits of these data we obtain torsional persistence lengths of 390 ( 30 and 530 ( 20 nm for the 4HB and the 6HB constructs, respectively. Compared to dsDNA this corresponds to an increase in torsional rigidity of 4.0- and 5.5-fold. The general stiffening is expected, but it appears small compared to the increase in bending rigidity. In order to understand the discrepancy between bending and twisting rigidity, we carried out finite-element-method (FEM) simulations of multihelix bundle-like geometries. For this the individual DNA double strands of the bundles were approximated by solid cylinders of 1.98 nm diameter and isotropic material properties. We simulated the following models that use different connections between the cylinders (Figure 5a, Supporting Information, Figure S8): (i) individual cylinders without connections (red), (ii) cylinders connected by solid continuous walls (blue), (iii) discrete 1.0 nm thick cylindrical connectors at positions of crossovers in the origami structure (green), and (iv) discrete 1.0 nm thick cylindrical connectors (as in iii) and additional slits in the main cylinder at positions of nicks (i.e., staple ends) in the origami structure (yellow). As expected, in the absence of connections between cylinders the bending and twisting rigidities increase 6- and 4-fold for 6HBs and 4HBs, respectively. Introducing intercylinder connections increases for all models the bending rigidities strongly, approaching the second moment of inertia expectation for the corresponding cross section (Figure 5b,c). The slightly reduced increase found for the models with discrete connectors is in good agreement with the measured values. For twisting, continuous intercylinder connections yield still a strongly increased rigidity just reduced to half the expected value from polar moment of inertia estimates, which is due to the imperfect cylinder symmetry of the bundle geometries. The measured moderate increase of the twisting rigidity is however only reproduced by the two models that have discrete connectors (Figure 5b,c). Modifying the parameters of the discrete connectors, e.g., using a different thickness, changes the obtained rigidities only

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Figure 5. Finite-element modeling of DNA-origami mechanics. (a) Drawing of the different simulated connections (see text) in the cylinder models that model multihelix bundles. (b, c) Simulated bending (left) and twisting (right) rigidities of six-cylinder and four-cylinder models normalized by the rigidity of a single cylinder. Colors of the bars correspond to the colors of the intercylinder connections shown in a. Measured values for the multihelix structures are shown as gray bars. The dashed gray lines represent the expectation from calculating the area and polar second moment of inertia for the corresponding multicylindrical cross section.

slightly and provides the same trend—a strong increase in bending but a comparably small increase in twisting rigidity. In summary, we here present the first measurements of the mechanics of multihelix DNA bundles by direct mechanical manipulation. In agreement with previous reports, we find that these structures have a greatly increased bending rigidity10,15,20 but exhibit an unexpected low twisting rigidity. We present a simple mechanical model that can nearly quantitatively describe the observed behavior. With this we validate the general applicability of simple rod models to describe the mechanics of 3D origami structures19 but also find an absolute requirement for the use of discrete rather than continuous connectors between the solid cylinders that approximate the DNA helices at crossover positions. Our modeling suggests that interruptions of the DNA helix structure by nicks at staple ends and by the Holliday-junction crossovers has only little influence on the mechanics of DNA origami structures. Especially the torsional mechanics should be sensitive to a major role of these lesions. We assume that stacking effects between neighboring bases contribute significantly to the helices’ stability. In general we expect that our modeling approach that quantitatively describes the mechanics of multihelix bundles is applicable also for more complex DNA origami structures. The defined and testable interfacing of DNA origami structures with surfaces, which we present here, will be helpful for further mechanical studies of such structures but more generally for the application of DNA origami as noise suppressor in forcebased single-molecule experiments that require extended spacers, such as studies of protein (un)folding dynamics32 or measurements of DNA
protein interactions.33 Replacing the typically used soft DNA spacers by much stiffer and rigidly attached DNAorigami spacers should significantly reduce Brownian fluctuations along the force direction and thus allow measurements at improved temporal and spatial resolution even under smaller external load. Also, defined attachments of DNA structures may be useful to better understand the role of boundary conditions in analyzing single-molecule force
extension experiments23 and to 5561

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Nano Letters develop structured and three-dimensional surface modifications with the help of DNA templates. The characterization of basic mechanical parameters of 3D DNA origami structures will be key for designing artificial nanostructures with tailored material properties for the future development of reliable nanoscopic agents, rulers, and sensors as well as for mimics of structural cellular proteins. Direct mechanical measurements as carried out here will become an important tool to develop, validate, and calibrate detailed models of origami mechanics and to study more complex DNA architectures, such as twisted, bent,34 or prestressed structures15 under tension, compression, and torsion. Methods. DNA-Origami Design, Assembly, and Analysis. DNA origami structures (Supporting Information, Figure S9) have been designed using CaDNAno.35 Reverse-phase cartridge purified oligonucleotides for the DNA origami objects were purchased from Eurofins MWG Operon. Single-stranded scaffold DNA was produced as described.3 The one-pot assembly reaction was performed as follows: A solution containing 10 nM of the scaffold p7560, 75 nM of each oligonucleotide, 5 mM TrisHCl, 1 mM EDTA, and 16 mM MgCl2 at pH 8.0 was heated to 80 °C for 4 min, cooled to 60 °C over the course of 80 min, and finally cooled to 25 °C over 14 h. To introduce anchors (Supporting Information, Figure S9) for the flexibly attached 6HB, one staple oligonucleotide at either end of the structure carried a biotin or a digoxigenin modification at its 50 -end. Anchors for the rigidly attached bundles were introduced by modifying all staple oligonucleotides that terminate with their 30 -ends at either origami end (9 and 10 oligonucleotides per end for 6HBs and 4HBs, respectively) enzymatically in a onepot reaction prior origami assembly using terminal end-transferase (Roche) and biotin- or digoxigenin-ddUTP. Each oligo (500 nM) was incubated together with 400 units of the terminal end-transferase in a 20 μL reaction. Control dsDNA of 1259 bp in length was prepared by PCR using one primer with a biotin and one primer with a digoxigenin modification at the 50 -end. The folded objects were investigated with gel electrophoresis at 3.5 V/cm on a 1% agarose gel containing 50 mM Tris borate (pH 8.3), 1 mM EDTA, and 14 mM MgCl2 (see Supporting Information, Figure S10). For subsequent measurements, origami objects were sliced out from the gel and purified using a commercial kit (Freez’N’Squeeze, Bio-Rad). To prevent damage of the origami structures, any exposure to ethidium bromide and UV light during the purification was avoided. A small fraction of the sample was run in an extra lane on the gel next to the main fraction. The extra lane was cut from the gel and stained with ethidium bromide and the band of the origami objects was marked with a scalpel during subsequent UV illumination. These marks were then used to locate and excise the corresponding band of the main fraction of the sample. For TEM imaging, a dilute solution containing the folded DNA origami objects was applied to glow-discharged carbon-coated grids. The samples were subsequently stained using a filtered 0.7% solution of uranyl formate in 5 μM NaOH. TEM was performed on a FEI Morgagni 268D transmission electron microscope at 80
100 kV. Magnetic Tweezers Experiments. Magnetic tweezers experiments were carried out as previously described.24,29 DNA origami constructs were bound to 1 μm streptavidin-coated superparamagnetic beads (Invitrogen) and flushed into a flow cell, whose bottom coverslip was coated with antidigoxigenin. All measurements were performed at room temperature in 5 mM Tris-HCl,

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16 mM MgCl2, 0.1% Tween 20, 10 mM NaN3, and 100 μg mL
1 BSA at pH 8.0 pH. For force
extension measurements the magnetic field was generated using a pair of permanent NdFeB magnets (W-05-N50-G, Supermagnete). For torsional measurements a stack of four cylindrical magnets with 10 mm diameter, 1 mm height, a central hole of 1 mm diameter and axial magnetization (Supermagnete) was used (see Supporting Information, Figure S4). The length of the DNA, i.e., the vertical position of the magnetic bead with respect to a nonmagnetic reference bead attached to the surface of the flow cell, was determined from video images taken at 120 Hz using a Pulnix TM-6710CL CCD camera and real-time 3D particle tracking with subnanometer accuracy24,36 (see Supporting Information, Figure S5 for the tracking of the angular bead position and the torsional measurements). Monte Carlo Simulations of Force
Extension Data. Coarsegrained Monte Carlo (MC) simulations of our bead-origami system were carried out as previously described.21 The DNA structures were approximated by a chain of discrete segments (20 nm segments for multihelix bundles, 2 nm segments for dsDNA) with harmonic, wormlike chain bending potentials set by pbend between the segments. In addition, the external stretching force as well as volume exclusion prohibiting the chain to penetrate the surfaces of bead and flow cell as well as the bead to penetrate into the flow cell were considered.21 To estimate the persistence length of multihelix bundles, the set of simulated force
extension curves for each construct was globally fitted using the formula from Bouchiat et al.,22 where the polynomial correction terms were taken as free parameters. The obtained parameter set was then used to fit the experimental force
extension curves with the persistence length and the molecule length as free parameters. FEM Simulations. FEM simulations of cylinder models of multihelix bundles were carried out using the structural mechanics module of COMSOL Multiphysics v3.5a. We used a Poisson ratio of 0.25 and Young’s moduli of 261 and 614 MPa for modeling bending and twisting, respectively. To simulate bending, the points in the center of the bottom faces of the isotropic rods were fixed and various displacements from 0.1 to 10 nm set for center points of the top faces. The software then solved for stresses and strains from which it would calculate the reaction forces acting on the top faces of the rods. The torque simulations were done in a similar way. The bottom edges were fixed and the top edges twisted from 0.005 to 0.5 rad around the center axis of the model. In all cases a linear mechanical response was found. Control FEM simulations of a single rod representing dsDNA provided the expected responses.

’ ASSOCIATED CONTENT

bS

Supporting Information. Discussion of direct torque measurements with magnetic tweezers and supporting figures. This material is available free of charge via the Internet at http:// pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected], [email protected].

’ ACKNOWLEDGMENT We gratefully acknowledge F. Schwarz, S. Kretschmar, S. Kempter, and D. Schiffels for technical support and comments. 5562

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Nano Letters This work was supported by Grant SE 1646/1-1 from the Deutsche Forschungsgemeinschaft (DFG) and a starting grant from the European Research Council (No. 261224) to R.S. and by the Cluster of Excellence NIM and Grant TI 329/5-1 both from the DFG to T.L.

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