Understanding the Mechanical Properties of DNA Origami Tiles and Controlling the Kinetics of Their Folding and Unfolding Reconfiguration

Transcription

1 Purue University Purue e-pubs Birck an NCN Publications Birck Nanotechnology Center Unerstaning the Mechanical Properties of DNA Origami Tiles an Controlling the Kinetics of Their Foling an Unfoling Reconfiguration Haorong Chen Purue University, Birck Nanotechnology Center, Te-Wei Wang Purue University, Birck Nanotechnology Center, Molly M. Riccitelli Purue University, Birck Nanotechnology Center, Yi Cui Purue University, Binley Bioscience Center, Joseph Iruayaraj Purue University, Birck Nanotechnology Center, Binley Bioscience Center, See next page for aitional authors Follow this an aitional works at: Part of the Nanoscience an Nanotechnology Commons Chen, Haorong; Wang, Te-Wei; Riccitelli, Molly M.; Cui, Yi; Iruayaraj, Joseph; an Choi, Jong Hyun, "Unerstaning the Mechanical Properties of DNA Origami Tiles an Controlling the Kinetics of Their Foling an Unfoling Reconfiguration" (2014). Birck an NCN Publications. Paper This ocument has been mae available through Purue e-pubs, a service of the Purue University Libraries. Please contact epubs@purue.eu for aitional information.

2 Authors Haorong Chen, Te-Wei Wang, Molly M. Riccitelli, Yi Cui, Joseph Iruayaraj, an Jong Hyun Choi This article is available at Purue e-pubs:

3 pubs.acs.org/jacs Unerstaning the Mechanical Properties of DNA Origami Tiles an Controlling the Kinetics of Their Foling an Unfoling Reconfiguration Haorong Chen, Te-Wei Weng, Molly M. Riccitelli, Yi Cui, Joseph Iruayaraj,, an Jong Hyun Choi*, School of Mechanical Engineering, Birck Nanotechnology Center, Binley Bioscience Center, Purue University, West Lafayette, Iniana 47907, Unite States Department of Agricultural an Biological Engineering, Binley Bioscience Center, Purue University, West Lafayette, Iniana 47907, Unite States *S Supporting Information ABSTRACT: DNA origami represents a class of highly programmable macromolecules that can go through conformational changes in response to external signals. Here we show that a two-imensional origami rectangle can be effectively fole into a short, cylinrical tube by connecting the two opposite eges through the hybriization of linker strans an that this process can be efficiently reverse via toehol-meiate stran isplacement. The reconfiguration kinetics was experimentally stuie as a function of incubation temperature, initial origami concentration, missing staples, an origami geometry. A kinetic moel was evelope by introucing the j factor to escribe the reaction rates in the cyclization process. We foun that the cyclization efficiency (j factor) increases sharply with temperature an epens strongly on the structural flexibility an geometry. A simple mechanical moel was use to correlate the observe cyclization efficiency with origami structure etails. The mechanical analysis suggests two sources of the energy barrier for DNA origami foling: overcoming global twisting an bening the structure into a circular conformation. It also provies the first semiquantitative estimation of the rigiity of DNA interhelix crossovers, an essential element in structural DNA nanotechnology. This work emonstrates efficient DNA origami reconfiguration, avances our unerstaning of the ynamics an mechanical properties of self-assemble DNA structures, an shoul be valuable to the fiel of DNA nanotechnology. INTRODUCTION The DNA origami technique has emerge as a powerful metho to synthesize programmable nanostructures with high precision. 1 4 This metho has create novel structures not only as static templates for organizing functional molecules 5 7 an nanoparticles 8 13 but also as ynamic platforms for sensing an actuation at the nanoscale. Several strategies have been evelope to achieve such ynamic, shape-changing origami structures. For instance, origami boxes 14 or clamlike switches 15 that can open in response to external stimuli an molecular forceps 16 that pinch upon bining to a molecular target have been emonstrate. These nanomechanical evices achieve conformation changes by using single-strane hinges to connect moving parts while treating ouble-strane omains as rigi boies. Reconfiguration can also be achieve via a releasean-reassemble strategy. A hierarchically assemble DNA tube has been shown to switch between ifferent chiralities, 17 an a simple origami structure can be switche into an back from a quasi-fractal pattern. 18 Recently, rectangular DNA origami sheets ensely functionalize with gol nanoparticles were shown to reaily roll up into short tubes upon aition of a linker set that connect the two opposite eges. 19 The rolling up of unfunctionalize origami rectangles was also briefly mentione in the same work. These results suggest that completely base-paire single-layer DNA origami has consierable flexibility that may be use as a new mechanism for ynamic reconfiguration. In orer to explore this possibility, the kinetics of this shapechanging mechanism is systematically stuie here. Our moel system is an origami tile that globally bens over an seals into a short tube. Unlike most other ynamic DNA structures, the eformation is istribute across the whole sheet instea of being localize at a few single-strane hinges. We fin that the foling kinetics an final yiel strongly epen on the incubation temperature, missing staples, an the imension of the rectangular structure. Elevating the incubation temperature or eliminating as few as seven staples allows foling yiels of over 90% to be achieve within 1 h. We also emonstrate that the foling process can be reverse by isengaging the linkers via Receive: January 24, 2014 Publishe: April 21, American Chemical Society 6995

4 toehol-meiate stran isplacement. 20 The unfoling process is typically complete in less than half an hour even at room temperature an leas to a yiel of almost 100%. Overall, the foling an unfoling kinetics are shown to be well-controllable an reasonably fast, making them useful reconfiguration mechanisms in the inventory of ynamic DNA origami. For example, the flat-to-circular transition can be use to controllably trigger see-catalyze DNA tubule growth. 21 In the fiel of DNA nanotechnology, there has been growing interest in the mechanical properties of self-assemble DNA structures, which are essentially bunles of DNA ouble helices interconnecte by crossovers. The torsional rigiity of such bunles has been irectly measure using magnetic tweezers, 22 an the bening stiffness has also been investigate by cyclization stuies 23 or by probing the persistence length via imaging methos. 24 However, the rigiity of the interhelix crossovers, the connecting part, is still largely unknown. As a result, it remains unclear to what extent one helix can rotate about another helix within the assemble structure. 23 Such uncertainty may pose ifficulties in preicting the ynamic behavior of DNA nanostructures. Because of its small length scale, the fluctuation of a single crossover is ifficult to monitor experimentally. However, within a typical DNA origami tile, the crossovers are arrange into an orere array, an their bening can be accumulate to prouce observable effects (the cyclization of an origami sheet in this work). From our kinetic stuy of the tile cyclization process, the activation energy is probe as a function of origami geometry an missing staples. The experimental observations can be wellescribe by a simple mechanical moel that inclues the bening flexibility of crossovers. From this moel, we estimate that the effective bening stiffness of a phosphate bon in crossovers is similar to that of a one-base-long single-strane DNA an that crossovers contribute most of the bening flexibility of a DNA origami sheet. This fining avances our unerstaning of DNA mechanics an shoul be important for the esign an preiction of self-assemble DNA structures. SCHEME AND MODEL SETUP In this work, a two-imensional rectangular DNA origami tile 32 helices in height an 224 bases in with is esigne as a moel system. A set of linker strans is use to connect the upper an lower eges of the origami, as illustrate in Figure 1a. Here the linkers (shown in re) are arrange parallel to the scaffols (shown in blue an black). They simultaneously hybriize with the scaffols on both eges an thus link them. To make the process reversible, we attache eight-base-long toehol segments (shown in green) of ranom sequences to both the 5 an 3 ens of each linker. The releaser strans, which are completely complementary to the linkers, first hybriize with the unpaire toehols an then completely base-pair with the linkers via branch migration, thereby releasing the linkage. The normal staples on the left an right eges were intentionally remove to prevent blunt en stacking. 1 To allow optical monitoring of the tile conformation, two staples on the upper an lower eges are labele with 6-carboxyfluorescein (FAM) an tetramethylrhoamine (TAMRA), respectively, which isplay iniviual emission signatures peaking at 520 an 580 nm. In a fole tile, the FAM an TAMRA labels on opposite eges are brought to close proximity with each other, an efficient Fo rster resonance energy transfer (FRET) occurs. When the tile unfols, the FAM onor an TAMRA acceptor are separate, causing a rastic ecrease in the FRET efficiency. As a result, the FAM fluorescence at 520 nm is no longer quenche an increases significantly. Figure 1 also illustrates the typical reaction pathways of the system. A flat origami tile (F1) can fol up an seal into a short hollow tube (C1). Other sie reactions inclue the imerization of two tiles into a flat imer (F2) an the cyclization of a imer into a tube with a larger iameter (C2). Although not illustrate here, even higher orer reactions involving more tiles are also possible. The generalize reaction pathways can be ivie into two types: cyclization an oligomerization. Cyclization is escribe by the following reaction: Jk a Fn + L Xooo Y Cn nk Oligomerization can be escribe by the following reactions: ka 2Fn + L F(2 n) k ka Fn + Fm + L XY oo F( n + m) 2k Figure 1. (a) Schematic of a fole scaffol with its opposite eges (black an blue) connecte an seale by a set of toehol-prime linker strans. The linkers an toehols are shown in re an green, respectively. Staple strans use to construct the origami tiles are shown in gray. The green an yellow ots represent FAM an TAMRA fluorophores. (b ) Illustration of possible reaction pathways. DNA ouble helices are presente as gray ros. Re lines represent seale eges. J, k a, an k are kinetic parameters that govern the reaction rates. (b) Monomer cyclization. A flat origami tile (F1) fols up an cyclizes into a short, cylinrical tube (C1). (c) Dimerization. Two flat monomers react an form a flat imer (F2). () Dimer cyclization. A imer seals its two eges an cyclizes into a short tube (C2). (e g) AFM images of various DNA origami species. The ientity of each origami is marke in the images. The striate pattern clearly shows the orientation of the DNA strans. The tiles are connecte in the irection perpenicular to the DNA strans. The F4 object twiste twice when it asorbe on the substrate. Scale bar: 200 nm. (1) (2) (3) 6996

5 where F an C enote the flat an cyclize origami conformations an n an m enote numbers of monomer tiles that particular DNA assemblies contain. L is use to represent the linker set. J enotes the j factor, an intrinsic property of a cyclizable molecule. It has the unit of nm an can be unerstoo as the effective local concentration of reactive ens: two ens of one molecule are always confine in the vicinity of each other, but the rate of their association epens on the probability of the molecule to ben into correct circular conformation. By serving as a kinetic parameter for the cyclization reaction, the j factor also characterizes the reainess of a molecule to flex over into a circular form. As a result, it is a goo inicator of the flexibility an conformation of a molecule. 23,25 27 The reverse reaction involves the breaking of existing linkages. Depening on the specific reaction pathway, the reverse process can be achieve through linkage breaking at one or more sites (see the Supporting Information for etails). Throughout this stuy, we use the same high linker concentration (200 nm, at least 45 times in excess with respect to the origami monomers) to make linker exhaustion negligible. Therefore, the linker concentration [L] is hel nearly constant at all times. Since the linkers are constantly an abunantly available, we treat oligomerization as a secon-orer bimolecular reaction an cyclization as a first-orer unimolecular reaction whose rate can be correlate with the bimolecular reaction rate by the j factor. The forwar an reverse reaction rate constants are enote as k a an k, which have units of nm 1 s 1 an s 1, respectively. As a common assumption, k a is assume to be inepenent of the size of the reacting DNA assembly, an every linkage in one oligomer has equal probability to break with issociation rate constant k. Uner such assumptions, the oligomerization rate can be presente as k a [Fn] [Fm]. To moel the cyclization reaction, we borrow the concept of the j factor (or J) from polymerization theory 28 an DNA cyclization stuies. 23,25 27 The j factor is efine by Shore et al. 27 as the ratio of the equilibrium constants for cyclization an for bimolecular association via the cohesive ens. By this efinition, the cyclization rate for species Fn is expresse as k a J [Fn]. In our experiments, we foun that the origami species are preominantly monomers (F1 an C1) an imers (F2 an C2), with some rare F3 an F4 species. Higher-orer species such as C3, C4, an F5 were never observe. Therefore, we consiere cyclization an oligomerization up to C2 an F4, respectively. The reaction equations can be liste as follows: Jk a F1 + L Xooo Y C1 k,c J k 2 a 2k,c F2 + L XoooY C2 ka 2F1 + L XY oo F2 k,f ka F2 + F1 + L XoooY F3 ka 2F2 + L XY oo F4 k,f 2k,f ka F3 + F1 + L XoooY F4 2k,f (4) (5) (6) (7) (8) (9) Because oligomers with ifferent sizes often have ifferent values of the j factor, a separate j factor, J 2, is assigne to imer tiles. Aitionally, cyclize species experience more mechanical strain than flat species (see Mechanical Analysis of Elastic Deformation, below). As a result, the linkages in cyclize species may be more prone to break. To be able to examine such an effect, we keep the kinetic moel general an assign separate issociation rate constants to flat an cyclize species, which are enote as k,f an k,c respectively. It is expecte that 0 k,f k,c. On the basis of the above reaction equations, a set of orinary ifferential equations (ODEs) can be evelope. We normalize the concentration of every species with the initial concentration of flat monomer, [F1] 0. The normalize concentrations are enote by a bar, an the imensionless set of ODEs is as follows: [C1] = ka [F1] 0 J [F1] k,c [C1] t [C2] = ka [F1] 0 J [F2] 2 k [C2] 2,c t (10) (11) 2 [F1] = ka [F1] 0 { 2 [F1] [F2] [F1] [F3] [F1] t J [F1]} + k {2 [F2] + 2 [F3] + 2 [F4]},f + k,c [C1] (12) 2 2 [F2] = ka [F1] 0 {[F1] [F2] [F1] 2 [F2] t J [F2]} + k { [F2] + 2 [F3] + 2 [F4]} 2,f + 2 k,c [C2] (13) [F3] = ka [F1] 0 {[F2] [F1] [F3] [F1]} t + k,f { 2 [F3] + 2 [F4]} (14) 2 [F4] = ka [F1] 0 {[F2] + [F3] [F1]} 3 k,f [F4] t (15) At the onset of the reaction (i.e., at t = 0), [F1] is equal to 1, while the normalize concentration of every other species is equal to 0. With these initial conitions, the set of ODEs can be numerically solve for a set of floating kinetic parameters (k a, k,c, k,f, J, an J 2 ). Resiual minimization was performe to extract the kinetic parameters that provie the best agreement between the numerical solution an the experimentally obtaine statistical ata. Aitional constraints were neee to make the parameter extraction robust. Since 0 k,f k,c, we examine an compare two extreme cases by ictating either k,f =0ork,f = k,c. The further simplification of ictating J = J 2 coul be mae to spee up the minimization process. This simplification i not significantly affect the extracte k a, k,c, an J values (see Figure S9 in the Supporting Information). All of the conitions yiele generally goo agreement an the extraction of similar k a an J values. The best fit was achieve by using the k,f = 0 constraint an an inepenent J 2. All of the kinetic curves presente here were obtaine from simulations uner these conitions. 6997

6 Journal of the American Chemical Society (C1) solution prepare by annealing 4.2 nm scaffol with 10 staples an 200 nm linkers in one pot (Figure S11). To enable fluorescence measurements, each tile was ecorate with two fluorescently labele staples (a FRET pair, as shown in Figure 1a), an the free, excess staples were remove by centrifugal filtration (Amicon Ultra-0.5, Ultracel-100 membrane, 100 kda) five times. The unfoling kinetics was stuie by monitoring the ecrease in the FRET signal (increase of FAM fluorescence at 520 nm) over time. Fluorescence measurements were performe with a spectrofluorometer (HORIBA Jovin Yvon Fluorolog3) an a StepOnePlus real-time polymerase chain reaction (RT-PCR) machine, which also measure the melting curve. To account for sample loss uring centrifugal filtration, the tile concentration of the filtere sample was reetermine by fluorescence correlation spectroscopy (FCS) (see the Supporting Information for etails). EXPERIMENTAL METHODS Since the concentration of DNA origami tiles is conserve at [F1]0 uring the cyclization/oligomerization reaction, the nonimensionalize concentration of one species is simply its mass fraction ivie by the total number of tiles. In this work, we statistically estimate the mass fraction by taking atomic force microscopy (AFM) images of a sample an counting the occurrences of each species. Similar to previous reports,29,30 the relative abunance of a species in an AFM image (or on a mica substrate) was assume to represent its relative abunance in solution. As shown in Figures S10 an S11, we also verifie this assumption by carrying out calibration measurements on stanar sample solutions. The reaction kinetics was characterize by measuring species fractions as functions of time. Factors such as temperature, DNA origami tile concentration, an the intrinsic structure of the tiles were stuie. The starting material for the cyclization/oligomerization reaction (i.e., flat DNA origami monomer tiles) was synthesize by annealing 4.2 nm m13mp18 scaffol (New Englan Biolabs) with 10 staples in TAEM buffer (1 TAE buffer containing 12.5 mm Mg2+, which was kept throughout the stuy) from 95 to 4 C at a rate of 1 C/min in a thermal cycler. To stuy the effect of temperature an tile concentration, part of the 4.2 nm tile solution was ilute to 1.3 nm with TAEM buffer. Concentrate linker solution (5.8 μm) was ae to the flat tile solution to a final concentration of 200 nm. The mixtures containing 4.2 or 1.3 nm tiles an 200 nm linkers were then ivie into 20 μl aliquots an incubate at the esignate temperature (35, 40, 45, or 50 C) in a thermal cycler for the esignate time (0.5, 1, 2, 4, or 8 h in the 35, 40, an 45 C cases; 10 min, 20 min, 0.5 h, 1 h, an 2 h in the 50 C case). The thermal cycler was programme to rapily cool the aliquot to 4 C when the incubation time was up. The 4.2 nm aliquots were then ilute to 1.3 nm an store at 4 C, while the 1.3 nm aliquots were irectly store at 4 C. Except uring incubation an brief exposure to room temperature, the tile solutions were always kept at 4 C, where no cyclization or oligomerization was observe even after 5 ays. The samples of the incubate aliquots were characterize by air-phase AFM. To eposit the DNA structures on a substrate, 20 μl of TAEM buffer was first eposite on freshly cleave mica, followe by 2 μl of sample solution. The mica substrate was incubate for 10 min in a Petri ish at room temperature an then blown ry with compresse air. The mica isc was immeiately washe by epositing 80 μl of washing solution (1:1 ethanol/water mixture10) on it an blowing it ry three times. Airphase AFM was performe with a Dimension Icon atomic force microscopy an a SCANASYST-AIR probe (Bruker). At least three 5 μm 5 μm AFM images were taken for each measurement. The DNA structures were then ientifie an counte. The total number of tiles counte for each measurement range from 300 to To stuy the effect of origami flexibility an origami geometry, special flat tiles were prepare by eliminating staples from the original complete staple set. To stuy the effect of isolate missing staples, 7, 14, or 21 nonajacent staples (at positions illustrate in Figure S4) were intentionally exclue. To stuy the effect of origami height, 5 or 10 consecutive rows of staples (at positions illustrate in Figure S19) were exclue to prouce shorter tiles that were 22 or 12 helices in height. The synthesis of these special tiles was performe in exactly the same way as for the original tile: 4.2 nm scaffol was mixe with 10 staples, an the mixture was anneale an ilute to 1.3 nm. The foling behaviors of these special tiles were examine at 40 C similarly as the original tiles: 20 μl aliquots containing 1.3 nm tiles an 200 nm linkers were incubate for the esignate time an characterize by air-phase AFM. To visualize the structure etails of the origami structures in their most native environment, liqui-phase AFM imaging was also performe for some samples. Sample eposition was achieve by incubating 20 μl of TAEM buffer an 1.6 μl of sample solution on freshly cleave mica for 5 min. The imaging was performe with a SCANASYST-Flui+ probe (Bruker). The reverse unfoling process was also stuie in this work. The starting material was highly homogeneous (>90%) fole monomer RESULTS External Parameters That Govern the Reconfiguration Reaction Kinetics. In this stuy, the starting tile ensembles were highly homogeneous. The flat tile solution (Figure 2a) i not appear to contain any fole species. The one-pot fole solution (represente by Figure 2b) containe over 90% cyclize monomer tiles. The flat origami tiles in Figure 2a measure Figure 2. AFM images of the DNA origami species. (a) Near 100% flat origami tiles (F1) prepare by annealing without linkers. (b) Over 90% cyclize origami (C1) prepare by one-pot annealing with linkers. (c) Mixture of species obtaine by foling of flat monomers from (a) at 45 C for 2 h. Multiple F1 an C1 as well as one C2 are present. () Nearly 100% F1 generate by unfoling of short tubes from (b) at room temperature. (e) Zoom-in image showing F1, C1, an C2 species excerpte from (c). (f) Cross-section profiles of the three tiles inicate in (e). C1 has exactly the same with as F1. The thicknesses of C1 an C2 are twice that of F1. Scale bars: 200 nm. The original 5 μm 5 μm AFM images are presente in the Supporting Information. 6998

7 Figure 3. Experimental (soli symbols) an numerical simulation (soli curves) results for the time evolution of the fraction of DNA origami species as a function of incubation temperature an initial monomer concentration. The fractions of origami species were statistically counte over time after the aition of linker strans to initiate structural reconfiguration. (a ) Fraction evolution from an initial monomer concentration of 1.3 nm at (a) 35, (b) 40, (c) 45, an () 50 C. (e h) Fraction evolution from an initial monomer concentration of 4.2 nm at (e) 35, (f) 40, (g) 45, an (h) 50 C. It shoul be note that the time scale in the 50 C cases is ifferent to capture their fast reaction kinetics. (i) Association (black squares) an issociation (blue triangles) rate constants as functions of temperature. The re symbols of corresponing shape enote the extracte k a an k,c values for tiles with 0, 7, 14, an 21 missing staples. Missing staples i not significantly change the two parameters. (j) Monomer j factor as a function of temperature extracte from fitting the kinetic moel. Black soli squares enote our original esign, while the other symbols represent origami samples with 0, 7, 14, or 21 staples exclue. Missing staples increase the structural flexibility of the origami, thus changing the cyclization efficiency or J. Note that the kinetic parameters are plotte as functions of temperature instea of the inverse of absolute temperature for clarity. The x-axis is scale such that the Arrhenius equation plots linearly. approximately 100 nm in height an 70 nm in with. The short cylinrical tubes forme by sealing the upper an lower eges collapse into a rectangular shape to maximize their contact with the mica substrate (Figure 2b). The size of the resultant rectangles measure about 70 nm 50 nm, half that of the flat monomer tiles. The thickness of a fole tile was about 4 nm, twice the thickness of a flat tile (Figure 2e,f). Figure 2c shows a typical AFM image after aition of linker strans. The image was taken after incubation at 45 C for 2 h, an we observe a mixture of origami species incluing cyclize monomers an imers (C1 an C2, respectively) along with unreacte flat monomers (F1). In this case, the cyclize short tubes, C1, took up approximately 70% of all the tiles. When the incubation temperature was increase to 50 C, the fraction of C1 was measure to be greater than 90%. The unfoling process was efficient even at room temperature ( 22 C). As shown in Figure 2, all of the origami structures isplaye the morphology of F1 30 min after the aition of releaser strans. The j factor of DNA has been shown to epen on temperature. 31 From our reaction moel, increase initial tile concentration was also expecte to influence the kinetic behavior by shifting the reaction towar the oligomerization pathway. Therefore, we examine the kinetic effect of these two parameters. The fraction of origami species as a function of incubation time was measure uner ifferent conitions. Figure 3a h shows the time evolutions of the fraction of DNA origami species at 35, 40, 45, an 50 C from two ifferent initial origami concentrations (1.3 an 4.2 nm). The experimental results are plotte as soli symbols; the numerical solutions from our kinetic moel are overlai as soli curves in corresponing colors. Since the fractions of F3 an F4 remaine nearly zero throughout all of the experiments, they were not plotte. The reaction kinetics was accelerate by increasing the incubation temperature, as expecte. More importantly, the cyclization yiel increase significantly from 10 to 90% when the temperature was elevate from 35 to 50 C. The en-joining reactions also became more efficient with increasing temperature, as inicate by the ecrease in the fraction of unreacte F1 from about 70 to 10%. However, the increase en-joining efficiency i not lea to increases in the fractions of of oligomerize species such as F2 an C2. In fact, the oligomer fractions ecrease steaily with increasing temperature. This opposition in trens inicates that the cyclization reaction rate increase faster than the oligomerization rate. As a result, cyclization suppresse oligomerization by rapily consuming reactive monomer tiles. The >20-fol increase in the j factor shown in Figure 3j confirms this qualitative conclusion. In a parallel observation, it is clear that a high initial monomer concentration, [F1] 0, favors oligomerization, as oligomerize 6999

8 Figure 4. Evolutions of species fractions as functions of time for origami sheets with (a) 0, (b) 7, (c) 14, an () 21 staples exclue. Front views of CanDo-simulate origami structures are presente besie the plots for visualization of the effect of eliminating staples. The overall structural shapes were little affecte by missing staples. species were always more abunant in the 4.2 nm case than in the 1.3 nm case. The agreement between the experimental results an our simulations is fairly goo. A set of kinetic parameters (k a, k,c, J, an J 2 ) simultaneously escribe the time evolutions from the two ifferent initial concentrations with reasonable accuracy. Most ata points coincie within the experimental uncertainty margin. The kinetic parameters for the best fit are plotte in Figure 3i,j. The association rate constant k a follows the Arrhenius equation with goo linearity in semilog plots. The activation energy for the association reaction was etermine to be 28.7 ± 2.5 kcal/mol. The values of the j factor below 50 C fit the Arrhenius equation excellently, with an activation energy of 32.4 ± 0.7 kcal/mol. This activation energy represents the energy barrier for bringing the origami rectangle into a correct circular conformation so that the linkers can effectively hybriize with both eges. As will be iscusse later, a simple mechanical moel can give a goo estimation of this energy barrier by moeling the ouble helices an crossovers as springs. The J value at 50 C is significantly larger than that preicte by the Arrhenius equation. This eviation is probably ue to the partial issociation of staples at a high temperature. Yan an coworkers mappe the thermal behavior of DNA origami by functionalizing neighboring staples with FRET yes an measuring the FRET efficiency as a function of temperature. 32 From their experimental results, the complete issociation of staples is rare at or below 50 C. However, partial issociation may be significant at that temperature. The single-strane omains resulting from partial issociation are mechanically much more compliant than ouble strans. As a result, the overall structure is softene an easier to ben over, leaing to the increase j factor. The melting temperature for our tiles was shown to be above 55 C (Figure S14b). Since the melting of DNA origami happens with a narrow temperature range, 32 we hypothesize that the effect of staple issociation is not significant at or below 45 C, which is over 10 C below the melting temperature. The excellent linearity of the J plot at 35, 40, an 45 C serves as a confirmation. To accurately extract the activation energy for completely base-paire origami tiles, the 50 C ata point was exclue from the Arrhenius analysis. While k a an J closely follow the Arrhenius equation, k,c ranges aroun 10 4 s 1 within a factor of 2. We hypothesize that k,c is etermine by two parallel processes. First, the cyclize tiles may have a low probability of opening up (i.e., linkage rupture) ue to their mechanical strain. This process is relatively insensitive to temperature. Secon, the linker strans can spontaneously issociate even when below the melting temperature. This process is rare at low temperatures but becomes significant at 50 C. Because of the ifferent temperature epenences of the two processes, k,c remains nearly constant at low temperatures an increases rapily at 50 C. Effect of Structural Properties. The intrinsic structural stiffness woul also be expecte to significantly affect the cyclization behavior. To examine this effect, origami reconfiguration uner isothermal conitions (40 C) was performe for origami tiles from which staples were intentionally exclue. Three types of tiles, with 7, 14, an 21 staples remove, were examine alongsie the original intact tiles that containe the complete staple set. The positions of the missing staples were sparsely istribute across the rectangular tile so that the resultant single-stran omains were isolate. The finite-element simulation results from CanDo 33,34 presente in Figures 4 an S18 show that the equilibrium global twisting is largely etermine by the helix pitch mismatch an little affecte by isolate single-stran holes. Since the global conformation is largely unchange, any increase in j factor shoul primarily correlate with increase origami flexibility rather than conformational change. Figure 4 shows the time evolutions of the species fractions as functions of the number of missing staples. The four sets of experimental ata can be fitte with the same set of k a, k,c, an J 2. The change in J alone can account for all of the ifferences in reaction kinetics. The foling kinetics for the intact tile (Figure 4a) was very close to the previously measure result at the same temperature an tile concentration (Figure 3b). In contrast, the kinetics was significantly change even when only seven staples were eliminate. The monomer j factor increase 12-fol to 150 nm. The accelerate foling reaction practically reache completion within 1 h, an the final foling yiel was over 90%. The reaction was accelerate even more when 14 staples were eliminate, an the reaction reache completion in about 0.5 h. When too many staples (e.g., 21) were eliminate, however, the foling efficiency starte to ecrease from the highest value, probably because of compromise structural integrity (see the comparison of the AFM images of the four tiles in Figures S12 an S13). The extracte k a, k,c an J values are plotte in Figure 3i,j alongsie the results of the previous section. It can be seen 7000

9 Journal of the American Chemical Society Figure 5. Representative AFM images of flat origami tiles (a c) before an ( f) after foling (30 min after aition of linkers). The origami tiles contain 12 helices in (a), (), an (g), 22 helices in (b), (e), an (h), an 32 helices in (c), (f), an (i). Scale bars: 200 nm. (g i) Zoom-in AFM images (240 nm 240 nm) with corresponing cross-section profiles. (j) Fractions of C1 (i.e., foling yiels) for ifferent tiles as functions of time. that ka an k,c are harly affecte by the missing staples while J sensitively epens on the number of missing staples. A high j factor of 320 nm was achieve when 14 staples were eliminate. Even higher values woul be expecte if we were to simultaneously exclue staples an increase the incubation temperature. From our reaction moel, the fraction of oligomerization proucts can be limite to <10% when the starting monomer concentration is less than 1/10 of the j factor. In DNA origami stuies, the concentration is typically below 10 nm. Therefore, by using rational esigns an/or choosing suitable incubation conitions, this foling mechanism can work effectively for typical DNA origami applications without the nee for ilution. Effect of Origami Geometry. To probe the effect of origami geometry, we synthesize shorter origami rectangles (12 an 22 helices in height) by eliminating 10 or 5 consecutive rows of staples from the initial 32-helix rectangle esign.6 New linker sets were esigne to brige the opposite eges of the shorter tiles in exactly the same configuration. The shorter tiles as well as the original one were mixe with 200 nm corresponing linkers an incubate at 40 C for 10, 20, or 30 min. Figure 5 shows representative AFM images. For the shorter tiles, the unuse scaffol segment appears as a ranom filament besie the istinct rectangular structure. The with of all of the tiles remaine at about 70 nm regarless of the tile height or whether the tile was fole. Before foling, the height of the 12-helix tile range from 30 to 35 nm, close to the expecte value of 35 nm. The height of the 22-helix tile measure from 60 to 65 nm, consistent with the expecte value of 65 nm. The height of the 32-helix tile was 100 nm, the same as measure before. Figure 5 f shows representative AFM images after 30 min of incubation with linkers. The corresponing zoom-in images an cross-section profiles are presente in Figures 5g i. While some tiles remain unchange, istinct new species appear in each image. The new species are about half the height an twice the thickness of the flat tiles, which unambiguously inicates their ientity as fole monomers (C1). The flat an fole tiles in an image can be clearly ientifie by their ifference in size an contrast. After 30 min of incubation, over half of the 12-helix tiles an most of the 22-helix tiles are fole, while only a small portion of the original 32-helix tiles are fole. The exact foling yiels as functions of time are presente in Figure 5j. It is unambiguous that the 22-helix tiles have the highest foling reaction rate, while the foling reaction rate of 32helix tiles is significantly lower than those of the other two types of tile. The nonimensionalize foling reaction rate is J ka. Since the three types of rectangles use the same linking mechanism, their association rate constants ka shoul be close. Therefore, we have the following relation: J(22 helix tile) > J(12 helix tile) > J(32 helix tile) 7001 (16)

10 Unfoling Process. The unfoling process was foun to be kinetically fast even at room temperature. Typical AFM oes not have enough temporal resolution to monitor it. Since only one reaction pathway is involve here (no sie reactions), we probe the kinetics by monitoring the FRET signals from FAM an TAMRA pairs. Figure 6a shows the fluorescence spectra of the Figure 6. (a) Fluorescence spectra of cyclize (fole) an flat (unfole) tiles. A FRET pair consisting of FAM (λ peak 520 nm, shown in green) an TAMRA (λ peak 580 nm, shown in yellow) inicates the conformation of the DNA origami. When the origami is fole, the FRET signature is evient, as both the FAM an TAMRA signals are istinct, whereas the FAM onor signal is ominant for flat origami. (b) Real-time fluorescence measurements before an after aition of the releaser strans. Black squares, experimental ata; blue line, linear fit of the ata before aition of releaser strans; re curve, exponential fit of the ata after aition of releaser strans. (c, ) Normalize fluorescence changes for (c) various releaser stran concentrations an () various incubation temperatures. Circles, experimental ata; soli lines, best single-exponential ecay fits. (e) Rate constant (k ) for the unfoling reaction as a function of releaser stran concentration at 30 C. The error bars were calculate from ifferences between two measurements. (f) Rate constant for the unfoling reaction as a function of temperature at a releaser stran concentration of 200 nm. Note that the x-axis is scale to make Arrhenius equation plot linearly. origami tiles before an after the unfoling reconfiguration. With excitation at 480 nm, FAM fluoresces at 520 nm, while the TAMRA emission signature exhibits its peak at 580 nm. The FRET signal is clearly visible for the fole tiles, as the FAM peak intensity is less than 40% of the value in the flat case an the TAMRA signature is much more istinct. In our experiments, the increase in the FAM peak value shoul be proportional to the amount of F1 species unfole from C1. The releaser strans were ae at least 50 times in excess to make their exhaustion negligible. As a result, the probability for each origami to unfol remaine nearly constant, an a single-exponential ecay curve was expecte for the FAM fluorescence change. Figure 6b shows the real-time fluorescence measure at 520 nm. When left with no releaser strans at room temperature, the fluorescence intensity of the sample increase slowly with time, inicating the spontaneous unfoling of fole monomers. As a control, flat tile solutions i not show a significant fluorescence change. The unfoling rate can be expresse as k,c [C1], where k,c is the issociation rate constant for cyclize species as efine before. Because of the efficiency of toehol-meiate stran isplacement, the fluorescence increase was ramatically accelerate by the aition of releaser strans. From the slopes of the two fitte functions in Figure 6b, the rate was increase by a factor of 16. We efine a new symbol k to enote the issociation rate constant in the presence of releaser strans. From the fit of the fluorescence curve to an exponential ecay function, k can be extracte. Since the fluorescence increase rate is proportional to the unfoling rate, the issociation rate constant in the absence of releasers may be calculate as k,c = k /16 = s 1. Previously, our reaction rate moel conclue that k,c remaine at about s 1 at low temperatures, in goo agreement with the irectly measure value. To further stuy the unfoling kinetics, we measure the unfoling rate constant as a function of temperature an releaser concentration. Figure 6c, shows the corresponing normalize fluorescence changes as functions of time. All of the experimental curves can be escribe well by exponential ecay functions. The extracte k values are plotte in Figure 6e,f. k is nearly proportional to the releaser concentration an follows the Arrhenius equation closely. The activation energy was etermine to be 30.2 ± 1.6 kcal/mol, which is close to the value of 33 kcal/mol measure for branch migration. 35 The overall agreement suggests that the unfoling kinetics is wellgoverne by that of stran isplacement. To control the unfoling kinetics, one may change the toehol length, 20 the concentration of releaser strans, or the incubation temperature. Mechanical Analysis of Elastic Deformation. In our esign, the crossovers are place perioically with a perio of 32 base pairs (bp). If ouble-strane helices were to complete one turn every bp, the esign woul result in a planar origami sheet. However, the helical pitch of unstraine B-form DNA in solution is approximately 10.5 bp. 36,37 The slight ifference causes the origami to assume a twist-ben curvature, 32,33 as shown in Figure 7a. Figure 7. Schematic illustration of the conceptual two-step foling process: (a) equilibrium curve origami sheet; (b) intermeiate planar origami sheet; (c) flexe-up origami reay for linker hybriization. The fole short tube after the aition of linkers is illustrate in Figure 7c. In view of the rotational symmetry of the structure, the ouble helices in the bunle shoul be straight an parallel to each other. Consequently, neighboring crossovers on the same ouble helix are expecte to have ientical orientations. Therefore, the ouble helix shoul complete an integer number of turns between crossovers. Since the crossover perio is still

11 bp as in our original esign, the helical pitch is force to have a value of bp/turn in the fole short tube. The correct orientation of reactive ens is important for cyclization reactions, 25 an the twist-ben curvature in Figure 7a is expecte to inhibit the linker set from working effectively because even if the sheet is eforme to a large extent, the two eges will still have lateral islocation an the two corresponing bining sites for a linker will still be too far apart. For the linkers to effectively seal the two eges, the ege helices nee to be correctly aligne an brought into close proximity. To account for this requirement, we moele the foling process by conceptually introucing an intermeiate planar conformation (Figure 7b). The correct ege alignment can be guarantee when such a planar sheet is flexe. The foling process can then be ivie into two steps: I. planarize the origami tile from the curve sheet; II. flex the planar sheet into a close form for sealing of the two opposite eges. Step I may be achieve by simply forcing the DNA ouble helices into a bp/turn pitch. As per our esign, the origami sheet will then assume a planar conformation. This step requires an energy enote as E 1. For a 32-helix tile, E 1 = 25.6 kcal/mol (see the Supporting Information for calculation etails). Step II requires the flat origami to be flexe out of plane an into a circular conformation. The bening flexibility of the planar origami originates from two sources, as illustrate in Figure 8. To calculate the total energy neee for cyclization, we use the efault moulus values from CanDo 33,34 (see the Supporting Information for etails). This set of rigiity values is compatible with previous DNA mechanics stuies an has provie goo preictions of three-imensional origami equilibrium geometry valiate by transmission electron microscopy (TEM). 34 To the best of our knowlege, there have been no reports on the rigiity of crossovers. Therefore, we treate this as an unknown parameter to be fixe by our experimental observations. By aing E 1 an E 2 from steps I an II, we calculate the total elastic energy as a function of origami height, as plotte in Figure 9 (see the Supporting Information for etaile calculations). The Figure 9. Calculate total elastic energy for bringing an origami tile into circular conformation as a function of origami height. The number near each curve enotes the crossover bening moulus use to calculate that curve, relative to the value for single-strane DNA. Figure 8. (a) Three-imensional view of the uneforme structural motif. Blue ros represent ouble-strane helices. Gray ros enote crossovers. (b) Twisting of the 16 bp omain between opposite crossovers moves neighboring ouble helices out of plane. This flexibility is enote by a torsional spring constant, k t. The re color highlights the eforme element. (c) Bening of crossovers also moves neighboring ouble helices out of plane. This flexibility is enote by a bening spring constant, k b. () Top view of the structural motif in DNA origami. (e) Sie view of the equivalent spring network for a planar tile in our mechanical analysis. First, the crossovers to ajacent rows are arrange in a staggere manner with a istance of 16 bp (Figure 8a,). The twist of the 16 bp ouble-strane helix between opposite crossovers sens ajacent helices out of plane (Figure 8b). Secon, a crossover between ouble helices consists of two phosphate bons (or only one if the crossover is locate on the ege) possessing certain bening flexibility. Bening of the crossovers woul flex the sheet further out of plane, as shown in Figure 8c. These flexible components can be moele as springs connecte into a network (Figure 8,e) whose effective spring constant may be calculate from formulas for springs in parallel an series. 38 Collectively, these flexible joints can create a global flexure of 360. This step requires an energy enote as E 2. bening rigiity of the crossover was varie from 0.4 to 5 times that of one-base-long single-strane DNA. For a longer origami tile of the same with, there are more ouble helix omains whose helical pitches must be force to take the value bp/ turn, an therefore, E 1 increases. However, a longer tile has more flexible joints in series an is easier to flex, resulting in a reuce E 2. If the crossovers are highly flexible, E 1 ominates an the total energy increases with the origami height (e.g., the curve marke as 0.4 in Figure 9). In contrast, if the crossovers are highly rigi, E 2 ominates an the total energy ecreases with increasing origami height (e.g., the curve marke 5 in Figure 9). When the crossover rigiity is between these extremes, E 1 an E 2 are comparable. A minimal elastic energy occurs for origami tiles of moerate height. From our experiment, we foun the relation in 16, which leas to E (32 helix) > E (12 helix) > E (22 helix) elastic elastic elastic This inequality can be satisfie only when the bening stiffness of a phosphate bon in a crossover is within a narrow range aroun 1 times that of the one-base-long single-strane DNA (the curve shown in re in Figure 9). Therefore, we estimate that the bening moulus of a crossover phosphate bon is similar to that of single-strane DNA. Corresponingly, the effective bening spring constant for the bon is 6.8 pn nm/ra (see the 7003

12 Supporting Information for etails). From this stiffness value, E 2 was calculate to be 6.7 kcal/mol. The total elastic energy neee to fol a 32-helix origami is 32.3 kcal/mol, which is very close to the experimentally erive value of 32.4 kcal/mol. The mechanical moel also preicts the effect of missing staples. When some staples are eliminate, the number of ouble-helix omains to be force to have a pitch of bp/ turn in step I ecreases, leaing to reuce E 1. The origami also becomes more flexible, as there are fewer parallel springs in the spring network. These effects collectively result in a ecrease energy barrier an an increase j factor. As an example, we consier the origami tile with seven staples eliminate. The ecrease in the energy barrier is calculate to be Δ E = 1.51 kcal/mol elastic At 40 C, the j factor is expecte to increase by a factor of exp( Δ E / k T) = 11 elastic B in excellent agreement with the 12-fol increase observe experimentally. DISCUSSION Flexibility of Crossovers. Since the crossovers consist of two phosphate bons an the two bons are not joine by base recognition at their ens, it is not surprising that the bon s bening flexibility is in a range similar to that of single-strane DNA. At least two effects influence the apparent crossover bening flexibility we observe in this work. First, the bening is likely to be a nonlinear process. When the crossovers are significantly bent, electrostatic an steric repulsion between the helices they connect increases rapily. This effect tens to ecrease the apparent crossover flexibility. Secon, crossovers create nicks in the ouble helices they connect. These nicks ten to reuce the local stiffness of the structure an may increase the apparent flexibility of crossovers. For our moel system, the two effects seem to offset each other. As a result, the phosphate bon behaves like that in single-strane DNA. The flexibility of the origami tile mostly originates from crossover flexibility. When we assume very large spring constants in the mechanical moel for crossovers, thereby eliminating their flexibility, E 2 increase ramatically from 6.7 to 51 kcal/mol. This result inicates that crossovers contribute most of the bening flexibility of the origami tile. Activation Energy for Cyclization. We experimentally observe a sharp temperature epenence of the cyclization efficiency, corresponing to large activation energy of 32 kcal/ mol. Such a large value can be expecte for the foling of macromolecules such as DNA origami or protein. 42 The linkers we use to connect the origami eges bin to one ege of the origami through a 24-base omain an to the other through an eight-base omain. When the origami sheet fols into a short tube, every linker stran contributes an aitional 8 bp ouble helix. Accoring to the nearest-neighbor moel, 43 the average ecrease in free enthalpy for an 8 bp ouble helix is 8.8 kcal/mol in 1 M Na + at 40 C. The 13-linker set thus ecreases the free enthalpy by 114 kcal/mol, which is more than enough to compensate for the energy barrier. If the number of linkers is reuce to four, the aitional base pairing can only ecrease free enthalpy by 35.2 kcal/mol, which is barely enough to overcome the energy barrier. In view of the fact that the bining between DNA strans is weaker in 12.5 mm Mg 2+ than in 1 M Na +, 44 at least five or six linkers are neee for effective foling of our tile uner 40 C. Experimentally, we observe that fole species starte to appear when the number of linkers was increase to six (Figure S16). The general agreement provies another confirmation of our analysis. Activation Energy for En Association. The 29 kcal/ mol activation energy for the en-association reaction between tiles is also quite large. This may explain the relatively ineffective linking in the vertical irection (in our esign, the ouble helices are oriente horizontally). When connecting the tiles vertically, we have never observe origami chains longer than four tiles ( 400 nm). In contrast, connecting the tiles horizontally can easily prouce ribbons longer than 1 μm ( 14 tiles; Figure S15). Sugiyama an co-workers have also observe a lower linking yiel for connecting origami tiles vertically compare with horizontally. 45 Interestingly, the activation energy for vertical en association (29 kcal/mol) is similar to E 1 (25.6 kcal/mol), the energy neee to planarize the tile. We speculate that the linking inefficiency in the vertical irection may be largely ue to the inhibitory effect of global twisting. Since the linkers are farther apart in the vertical linking scheme than in the horizontal linking scheme (istance between linkers: 10 nm vs 5 nm, respectively), they may be more sensitive to the misalignment between bining sites cause by curve eges. Guielines for Designing Dynamic Origami Structures That Use Crossover Flexibility. Our experimental results have emonstrate efficient foling/unfoling origami reconfiguration. For future applications of this reconfiguration mechanism, our mechanical moel can provie a few esign guielines base on estimates of the energy barrier: (1) A minimum number of linkers is require. Because the energy barrier is relatively large (typically >20 kcal/mol), a minimum number of linkers is neee to compensate for it. Our mechanical moel can be aapte to calculate the elastic energy barrier for foling of an origami sheet an thereby estimate the minimum number of linkers. To enhance the reaction kinetics an to account for any estimation uncertainty, aitional linkers are recommene to effectively rive the foling process. (2) The energy barrier shoul be lowere by reucing the global twist of the origami tile. From our calculations, E 1 contributes about three-fourths of the cyclization energy barrier. This portion of the energy barrier has little epenence on the aspect ratio of the origami tile. Therefore, the global twist poses a major obstacle for origami tile foling. Fortunately, the global twist can be reuce by rational esign. 30,36 Designs that follow the natural 10.5 bp/turn helical pitch are expecte to have a much higher reconfiguration efficiency. CONCLUSIONS We have stuie the foling an unfoling kinetics of a rectangular DNA origami tile, which represents an alternative mechanism for ynamic shape-changing DNA origami. The foling process utilizes the intrinsic flexibility of an origami sheet an is riven by linkers that connect the two opposite eges. Eliminating a few staple strans or increasing the incubation temperature resulte in foling yiels of over 90% within 1 h. The foling process can also be efficiently reverse via toeholmeiate stran isplacement. A simple chemical reaction moel has been propose to escribe the cyclization/oligomerization kinetics uring the foling reconfiguration. The reaction parameters, such as the association rate constant an j factor, were extracte from the numerical calculations. A two-step mechanical moel has been create to correlate microscopic origami structure etails with 7004