Bowen LiangDepartment of Mechanical and

Aerospace Engineering,

The Ohio State University,

Columbus, OH 43210

Anand NagarajanDepartment of Mechanical and

Aerospace Engineering,

The Ohio State University,

Columbus, OH 43210

Michael W. HudobaDepartment of Engineering,

Otterbein University,

Westerville, OH 43081

Ricardo AlvarezDepartment of Mechanical and

Aerospace Engineering,

The Ohio State University,

Columbus, OH 43210

Carlos E. CastroDepartment of Mechanical and

Aerospace Engineering,

The Ohio State University,

Columbus, OH 43210

Soheil Soghrati1Department of Mechanical and

Aerospace Engineering,

The Ohio State University,

Columbus, OH 43210;

Department of Materials

Science and Engineering,

The Ohio State University,

Columbus, OH 43210

e-mail: soghrati.1@osu.edu

Automated Quantificationof the Impact of Defectson the Mechanical Behaviorof Deoxyribonucleic AcidOrigami NanoplatesDeoxyribonucleic acid (DNA) origami is a method for the bottom-up self-assembly of com-plex nanostructures for applications, such as biosensing, drug delivery, nanopore technolo-gies, and nanomechanical devices. Effective design of such nanostructures requires a goodunderstanding of their mechanical behavior. While a number of studies have focused on themechanical properties of DNA origami structures, considering defects arising from molecu-lar self-assembly is largely unexplored. In this paper, we present an automated computa-tional framework to analyze the impact of such defects on the structural integrity of a modelDNA origami nanoplate. The proposed computational approach relies on a noniterativeconforming to interface-structured adaptive mesh refinement (CISAMR) algorithm, whichenables the automated transformation of a binary image of the nanoplate into a high fidelityfinite element model. We implement this technique to quantify the impact of defects on themechanical behavior of the nanoplate by performing multiple simulations taking intoaccount varying numbers and spatial arrangements of missing DNA strands. The analysesare carried out for two types of loading: uniform tensile displacement applied on all theDNA strands and asymmetric tensile displacement applied to strands at diagonal corners ofthe nanoplate. [DOI: 10.1115/1.4036022]

Keywords: DNA origami, mechanical behavior, nanoplate, CISAMR, mesh generation,uncertainty quantification

1 Introduction

In addition to its biological function of encoding genetic infor-mation, DNA is now recognized as a versatile nanomaterial toconstruct devices for applications, such as drug delivery [1–3],biosensing [4,5], and measurement tools [6,7]. Decades of researchin structural DNA nanotechnology have enabled the design ofintricate structures with dimensions of 1–100 nm [8,9], positioningresolution even down to the subnanometer scale [10], and latticeassemblies up to the micron [11] and even millimeter scale [12].The scaffolded DNA origami approach [13] led to the design ofnanostructures with unprecedented geometric complexity. In thisapproach, a long “scaffold” strand is folded into a compact struc-ture via base-pairing interactions with 150–200 shorter “staple”strands typically 20–50 bases long. This folding process is illus-trated schematically in Fig. 1 for a model nanoplate, with reducedsize and number of staple strand components for simplicity.Single-stranded DNA tile [14] and single-stranded DNA brick[15] approaches were developed to build structures of similar geo-metric complexity and underlying architecture using purelyshorter strands. More recently, approaches have been developedto automate the design of a range of solid three-dimensional (3D)

structures with considerable geometric versatility based on com-puter aided design models [16,17].

The increasing interest in DNA-based materials and devices hasled to efforts to understand the mechanical properties of variousDNA assemblies [18]. Mechanical modeling studies have largelyfocused on predicting the assembled structure geometry and flexi-bility [19], while a few experimental studies have used force spec-troscopy [20,21] and imaging of thermal fluctuations [22] toquantify the mechanical properties of DNA nanostructures. Theseprior studies have led to a basic understanding of the mechanicalstiffness, in particular bending stiffness, of various DNA assem-blies and the ability to predict folded shapes including caseswhere local stresses lead to curvature [23,24]. In addition, thefinite element method (FEM) [20,25] and molecular dynamics(MD) [26] have been demonstrated as viable tools for the analysisof DNA origami nanostructures to predict mechanical properties.In particular, the finite element (FE) based tool, computer-aidedengineering for DNA origami (CanDo) [25,27], which describesDNA base pairs as two-node beam elements with effective elasticand geometric properties, has been widely used to predict foldedgeometries and local flexibility of DNA origami structures.

The studies outlined above have exclusively considered nano-structures with perfect assembly, where all of the strand compo-nents are correctly incorporated. However, a recent study [28]demonstrated that the DNA origami molecular self-assembly pro-cess generally leads to one or a few strands missing, which results

1Corresponding author.Manuscript received October 8, 2016; final manuscript received February 3,

2017; published online March 1, 2017. Assoc. Editor: Jeffrey Ruberti.

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in pre-existing structural defects. The mechanical impacts of thesedefects have remained unexplored largely because of the difficultyof screening a large variety of possible defects, as there are over150 strands that could potentially be missing. Further, consideringvarying spatial arrangements of multiple defects leads to anextremely large set of possible combinations, even for just twomissing strands. Although self-assembly conditions may be opti-mized to minimize defects, that would be a timely process, whichis still unlikely to lead to a perfectly folded structure. Thus, sincethe presence of missing strand defects in DNA origami nanostruc-tures is challenging to avoid and costly to minimize, it is criticalto understand the impact of defects on the mechanical behavior.Given the large number of possible defects and experimental diffi-culties, a computational approach to rapidly screen the uncertaintyof mechanical properties would be highly desirable. Consideringso many cases by MD simulations is intractable; and it is possiblevia existing FEM approaches that capturing the local effects ofmissing strands requires a more detailed description of the DNAstructure than beam elements [25].

Similar problems are encountered in the field of computationalmaterial engineering, where quantifying the uncertainty associatedwith pre-existing defects in the mechanical behavior is essentialfor the reliable design of a materials system. Several techniquessuch as data-driven approaches [29] and micromechanical models[30] have been developed to accomplish this goal. However, theuses of numerical techniques such as FEM for the treatment ofsuch uncertainty quantification (UQ) problems could still be alaborious process. Two major barriers toward this task are (i) cre-ating multiple realistic geometrical models of the problem withvarying shapes and spatial distributions of defects and (ii) con-structing an appropriate conforming mesh to discretize each geo-metrical model [31].

Two metrics are frequently used to determine the quality ofan FE mesh: the geometric discretization error and aspect ratiosof elements [32]. Several techniques have been developed forthe construction of conforming meshes, such as the Delaunay

triangulation [33], advancing front [34], and quadtree/octree-based methods [35]. Creating a high-quality mesh via such algo-rithms often involves an iterative smoothing or optimizationphase, together with other techniques, such as node relocation andedge swapping. This process could be computationally demandingwhen multiple FE models are required for a UQ, as even smallchanges in the domain morphology often necessitate the recon-struction of a whole new mesh. Recently, Soghrati et al. [36]introduced a conforming to interface-structured adaptive meshrefinement (CISAMR) technique that enables the automated FEmodeling of problems with complex geometries. CISAMR relieson a noniterative algorithm to transform a structured grid into ahigh-quality conforming mesh. A unique advantage of this methodis the ability to locally modify the mesh by adding/removing ageometric entity (e.g., a defect), which highly facilitates creatingmultiple models of a materials system (e.g., a DNA origami nano-plate) with varying morphological features.

The aim of this paper is to demonstrate the application of afully automated computational framework relying on CISAMRfor the UQ of the impact of defects (missing staples) on themechanical behavior of a model DNA origami nanoplate. Wechose to focus on a nanoplate structure (Fig. 2), since they arewidely used as templates for nanoparticles, proteins, chemicalreactions, and biomarker detection [37]. In addition, smaller ver-sions of DNA origami nanoplates have been the subject of mechan-ical analysis by force spectroscopy [38] and can serve as a basis fora wide range of materials, such as DNA origami ribbons [39], illus-trated in Fig. 2(b). Further, varying arrangements of nanoplatescould serve as a basis for metamaterials, where local reorientationcontributes to the overall mechanical behavior (Fig. 2(c)), similarto structures realized with elastomeric materials [40].

2 CISAMR Algorithm

In this section, we provide an overview of the CISAMR algo-rithm, as originally presented in Ref. [36]. CISAMR implements

Fig. 2 (a) Atomic-force microscopy image of DNA origami nanoplates, togetherwith example DNA origami materials composed of an array of these nanoplatesconnected (b) along a complete edge and (c) at varying corner points

Fig. 1 Many staple strands bind piecewise to the scaffold strand to fold that into a compactstructure for a small model of a DNA origami nanoplate

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three noniterative steps to create a hybrid conforming mesh com-posed of quadrilateral and triangular elements: h-adaptivity, r-adaptivity, and subtriangulation of the background mesh, whichare described in more detail in Secs. 2.1–2.3.

2.1 Step 1: h-Adaptivity. As the first step, CISAMR uses anh-adaptive refinement algorithm to subdivide the background ele-ments in the vicinity of materials interfaces to accurately approxi-mate the gradient field and minimize the geometric discretizationerror. As shown in Fig. 3(a), at each level, the elements cut by theinterface and their selected neighboring elements are subdividedinto four smaller quadrilateral elements. In this algorithm, if oneof the nodes of a nonconforming element is located in a differentmaterial phase than one of the element edges connected to that,all the neighboring elements sharing that node are subjected torefinement.

2.2 Step 2: r-Adaptivity. Next, an r-adaptivity algorithm isemployed to transform the refined grid constructed after applyingthe SAMR step into a deformed mesh in the vicinity of materialsinterfaces, as illustrated in Fig. 3(b). This process begins by calcu-lating intersection points of interfaces with the edges of back-ground elements. We then visit the nodes of elements cut bymaterials interfaces to determine whether they need to be relo-cated by moving to the interface. As shown in Fig. 3(b), afterapplying this algorithm, the original nonconforming elementseither transform into conforming elements or are diagonally cutby the interface. Assuming that h is the length of element edgesconnected to node N and d is the distance between this node andthe intersection point of the interface with one of these edges, thefollowing algorithm is employed to update the location of N :

(1) One of the edges intersects the interface:(a) if d � 0:5h : do not move N and(b) if d < 0:5h : snap N to the interface/edge intersection

point.(2) Two perpendicular edges intersect the interface:

(a) if d1 � 0:5h1 and d2 � 0:5h2 : do not move N ,(b) if d1 < 0:5h1 and d2 � 0:5h2 : snap N to the intersection

point at distance d1, and(c) if d1 < 0:5h1, d2 < 0:5h2, and d1 < d2 : eliminate the

intersection point at distance d2 and snap N to the inter-section point at distance d1.

2.3 Step 3: Subtriangulation. Finally, all the backgroundelements deformed during the r-adaptivity process, as well as ele-ments with hanging nodes due to applying SAMR to their neighbor-ing elements, are subtriangulated to create the final conformingmesh (Fig. 3(c)). As noted previously, all the remaining noncon-forming quadrilateral elements after the r-adaptivity phase are cutdiagonally by the interface. Using the following rules for the sub-triangulation of these elements guarantees that the aspect ratios ofthe resulting subelements are lower than three: (i) Wheneverpossible, i.e., if the element is not cut by the interface along thediagonal emanating from its smallest angle, the cut used for

subdividing that into two triangular elements must emanate fromits largest angle. (ii) If the element is already cut along the diago-nal emanating from its largest angle, and this angle is smaller than60 deg, cut the element along both its diagonals to subdivide thatinto four subtriangles.

It is worth mentioning that although the aim of the currentpaper is to establish an automated computational framework formodeling two-dimensional DNA origami nanoplates, there is noinherent limitation for expanding CISAMR to 3D. Thus, a similarthree-step process involving h-adaptivity, r-adaptivity, and subtetra-hedralization can be implemented to create high-fidelity FE modelsof DNA origami objects with more complex 3D nanostructures.

3 DNA Origami Nanoplate

3.1 Design and Assembly. To demonstrate the utility of CIS-AMR for UQ in DNA origami nanostructures, we focused on ananoplate modeled after the Rothemund rectangle [13] as anexemplary structure. This nanoplate consists of 26 helices joinedtogether side by side to make a rectangle that is approximately65 nm wide� 105 nm long, as shown in Fig. 4(a). Many flat DNAorigami nanostructures, including the Rothemund rectangle,exhibit an irregular underlying strand architecture due to the pres-ence of a scaffold seam that is required for a circular scaffold.Here, we focus our analysis on a nanoplate with a regular underly-ing strand architecture to avoid potential stress concentrations thatmay result from an irregular strand architecture. This regularstrand design can be achieved using a linearized scaffold similarto the square- and star-shaped structures presented in Rothe-mund’s original paper [13] or via a tile approach that exclusivelyutilizes shorter DNA strands [14]. The upper inset in Fig. 4(a)illustrates a simplified cylinder model of the nanoplate, which rep-resents the underlying helices and strand architecture.

DNA origami fabrication is performed via molecular self-assembly, where the scaffold strand is mixed with all of the com-ponent staple strands, typically with each staple strand in tenfoldexcess relative to the scaffold. The scaffold and staple strandsmixture is suspended in a folding reaction and subjected to a ther-mal annealing process as described previously [27]. The atomic-force microscopy image of the resulting rectangular nanoplates isshown in Fig. 2. The assembly process can be optimized withregards to the solution conditions, such as ion concentrations, thedetails of the thermal ramp, the DNA component concentrations,and the underlying structure design. However, even optimizedassembly conditions typically result in incomplete assembly withone or a few strands missing from a structure [28]. Therefore,understanding the impact of defects on the structure behavior iscritical for effective design of nanodevices and nanomaterials.

3.2 Automated Finite Element Modeling. The presence ofdefects in a DNA origami structure could affect both global struc-ture mechanical properties and local stresses, which affect mate-rial failure. Here, we investigate the impact of defects resultingfrom incomplete self-assembly on the effective stiffness and max-imum normal strain (as a precursor for damage) when the

Fig. 3 CISAMR transformation of a structured grid into a conforming mesh: (a)SAMR, (b) r-adaptivity, and (c) subtriangulation of background elements

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nanoplate is subject to uniform and asymmetric tensile loadsapplied as a prescribed displacement of 1 nm, as shown in Fig. 5.These boundary conditions are selected such that they replicatethe loads applied to the nanoplates used for the construction of thenanostructures depicted in Fig. 2. In particular, the asymmetricloading condition (Fig. 5(b)) is similar to a previous experimentalstudy developing a DNA origami nanomechanical sensor [38].

In this work, we improve on the simplified cylinder model ofthe nanoplate with a more realistic model of its molecular struc-ture, as shown in Fig. 4(b), to enable the prediction of mechanicalbehavior and stress concentrations in the presence of defects. Thewavy geometry of each DNA strand in this model is based on acryo-electron microscopy study that reconstructed the helices in aDNA origami nanostructure [41]. The underlying DNA architec-ture and a defect caused by a missing staple strand are illustratedin Figs. 4(c) and 4(d), respectively. Although single-strandedDNA remains (dashed lines) at the location of the defect, it doesnot support any load since it is much more flexible than double-stranded DNA. Hence, it is analogous to replacing load-bearingmaterial with a slack string. The unique capability of CISAMRfor creating high-quality conforming meshes enables the auto-mated construction of appropriate FE models of the nanoplatewith varying numbers and spatial arrangements of defects. Usinga 400� 256 background grid to discretize the bounding box of thenanoplate, Fig. 4(e) shows a small portion of the conforming

mesh generated using CISAMR for modeling the nanoplate. Twolevels of refinement are used in the SAMR phase to reduce thegeometric discretization error and accurately approximate thestrain field in the vicinity of boundaries.

The CISAMR ability to transform a simple structured grid intoa conforming mesh also eliminates the need for the use of com-puter aided design drawings for creating the FE model. Instead,one can easily create a high-quality conforming mesh startingwith a binary image of the nanoplate, as shown in Fig. 6. In thisapproach, after identifying the binary pixels corresponding to thenodes of the background grid that represent each material phase(1: DNA and 0: no material), we determine whether each elementis located entirely inside/outside each DNA strand or intersectingwith its boundaries. After recursive SAMR of the elements cut bythe domain boundaries and their selected neighboring elements,we employ the split-half search algorithm along the edges of eachnonconforming element to evaluate their intersection points withdomain boundaries. The r-adaptivity and subtriangulation steps ofCISAMR are then executed to build the final conforming mesh.This technique fully automates the modeling process by allowingthe implementation of a high-resolution image of the nanoplate todirectly predict its mechanical behavior. Thus, one can simplyoverlap the image of a perfect nanoplate with multiple virtualdefects, similar to that shown in Fig. 4(b), to simulate varyingnumbers and spatial arrangements of defects.

Fig. 4 (a) Cylinder and (b) realistic models of the nanoplate, (c) and (d) underlying molecular structure showingthe helices and staple strand, and (e) small portion of the resulting CISAMR mesh using a 400 3 256 structuredgrid to discretize the domain

Fig. 5 Boundary conditions for nanoplate subjected to (a) uniform and (b) asymmetric pre-scribed tensile displacements

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4 Numerical Results and Discussion

The automated image-based CISAMR technique described inSec. 3.2 was employed to analyze the mechanical response of 42nanoplates with varying pre-existing defects, as shown in Fig. 7.The spatial arrangement of defects in these nanoplates is not com-pletely random, as each plate has two axes of symmetry, whichleads to similar mechanical behavior for some nonsimilar arrange-ments of defects. Instead, the 42 cases depicted in Fig. 7 areselected such that none of them is symmetric, thus representingunique behaviors subject to varying loading conditions. As notedpreviously, two types of simulations with the BCs shown in Fig. 5are carried out for each model to perform the UQ. Here, we com-pare the mechanical behavior of a nanoplate with no defect tothese 42 nanostructures with either one or two missing staplestrands. In addition to studying the variation of the nanoplate stiff-ness in the presence of defects, we also investigate their impact onthe maximum normal strain in the underlying DNA structure as aprecursor for the initiation of damage. According to Kim andKim [42], the elastic modulus and the Poisson’s ratio of DNA inthe FE models are considered as E¼ 244 MPa and � ¼ 0:499,respectively.

4.1 Uniform Tensile Displacement. Figure 8 illustrates thevariations of the effective modulus of elasticity Eeff and maximumtensile strain emax versus the number/arrangement of defects in the42 nanoplates depicted in Fig. 7. Values of both parameters arenormalized with those associated with a perfect nanoplate with nopre-existing defect, i.e., E0

eff ¼ 160:3 MPa and e0max ¼ 0:028. As

shown in Fig. 8(a), missing only one staple in manufacturing thenanoplate leads to an average decrease of 6.5% in Eeff , with asmall standard deviation of approximately 1%. However, the pres-ence of two defects in the nanoplate leads to a considerably higheruncertainty in Eeff , with minimum and maximum reductions of8.4% and 12%. Analyzing the spatial distribution of defects in thenanoplates with least decrease in Eeff (36) shows that the defectsare in the same row, which roughly replicates a nanostructurewith only one missing staple. However, for the nanoplates withthe lowest effective modulus of elasticity (e.g., 20–22 and32–34), the defects were either in two adjacent rows or far fromone another; thus, no clear correlation can be made between theirspatial arrangement and the effective stiffness.

Studying the variation of the maximum tensile strain in thedefective nanoplates as shown in Fig. 9 reveals that even onemissing staple could lead to more than a twofold increase in emax

Fig. 6 Schematic of the process of identifying the background elements cut byDNA strands and performing the h-adaptivity phase during the construction of anFE model of the nanoplate using CISAMR

Fig. 7 Different models analyzed to quantify the impact of defects on the DNAnanoplate mechanical behavior

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(e.g., nanoplate 1). As expected, on average, missing two staplesresults in a higher increase in emax, although for both cases thestandard deviation is also significant (nearly 45%). Further, theincrease in emax has no direct correlation with the decrease in Eeff .Note that since a displacement of 1 nm is employed to generatetension in the nanoplate, reduction in its effective stiffness meansthat the amplified values of emax correspond to lower applied trac-tions along the left and right boundaries. For example, for nano-plate 16, although the applied force required to achieve theboundary displacement decreases by 11%, the maximum tensilestrain is increased by a factor of 2.27.

A closer look at the spatial arrangement of defects in nanoplateswith largest values of emax shows that either one of the missingstaples is located near one of the corners or two missing staplesare in two consecutive rows of the nanoplate. A more importantobservation pertains to the location of emax, in which all the 42nanoplates occur in the DNA strand right below or above themissing staple. Figure 9 illustrates the strain field in two nano-plates (10 and 11), which clearly shows this common feature inthe vicinity of defects. Since the rupture of DNA strands occursdue to overstretching, this important observation suggests that amissing staple strand could lead to local strain concentrations inthe neighboring strands that accelerate local failure. In addition, iflocal failure occurs, the emax would be transferred to the adjacent

row and the damage initiated near the original defect couldquickly propagate in perpendicular to the DNA strands directionuntil the entire nanoplate fails.

4.2 Asymmetric Tensile Displacement. The variations ofthe reaction force R and the maximum tensile strain emax in nano-plates subjected to asymmetric tension (Fig. 5(b)) are depicted inFigs. 10(a) and 10(b), respectively. The reaction force is com-puted for a 1 nm displacement applied on a single DNA strand onthe top right of the nanoplate, while the bottom left is held fixed.Interestingly, the reaction force is only affected for the four cases(nanoplates 11; 14; 28, and 31), where a defect is in close prox-imity to the applied displacement. In other words, unless thedefect is located near one of the two corners where tension isapplied, the decrease in the stiffness for this type of loading isnegligible. Note that the closer the defect is located to the edge ofnanoplate where the force is applied, the larger the reduction inthe reaction force. Nanoplate 11 where the defect occurs one rowabove the edge near the bottom left corner exhibits an 11% reduc-tion in reaction force compared to 7% for 14; 28, and 31 thatoccur on the second row from the edge near the top right corner.

Studying the relationship between number/distribution ofdefects and the emax (Fig. 10(b)) shows that except for nanoplate11, the variation of emax is negligible. More interestingly, unlike

Fig. 8 Variations of (a) normalized effective stiffness and (b)normalized maximum normal tensile strain in the 42 DNA ori-gami nanoplates shown in Fig. 7 subject to uniform tension

Fig. 9 Deformed shape and normal strain in nanoplates 10 and 11 subject to uniform tension

Fig. 10 Variations of (a) normalized reaction force and (b) nor-malized maximum normal tensile strain in the 42 DNA origaminanoplates shown in Fig. 7 subject to asymmetric tension

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the case of uniform tensile loading, the presence of defects in thisnanoplate leads to a reduction in emax if a defect is near the cornerwhere the reaction force occurs or the displacement is applied.The deformed shape and normal strain field for this nanoplate areillustrated in Fig. 11. Since emax can be considered as a precursorof the damage (rupture), this study shows that regardless of thenumber and arrangement of defects in the nanoplate subjected toasymmetric tension, failure always occurs at the supports or loca-tions of the applied load.

The computational framework presented in this paper enablesthe construction of many models of DNA origami objects withvarying nanostructural features, which is critical to consider theeffects of structural uncertainty resulting from self-assembly. Thiswork establishes a foundation to consider the detailed underlyingstrand structure of DNA origami objects in an FE framework.Compared to prior FE-based models approximating DNA basepairs as cylinders, a more realistic description of the DNA struc-ture in the current model provides higher fidelity for consideringlocal effects that govern the onset of failure, although it alsoincreases the computational burden. The image-based CISAMRalgorithm streamlines the consideration of multiple models byautomating the modeling process. Note that continuum modelsgenerally do not provide a similar level of accuracy or mechanis-tic insight as MD simulations, but MD simulations are consider-ably more computationally expensive. Further, the use of acontinuum model for predicting the failure response of DNA ori-gami nanostructures requires the use of an appropriate damagemodel and the 3D geometry of base pairs, which could be the sub-ject of future studies.

5 Conclusion

An automated computational framework relying on a nonitera-tive conforming to interface structured adaptive mesh refinement(CISAMR) algorithm was introduced to quantify the impact ofmissing staples on the mechanical behavior of a DNA origaminanostructure. The CISAMR approach simply requires input of abinary image of the nanostructure, together with a structured grid,which is then transformed into a high-quality conforming mesh.The proposed image-based CISAMR technique automates thegeneration of high-fidelity FE models for DNA origami nano-structures, which enables the mechanical uncertainty quantifica-tion for a large number of possible defects (missing staples). Inthis work, we focused on a model nanoplate subject to uniformand asymmetric prescribed tension. The key observations made inthis study are summarized below:

(1) When subjected to uniform tensile displacement, missingone or two staples in the plate nanostructure could lead toan average decrease of 6.5% and 10% in the effective stiff-ness, respectively, with a considerably higher standarddeviation (uncertainty) for varying configurations of twomissing strands. This suggests the importance of under-standing whether defects are random or systematicallyoccur at specific sites.

(2) The presence of defects can amplify the maximum tensilestrain more than two times and thus accelerate the initiationof damage in the direction perpendicular to the DNAstrands subject to uniform tension. This observation couldguide the design strategies for robust mechanical behaviorto increase local thermodynamic binding stability near thecorners to maximize proper incorporation or to minimizethe occurrence of neighboring staples with low annealingprobabilities.

(3) When subjected to asymmetric tension applied on two diag-onal corners of the nanoplate, the pre-existing defects haveno impact on the stiffness and maximum tensile strainunless one of them is close to one of the corners. Further,the maximum strain (and thus failure) always occurs in thecorner DNA strand where the force is applied, which sug-gests that reinforcement of the structure near the sites offorce application could strengthen origami structures formechanical applications.

Acknowledgment

This work was supported in part by The Ohio State UniversityMaterials Research Seed Grant Program, funded by the Center forEmergent Materials, an NSF-MRSEC Grant No. DMR-1420451,the Center for Exploration of Novel Complex Materials, and theInstitute for Materials Research.

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Fig. 11 Deformed shape and normal strain in nanoplate 11 subject to asymmetric tension

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