### Tech Briefs

**CanDo: Computer-aided Engineering for DNA Origami**

**Movie 1** Thermal fluctuations of a robot-like DNA origami structure

Origami is a traditional art: a flat sheet is folded into a beautiful complex structure (http://en.wikipedia.org/wiki/Origami). Scaffolded DNA origami is a novel technique in which structural forms are constructed of two- and three-dimensional shapes, at the nano-scale, see Rothemund, Shih, M. Bathe, Dietz.

Such miniature structures may be useful in many devices, for example, in tiny components of computers and in nano carriers used to target and destroy abnormal cells or deliver therapeutics. Indeed, numerous applications are on the horizon for this novel approach to nano-scale construction.

The field of scaffolded DNA origami technology aims at the technological synthesis of complex nano-scale objects of precise shape and mechanical properties – and here finite element methods are now used in a novel and ingenious way.

The aim is to rationally design shapes for specific purposes, specifically technological and biomedical applications. The first step therein is to conceive a target shape, perhaps mimicking or inspired by nature, that meets certain functional requirements.

In this Brief, we present a computational tool called CanDo (__C__omputer-__a__ided e__n__gineering for __D__NA __o__rigami) that is used to perform, among other functions, finite element analysis using ADINA to predict the 3D solution shape and the flexibility of scaffolded DNA origami structures. The use of CanDo is illustrated in Refs. [1] and [2] for a range of nonlinear DNA structures that include internal curvature and twist — which are complex phenomena but important to include.

**Figure 1** DNA double helix: atomic structure (left); homogeneous elastic rod model (middle); and finite element representation using two-node beam elements (right)

Figure 1 shows DNA modeled as a homogeneous elastic rod with default geometric data (length = 0.34 nm per base pair and diameter = 2.25 nm) and mechanical properties (stretching stiffness = 1100 pN, bending stiffness = 230 pN nm^{2}, and twisting stiffness = 460 pN nm^{2}) that are represented computationally using two-node beam finite elements. The finite element nodes contain three translational and three rotational degrees of freedom that represent the neutral axis and cross-sectional orientation of DNA in stretching, bending, and twisting. Strand crossovers that constrain neighboring helices are modeled as rigid links.

**Figure 2** Initial configuration (left); stressed configuration (middle); relaxed configuration (right)

Local insertions and deletions of DNA base-pairs are used to design curved, twisted DNA origami structures. The 3D solution shape is computed by introducing three conceptual configurations: the initial configuration, the stressed configuration where axial and torsional strains are locally induced, and the final relaxed configuration where these local strains are gradually relieved by a global deformation of the entire structure, see Figure 2.

The complete simulation is performed as follows —

Use of the automatic time stepping algorithm of ADINA for the geometrically highly nonlinear analysis with severe local buckling (see Movie 2).

Solution of frequencies and mode shapes to establish the flexibility of the deformed origami structure (see Movie 1).

It should be emphasized that the analysis requires first the complex geometrically nonlinear solution and then the calculation of the frequencies in the deformed geometry — ADINA is a powerful tool for these tasks.

**Movie 2** Load steps of the 3D solution shape computation

Who would have thought half a century ago, when the finite element method was used first in the analysis of airplane structures, see Refs. [3] and [4], that these techniques would now be applied in the design and analysis of DNA origami — that origami would no longer be just for paper, see MIT News, April 27 (2011).

*Keywords:*

DNA, origami, finite elements, nano-technology, miniature structures, biomechanics, frequencies, mode shapes, deformed configuration, geometrically nonlinear

**References**

- Kim, D.N., Kilchherr, F., Dietz, H., and Bathe, M., manuscript in preparation.
- Castro, C.E., Kilchherr, F., Kim, D.N., Shiao, E.L., Wauer, T., Wortmann, P., Bathe, M., and Dietz, H., "A primer to scaffolded DNA origami",
*Nature Methods*, 8:221-229, 2011. - Argyris, J.H. and Kelsey, S., "Energy Theorems and Structural Analysis",
*Aircraft Engineering*, Vols. 26 and 27, Oct. 1954 to May 1955, Part I is by J.H. Argyris and Part II is by J.H. Argyris and S. Kelsey. - Turner, M.J., Clough, R.W., Martin, H.C. and Topp, L.J., "Stiffness and Deflection Analysis of Complex Structures",
*Journal of the Aeronautical Sciences*, 23:805-823, 1956.