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Research Papers

Pseudorigid-Body Models of Compliant DNA Origami Mechanisms

[+] Author and Article Information
Lifeng Zhou

Department of Mechanical and
Aerospace Engineering,
The Ohio State University,
Columbus, OH 43210
e-mail: zhou.809@osu.edu

Alexander E. Marras

Department of Mechanical and
Aerospace Engineering,
The Ohio State University,
Columbus, OH 43210
e-mail: marras.3@osu.edu

Carlos E. Castro

Department of Mechanical and
Aerospace Engineering,
The Ohio State University,
Columbus, OH 43210
e-mail: castro.39@osu.edu

Hai-Jun Su

Department of Mechanical and
Aerospace Engineering,
The Ohio State University,
Columbus, OH 43210
e-mail: su.298@osu.edu

1Corresponding author.

Manuscript received September 14, 2015; final manuscript received November 25, 2015; published online May 4, 2016. Assoc. Editor: Andrew P. Murray.

J. Mechanisms Robotics 8(5), 051013 (May 04, 2016) (11 pages) Paper No: JMR-15-1263; doi: 10.1115/1.4032213 History: Received September 14, 2015; Revised November 25, 2015

In this paper, we introduce a strategy for the design and computational analysis of compliant DNA origami mechanisms (CDOMs), which are compliant nanomechanisms fabricated via DNA origami self-assembly. The rigid, compliant, and flexible parts are constructed by bundles of many double-stranded DNA (dsDNA) helices, bundles of a few dsDNA helices or a single dsDNA helix, and single-stranded DNA (ssDNA) strands, respectively. Similar to its macroscopic counterparts, a CDOM generates its motion via deformation of at least one structural member. During the motion, strain energy is stored and released in the compliant components. Therefore, these CDOMs have the advantage of suppressing thermal fluctuations due to the internal mechanical energy barrier for motion. Here, we show that classic pseudorigid-body (PRB) models for compliant mechanism are successfully employed to the analysis of these DNA origami nanomechanisms and can serve to guide the design and analysis method. An example of compliant joint and a bistable four-bar CDOM fabricated with DNA origami are presented.

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References

Figures

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Fig. 1

(a) The cylinder model of single dsDNA helix and (b) two parallel dsDNA helices

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Fig. 2

(a) An example of a hinge joint design. (b) A bistable CDOM and the molecular model (lower right corner). (c) Two types of cross sections used in the bistable nanomechanism design.

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Fig. 3

An example of compliant DNA origami joint: (a) 3D model and (b) deformed compliant DNA origami joints

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Fig. 4

Sketch of single polymer

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Fig. 5

The cross section of a bundle of six dsDNA helices, each circle represents a dsDNA helix

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Fig. 6

PRBM for cantilever beam with a nonrigid-fixed end

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Fig. 7

Comparison between PRBM (red dots or lines) and beam model (blue dots or lines) for nonrigid-fixed end cantilever beam. (a) η = 0.5 and n is chosen from a list given in Table 3 in the Appendix. (b) n = 0 (ϕ = 90 deg), (c) n = − 1.0 (ϕ = 45 deg), and (d) n = 1 (ϕ = 135 deg), η∈{0.5, 1, 2, 4, 8, 20, 80, 200, 400, 1000}.

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Fig. 8

Three segments cantilever beam

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Fig. 9

One revolute joint PRBM for the three segment cantilever beam. (a) Sketch of the PRBM. (b) ρ for different (ε1, ε2). (c) Comparison of end tip position and energy between PRBM and beam model.

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Fig. 10

PRB-3R model for nonuniform cross section beam. (a) Sketch of the model. (b) ρ for different (ε1, ε2). ((c)–(e)) Comparisons of end tip position, end tip angle, energy and their relative errors, and average errors between PRB-3 R model and beam model.

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Fig. 11

Test the PRB-3 R model for different bending stiffness of different segment. (a) Sketch of the model. (b) ρ for different (e1, e2). ((c)–(e)) Comparisons of end tip position, end tip angle, energy and their relative errors, and average errors between PRB-3 R model and beam model.

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Fig. 12

PRB-3R model applied on the nonrigid-fixed multicross section cantilever beam. (a) Sketch of the model. ((b) and (c)) End tip position, stored energy calculated by the PRB-3 R model and the beam model with η=0.5 and η=2.0, respectively.

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Fig. 13

PRBM of the CDOM hinge joint

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Fig. 14

(a) TEM images of CDOM hinge joint and (b) comparison of experiment and model results, scale bar = 20 nm

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Fig. 15

(a) The PRBM of the bistable mechanism (unit: nm) and (b) simplified model sketch

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Fig. 16

End tip position (left) and energy (right) calculated by beam model (blue dots), PRB-1 R model (purple dots), and PRB-3 R model (red dots)

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Fig. 17

(a) Typical TEM images, most particles stay at the open or closed stable configuration (top and bottom) and only a few samples are stuck at the unstable configuration (middle). (b) Comparisons of experiment and PRBMs results.

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