Origami Methods

Introduction

Origami folding for DNA self-assembly starts with a single strand of DNA, called a scaffolding strand. Other shorter additional DNA strands (called staple strands) then join with two non-adjacent sequences of nitrogenous bases on the scaffolding strand. DNA is a very flexible material, and so by attaching these staple strands, different sections of the scaffolding strand will be folded at specific angles and held in place to form the target structure. (See [Rot06])

For a visual representation of DNA origami, watch this video.

Threading

To address the challenges of this assembly method for graph-like targets (as opposed to filled surfaces), our group has considered different 3D skeletal polyhedra and found Euler circuits for them (see graph theory conventions page). If an Euler circuit can be found within a 3D figure, then it may be used as a route along which a scaffolding strand can traverse to form that particular shape. This circuit becomes a threading for the construct. The following objectives are required to both facilitate assembly and prevent edges at a vertex from detaching. However, for certain polyhedra some of these may not be simultaneously attainable.

• If the target graph-like structure is not Eulerian, then augmenting edges must first be added to make it so.
• Every edge must be covered exactly once by the scaffolding strand, and thus the number of edges directed inward must equal the number of edges directed outward at each vertex.
• To the extent that it is possible, the threading should follow faces.
• There should be as few unique vertex configurations as possible
• Symmetry of the circuit should be maximized.

Stapling

Staple strands follow the same general constraints as the scaffolding strand. Some additional restrictions are as follows:

• Staples are oriented in the opposite direction from the scaffolding strand, so that each edge is covered in one direction by the scaffolding strand and in the other direction by staples.
• Staples can not follow the threading through the vertex, but must turn at the vertex to follow an adjacent edge of the scaffolding strand (thus facilitating the above-mentioned pattern of threading follow faces). See Figure 3.
• In general, the staple configuration must prevent any detachment at each vertex.
• If the staples are imagined to be connected into circular strands, this need not form an Euler circuit, but only a cycle family.