Investigating structural mechanics of ligated DNA crystals via molecular dynamics simulation

DNA nanotechnology is a rapidly advancing field that utilizes the base-pairing properties of DNA molecules to create arbitrary nanostructures with exceptional precision and programmability. Through different techniques such as tile-based assembly, DNA origami, and DNA bricks, a wide range of static and dynamic constructs have been developed for drug delivery systems, biosensors, and nanomachines. Among these, DNA crystals, periodic lattices formed by assembling DNA motifs through sticky-end cohesion, are particularly unique, as they can grow to sizes exceeding 100 µm. Unlike smaller nanostructures, which are often unsuitable for mechanical studies due to their small dimension, macroscopic DNA crystals provide an ideal platform to study structural properties and deformation behaviors of DNA assemblies.

This thesis uses coarse-grained molecular dynamics (MD) simulations to investigate the structural mechanics of DNA crystals made of tensegrity triangle motifs with different ligation patterns. Coarse-grained models simplify groups of atoms into single particles, enabling the simulation of large and complex systems with a reasonable amount of computational time. This approach is well-suited for investigating the properties of large crystal structures. Here, we approximated DNA crystals using 5´5´5 motifs (a total of 125 units) on oxDNA, an open-source coarse-grained simulation platform based, and examined four distinct ligation patterns: full ligation, major direction ligation, connector ligation, and in-plane ligation. Tensile forces were applied along one axial direction and resulting deformation behaviors were analyzed in detail.

The computational results indicate that the number and the location of the ligated nucleotides have significant effects on structural mechanics of the DNA crystals. Fully ligated crystals exhibit a Young’s moduli of approximately 1-3 MPa with yield stresses between 0.4 and 0.7 MPa. These structures maintain high structural integrity with no visible signs of failure until reaching a breaking point near 20 MPa. Crystals ligated along major directions and connectors display similar Young’s moduli but a lower yield point (0.2 - 0.4 MPa). However, both fully ligated and major-direction ligated crystals exhibit distinct deformation stages: (i) entropic elasticity, (ii) linear elasticity, (ii) dsDNA dissociation, and (iv) ssDNA stretching. In contrast, the connector ligated crystals fail during dsDNA dissociation, while in-plane ligated crystals break before entering the linear elasticity regime due to the lack of structural resilience (which should come from ligation along the loading direction).

We also have investigated the influence of motif length by comparing fully ligated crystals with four different motif lengths. The 2-turn crystal, that is, the crystal made of the shortest motif length of 2 helical turns, shows no entropic elasticity stage and starts deforming directly into the linear elasticity range. In contrast, crystals with longer motifs display a distinct entropic elasticity stage, with the 4-turn crystal exhibiting strain up to ~0.5, the 6-turn crystal around 1, and the 8-turn crystal approximately 1.5 during this initial regime. Longer motifs also result in greater overall extension. For example, the 2-turn crystal can be stretched to a strain of 1 before breaking, while the 8-turn crystal can be stretched until a strain of ~3. These findings suggest that a longer motif (e.g., 8-turn motif) produces more relaxed and loose crystals leading to a greater entropic elasticity range and total extension compared to shorter motifs. However, excluding the entropic elasticity stage, all crystals with various motif lengths show similar deformation stages (linear elasticity, dsDNA dissociation, and ssDNA stretching). This confirms that the length of motif influences initial stage but does not affect the overall deformation behavior of DNA crystals.

Overall, this thesis elucidates how ligation patterns and motif design affect the mechanical behavior of DNA crystals. The findings may be combined with experiments and used as guidelines to provide insights on designing and improving DNA assemblies, which should be invaluable in the field of structural DNA nanotechnology.