Lattice models and Monte Carlo methods for simulating DNA origami self-assembly

TL;DR

This paper introduces a lattice-based model and Monte Carlo simulation methods for DNA origami self-assembly, balancing detail and computational efficiency, to better understand assembly pathways and design effects.

Contribution

It presents a novel lattice model with Monte Carlo methods that efficiently simulate DNA origami assembly, capturing key structural constraints and enabling exploration of assembly pathways.

Findings

Model accurately samples configurations of small origami designs.

Simulation can handle longer staple segments and complex structures.

Method improves understanding of assembly pathways and design impacts.

Abstract

The optimal design of DNA origami systems that assemble rapidly and robustly is hampered by the lack of a model for self-assembly that is sufficiently detailed yet computationally tractable. Here, we propose a model for DNA origami that strikes a balance between these two criteria by representing these systems on a lattice at the level of binding domains. The free energy of hybridization between individual binding domains is estimated with a nearest-neighbour model. Double helical segments are treated as rigid rods, but we allow flexibility at points where the backbone of one of the strands is interrupted, which provides a reasonably realistic representation of partially and fully assembled states. Particular attention is paid to the constraints imposed by the double helical twist, as they determine where strand crossovers between adjacent helices can occur. To improve the efficiency of sampling configuration space, we develop Monte Carlo methods for sampling scaffold conformations in near-assembled states, and we carry out simulations in the grand canonical ensemble, enabling us to avoid considering states with unbound staples. We demonstrate that our model can quickly sample assembled configurations of a small origami design previously studied with the oxDNA model, as well as a design with staples that span longer segments of the scaffold. The sampling ability of our method should allow for good statistics to be obtained when studying the assembly pathways, and is suited to investigating in particular the effects of design and assembly conditions on these pathways and their resulting final assembled structures.