Multi-scale coarse-graining for the study of assembly pathways in DNA-brick self-assembly

In this thesis, we develop a novel approach for modelling self-assembling systems that use the single-stranded-tile (SST) assembly method, an increasingly popular nanoconstruction approach in the field of DNA nanotechnology, developed primarily in the Molecular Systems Lab (Harvard University). In the SST method, a desired target structure is produced by mixing together a set of short DNA molecules (called SSTs) where each SST is provided with a judiciously chosen base sequence such that it will bind to a predetermined set of local neighbours in the target structure. Our approach for modelling these systems involves the use of simulations with a relatively fine-grained model of DNA (here we opt for oxDNA [1]) to parametrise coarser stochastic models that represent these systems at the level of the SST (the basic subunit of the method), and can probe effectively the timescales required for self assembly. As a test system for our approach we choose a rectangular-shaped SST-based object made out of 334 42-base-long SSTs, first reported in Ref. [2]. We first introduce a stochastic model that describes the growth of one target structure under a fixed background concentration of SSTs. We use the model to study nucleation pathways, finding that structures with a high number of bonds between SSTs and compact shapes are typically the most likely to form. However, we also find that for certain (recurrent) sizes, maximally-bonded structures are actually disfavoured due to statistical factors. We then devise a simple model that describes the bonding of incorrect SSTs to a (otherwise correctly formed) structure, finding that these bonds are typically very weak, and have a relatively minor impact on the overall kinetics and thermodynamics of self assembly. We then introduce a stochastic model that describes the simultaneous growth of multiple target structures in a system where subunits are present in finite numbers (rather than present at constant supply). Under isothermal conditions the model predicts that there is only a small temperature window (∼2ºC) where self assembly is not hindered by excessively high nucleation barriers nor depletion traps. Finally, we simulate a cooling ramp similar to the original experiments of Refs. [2, 3]. The model predicts a peak in base-pairing formation in close agreement with Ref. [3]. However, the models predicts assembly yields that are significantly above those achieved in experiments. This differences are attributed to non-specific contacts between structures, a type of assembly that is not yet well understood, and thus not described by the model.