Cooperativity in the annealing of DNA origamis

DNA based nanostructures built on a long single stranded DNA scaffold, known as DNA origamis, offer the possibility to organize various molecules at the nanometer scale in one pot experiments. The folding of the scaffold is guaranteed by the presence of short, single stranded DNA sequences (staples), that hold together separate regions of the scaffold. In this paper, we modelize the annealing-melting properties of these DNA constructions. The model captures important features such as the hysteresis between melting and annealing, as well as the dependence upon the topology of the scaffold. We show that cooperativity between staples is critical to quantitatively explain the folding process of DNA origamis.

💡 Research Summary

In this paper the authors present a quantitative statistical‑mechanical model of the annealing and melting behavior of DNA origami nanostructures, and they validate the model against UV‑absorbance experiments. The study begins with a minimal “small origami” system composed of a 64‑base single‑strand scaffold and two 32‑base staples. Each staple is split into two contiguous domains that bind to non‑adjacent regions of the scaffold in a two‑step process: first one domain hybridizes, forming a short double‑helical segment, then the second domain completes the bridge. Depending on whether a staple occupies an “outer” (bulge) or “inner” (opposite‑side) position relative to the scaffold, the entropic penalty and mechanical strain differ markedly. Experiments using AT‑rich (B1) and GC‑rich (B2) staples with widely separated melting temperatures (57 °C vs 91 °C) show that when the higher‑Tm staple (B2) is already bound, the lower‑Tm staple (B1) folds at a higher temperature and with a narrower transition, evidencing cooperative binding. The converse is not observed: B1 does not significantly affect B2. A second set of staples (B1m, B2m) with similar Tm values displays the same qualitative trend but with weaker cooperativity. These observations establish that (i) the location of a staple (inner vs outer) strongly influences its stability, and (ii) the presence of a pre‑bound staple can reduce the effective free‑energy barrier for a neighboring staple, a phenomenon the authors term “cooperativity”.

Building on these insights, the authors formulate a model for full‑scale DNA origami. They adopt three key hypotheses: (1) each staple domain is either fully hybridized or fully unbound (binary state), and mis‑paired configurations are ignored; (2) non‑contiguous hybridized domains are forbidden, reflecting the dominance of the central domain in typical 32‑base staples; (3) strong correlations exist among staples, allowing a high‑correlation approximation in which the probability of a staple being present is ordered relative to its neighbors. A staple Si is divided into parts Si,1, Si,2,… and a configuration Si(k,l) denotes a contiguous block of hybridized parts from k to l. The probability p(Si(k,l),T) of being in that state at temperature T is computed recursively. For each staple a set of neighboring staples Nα(Si) is defined, limited to those whose crossovers lie in the same row and are within 75 bases. The equilibrium reaction Si(k,l)+Nα ↔ Nα·Si(k,l) yields a conditional probability p(Si|Nα). The overall probability is then p(Si,T)=∑α p(Si,T|Nα)·p(Nα,T). In practice the recursion is implemented as an iteration over temperature steps dT, with p(Nα,T) taken from the previous temperature step, thereby reproducing the hysteresis observed experimentally.

The model incorporates three classes of parameters: (i) thermodynamic free‑energy contributions for each domain, derived from nearest‑neighbor rules and adjusted for GC content; (ii) an entropic penalty term for loop or bulge formation, which depends on the length of the unpaired scaffold segment between the two domains of a staple; (iii) a geometric coupling term that accounts for the proximity of neighboring crossovers (the 75‑base cutoff). By fitting these parameters to the UV‑absorbance melting curves of the small origami, the model accurately reproduces the two‑peak structure (inner and outer staple melting), the shift in melting temperature caused by cooperativity, and the different half‑widths of the transitions. Importantly, when the same parameter set is applied to larger, experimentally characterized 2‑D origami (≈100 nm square lattices), the simulated melting curves match the measured ones within 1–2 °C, and the predicted hysteresis between annealing and melting is consistent with observations.

The authors discuss the implications for origami design. Because cooperative effects arise primarily from the reduction of entropic penalties when a neighboring staple is already bound, arranging staples so that high‑Tm staples occupy inner positions and low‑Tm staples occupy outer positions can enhance overall yield. Conversely, avoiding configurations that generate large internal loops minimizes destabilizing strain. The model thus provides a computational tool for predicting the thermal stability and folding yield of a given staple layout without the need for exhaustive experimental screening.

In conclusion, the paper demonstrates that (a) staple‑staple cooperativity and scaffold topology are essential determinants of DNA origami folding, (b) a relatively simple statistical‑mechanical framework, grounded in experimentally measured thermodynamic parameters and a high‑correlation approximation, can capture the essential physics of the process, and (c) this framework can be used to guide the rational design of more robust DNA nanostructures, potentially extending to multi‑layered or non‑planar architectures in future work.