Modelling the folding of DNA origami

DNA-based nanostructures built from a long single-stranded DNA scaffold, known as DNA origamis, are at the basis of many applications. Despite their widespread development, many basic questions concerning the mechanisms of formation of DNA origamis have not yet been addressed. For instance, the robustness of different designs against factors such as the internal topology, or the influence of the staple pattern, are handled empirically. We have developed a model for the folding and melting processes of DNA origamis that is able to reproduce accurately several thermodynamic quantities measurable from UV absorption experiments. This model incorporates not only the origami sequence but also its topology. We show that cooperativity is key to quantitatively understand the folding process. The model can also be used to design a new distribution of crossovers that increases the robustness of the DNA template, a necessary step for technological development. Copyright c © EPLA, 2012 Introduction. – Self-assembly with scaffolded DNA origamis [1] enables the fabrication of template biosensing structures or dynamical systems in 2D and 3D with nanometer scale accuracy in a simple bottom-up approach. Besides immediate applications such as biosensors [2], many strategies make use of the DNA dynamical behaviour to achieve complex functions or structure reconfiguration. Prescribed tracks have been used for the development of nanomachines and nanorobots [3–5] while strand displacement techniques [6] have been employed to reorganise origami structures [7,8]. However, despite these innovative realisations, the folding process of DNA origamis remains poorly understood. DNA origamis are made of a 7249 bases long ssDNA scaffold (M13mp18) folded with a set of about 200 complementary short ssDNA (32 bases long) called staples. DNA origamis form as the result of an annealing process. The fraction of hybridized bases (degree of pairing θ(T )) can be obtained from raw absorbance measurements as indicated in [9,10]. The derivative of the melting curve of a short dsDNA displays a maximum that is often used to determine the melting temperature (Tm). For more complex structures, melting and annealing curves do not match, the temperatures corresponding to the maximum of their derivative are also different. In this paper, we show that well-established models of dsDNA folding do not apply to DNA origamis. In fig. 1 we compare the predictions of the simplest model of DNA origami folding (where the staples fold independently) with the experimentally obtained melting curves from three different origamis. These data show that the hypothesis of independent folding leads to completely erroneous predictions of the melting stability. Staples are designed to hold together regions of the scaffold that, otherwise, would be separated by a long portion of the scaffold. The binding of a staple to the scaffold is hindered by an entropic penalty that depends on the length of this region: the longer the region, the lower the probability that the regions complementary to the staple are close to each other. Moreover, depending on the melting temperature at which each staple binds, it may happen that other staples are already bound to this portion, reducing its effective entropy. Therefore, the binding of any staple depends on the binding state of the other staples, leading to a field of interacting loops of various sizes. In this work, we characterize the type of configurations that may influence the binding of any staple. We show that the key issue to disentangle the folding process is to take into account the cooperativity of staple association with the scaffold. More precisely, we show that only the staples contained in a close neighborhood of any staple influence its binding. Small origamis. – We first investigate a simple structure, hereafter named small origami, which highlights the