The folding of biological macromolecules is a fundamental process of which we lack a full comprehension. Mostly studied in proteins and RNA, single-stranded DNA (ssDNA) also folds, at physiological salt conditions, by forming nonspecific secondary structures that are difficult to characterize with biophysical techniques. Here, we present a helix-coil model for secondary-structure formation, where ssDNA bases are organized in two different types of domains (compact and free). The model contains two parameters: the energy gain per base in a compact domain, $\epsilon$, and the cooperativity related to the interfacial energy between different domains, $\gamma$. We test the ability of the model to quantify the formation of secondary structure in ssDNA molecules mechanically stretched with optical tweezers. The model reproduces the experimental force-extension curves in ssDNA of different molecular lengths and varying sodium and magnesium concentrations. Salt-correction effects for the energy of compact domains and the interfacial energy are found to be compatible with those of DNA hybridization. The model also predicts the folding free energy and the average size of domains at zero force, finding good agreement with secondary-structure predictions by mfold. We envision the model could be further extended to investigate native folding in RNA and proteins.

中文翻译：

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单链 DNA 的协同依赖折叠

生物大分子的折叠是一个我们缺乏充分理解的基本过程。主要在蛋白质和 RNA 中进行研究，单链 DNA (ssDNA) 在生理盐条件下也会折叠，通过形成难以用生物物理技术表征的非特异性二级结构。在这里，我们提出了一个用于二级结构形成的螺旋线圈模型，其中 ssDNA 碱基被组织在两种不同类型的域（紧凑型和自由型）中。该模型包含两个参数：紧凑域中每个碱基的能量增益，$\epsilon$，以及与不同域之间的界面能相关的协同性， $\gamma$. 我们测试了模型量化用光镊机械拉伸的 ssDNA 分子中二级结构形成的能力。该模型再现了不同分子长度和不同钠和镁浓度的 ssDNA 中的实验力-延伸曲线。发现致密结构域能量和界面能的盐校正效应与 DNA 杂交的效应相容。该模型还预测了零力时的折叠自由能和域的平均大小，与mf old 的二级结构预测非常吻合。我们设想该模型可以进一步扩展以研究 RNA 和蛋白质的天然折叠。