Abstract
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 non-specific 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 tested 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.
Highlights
Single-stranded nucleic acids participate in a myriad of processes [1,2]
The first two terms account for the total energy of the compact domains pulled at a force f; MCðfÞ is the number of C domains, each contributing with an extension dCðfÞ; the third term is the stretching energy of F-type monomers with the extension per monomer xFðfÞ, obtained by Eq (2) or (3) [58]; and the last term stands for the interfacial energy between adjacent monomers
A dependence of the force-extension curves (FECs) with the single-stranded DNA (ssDNA) length might be the signature of long-range interactions along the chain, giving information about the nature of the secondary structure
Summary
Single-stranded nucleic acids participate in a myriad of processes [1,2]. Bases in single-stranded DNA (ssDNA) and ssRNA tend to form base pairs of different geometries and stabilities, from the most stable Watson-Crick to the weaker Hoogsteen or wobble base pairs [3]. Secondary-structure formation in nucleic acids can be investigated with pulling experiments with optical and magnetic tweezers [26], which allow stretching individual molecules by applying mechanical forces in the piconewton range and measuring their force-extension curves (FECs) [27,28,29]. These experiments show that ssDNA behaves as a semiflexible polymer, with FECs described using ideal elastic polymer models [such as the wormlike chain (WLC) model [30] ]. The model is compatible with MFold secondarystructure predictions, showing its power for predicting cooperativity-dependent folding of ssDNA
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