• Open Access

Cooperativity-Dependent Folding of Single-Stranded DNA

X. Viader-Godoy, C. R. Pulido, B. Ibarra, M. Manosas, and F. Ritort
Phys. Rev. X 11, 031037 – Published 17 August 2021
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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 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, ε, and the cooperativity related to the interfacial energy between different domains, γ. 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.

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  • Received 12 December 2020
  • Revised 18 May 2021
  • Accepted 16 June 2021
  • Corrected 23 August 2022

DOI:https://doi.org/10.1103/PhysRevX.11.031037

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Physics of Living SystemsStatistical Physics & Thermodynamics

Corrections

23 August 2022

Correction: Equations (11) and (G28) contained errors and have been fixed.

Authors & Affiliations

X. Viader-Godoy1,‡, C. R. Pulido2, B. Ibarra2, M. Manosas1,†, and F. Ritort1,*

  • 1Small Biosystems Lab, Departament de Física de la Matèria Condensada, Facultat de Física, Universitat de Barcelona, Carrer de Martí i Franquès, 1, 08028 Barcelona, Spain
  • 2Instituto Madrileño de Estudios Avanzados en Nanociencia, IMDEA Nanociencia, 28049 Madrid, Spain

  • *Corresponding author. fritort@gmail.com
  • Corresponding author. mmanosas@gmail.com
  • Present address: Department of Physics and Astronomy, University of Padova, via Marzolo 8, 35131 Padova, Italy.

Popular Summary

Proteins and nucleic acids are linear chains that fold into specific 3D shapes to perform their biological functions. Mostly studied in proteins and RNA, a full understanding of the process of molecular folding still eludes researchers. Here, we develop a mathematical model to interpret how single-stranded DNA (ssDNA) folds, at salt concentrations typical of living cells, forming nonspecific secondary structures.

Our model considers that ssDNA bases are organized into two types of domains: compact, where a chain of bases folds to form loops and other structures, and free, where the chain of bases remains relatively straight. The model also has two energy parameters, the average energy per base and the interfacial energy, which quantify secondary structure formation.

We test the validity of the model to predict secondary structure formation in individual ssDNA molecules manipulated with optical tweezers. The model reproduces experimental relations between applied force and ssDNA extension for over three decades of ssDNA lengths and varying sodium and magnesium concentrations. This implies that folding, at the most basic level of monomer interactions, is a cooperative process. We find that the dependence on salt concentration for the energy of the compact domains and the interfacial energy is compatible with those observed when ssDNA bonds to a complementary DNA strand (hybridization), suggesting similar underlying mechanisms.

Notably, the model’s predicted folding structures at zero force agree with those given by mfold, a software for secondary structure prediction of nucleic acids. We envision that our model could be further extended to investigate native folding in RNA and proteins, with the ability to predict zero-force structures from force-spectroscopy measurements.

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Vol. 11, Iss. 3 — July - September 2021

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