Torsional Stiffness of Extended and Plectonemic DNA

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Torsional Stiffness of Extended and Plectonemic DNA

Xiang Gao, Yifeng Hong, Fan Ye, James T. Inman, and Michelle D. Wang

Phys. Rev. Lett. 127, 028101 – Published 7 July 2021

See Viewpoint: A Gentle Twist on DNA

Abstract

DNA torsional elastic properties play a crucial role in DNA structure, topology, and the regulation of motor protein progression. However, direct measurements of these parameters are experimentally challenging. Here, we present a constant-extension method integrated into an angular optical trap to directly measure torque during DNA supercoiling. We measured the twist persistence length of extended DNA to be 22 nm under an extremely low force ( $\sim 0.02 pN$ ) and the twist persistence length of plectonemic DNA to be 24 nm. In addition, we implemented a rigorous data analysis scheme that bridged our measurements with existing theoretical models of DNA torsional behavior. This comprehensive set of torsional parameters demonstrates that at least 20% of DNA supercoiling is partitioned into twist for both extended DNA and plectonemic DNA. This work provides a new experimental methodology, as well as an analytical and interpretational framework, which will enable, expand, and enhance future studies of DNA torsional properties.

Received 21 December 2020
Accepted 15 April 2021

DOI:https://doi.org/10.1103/PhysRevLett.127.028101

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.

Physics Subject Headings (PhySH)

Bending Elastic deformation Elastic forces Fluctuations & noise Persistence length Phase diagrams Phase transitions

DNA

Polymers & Soft MatterStatistical Physics & Thermodynamics

Viewpoint

A Gentle Twist on DNA

Published 7 July 2021

A new technique allows measurements of DNA’s resistance to twisting under previously hard-to-access, biologically relevant conditions.

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Authors & Affiliations

Xiang Gao ^1,2, Yifeng Hong ³, Fan Ye ^1,2, James T. Inman ^1,2, and Michelle D. Wang ^1,2,*

¹Howard Hughes Medical Institute, Cornell University, Ithaca, New York 14853, USA
²Department of Physics, Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853, USA
³Department of Electrical and Computer Engineering, Cornell University, Ithaca, New York 14853, USA

^*mwang@physics.cornell.edu

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Issue

Vol. 127, Iss. 2 — 9 July 2021

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Images

Figure 1
Torque measurements by an AOT during DNA supercoiling using either the constant-force or the constant-extension method. In both methods, a DNA molecule was torsionally constrained between a coverslip surface and a nanofabricated quartz cylinder held in the AOT. For each experimental condition, the number of traces ( $N$ ) is also indicated. (a) Constant-force method. As turns were introduced to DNA with the force in the DNA held constant, the DNA extension and torque were simultaneously measured. (b) Constant-extension method. As turns were introduced to DNA with the DNA extension held constant, the force and torque on the DNA were simultaneously measured. Notably, the force on the DNA in constant-extension experiments can be much lower than the smallest attainable force in previous constant-force measurements.
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Figure 2
The effective twist persistence length $C_{eff}$ of extended DNA versus force $F$ . Data are from constant-force [blue symbols, Fig. 1] and constant-extension [red symbols, Fig. 1] experiments. The vertical error bars represent the SEM of the slope obtained from fitting individual traces. For each constant-extension condition, the force value indicated is the mean force of the fitting range in Fig. 1, the error bars represent the minimum and maximum force in the same range. Also shown are predictions from Bouchiat-Mézard (BM) model, Moroz-Nelson (MN) model, and modified Moroz-Nelson (modified-MN) model. $C = 109.3 nm$ is indicated as the gray solid line.
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Figure 3
Direct measurement of the twist persistence length $P$ of plectonemic DNA and theoretical predictions of DNA buckling transition. (a) Direct measurement of the torsional twist persistence length of $P$ plectonemic DNA, compared with the Marko model. The DNA was torsionally anchored between a coverslip surface and a nanofabricated quartz cylinder under a constant extension of 500 nm. Both force (top) and torque (bottom) were simultaneously measured as a function of turns (red curves). $P$ was determined by the slope of a linear fit to the torque-turns relation (bottom panel, black line) between $+ 24$ turns and $+ 190$ turns. The linear fit yields $P = 24 \pm 0.3 nm$ . For comparison, the torque measured from constant-force experiments in Fig. 1 (blue crosses) under the same conditions are shown. For the force versus turns relation, the grey solid line shows the Marko model prediction. (b) Marko model predictions of the DNA buckling transition at constant force. Data are from Fig. 1 (blue curves), and predictions from the Marko model (black curves) using $A = 43 nm$ , $C = 109 nm$ , and $P = 24 nm$ .
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