DNA Twist Stability Changes with Magnesium($2+$) Concentration

DNA Twist Stability Changes with Magnesium( $2 +$ ) Concentration

Onno D. Broekmans, Graeme A. King, Greg J. Stephens, and Gijs J. L. Wuite

Phys. Rev. Lett. 116, 258102 – Published 21 June 2016

Abstract

To understand DNA elasticity at high forces ( $F > 30 pN$ ), its helical nature must be taken into account, as a coupling between twist and stretch. The prevailing model, the wormlike chain, was previously extended to include this twist-stretch coupling. Motivated by DNA’s charged nature, and the known effects of ionic charges on its elasticity, we set out to systematically measure the impact of buffer ionic conditions on twist-stretch coupling. After developing a robust fitting approach, we show, using our new data set, that DNA’s helical twist is stabilized at high concentrations of the magnesium divalent cation. DNA’s persistence length and stretch modulus are, on the other hand, relatively insensitive to the applied range of ionic strengths.

Received 14 February 2015

DOI:https://doi.org/10.1103/PhysRevLett.116.258102

Physics Subject Headings (PhySH)

DNA folding

DNA

Physics of Living Systems

Authors & Affiliations

Onno D. Broekmans, Graeme A. King, Greg J. Stephens, and Gijs J. L. Wuite

LaserLaB Amsterdam and Department of Physics and Astronomy VU University Amsterdam, 1081 HV Amsterdam, Netherlands

Corresponding author. g.j.l.wuite@vu.nl

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Vol. 116, Iss. 25 — 24 June 2016

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Images

Figure 1
Typical force-extension data for double-stranded DNA (open circles) stretched using optical tweezers (schematically shown: a DNA molecule is tethered between two microbeads held in optical traps). Whereas the extensible wormlike chain (dashed line) only fits the data for forces up to $\sim 30 pN$ , the twistable wormlike chain (solid line) expands this range to $\sim 60 pN$ . Shown is averaged data for buffer conditions ( $500 m M$ NaCl, no ${Mg}^{2 +}$ , $N = 151$ ). For comparison, a single low-salt curve ( $75 m M$ NaCl, dash-dotted line) is shown, illustrating the effects of end-unpeeling.
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Figure 2
(a) A “toy model” of DNA twist-stretch coupling, based on [9]. For positive values of the twist-stretch coupling $g$ , the right-handed DNA helix (blue, solid line) would unwind (green, dashed line) when stretched (increasing relative extension $e$ ). In reality, for forces up to $\sim 35 pN$ , DNA overwinds when stretched (red, dash-dotted line). (b) The force dependence of the twist-stretch coupling $g$ of dsDNA is modeled in the twistable wormlike chain as a piecewise linear function [8]: constant up to a critical force $F_{c}$ (30.6 pN); above $F_{c}$ , a linear approximation $g (F) = g_{0} + g_{1} F$ is used.
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Figure 3
Double-stranded DNA force-extension data for increasing concentrations of ${MgCl}_{2}$ (in a background of $500 m M$ NaCl and $10 m M$ TrisHCl, pH 7.6; light to dark: 0, 25, 50, and $100 m M$ of ${MgCl}_{2}$ , respectively). For high magnesium concentrations, a clear stiffening of the DNA before the onset of overstretching is observed. Shown is data averaged per magnesium concentration ( $N \geq 12$ ), after correction for systematic measurement errors (see main text).
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Figure 4
When fitting optical tweezers force-extension data with the extensible wormlike chain (eWLC) equation as expressed analogously to Eq. (1), with $d$ as the dependent variable, the fit results are highly dependent on the data range used for fitting. As an illustration of this, fragments of simulated data were fitted using nonlinear least squares, using only the data between a distance $d_{\min}$ and the eWLC’s upper limit of 30 pN (inset). The values found for the persistence length $L_{p}$ (solid circles) as $d_{\min}$ is varied significantly underestimate the actual value (dashed line) and depend strongly on $d_{\min}$ (missing points indicate a lack of convergence of the fit). When using an inverted version of the eWLC equation, which expresses $F$ as a function of $d$ , a robust and reliable value for $L_{p}$ is found instead (open circles).
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Figure 5
As the concentration of $magnesium (2 +)$ ( ${MgCl}_{2}$ ) is increased from 0 to 150 m $M$ (in a background of $500 m M$ NaCl), the twist-stretch coupling parameter $g_{1}$ decreases, indicating a stabilization of dsDNA twist (error bars: bootstrap error, $N \geq 12$ ). In contrast, the persistence length $L_{p}$ and stretch modulus $S$ are relatively insensitive to these changes in divalent cation concentration.
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