Arrhenius-law-governed homo- and heteroduplex dissociation

Open Access

Arrhenius-law-governed homo- and heteroduplex dissociation

Matthias Bochtler

Phys. Rev. E 101, 032405 – Published 9 March 2020

Abstract

A simple model of temperature-increase-driven homo- or heteroduplex dissociation is analyzed. It features a temperature-independent association constant, and a dissociation constant that increases with temperature according to an Arrhenius law. The model is analytically tractable for quasiequilibrium conditions, for two special cases in the intermediate regime, and in the strongly irreversible regime. In the latter, the fraction of isolated components depends on temperature according to a Gumbel minimal value distribution. The model suggests a logarithmic dependence of the dissociation temperature on the rate of temperature increase. It further predicts that the dissociation occurs in a twice broader temperature interval for slow than fast temperature increase. Finally, the model points to a previously overlooked source of discrepancy between apparent van't Hoff and calorimetric enthalpies. Applied to short double stranded DNA, the model explains the dependence of the melting temperature on the rate of temperature increase, and the twice lower width of the melting transition in low salt compared to high salt conditions.

Received 7 January 2019
Revised 21 January 2020
Accepted 14 February 2020

DOI:https://doi.org/10.1103/PhysRevE.101.032405

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)

Nonequilibrium & irreversible thermodynamics Nonequilibrium statistical mechanics Phase transitions

Statistical Physics & Thermodynamics

Authors & Affiliations

Matthias Bochtler ^*

IIMCB, Trojdena 4, 02-109 Warsaw, Poland and Polish Academy of Sciences, IBB, Pawinskiego 5a, 02-106 Warsaw, Poland

^*mbochtler@iimcb.gov.pl

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Issue

Vol. 101, Iss. 3 — March 2020

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Images

Figure 1
Predicted dependence of the free fraction $y$ and its derivative $d y / d θ$ on $θ$ in the $ξ \to 0$ limit. Black curves are based on numerical integration of master Eq. (24). The gray curves below show the analytical solutions for quasiequilibrium [Eq. (32)], $α = 1$ [Eq. (42)], $α = 2$ [Eq. (76)], and large $α$ [Eq. (61)].
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Figure 2
Characteristics of the dissociation curves $y (θ)$ for various $α$ in the $ξ \to 0$ limit. The black curves are based on numerical solution of the master Eq. (24). The gray curves for $θ_{av}$ , $Δ θ$ and $s$ are based on the approximate solution in Eqs. (71) and (72), for $f (α) = α^{2} / 2$ . Note that the approximate solution predicts an incorrect asymptotic $s$ value for large $α$ . The correct value is obtained from the Gumbel solution of Eq. (61), according to Eq. (66) (see Table 1).
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Figure 3
Van't Hoff analysis in the $ξ \to 0$ limit. Panels (a) and (b) $ln \frac{y^{2}}{1 - y}$ and $d (ln K_{app}) / d θ$ as a function of temperature $θ$ , for selected parameters $α$ . Black lines show results for the numerical solution of the master equation, faint gray lines are analytical results in the quasiequilibrium limit, and for the special case $α = 2$ . The legend in panel (a) applies also to panel (b). In the $ξ \to 0$ limit, the ratio $κ = Δ H_{app} / Δ H$ is equal to $d (ln K_{app}) / d θ$ . Measurements of $K_{app}$ are typically made near $y = 1 / 2$ to have well-defined $y$ and $1 - y$ values. Panel (c) shows the typical correction factors for measurements in the (immediate) vicinity of $y = 1 / 2$ , as a function of the parameter $α$ .
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Figure 4
Dissociation curve characteristics for small finite $ξ$ . The legend in panel (a) applies to all panels.
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Figure 5
Thermodynamic values for small finite $ξ$ . The legend in panel (a) applies to all panels.
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Figure 6
Change of apparent melting temperature (a) and melting width (b) with changing $α$ . In the experiment shown in (a), carried out by Li and colleagues [10], three DNA duplexes of different length were studied, and $α$ was varied by changing the melting rate $Γ$ for fixed salt concentration $a$ . Gray lines represent best least square fits assuming a logarithmic dependence of apparent melting temperature on $α$ or $Γ$ , as predicted by Eq. (82). In the experiment shown in (b), carried out by Hillen and colleagues [13], $α$ was varied by changing the salt concentration $a$ for fixed melting rate $Γ$ . Data are shown for a 300-mer duplex. The gray curve illustrates the theoretical expectation based on Eq. (84) for fit parameters $p = 3.7$ , $a_{0} = 0.2 M$ and $Δ T_{vH} = 0 . 43^{\circ} C$ . The $p$ value is typical for a DNA of this length [12], and the $Δ T_{vH}$ value is in fair agreement with the expected $Δ T_{vH} = 0 . 34^{\circ} C$ based on the melting point of the 300-mer duplex assuming a melting entropy per base pair of 23 cal/(molK). Hillen and colleagues also studied two shorter duplexes that exhibit qualitatively similar behavior. Data for these are not shown, because the change in melting width occurs at the edge of the studied range of salt concentrations.
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