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. 2017 Dec;43(4):535-550.
doi: 10.1007/s10867-017-9468-1. Epub 2017 Sep 14.

Ionic effects on the temperature-force phase diagram of DNA

Sitichoke Amnuanpol  1
Affiliations

Ionic effects on the temperature-force phase diagram of DNA

Sitichoke Amnuanpol. J Biol Phys. 2017 Dec.

Abstract

Double-stranded DNA (dsDNA) undergoes a structural transition to single-stranded DNA (ssDNA) in many biologically important processes such as replication and transcription. This strand separation arises in response either to thermal fluctuations or to external forces. The roles of ions are twofold, shortening the range of the interstrand potential and renormalizing the DNA elastic modulus. The dsDNA-to-ssDNA transition is studied on the basis that dsDNA is regarded as a bound state while ssDNA is regarded as an unbound state. The ground state energy of DNA is obtained by mapping the statistical mechanics problem to the imaginary time quantum mechanics problem. In the temperature-force phase diagram the critical force F c (T) increases logarithmically with the Na+ concentration in the range from 32 to 110 mM. Discussing this logarithmic dependence of F c (T) within the framework of polyelectrolyte theory, it inevitably suggests a constraint on the difference between the interstrand separation and the length per unit charge during the dsDNA-to-ssDNA transition.

Keywords: DNA denaturation; DNA unzipping; Debye-Hückel potential; Imaginary time quantum mechanics.

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Conflict of interest statement

The author declares that he has no conflicts of interest.

Figures

Fig. 1
Fig. 1
In the absence of force, an increase in temperature above the melting temperature T m transits dsDNA to ssDNA. For temperatures T < T m, the dsDNA-to-ssDNA transition is achieved by applying an external force F larger than the critical force F c(T)
Fig. 2
Fig. 2
DNA is smeared out to form two continuous curves r 1(s) and r 2(s) interacting to each other by the attractive Debye-Hückel potential U(r 2(s) −r 1(s)). The constant force F acts uniformly along the curves r 1(s) and r 2(s) with equal magnitude but opposite direction. Elastic energy is contributed from the spatially varying orientation described by the tangent vectors t 1(s) = d r 1/ds and t 2(s) = d r 2/ds
Fig. 3
Fig. 3
Dependence of melting temperature T m on the Na + concentration, calculated by Eq. (28), is compared with T m, shown as dots, determined from the calorimetric measurements. Note that T m obtained from Eq. (28) is in unit of Kelvin and is converted to unit of Celsius for comparison with experiments. Experimentally, the melting temperature is identified to be the temperature at which heat capacity is maximum, shown as an inset for six values of sodium ions 32, 50, 75, 110, 125, and 200 mM (Copyright 1999 National Academy of Sciences) [19]
Fig. 4
Fig. 4
The critical force F c is determined from the zero of the ground state eigenenergy E 0, (22). a At [Na+] = 0.110 M the critical force F c is 11.6 pN at 300 K (27 °C) and 11.0 pN at 320 K (47 °C). b At [Na+] = 0.200 M the critical force F c is 15.0 pN at 300 K (27 °C) and 14.3 pN at 320 K (47 °C)
Fig. 5
Fig. 5
The DNA in high Na+ concentration requires the larger critical force F c(T) for the dsDNA-to-ssDNA transition. For comparison, the dots are the experimentally measured critical force of the lambda bacteriophage virus at [Na+] = 0.110 M [22]
Fig. 6
Fig. 6
At a temperature of 300 K (27 °C), the critical force exhibits a linear relation with ln[Na+] for the Na+ concentration ranging from 0.032 to 0.110 M. The dashed line, which is a linear fit to the calculated results, has a slope 5.9 pN. At too high Na+ concentration, the perturbative expansion from the ground state eigenenergy E0(0) for the Coulomb interstrand potential is less reliable, giving rise to a deviation from the linear fit
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