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Research Papers

Extensional Response and Equilibrium Kinetics of Torsionally Relaxed dsDNA Under Tension: A Brownian Dynamics Study

[+] Author and Article Information
Ikenna D. Ivenso

Department of Mechanical Engineering,
Texas Tech University,
Lubbock, TX 79409
e-mail: ikenna.ivenso@ttu.edu

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received May 24, 2015; final manuscript received September 18, 2016; published online December 5, 2016. Assoc. Editor: Zdravko Terze.

J. Comput. Nonlinear Dynam 12(3), 031001 (Dec 05, 2016) (7 pages) Paper No: CND-15-1140; doi: 10.1115/1.4034834 History: Received May 24, 2015; Revised September 18, 2016

Deoxyribonucleic acid (DNA) is a long flexible polyelectrolyte that is housed in the aqueous environment within the cell of an organism. When a length of torsionally relaxed (untwisted) DNA is held in tension, such as is the case in many single molecule experiments, the thermal fluctuations arising from the constant bombardment of the DNA by the surrounding fluid molecules induce bending in it, while the applied tension tends to keep it extended. The combined effect of these influences is that DNA is never at its full extension but eventually attains an equilibrium value of end-to-end extension under these influences. An analytical model was developed to estimate the tension-dependent value of this extension. This model, however, does not provide any insight into the dynamics of the extensional response of DNA to applied tension nor the kinetics of DNA at equilibrium under said tension. This paper reports the results of Brownian dynamics simulations using a discrete wormlike-chain model of DNA that provide some insight into these dynamics and kinetics.

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Figures

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Fig. 1

The DNA strand represented in this figure is anchored at its lower end while a tensile force applied to its upper end. The bombardment from the surrounding fluid particles tends to bend it, while the applied tension tends to keep it extended. The resulting end-to-end extension of the DNA is always less than its contour length.

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Fig. 2

A representation of the dWLC model

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Fig. 3

Figure showing the evaluation of αi and γi, the two components of the bend angle τi (see text)

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Fig. 4

Comparison between the equilibrium relative extensions obtained from BD simulations (circles) and those obtained from the theoretical estimate (inverted triangles)

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Fig. 5

Extensional trajectories obtained from simulations of torsionally relaxed DNA under applied tensions. The value of the equilibrium relative extension increases with the magnitude of the applied tension. For clarity, this plot shows only the first 8 ms of the extensional response.

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Fig. 6

The dependence of the timescale for extensional response of torsionally relaxed DNA on the magnitude of applied tension decays exponentially with increasing magnitude of applied tension

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Fig. 7

The size of the fluctuations in the end-to-end extensions at equilibrium decay exponentially with increasing magnitude of applied tension. The solid line is the fit of a single exponential function to the data.

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Fig. 8

The mean bend angle decreases with increasing magnitude of applied tension. This indicates that the applied tension reduces the influence of entropic forces that cause bending in DNA.

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Fig. 9

Influence of hydrodynamics interactions on the timescale for the extensional response of torsionally relaxed DNA under an applied tension. (a) comparison of the timescales for extensional response with (circles) and without (diamonds) hydrodynamic interactions and (b) the difference in timescales decays with increasing magnitude of applied tension.

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Fig. 10

Influence of hydrodynamics interactions on the thermal fluctuations at extensional equilibrium: (a) comparison of the standard deviations in extensions at equilibrium with (squares) and without (diamonds) hydrodynamic interactions and (b) comparison between the corresponding mean bend angles

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