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Research Papers

Modeling the Abrupt Buckling Transition in dsDNA During Supercoiling

[+] 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 September 30, 2015; final manuscript received May 16, 2016; published online June 22, 2016. Assoc. Editor: Firdaus Udwadia.

J. Comput. Nonlinear Dynam 11(6), 061003 (Jun 22, 2016) (7 pages) Paper No: CND-15-1308; doi: 10.1115/1.4033308 History: Received September 30, 2015; Revised May 16, 2016

When deoxyribonucleic (DNA), held at a fixed tension, is subjected to torsional deformations, it responds by forming plectonemic supercoils accompanied by a reduction in its end-to-end extension. This transition from the extended state to the supercoiled state is marked by an abrupt buckling of the DNA accompanied by a rapid “hopping” of the DNA between the extended and supercoiled states. This transition is studied by means of Brownian dynamics simulations using a discrete wormlike-chain (dWLC) model of DNA. The simulations reveal, among other things, the distinct regimes that occur during DNA supercoiling and the probabilities of states within the buckling transition regime.

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Figures

Grahic Jump Location
Fig. 1

Cartoon illustrating the formation of plectonemic supercoils in DNA by means of the magnetic tweezer apparatus

Grahic Jump Location
Fig. 2

A representation of the dWLC model

Grahic Jump Location
Fig. 3

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

Grahic Jump Location
Fig. 4

The three regimes that occur during plectonemic supercoiling of DNA. The regimes are demarcated by the black vertical broken lines with the prebuckling regime on the left, the buckling transition regime in the middle, and the post-buckling regime on the right.

Grahic Jump Location
Fig. 5

Two metastable states exist within the buckling transition regime. The data in this plot were obtained for a linking number at which both states have equal probabilities. (Top) Rapid “hopping” between the two equilibrium states and the fluctuation about the mean value of each state. (Bottom) Histogram of end-to-end extensions within the buckling transition.

Grahic Jump Location
Fig. 6

The probability of finding DNA in one of the looped (circles) or extended (inverted triangles) states, within the buckling transition regime, depends on the number of turns at which it is held. An equilibrium point at which both states are equally probable can be estimated by the point of intersection of linear fits to the probability data.

Grahic Jump Location
Fig. 7

Within the buckling transition regime, increasing number of turns not only increases the probability of finding the DNA in the looped state but also increases the size of the extension jump between both states. With increasing number of turns, while the change in the equilibrium position of the extended state remains virtually unchanged, a shift is noticed in the equilibrium position of the looped state to the left.

Grahic Jump Location
Fig. 8

A strong correlation exists between the elastic energy (top) of DNA and its end-to-end extension (bottom) as it hops between the looped and extended states within the buckling transition regime

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