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Research Papers

# Resolving the Sequence-Dependent Stiffness of DNA Using Cyclization Experiments and a Computational Rod Model

[+] Author and Article Information
Sachin Goyal

Woods Hole Oceanographic Institution, MS 7, Woods Hole, MA 02543sgoyal@umich.edu

Noel C. Perkins

Mechanical Engineering, 2350 Hayward, University of Michigan, Ann Arbor, MI 48109-2125ncp@umich.edu

Jens-Christian Meiners

Physics (Biophysics Research Division), 930 North University Avenue, University of Michigan, Ann Arbor, MI 48109-1055meiners@umich.edu

A palindromic sequence over one helical turn would also cancel the intrinsic curvature over many helical turns, provided a helical turn contains exactly an integral number of base pairs. Otherwise, a small aperiodicity would ultimately increase the curvature over many helical repeats.

For perfectly homogeneous DNA, the equilibrium is a circle of radius $R=L∕2π$, for which the strain energy can also be calculated directly as $1∕2A(1∕R)2L$, where $A=50kTnm$ is the bending stiffness. This direct calculation gives exactly the same value of strain energy $(=22.6kT)$ as computed by the numerical simulation, validating the accuracy of our computational rod model. In addition, we have shown in Ref. 8 that our computational rod model faithfully reproduces the strain energies of protein-mediated homogenous B-DNA loops as computed by the elastic rod model of Balaeff et al. (37).

J. Comput. Nonlinear Dynam 3(1), 011003 (Nov 02, 2007) (6 pages) doi:10.1115/1.2802582 History: Received May 06, 2007; Revised July 12, 2007; Published November 02, 2007

## Abstract

Structural deformations of DNA play a central role in many biological processes, including gene expression. The structural deformations are sensitive to the material properties of the molecule, and these, in turn, vary along the molecule’s length according to its base-pair sequence. Examples of “sequence-dependent” material properties include the stress-free curvature and the stiffness for bending and torsion. Quantifying and separating these sequence-dependent properties from experimental data remains a significant challenge as they often work in unison in nature. In this paper, we offer a method for resolving and quantifying the sequence-dependent stiffness of DNA from cyclization (loop closure) experiments using a computational rod model of the molecule.

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Topics: Stiffness , DNA

## Figures

Figure 1

DNA shown on three length scales. Smallest scale (left) shows a double-helix structure (sugar-phosphate chains and base pairs). The intermediate scale (middle) shows how multiple double helices form a continuous molecule of double-stranded DNA (ds-DNA). The largest scale (right) shows how the molecule curves and twists in forming supercoils including the idealized plectonemic and solenoidal supercoils depicted here. (Courtesy: Branden and Tooze (2) and Lehninger (3).)

Figure 2

Dynamical rod model describing the deformation of the helical axis of DNA

Figure 3

A schematic of DNA cyclization in which a segment of DNA ultimately forms a complete loop under thermal fluctuations

Figure 5

Cyclization of two sequences, which have nearly straight (hence nearly identical) stress-free states yet substantially different stiffnesses. Sequence 1 is rich in GC pairs, while Sequence 2 is rich in AT pairs.

Figure 4

Block diagram of rod model computation leading from the base-pair sequence to the J factor

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