Physical Properties of DNA

Sonny Vo
October 31, 2007

(Submitted as coursework for Physics 210, Stanford University, Spring 2007)

Brief Overview

DNA contains genetic instruction essential to the development and functionality in all living organisms. The double helix is 2.2-2.6 nm in width, can range from 2 to 8 cm in length when uncoiled, and is made up of millions of nucleotides. The networks of covalent bond between the base groups: A-T, C-G, orchestrates the construction of RNA, which then codes ribosome. The ribosome in turn manufacture the proteins that drive the biochemical reactions to sustain all life forms. This is the recipe for life and is popularly regarded as the "central dogma" of biology.

Recent advances in optical and magnetic tweetzers can trap a nanometer size polysterene beads in a potential and measure its displacement with nanometer precision. By coating the bead with biological samples such as DNA strands and using a set of permanent magnets, the physical properties of DNA such as its twist-strain coupling factor can be probed.

Fig. 1: Sample Set-up


A DNA segment is stretched and attached between a glass coated slip and a 2.8 μm magnetic bead as presented in Fig. 1. The magnetic bead is chemically attached to the DNA with streptavidin. The application of a magnetic field will cause the magnetic moments of the magnetic bead to align to the field line, resulting in a stretching the bead. The rotor bead is fluorescently labeled with an avidin coat and attached to a biotinylated patch. Central to the experiment is the magnetic tweezer [4]. Selectively changing the height of the magnet introduces tension to the DNA. Extension changes in the DNA can be measured by gauging the change in the focal depth of the magnetic bead. Moreover, the twist of the DNA can be manipulated by rotating the fluorescent rotor bead. A 100 Hz electron multiplying camera is used to capture the bead motion to measure its rotational velocity and applied torque on the DNA.

Physical Parameters of DNA

DNA can be modeled as an isotropic rod under conditions of small perturbations. The various categories of rigidity can be summarized in Table 1.

The total energy or Hamiltonian of a twisted and stretched DNA is given by

where C, L, and S are the given parameters displayed in Table 1, and theta is the angle DNA subtends from its equilibrium position. G is the twist-stretch coupling parameter. One can see from unit analysis that each term in the equation yields units of energy. Previously, G was thought to have a positive value implying that DNA will unravel as its length is stretched. However, this was recently showed to be incorrect from quantatitive analysis of DNA structure and conformation using magnetic tweetzers[1]. It was shown experimentally that DNA has a negative G coupling value. By using isolated DNA molecules, a G value of -90 ± 20 pN nm were found. The DNA will twist up to an applied stretched tension of about 30 pN. Furthermore, every 1% of DNA stretched led to about 0.1% twist of the DNA.

Table 1: Physical Properties of DNA under small deformation [1]
Bending Rigidity (B) 230±20 pN nm2
Twist Rigidity (C) 460±20 pN nm2
Stretch Modulus (S) 1100±200 pN

A corollary experiment was then performed to measure the extension of the DNA as it is twisted. This would add confidence to the measured observation of a negative G value.The Hamiltonian of equation 1 is modified by adding a negative xF term. Minimizing this new energy with respect to distance, x, gave a predicted stretched length of 0.5 ± 0.1 nm. Using the magnetic tweetzers and assayed in the literature, a value of 0.5 nm per turn were found.

What is the physical reason for the negative twist-stretch coupling? Simulation of the DNA structure using all-atom potentials showed that certain DNA conformations are energetically favorable in an off-equilibrium state[3]. The technique replicates the natural chemical environment of the DNA by taking into account the salt condition, distant-dependence of the dielectric constant and atomic charges. Minimalizing the conformation energy yield several helical structures which are consistent with crystal structure data. This information opens up novel research direction for understanding the discoveries of the physical properties of DNA. Progress is still underway to understand the mechanism behind the negative twist-stretch coupling parameter.


Understanding the physical mechanism of DNA leads to the understanding of the binding or unbinding of proteins to DNA bases. One can imagine the important implications this may have in the long term. For example, helicases, which are responsible for unwinding DNA duplexes, are essential to the reproduction of HIV-C virus. Destabilizing the effects of this helicase by introducing an agent that changes the conformation of DNA might lead to the eradication of this virus.

DNA is the fundamental framework of life. Human beings are only at the beginning stage of understanding the extraordinary precision that DNA and its constituent parts can read and code information. Understanding biological systems at the single molecular level has opened up new frontiers in science. Complicated biological actions such as allostery, whereby protein conforms to a certain chemical signal, can be better understood. Scientists have been able to change the conformation of proteins by applying tension exerted by DNA attached end-to-end with the the proteins [5]. There is no doubt that given the complexities in a small system like a living cell, biology holds many laboratories for future exploration and exciting science experiments.

©2007 Sonny Vo. The author grants permission to copy, distribute and display the work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.


[1] J. Gore et al. Nature 442, 836 (2006)

[2] T. R. Strick et al., "The Elasticity of a Single Supercoiled DNA Molecule," Science 271, 1835 (1996).

[3] K. M. Kosikov et al., "DNA Stretching and Compression: Large-Scale Simulations of Double Helical Structures," J. Mol. Biol. 289, 1301 (1999).

[4] J. Sung, "Single Molecule Study Using Magnetic Tweezers,", (2007).

[5] B. Choi and G. Zocchi, "Guanylate Kinase, Induced Fit, and the Allosteric Spring Probe," Biophys. J. 92, 1651 (2007).