Single-molecule magnetic tweezer tests on DNA: bounds on topoisomerase relaxation

Abstract

Biomedical researchers regularly stretch and twist single DNA molecules in magnetic tweezer experiments. By making the molecule writhe into a plectoneme (ply) and plotting its load-extension curves, key DNA parameters, such as effective radius, can be estimated. Adding untangling enzymes (topoisomerases) to the DNA's environment, their individual cuts are detected as jumps in extension.Sufficient information is now known about the topoisomerases for us to make good idealizations about their kinematics and mechanics. The novelty of this paper is to study their actions in the context of accurate ply solutions from the theory of elastic rods. To do this, we define an extended rod-plus-tension system that allows us to determine the stored energies from areas in the conventional link versus writhe plane.After a cut, the molecule relaxes dynamically to a new equilibrium state, and often there will be two or more alternative stable configurations onto which it might settle. Knowing the energy levels allows us to identify which states can and cannot be reached over the unstable mountain passes, and which of the accessible states offer the greatest energy relaxation. Strict energy bounds on behaviour are established.This knowledge has medical value because topoisomerase inhibitors, lethal for cells, are used as antibiotics and in chemotherapy for cancer.

A Bracing Nonlinear Walk in Applied Mechanics: Memoirs and Reflections

“…We also used our energy method to derive the equations for a novel ply made of imperfect anisotropic rods, and examined its helical solutions. Further contributions examined the mechanics of DNA [Travers & Thompson, 2004], analysed singlemolecule tweezer tests [Thompson, 2008a], and the cutting actions of the untangling topoisomerase enzymes [Thompson, 2008b] as illustrated in figure 18.…”

DNA information: from digital code to analogue structure

“…Here, departures from ideal behaviour found by Olson and collaborators include intrinsic bending (in the roll variable), bending anisotropy, inhomogeneity in twisting to bending stiffness ratio, twist-roll coupling, twist-stretch coupling and shearing anisotropy. Some other experimental methods used to examine elastic behaviour of longer segments in which the effects of individual base-pair steps are spatially averaged are as follows: cyclization [85,86]; fluorescence resonance energy transfer [87]; gel mobility [88]; single-molecule stretching [89,90], and twisting [91][92][93]. The sequence-dependent nature of DNA deformability has been independently confirmed by research aiming to deduce DNA elastic properties from molecular dynamics simulations [94,95].…”

Helical post-buckling of a rod in a cylinder: with applications to drill-strings

“…(Schneider 2003). Helical buckling and ply formation also play a key role in the functioning of the DNA molecule (Thompson et al 2002;Calladine et al 2004;Travers & Thompson 2004;Thompson 2008).…”

“…During its use, the surgeon relies on the longitudinal and twisting movement on the input end to control the leading-end movement (Schneider 2003). Helical buckling and ply formation also play a key role in the functioning of the DNA molecule Calladine et al 2004;Travers & Thompson 2004;Thompson 2008).…”