Torque measurement at the single-molecule level

Abstract

Methods for exerting and measuring forces on single molecules have revolutionized the study of the physics of biology. However, it is often the case that biological processes involve rotation or torque generation, and these parameters have been more difficult to access experimentally. Recent advances in the single-molecule field have led to the development of techniques that add the capability of torque measurement. By combining force, displacement, torque, and rotational data, a more comprehensive description of the mechanics of a biomolecule can be achieved. In this review, we highlight a number of biological processes for which torque plays a key mechanical role. We describe the various techniques that have been developed to directly probe the torque experienced by a single molecule, and detail a variety of measurements made to date using these new technologies. We conclude by discussing a number of open questions and propose systems of study that would be well suited for analysis with torsional measurement techniques.

Figure 1. Examples of biological systems involving torque

(top) Transcription, the process of copying genomic DNA into RNA, involves the rotation of the RNA polymerase enzyme relative to its helical DNA track. Due to the size and typical confinement of the polymerase and associated machinery, the DNA is overtwisted (positive supercoiling) in front of the motor, and undertwisted (negative supercoiling) behind, in accordance with the “twin-supercoiled domain” model. (middle) During DNA replication, two identical copies are made of a single original DNA molecule. Just as during transcription, positive supercoiling is generated in front of the repliosome complex as it progresses along the DNA track. Behind the replication fork, daughter DNA strands can be twisted and intertwined, forming positive precatenanes. Topoisomerases of various types act during both processes in order to relieve the torsional stress generated along the DNA. (bottom) Two rotary motors are shown; the F₀F₁-ATPase, which uses the potential energy from a proton gradient to mechanically rotate and generate ATP from ADP and P_i, and the bacterial flagellar motor, which similarly uses a proton gradient to rotate and provide motility to a swimming bacterium.

Figure 2. Experimental configurations for single molecule torque measurements

(a) Electrorotation of a single bacterium with its flagella bound to the surface (8). (b) Rotation of the F₁-ATPase can be observed by monitoring the rotational orientation of a fluorescent actin filament (78). (c) The rotor bead tracking assay utilizes the rotation of a small bead to monitor and/or generate torque. Force and externally imposed twist can be controlled at the DNA ends by microsphere handles (19). (d) The angular optical trap angularly orients a quartz cylinder with the linear polarization of the input trapping laser beam. The polarization state of the transmitted beam, as measured by the transmitted light intensities in the right and left-handed circular polarizations, directly determines the applied torque on a dsDNA molecule and the angular orientation of the DNA (29, 59). (e) A magnetic tweezers setup by Celedon et al. (21) consists of a magnetic bead and nanorod torque arm to angularly orient one end of a dsDNA tether; twist is introduced by rotating the microscope coverglass. (f) Magnetic torque tweezers incorporate a supplementary side magnet to add a small horizontal perturbation to the vertical magnetic field created by a cylindrical magnet, producing a low-stiffness angular trap to orient a magnetic bead (65). (g) Soft magnetic tweezers use a six pole electromagnet to create a rapidly rotating horizontal magnetic field of varying intensity in order to produce either a constant torque or a magnetic angular trap of tunable stiffness (77). (h) Electromagnetic torque tweezers use two pairs of Helmholtz coils for dynamic control of the horizontal magnetic field (47).

Figure 3

DNA force-torque phase diagram. Phase transitions between specific states of DNA are represented by solid black lines (19, 73, 96). Red points indicate torque values measured during phase transitions using an angular optical trap (29, 33, 98, 99). Adapted from Sheinin et al. (98).

Figure 4. Torque measurements on single biological molecules

(a) Averaged torque trace obtained using rotor bead tracking during under- and over-winding of 14.8 kb DNA molecules held at 15 and 45 pN of force. Torque plateaus correspond to transitions to P-DNA (positive twist) or melted L-DNA (negative twist). The torsional modulus was extracted from the slope of the linear region. Adapted from Bryant et al. (19). (b) Individual torque traces obtained with an angular optical trap as a single 2.2 kb DNA molecule was overwound under tension. The torsional modulus was extracted from the slopes of the linear regions. Torque plateaued as the DNA buckled to form plectonemes (scB-DNA). Adapted from Forth et al. (33). (c) The torque-force relationship during the migration of a fully homologous Holliday junction, as determined by an angular optical trap. Shown are the mean torque values as a function of force (points) and theoretical prediction (line; not a fit). Adapted from Forth et al. (32). (d) Torsional response of a RecA filament at 3.5 pN, obtained with magnetic torque tweezers. The wide spread in torque values reflects the dynamic nature of the RecA filament (Lipfert, personal comm.). Adapted from Lipfert et al. (65). (e) Torque-speed relationship measured for the Na⁺-driven flagellar motor of Vibrio alginolyticus by monitoring rotation of a bead attached to the flagellum. Adapted from Sowa et al. (104). (f) Rotational trajectories of a single F₁-ATPase motor, under external torque, in the presence of ATP, ADP and P_i. At the stalling torque (~31 pN·nm), the motor still exhibited bidirectional stepwise fluctuations. Adapted from Toyabe et al. (108).