Magnetic tweezers are micromanipulation devices that are able to exert and measure forces on magnetic particles by introducing magnetic gradients. They are emerging as a powerful tool to study biological problems both at the cellular and single molecule level.
The first models of magnetic tweezers were developed from as early as the 1940s for the in vivo study of cytoplasmic viscosity . In 1996, Croquette et al developed the first magnetic tweezers that could manipulate single molecules. This was used to study the elasticity of supercoiled DNA . Since then the use of magnetic tweezers in cell biology, as well as mechanobiology, has increased significantly.
Current magnetic tweezers can achieve forces ranging from sub-piconewtons (pN) to nanonewtons (nN). Depending on the setup, the forces generated can be translational or rotational and in certain multiple magnet setups 3D manipulations are also possible. Magnetic tweezers present a robust means to quantitatively apply forces to a system of interest and at a relatively low cost when compared to other micromanipulation tools.
The individual design of magnetic tweezers varies greatly, and this produces different capabilities. However the underlying principle remains the same – to apply forces to a system of interest by generating a magnetic field gradient on a magnetic particle introduced into the system. The magnetic field is created either by a permanent magnet or an electromagnet.
A basic magnetic tweezers setup consists of a pair of magnets mounted on a manipulator above an inverted microscope. The image of the magnetic particle is captured by a CCD camera and analyzed on a computer. One of the basic considerations in designing magnetic tweezers is the direction in which force is applied to the system. This direction, which is relative to the microscope objective, determines the type of force applied and the extension of the object being targeted. There are two types of setups: horizontal and vertical. Horizontal setups are more suitable for studying long tethers ranging from 5 µm to more than 50 µm , whereas vertical setups are more suited for shorter tethers.
In single molecule manipulation experiments, the extension of the molecule is measured by determining the position of the magnetic bead that the molecule is attached to. Different methods are utilized depending on whether a horizontal or vertical magnetic tweezers setup is used.
For horizontal tweezers, image analysis is the main technique employed. Images of the magnetic bead are normally acquired by CCD camera and are then used to identify the centroid of the bead. This method can calculate the bead position in the order of one to two nanometers, when using micron sized beads.
For vertical tweezers, as the direction of the molecule extension is along the axis of the objective, the centroid method cannot be applied. Instead, two methods may be used to determine the position of the bead. One method utilizes the diffraction ring pattern of the bead under bright field microscopy , whilst the other uses the intensity change of the bead in TIRF (Total Internal Reflection Fluorescence) microscopy as means of detecting the distance of the bead to the surface .
For single molecule experiments, the force exerted on the magnetic bead is calculated from its transverse fluctuations. In the case of a magnetic bead attached to a stretched DNA molecule, the system can be considered in terms of a pendulum.
The transverse rigidity (stiffness, kx) is therefore determined by the force applied (F) and the length of the DNA molecule (l) which is equivalent to the distance of the bead from the surface.
kx = F/l
The transverse rigidity (kx) relates to the transverse fluctuations (dx) of the magnetic bead in the following manner:
dx2 = kBT/kx
The above two equations can be used to calculate the force applied to the magnetic bead from its transverse fluctuations, as shown below:
F = kBTl/dx2
Further details on force determination can be found in a review by Croquette et al . Traditionally this method only applies to tethers longer than 1 micron, as for shorter tethers the fluctuations of the bead are too fast to be captured by CCD camera. Recent theoretical and instrumentation improvements have however improved force determination measurements for shorter tethers .
Magnetic tweezers were first used to study the elasticity of supercoiled DNA . The ability of magnetic tweezers to carry out long term measurements and to rotate molecules makes them amenable to the study of DNA supercoiling. It has been extensively used in studies of topoisomerases and helicases, which can regulate the supercoiled state of DNA .
The effect of DNA binding proteins on the structure of DNA has also been studied using magnetic tweezers. Theoretical models have been proposed to describe the effect of protein binding on the extension of DNA molecules . Different DNA binding proteins can induce changes in the structure of DNA, such as stiffening and bridging. Magnetic tweezers have been used to obtain experimental data on these changes upon binding of a range of different proteins including; H-NS , SsrB  and Rad51 . It has also been widely used to study in vitro chromatin assembly .