Magnetic Tweezers - Construction Principle and Physics of Magnetic Tweezers - Magnetic Particles

Magnetic Particles

Magnetic particles for the operation in magnetic tweezers come with a wide range of properties and have to be chosen according to the intended application. Two basic types of magnetic particles are described in the following paragraphs; however there are also others like magnetic nanoparticles in ferrofluids, which allow experiments inside a cell.

Superparamagnetic beads

Superparamagnetic beads are commercially available with a number of different characteristics. The most common is the use of spherical particles of a diameter in the micrometer range. They consist of a porous latex matrix in which magnetic nanoparticles have been embedded. Latex is auto-fluorescent and may therefore be advantageous for the imaging of their position. Irregular shaped particles present a larger surface and hence a higher probability to bind to the molecules to be studied. The coating of the microbeads contains also ligands to be able to attach the molecules of interest. For example, the coating may contain streptavidin which couples strongly to biotin, which itself may be bound to the molecules of interest.

When exposed to an external magnetic field, these microbeads become magnetized. The induced magnetic moment is proportional to a weak external magnetic field :

where is the vacuum permeability. It is also proportional to the volume of the microspheres, which stems from the fact that the number of magnetic nanoparticles scales with the size of the bead. The magnetic susceptibility is assumed to be scalar in this first estimation and may be calculated by, where is the relative permeability. In a strong external field, the induced magnetic moment saturates at a material dependent value . The force experienced by a microbead can be derived from the potential of this magnetic moment in an outer magnetic field:

The outer magnetic field can be evaluated numerically with the help of finite element analysis or by simply measuring the magnetic field with the help of a Hall effect sensor. Theoretically it would be possible to calculate the force on the beads with these formulae; however the results are not very reliable due to uncertainties of the involved variables, but they allow estimating the order of magnitude and help to better understand the system. More accurate numerical values can be obtained considering the Brownian motion of the beads.

Due to anisotropies in the fortuitous distribution of the nanoparticles within the microbead the magnetic moment is not perfectly aligned with the outer magnetic field i.e. the magnetic susceptibility tensor cannot be reduced to a scalar. For this reason, the beads are also subjected to a torque which tries to align and :

The torques generated by this method are typically much greater than, which is more than necessary to twist the molecules of interest.

Ferromagnetic nanowires

The use of ferromagnetic nanowires for the operation of magnetic tweezers enlarges their experimental application range. The length of these wires typically is in the order of tens of nanometers up to tens of micrometers, which is much larger than their diameter. In comparison with superparamagnetic beads, they allow the application of much larger forces and torques. In addition to that, they present a remnant magnetic moment. This allows the operation in weak magnetic field strengths. It is possible to produce nanowires with surface segments that present different chemical properties, which allows controlling the position where the studied molecules can bind to the wire.