The principle of Magnetic Twisting Cytometry is best explained with a figure:

(Wang and Ingber, Science 260: 1124-1127, 1993)

The black circles represent small (4.5 um) ferrimagnetic beads that are firmly attached to the surface of cultured cells via specific surface receptors. First, the ferrimagnetic beads are magnetized in the horizontal direction with a brief, 1000-Gauss homogeneous magnetic pulse. Then the beads can be rotated (twisted) in a homogeneous magnetic field. The cell, of course, resists this bead rotation, and depending on the cell mechanical properties, the beads succeed to move more or less. If we know the amount or bead movement, then we can determine the cell's mechanical properties, such as cell stiffness, viscosity, etc. Obviously, three main components are required for this to work: a magnetizer, a twister, and a device to measure the bead movement.

A: The Magnetizer

B: The Twister

C: Measurement of the bead's movement

The bead movement consists of two components: rotation and lateral translation. The beads rotate due to the twisting field, and they can also translate unless they are completely internalized by the cell. This is best compared to the movement of a tire on a car: a torque on the weel will both cause a rotation and translation. Depending on whether we want to measure bead rotation or bead translation, we need two different methods.

Measurement of bead rotation

Traditionally, four fluxgate magnetometers (Foerster, Reutlingen, Germany) are used to measure the remanent magnetic field of the beads in the horizontal direction (Br). Values for Br are typically on the order of 1 nT. To improve signal-to-noise ratio, the well (Petri-dish) with the cells and the beads is rotated around the vertical axis at 6.5 Hz, and Br is determined by lock-in amplification. Also, the entire apparatus must be shielded from external magnetic fields. We use four concentric mu-metal cylinders that are closed on both ends (Amuneal, Philadelphia, USA). To achieve a reasonable signal-to-noise ratio, we need approximately 20,000 beads on about the same number of cells.

This figure explains how the horizontal component of the bead's remanent field vector (Br, as measured with an in-line magnetometer) can be used to compute the bead's angular rotation. B0 denotes the absolute value of the bead's remanent field (measured immediately after magnetization).

This scanning EM image shows how a magnetic bead is (usually) attached to a cell. The bead is coated with a synthetic RGD-containing peptide - a ligand for a number of integrin receptors that are expressed on the cell surface of many cells. This image shows a human airway smooth muscle cell.

A 6mm cell well contains about 20,000 cells, and we add about the same number of beads. The magnetic signal from those 20,000 beads is tiny (on the order of 1 nT at a distance of 2 cm), and a great deal of care must be taken to obtain usable signals. This figure shows a representative measurement of the bead's remanent field in human airway smooth muscle cells. The curve labelled "relaxation" shows how the remanent field slowly decays over time, which is thought to be due to cell motility. The curve labelled "twist" shows how the remanent magnetic field suddenly decreases and levels off after a few seconds when a twisting field of 30 Gauss is applied. After removing the twisting field (here at 80 seconds), the remanent field partially recovers. The ratio between the "twist" signal and the "relaxation" signal can be interpreted as bead rotation with the formula shown above. Generally, the more the "twist" and the "relaxation" signals differ, the more did the beads rotate. A large bead rotation can either mean that the cell is floppy, or that the bead is not or only weakly bound to the cytoskeleton that (as the skeleton in humans) sets mechanical stability.

If we know the angular bead rotation and the magnetic torque that we apply, we can compute an apparent cell stiffness. For an internalized bead, the magnetic torque and the shear stress in the cell during twisting scales with a calibration constant cbead. This calibration constant can be obtained from measurements of beads in a viscous standard. And of course, the magnetic torque increases with the twisting field Htwist. The torque also decreases with cos(a) as the bead aligns with the twisting field.

This figure shows a typical application of MTC: In this study by Hubmayr et al. Am J Physiol 271: C1660, 1996, a number of broncho-dilatory agonists have been tested to evaluate their effects on smooth muscle contraction. As cell stiffness and the contractile status of the cell are directly related, MTC can be used as a tool to measure the effectiveness of broncho-dilatory drugs. It can be (and has been) shown that relative changes of cell stiffness (as measured with MTC) correlate well with relative changes in airway resistance when these drugs are administered in vivo

We measure the magnetic properties (magnetic moment) of our microbeads by rotating them in a viscous standard (find out more)