1. THEORY

As described by Pohl [1] non-uniform fields can sometimes induce a torque on a particle, causing it to rotate. However, the controlled way to induce cellular spin is to subject the cell to a rotating electrical field, and the first reports of this were given by Arnold and Zimmerman[2] and Mischel et al [3]. The polynomial electrodes shown in Figure 1 can be used to perform near simultaneous measurements of both dielectrophoresis and electrorotation [4]. By arranging the electrical connections to give 90^o phase difference between adjacent electrodes (see Figure 1) a rotating electric field is generated, and the resulting rotational torque exerted on a particle is given by:

(1)

The symbol Im indicates that the imaginary component of the dipole moment determines the rate and sense of the induced electrorotation. Thus, if the imaginary component of m is positive, then from equation (1) the torque exerted will be negative and cause the particle to rotate in a sense that opposes that of the rotating field. A physical insight into this, perhaps counter-intuitive effect, is provided in Figure 1(b).

Arnold and Zimmerman (see reference 5 for a review) have demonstrated that electrorotation measurements provide a very sensitive method for monitoring the physiological state of cells and determining their sensitivity to exposure to chemicals and other agents. In our laboratory we are developing, with Genera Technologies Ltd., an electrorotation assay for determining the concentration and viability of toxic organisms in drinking water [6,7].

Figure 1 (a) A rotating field can be generated between four electrodes by applying sinusoidal voltages to them with phases spaced 90o apart. (b) Depending upon the phase angle of the induced dipole moment, defined by equation (2), the rotational torque acting on the particle will be either co- or anti-field. In the case shown here, and as a result of charge repulsion effects, the particle will rotate counter to the clockwise rotating field.

The phase angle between the applied field and the induced dipole moment is given by:

(2)

The factor Im{m} is positive for phase angles between 0^o and +180^o so that according to equation (1) the particle will rotate in an antifield sense, whilst Im{m} is negative for values between 0^o and -180^o and the rotation will be cofield.

For symmetrical electrode geometries, such as that shown in Figure 1, the rotating electric field is uniform over the central inter-electrode gap and the electrorotation behaviour is well described by equation (1). However, near the electrode edges both dielectrophoretic forces and rotational torques influence the kinetic behaviour of particles, or in other words the electrokinetic properties of the particle are influenced by both the real and imaginary components of the induced dipole moment. The frequency dependencies of these two components are shown in Figure 2 for model cases of a viable cell with an intact membrane and a non-viable cell having a "leaky" membrane.

Figure 2 Frequency variations of the real and imaginary components of the induced dipole moment for model cases of (a) a viable cell with an intact membrane, and (b) a cell with a porous membrane. Translational motion under the influence of travelling fields can occur in frequency ranges f1 and f2 . (see Traveling Wave Dielectrophoresis)

2. REFERENCES

1. Pohl, H. A. (1978) Dielectrophoresis, Cambridge University Press, Cambridge
2. Arnold, W. M. and Zimmerman, U. (1982) Z. Naturforsch. 37c, 908-915
3. Mischel, M., Voss, A. and Pohl, H. A. (1982) J. Biol. Phys. 10, 223-226
4. Huang, Y., Hölzel, R., Pethig, R. and Wang, X.-B. (1992) Phys. Med. Biol. 37, 1499- 1517
5. Arnold, W. M. and Zimmerman, U. (1988) J. Electrostatics 21, 151-191
6. Parton, A., Pethig, R. and Burt, J. P. H. (1992) Methods of Analysis, Patent Application GB92/02705.1
7. Coghlan, A. (15 May 1993) New Scientist No. 1873, 21