Theoretical Background of the Electrorotation Technique
Supplementary Data
This section illustrates the main aspects of the biophysical approach based on electrorotation. This work is highly interdisciplinary, most of the techniques employed throughout the study are well known to the molecular/cellular biologist. However, the electrorotation which provides important information about the structure/function of the cell membrane is a typical domain of biophysicists. Therefore, for a full understanding of the results obtained by this technique, we describe here in some detail the theory and the treatment of the experimental data.
1. Electrorotation
1.1Theory.
Anelectric field applied to cell suspensionsinduces on each single cell an effective dipole moment deriving from the different polarizability of the solvent and the plasma membrane. The applied electric field is rotating when using this technique. If the mechanism of interfacial polarization is in phase with the electric field,the induced dipole moment is aligned. Increasing the frequency of the field, the polarization mechanism undergoes a phase delay (dielectric relaxation) causing a torque moment, therefore cells rotate in an anti-field fashion. The phenomenon is generated in the range of approximately 104 - 106 Hz; if the frequency increases further (higher that 10 MHz), the electric field traverses the plasma membrane and the sense of rotation of the cell is inverted in aco-field fashion. The interface is now between membrane and cytoplasm. In the kHz range, anotherrelaxation occurs associated to the double electrical layer formed by the counter-ions and the mechanisms of surface conductivity. These relaxations are known as, and dispersions.In this study we take into account only on the dispersion, directly related to the dielectric properties of the plasma membrane (Foster et al. 1992; Gimsa 2001).The rotation period (T) of the cell depends on the frequency (f)of the applied field, according to equation (1), which describes a Debye-like relaxation:
(1)
where, f*is the relaxation frequency and Tminis the corresponding value of the period. The value of f* depends on the solvent conductivity according to the expression (2):
(2)
where C and G are, respectively, the specific capacitance and conductance of the plasma membrane of a cell with a radius R, e is the solvent conductivity and iis the conductivity of the cytoplasm considered as homogeneous. Since in general ei, equation (2) becomes:
(3)
The experimental approach is based on the measurement of the relaxation frequency as a function of the conductivity of the dispersing medium, from which C and G can be calculated by a linear fit taking into account the cell radius.
The Debye model mimics the cell as a sphere surrounded by a thin homogeneous layer simulating the plasma membrane. In comparison to the complexity of the real biological system this model is rather coarse;however it proved to be very effective to evaluate even slight changes in the dielectric properties of the cell membrane (Gimsa et. 1989; Gimsa et al. 1991; Wand et al. 1995; Dalton et al. 2004: Bonincontro et al. 2007). The capacitance C is influenced by the biochemical and physical properties of the membrane. The conductance G is informative of the membrane function in terms metabolism/ion-transport. Therefore, this simplified model is commonly acccepted as a good tool to investigate the biological membrane condition (see for instance ; Gimsa et al. 1989; Gimsa 2001; Cosimati et al. 2013).
1.2 Experimental results.
The rotation period of all control and resveratrol treated samples was measured as function of the frequency of the rotating field. The data were analyzed by fitting according to equation (1) to obtain the various relaxation frequencies. As an example of this analysis, Figure 1 reports the typical dependence of the periods by the field frequency in a control, non-treated cell suspension in 0.3M sucrose. This procedure was repeated for both untreated and RV-treated samples, varying the ion strength of the dispersing medium. Four different dispersion media were used, obtained from the same osmolar sucrose solution (300 mM) which was supplemented with three NaCl concentrations: (0.5; 1.0; 1.5mM). The conductivities of the four solvents were accurately measured by an automatic impedance meter (HP 4194A). The electrorotation apparatus, previously described in detail (Bonincontro et. 2007, Berardi et al. 2009; Cosimati et al. 2013), was connected to a video-recording system that permitted a more accurate off-line image analysis. A minimum number of 15 cells was considered at each frequency.
As expected from equation (2), the relaxation frequencies f*,as a function of the solvent conductivity, form the straight lines shownin Figure 2. The upper panel shows that the straight linescontrol and 24 hours resveratrol-treated cells are coincident demonstrating that no effect is present. On the contrary, as shown in the lower panel, the slope and the intercept for the control and 48 hours Resveratrol-treated are different. The cell radius was also measured obtaining an average value of 8.8±0.4 which did not vary in control and treated cells. This allows the final calculation of C and G reported in the main text.
References to the Supplementary Data
Berardi V, Aiello C, Bonincontro A, Risuleo G (2009) Alterations of the Plasma Membrane Caused by Murine Polyomavirus Proliferation: An Electrorotation Study. J Membrane Biol 229:19-25
Bonincontro A, Di Ilio V, Pedata O, Risuleo G (2007) Dielectric properties of the plasma membrane of cultured murine fibroblasts treated with a non a terpenoid extract of A. indica seeds. J. Membrane Biol. 215:75-79
Cosimati R,Milardi GL, Bombelli C, Bonincontro A, Bordi F,Mancini G, Risuleo G(2013) Interactions of DMPC and DMPC/gemini liposomes with the cell membrane investigated by electrorotation. BBA Biomem 1828:352-356. doi: 10.1016/j.bbamem.2012.10.021. Epub 2012 Oct 27
Dalton C, A. D. Goater, J. P. H. Burt, H. V. Smith, Analysis of parasites by electrorotation, J. Applied Microbiol. 96 (2004) 24-32.
Foster KR., Sauer FA, Schwan HP(1992) Electrorotation and levitation of cells and colloidal particles. Biophysical J 63:180-190
Gimsa J, Pritzen C, Donath E (1989) Characterisation of virus-red cell interaction by electrorotation. Stud Biophys 130:123-131
Gimsa J, Marszalek P, Loewe U, Tsong TY (1991) Dielectrophoresis and electrorotation of neurospora slime and murine myeloma cells. Biophys J 60:749 -760
Gimsa J (2001) A comprehensive approach to electro-orientation, electrodeformation, dielectrophoresis, and electrorotation of ellipsoidal particles and biological cells Bioelectrochem.54 23-31.
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Legends to the Figures
Figure 1. The figure shows the rotation period T as a function of the electric field frequency f. Cells were suspended in 0.3M sucrose. The curve results from the best fit according to equation (1).
Figure 2. The figures show the relaxation frequencies f* as a function of the conductivity e of the dispersing medium. Upper Panel: Empty circles, untreated control cells. Full circles, 100 M Resveratrol-treated cells. Both samples were grown for 24 hours. Lower Panel: Empty circles, untreated control cells. Full circles, 100 M Resveratrol-treated cells. Both samples were grown for 48 hours.