The DEP force (ƒDEP) depends on the applied field (E) according to Equation 1:
where ∊m is the absolute permittivity of the surrounding medium, R is the particle radius, and Re[CM] is the real component of the Clausius-Mossotti polarization factor. This relationship assumes that the length scale of the field gradient is large compared to the cell size (2). The polarizability parameter Re[CM] can have a value ranging between +1.0 and -0.5, depending on the particle's effective polarizability compared to that of the surrounding medium. Thus, a particle can respond by moving either up (positive DEP) or down (negative DEP) the field gradient generated at the energized electrode tip (Figure 1, B and D).
The experimental arrangement we used for initial testing and use of the DEP microelectrode was comprised of an inverted microscope, an AC signal generator capable of reaching frequencies in the megahertz, an aluminum foil ground, and a micromanipulator positioned with an electrode holder to enable precise three-dimensional control over the DEP microelectrode with reference to a target cell (see the Supplementary material). The AC signal generator enables control of positive (attractive) and negative (repulsive) DEP forces of the electrode through controling amplitude and frequency settings. The counter electrode, acting as the electrical return path to ground potential, can be located either in the cell suspension fluid or as an aluminum foil ground placed outside the bath, between the microscope stage and the bottom of the cell culture dish (see the Supplementary material). For the case of the grounded aluminum foil beneath a 35 × 10 mm Petri dish (Becton Dickinson), the parallel capacitance and resistance of the electrical coupling between the electrode and ground was measured at 9.94 pF and 6.6 kΩ, respectively, with the electrode tip submerged 0.25 cm below the fluid surface. These values changed, as measured with an impedance bridge,to 10.04 pF and 5.9 kΩ at an electrode tip submersion depth of 1.0 cm. Thus, the effective capacitive reactance of the single electrode is such that capacitive coupling to ground exists for frequencies above ∼50 kHz. It was found that single electrode DEP can be operated without a grounded foil or counter electrode altogether. In either case, the electrical return path used is the microscope or nearest ground plane. Without a grounded counter electrode, however, the DEP forces were observed to be slightly weaker.
To demonstrate the overall usefulness of the single DEP electrode in spatial manipulation of living cells, mammalian clonal cell lines Chinese hamster ovary (CHO) and HeLa, were separated from heterogeneous populations (see the Supplementary material for HeLa results). In Figure 2, a mixed population of calcein-AM loaded and nonloaded CHO cells were plated on a cushion of 1% agarose in a Petri dish containing 114 mS/m 10% HBSS supplemented with sucrose as an osmoticum (300 mOsm). No significant cell death was observed within these conditions after 2 hours for both CHO and HeLa cell lines, as measured by cell viability assays (data not shown). Cells labeled with calcein-AM and nonloaded cells were actively separated from the mixed population using single electrode DEP. Voltage amplitude [root mean squared (rms)] and frequency settings of 1 V, 10 MHz and 1 V, 50 kHz were used for positive DEP and negative DEP, respectively. Disruptive effects such as electrolysis and electro-osmotic driven fluid flow were avoided by operating in a low conductive solution (≤250 mS/m), under low voltage (≤4 V rms) and high frequency (≥10 kHz), with no DC voltage bias coupled to the electrode (7, 12-14).
The organization of cells shown in Figure 2B was achieved by actively positioning the single electrode within 50 μm of a target cell, applying a 10 MHz signal to attract the cell to the electrode tip, repositioning (by use of micromanipulator or stage), and then repelling the cell from the electrode by changing the frequency to 50 kHz. Using this approach, a single cell or multiple cells (up to 10) can be moved simultaneously. The frequency values of 10 and 50 kHz were determined through preliminary tests to identify optimal frequencies for cell capture and cell repulsion, by positive and negative DEP, respectively. The experimental parameter of relevance is the DEP cut-off frequency (ƒxo) that defines where a particle makes the transition from a negative to positive DEP response. An estimate of ƒxo for a viable cell can be derived from Equation 2 (1)(2)(7):