Frequency-Modulated Wave Dielectrophoresis of Vesicles And Cells: Periodic U-Turns at the Crossover Frequency

Frusawa Nanoscale Research Letters Frequency-Modulated Wave Dielectrophoresis of Vesicles And Cells: Periodic U-Turns at the Crossover Frequency Hiroshi Frusawa 0 0 School of Environmental Science & Engineering, Kochi University of Technology , Tosa-Yamada, Kochi 782-8502 , Japan We have formulated the dielectrophoretic force exerted on micro/nanoparticles upon the application of frequency-modulated (FM) electric fields. By adjusting the frequency range of an FM wave to cover the crossover frequency fX in the real part of the Clausius-Mossotti factor, our theory predicts the reversal of the dielectrophoretic force each time the instantaneous frequency periodically traverses fX . In fact, we observed periodic U-turns of vesicles, leukemia cells, and red blood cells that undergo FM wave dielectrophoresis (FM-DEP). It is also suggested by our theory that the video tracking of the U-turns due to FM-DEP is available for the agile and accurate measurement of fX . The FM-DEP method requires a short duration, less than 30 s, while applying the FM wave to observe several U-turns, and the agility in measuring fX is of much use for not only salty cell suspensions but also nanoparticles because the electric-field-induced solvent flow is suppressed as much as possible. The accuracy of fX has been verified using two types of experiment. First, we measured the attractive force exerted on a single vesicle experiencing alternatingcurrent dielectrophoresis (AC-DEP) at various frequencies of sinusoidal electric fields. The frequency dependence of the dielectrophoretic force yields fX as a characteristic frequency at which the force vanishes. Comparing the AC-DEP result of fX with that obtained from the FM-DEP method, both results of fX were found to coincide with each other. Second, we investigated the conductivity dependencies of fX for three kinds of cell by changing the surrounding electrolytes. From the experimental results, we evaluated simultaneously both of the cytoplasmic conductivities and the membrane capacitances using an elaborate theory on the single-shell model of biological cells. While the cytoplasmic conductivities, similar for these cells, were slightly lower than the range of previous reports, the membrane capacitances obtained were in good agreement with those previously reported in the literature. Dielectrophoresis; Frequency-modulated wave; The Clausius-Mossotti factor; Crossover frequency; Cell; Vesicle; Spectroscopy Background The polarizability of an electrical phenotype is primarily due to the cell membrane and the cytoplasmic electrical properties that depend on the frequency of the applied electric field. Accordingly, individual cells can be identified by the differences in the dielectric spectra using noninvasive electrical techniques. The electrical techniques are currently competent for separating cells with useful phenotypes from unknown samples [ 1–15 ]. Compared with other separation methods, these offer the major advantage that cell modification by antibodies or adherence to foreign material is unnecessary, whereby the potential for cell damage or activation by these probes is avoided [ 1–16 ]. The characterization of the cellular dielectric properties has been performed mainly using either impedance spectroscopy [ 10, 12, 13 ] or alternatingcurrent (AC) electrokinetics such as dielectrophoresis (DEP), traveling-wave DEP (twDEP), and electrorotation [ 1, 9, 15 ]. Among them, we focus on extending the ACDEP method to develop a new method for dielectric characterization using the frequency-modulated (FM) waves instead of AC fields. In general, the DEP occurs in an electric-field gradient that creates an electrokinetic force exerted on any polarizable object, charged or neutral, in the direction determined not only by the gradient vector, but also by the real part of the Clausius-Mossotti (CM) factor [ 1–15, 17–21 ]. For instance, we consider the DEP force induced by the AC electric field EAC(r, t) whose space-time dependence is expressed as EAC(r, t) = A(r) cos θAC(r, t) using the amplitude vector A(r) and the phase θAC(r, t). The ACDEP force is generated by the spatial gradient of the amplitude (i.e., ∇A) multiplied by the real part of the CM factor, as mentioned above, whereas the spatial gradient of the phase (i.e., ∇θAC) multiplied by the imaginary part of the CM factor creates the force of either twDEP or electrorotation, which therefore provides complementary information to the AC-DEP method in terms of the dielectric characterization [ 9, 15, 20, 21 ]. In this letter, we aim to formulate the DEP force induced by an FM field and compare the AC- and FM-DEP methods, so that neither the AC nor the FM field considers the spatial dependence of the phase; therefore, we will set θAC(t) = 2π fACt in proportion to the applied frequency fAC. A significant feature of the AC-DEP is that the force direction as well as its strength depends on fAC. Most notably, the force direction (...truncated)