Dielectrophoresis (DEP) is a phenomenon in which a force is exerted on a polarizable particle when it is subjected to a non-uniform electric field. This force does not require the particle to be charged. All particles exhibit dielectrophoretic activity in the presence of electric fields. However, the strength of the force depends strongly on the medium and particles' electrical properties, on the particles' shape and size, as well as on the frequency of the electric field. Consequently, fields of a particular frequency can manipulate particles with great selectivity. This has allowed, for example, the separation of cells or the orientation and manipulation of nanoparticles and nanowires. Furthermore, a study of the change in DEP force as a function of frequency can allow the electrical (or electrophysiological in the case of cells) properties of the particle to be elucidated.
Background and properties Although the phenomenon we now call dielectrophoresis was described in passing as far back as the early 20th century, it was only subject to serious study, named and first understood by Herbert Pohl in the 1950s. Recently, dielectrophoresis has been revived due to its potential in the manipulation of microparticles, nanoparticles and cells.
Dielectrophoresis occurs when a polarizable particle is suspended in a non-uniform electric field. The electric field polarizes the particle, and the poles then experience a force along the field lines, which can be either attractive or repulsive according to the orientation on the dipole. Since the field is non-uniform, the pole experiencing the greatest electric field will dominate over the other, and the particle will move. The orientation of the dipole is dependent on the relative polarizability of the particle and medium, in accordance with Maxwell–Wagner–Sillars polarization. Since the direction of the force is dependent on field gradient rather than field direction, DEP will occur in AC as well as DC electric fields; polarization (and hence the direction of the force) will depend on the relative polarizabilities of particle and medium. If the particle moves in the direction of increasing electric field, the behavior is referred to as positive DEP (sometime pDEP), if acting to move the particle away from high field regions, it is known as negative DEP (or nDEP). As the relative polarizabilities of the particle and medium are frequency-dependent, varying the energizing signal and measuring the way in which the force changes can be used to determine the electrical properties of particles; this also allows the elimination of electrophoretic motion of particles due to inherent particle charge.
Phenomena associated with dielectrophoresis are electrorotation and traveling wave dielectrophoresis (TWDEP). These require complex signal generation equipment in order to create the required rotating or traveling electric fields, and as a result of this complexity have found less favor among researchers than conventional dielectrophoresis.
Dielectrophoretic force The simplest theoretical model is that of a homogeneous sphere surrounded by a conducting dielectric medium. For a homogeneous sphere of radius and complex permittivity in a medium with complex permittivity the (time-averaged) DEP force is:
The factor in curly brackets is known as the complex Clausius-Mossotti function and contains all the frequency dependence of the DEP force. Where the particle consists of nested spheres – the most common example of which is the approximation of a spherical cell composed of an inner part (the cytoplasm) surrounded by an outer layer (the cell membrane) – then this can be represented by nested expressions for the shells and the way in which they interact, allowing the properties to be elucidated where there are sufficient parameters related to the number of unknowns being sought. For a more general field-aligned ellipsoid of radius and length with complex dielectric constant in a medium with complex dielectric constant the time-dependent dielectrophoretic force is given by:
The complex dielectric constant is , where is the dielectric constant, is the electrical conductivity, is the field frequency, and is the imaginary unit. This expression has been useful for approximating the dielectrophoretic behavior of particles such as red blood cells (as oblate spheroids) or long thin tubes (as prolate ellipsoids) allowing the approximation of the dielectrophoretic response of carbon nanotubes or tobacco mosaic viruses in suspension. These equations are accurate for particles when the electric field gradients are not very large (e.g., close to electrode edges) or when the particle is not moving along an axis in which the field gradient is zero (such as at the center of an axisymmetric electrode array), as the equations only take into account the dipole formed and not higher order polarization. When the electric field gradients are large, or when there is a field null running through the center of the particle, higher order terms become relevant, and result in higher forces. To be precise, the time-dependent equation only applies to lossless particles, because loss creates a lag between the field and the induced dipole. When averaged, the effect cancels out and the equation holds true for lossy particles as well. An equivalent time-averaged equation can be easily obtained by replacing E with Erms, or, for sinusoidal voltages by dividing the right hand side by 2. These models ignores the fact that cells have a complex internal structure and are heterogeneous. A multi-shell model in a low conducting medium can be used to obtain information of the membrane conductivity and the permittivity of the cytoplasm. For a cell with a shell surrounding a homogeneous core with its surrounding medium considered as a layer, as seen in Figure 2, the overall dielectric response is obtained from a combination of the properties of the shell and core.
where 1 is the core (in cellular terms, the cytoplasm), 2 is the shell (in a cell, the membrane). r1 is the radius from the centre of the sphere to the inside of the shell, and r2 is the radius from the centre of the sphere to the outside of the shell.
Applications Dielectrophoresis can be used to manipulate, transport, separate and sort different types of particles. DEP is being applied in fields such as medical diagnostics, drug discovery, cell therapeutics, and particle filtration.
DEP has been also used in conjunction with semiconductor chip technology for the development of DEP array technology for the simultaneous management of thousands of cells in microfluidic devices. Single microelectrodes on the floor of a flow cell are managed by a CMOS chip to form thousands of dielectrophoretic "cages", each capable of capturing and moving one single cell under control of routing software.
As biological cells have dielectric properties,Pethig R. Dielectric Properties of Biological Materials, 1979. dielectrophoresis has many biological and medical applications. Instruments capable of separating cancer cells from healthy cells have been madePolzer et al., EMBO 2014, Molecular profiling of single Circulating Tumor cells with diagnostic intention Polzer Et all EMBO 2014 DOI 10.15252/emmm.201404033Mesquita et al., Nature 2016, "Molecular analysis of circulating tumor cells identifies distinct copy-number profiles in patients with chemosensitive and chemorefractory small-cell lung cancer", https://doi.org/10.1038/nm.4239Bolognesi et al., Scientific Reports, 2017, "Digital Sorting of Pure Cell Populations Enables Unambiguous Genetic Analysis of Heterogeneous Formalin-Fixed Paraffin-Embedded Tumors by Next Generation Sequencing", https://doi.org/10.1038/srep20944 as well as isolating single cells from forensic mixed samples. Fontana et al., FSI 2017, "Isolation and genetic analysis of pure cells from forensic biological mixtures: The precision of a digital approach", https://doi.org/10.1016/j.fsigen.2017.04.023 Platelets have been separated from whole blood with a DEP-activated cell sorter.
DEP has made it possible to characterize and manipulate biological particles like blood cells, stem cells, neurons, pancreatic β cells, DNA, chromosomes, proteins and viruses. DEP can be used to separate particles with different sign polarizabilities as they move in different directions at a given frequency of the AC field applied. DEP has been applied for the separation of live and dead cells, with the remaining live cells still viable after separation or to force contact between selected single cells to study cell-cell interaction.Tellez Gabriel , EJCB, 2017, "Analysis of gap junctional intercellular communications using a dielectrophoresis-based microchip", DOI.org/10.1016/j.ejcb.2017.01.003 DEP has been used to separate strains of bacteria and viruses.Burt, J.P.H., R. Pethig, and M.S. Talary, Microelectrode devices for manipulating and analysing bioparticles. Transactions of the Institute of Measurement and Control, 1998. 20(2): p. 82–90 DEP can also be used to detect apoptosis soon after drug induction measuring the changes in electrophysiological properties.Chin, S., et al., Rapid assessment of early biophysical changes in K562 cells during apoptosis determined using dielectrophoresis. International Journal of Nanomedicine, 2006. 1(3): p. 333–337
As a cell characterisation tool DEP is mainly used for characterising cells measuring the changes in their electrical properties. To do this, many techniques are available to quantify the dielectrophoretic response, as it is not possible to directly measure the DEP force. These techniques rely on indirect measures, obtaining a proportional response of the strength and direction of the force that needs to be scaled to the model spectrum. So most models only consider the Clausius-Mossotti factor of a particle. The most used techniques are collection rate measurements: this is the simplest and most used technique – electrodes are submerged in a suspension with a known concentration of particles and the particles that collect at the electrode are counted;Labeed, F.H., Coley, H.M., Hughes, M.P. (2006), Biochim Biophys Acta 1760, 922–929 crossover measurements: the crossover frequency between positive and negative DEP is measured to characterise particles – this technique is used for smaller particles (e.g. viruses), that are difficult to count with the previous technique;Hughes, M.P., Morgan, H., Rixon, F.J., Burt, J.P.H., Pethig, R. (1998), Biochim Biophys Acta 1425, 119–126 particle velocity measurements: this technique measures the velocity and direction of the particles in an electric field gradient;Watarai, H., Sakomoto, T., Tsukahara, S. (1997) Langmuir 13, 2417–2420 measurement of the levitation height: the levitation height of a particle is proportional to the negative DEP force that is applied. Thus, this technique is good for characterising single particles and is mainly used for larger particles such as cells;Kaler, K.V., Jones, T.B. (1990) Biophysical Journal 57, 173–182 impedance sensing: particles collecting at the electrode edge have an influence on the impedance of the electrodes – this change can be monitored to quantify DEP.Allsop, D.W.E., Milner, K.R., Brown, A.P., Betts, W.B. (1999) Journal of Physics D: Applied Physics 32, 1066–1074 In order to study larger populations of cells, the properties can be obtained by analysing the dielectrophoretic spectra.
Implementation
Electrode geometries At the start, electrodes were made mainly from wires or metal sheets. Nowadays, the electric field in DEP is created by means of electrodes which minimize the magnitude of the voltage needed. This has been possible using fabrication techniques such as photolithography, laser ablation and electron beam patterning. These small electrodes allow the handling of small bioparticles.