The Dielectrophoresis Network

at the University of Surrey  # An Introduction to Dielectrophoresis

Dielectrophoresis (often abbreviated DEP) was first observed early in the 20th century, but described fully (and named) Herbert Pohl in 1950. It is an electrostatic phenomenon, distantly related to electrophoresis, and describes the motion of suspended particles resulting from polarisation forces produced by an inhomogeneous electric field.

If an object consists or positive and negative charges, but the average positions of those charges do not lie in the same place, the object is a dipole. You can get permanent dipoles (e.g. water) and induced dipoles (e.g. a capacitor); particles are polarised when the average positions of positive and negative charge are moved apart by an electric field.

Coulomb's law states that a force acts on free charges, so our dipole in an electric field will experience  forces applied to both charges moving in opposite directions.  If the electric field is equal everywhere, then the forces on the dipole are equal and opposite, and theparticle will not move (though it may align with the field).  However, if the electric ifeld is non-uniform - that is, there is a gradient - then the force on the charge at the higher electric field will be greater than the force on the diple in the lower electric field.  The particle will then move in the direction governed by the charge in the highest field, along the direction of the field gradient. The force can be in the direction of increasing or decreasing electric field - these are termed "positive dielectrophoresis" and "negative dielectrophoresis" respectively. Positive dielectrophoresis is shown in the figure, left.

What governs whether the particle experiences positive or negative DEP? In reality, all materials have capacitance and resistance.  We can treat this as a resistor and capacitor in parallel. Any charged capacitor will accumulate charges at its surfaces. Where two different materials meet, the net charge on the dipole depends on the charges on both sides of the interface. The effect can be to change the direction of a net dipole on a particle without actually changing the sign of the dipole on the particle. This is called the Maxwell-Wagner interfacial polarisation (see figure, left). Where two such materials – say, a cell and water – meet, there will be different amounts of charge on either side of the interface, depending on which material is mostly conductive and which is mostly capacitive. As the ratios of charge either side of the interface changes, the cumularive effect is that the dipole can change in both magnitude and direction.  This effect depends on the impedance and reactance of the materials and is therefore frequency dependent, producing different behaviours at different frewquencies.  If we determine the DEP behaviour as a function of frequeency, we can then use mathematical techniquies to determine the electrical properties of the particle.

The dielectrophoretic behaviour of cells

Dielectrically, cells can be reduced to an insulating membrane enclosing a conductive cytoplasm (possibly enclosed by a cell wall) (see figure). The cell nucleus has little effect unless it is over 50% of the cell volume.

Each component has its own resistance and capacitance –these combine, like little filters, to produce an overall value of polarisability relative to the suspending medium. If we can determine the dielectrophoretic spectrum of the cells of interest, then from theory we can determine the electrical properties of the different components by fitting a theoretical model to the spectrum (see figure).

From the dielectrophoretic response of cells, we can determine four parameters:

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• Effective membrane conductance -which describes the ionic transport across the membrane

• Effective membrane capacitance -which relates to membrane morphology

• Cytoplasm Conductivity-which relates to ionic strength

• Cytoplasm permittivity – indicative of high concentration of polar molecules (proteins etc)

• Can also determine cell wall properties, where present

Determining the DEP spectrum

In order to determine the dielectric properties via DEP, it is necessary to find an observable metric related to the polarisability (i.e. the DEP spectrum). Since the force cannot be measured directly, it is necessary to detect something related to it. At these scales, particles achieve terminal velocity in about 1ms, so the observed particle velocity is directly proportional to the force. We then need to measure the velocity in some way, and hence relate it to the force.  A number of techniques have been attempted, with varying degrees of success.

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• Particle velocity tracking via image processing:  cell velocity is compared to a known map of electric field strength.  Pros: accurate: Cons: depends on accurately knowing the field gradient at every point; computationally intensive; only a few cells can be used.

• Electrorotation (see figure, left): measure the velocity of rotation of particles when the field is rotated.  Pros: very accurate for single cells. Cons: slow; cells cannot be compared if they move, single cells only.

• Crossover measurements: the frequency where the DEP force is zero (i.e. where it crosses over from negative to positive) can be used to determine the cell properties. Pros: easy to achieve. Cons: only gives one measurable variable, so can’t be used to determine four unknowns

• Collection rate studies: count the number of cells collecting at a point (or moving towards it) in a given period of time. Pros: simple, can do very large numbers of cells.  Cons: can be time consuming.      