Protein Dielectrophoresis: A Tale of Two Clausius-Mossottis—Or Something Else?

Abstract

Standard DEP theory, based on the Clausius–Mossotti (CM) factor derived from solving the boundary-value problem of macroscopic electrostatics, fails to describe the dielectrophoresis (DEP) data obtained for 22 different globular proteins over the past three decades. The calculated DEP force appears far too small to overcome the dispersive forces associated with Brownian motion. An empirical theory, employing the equivalent of a molecular version of the macroscopic CM-factor, predicts a protein’s DEP response from the magnitude of the dielectric β-dispersion produced by its relaxing permanent dipole moment. A new theory, supported by molecular dynamics simulations, replaces the macroscopic boundary-value problem with calculation of the cross-correlation between the protein and water dipoles of its hydration shell. The empirical and formal theory predicts a positive DEP response for protein molecules up to MHz frequencies, a result consistently reported by electrode-based (eDEP) experiments. However, insulator-based (iDEP) experiments have reported negative DEP responses. This could result from crystallization or aggregation of the proteins (for which standard DEP theory predicts negative DEP) or the dominating influences of electrothermal and other electrokinetic (some non-linear) forces now being considered in iDEP theory.

Dielectrophoresis from the System’s Point of View: A Tale of Inhomogeneous Object Polarization, Mirror Charges, High Repelling and Snap-to-Surface Forces and Complex Trajectories Featuring Bifurcation Points and Watersheds

“…We believe that our model can explain experimental findings such as the paradoxical accumulation of viruses and proteins in field cages or at electrode edges, where the dipole approach cannot account for sufficiently high trapping forces to withstand Brownian motion [ 16 , 17 , 42 , 43 , 44 ]. Forces large enough to trap small objects can result from inhomogeneous object polarization at electrodes or other surfaces and near to other objects.…”

“…The CMFs of Equation (2) are three times larger than the usual expressions because the depolarization coefficient of 1/3 of the 3D sphere has not been separated and truncated against the 1/3 in the volume term; a step that is historically justified but is a simplification only for 3D spheres [9,17]. This allowed us to retain the full volume term in Equation (17), which reflects the ponderomotive (bodily) nature of the DEP force.…”

“…However, in microchambers, complicated field distribution and inhomogeneous object polarization is typical, because the objects are relatively large with respect to the chamber [ 10 , 11 , 12 , 13 , 14 , 15 ]. The simple CMF description becomes problematic because the total force results from the superposition of polarization contributions from the entire volume of the inhomogeneously polarized object with the inhomogeneous field [ 16 , 17 ]. Examples include individual objects inducing mirror charges at the electrode surface or the attraction of two adjacent objects of the same size, where each object is subject to the field resulting from the inhomogeneous polarization of the respective other object.…”

Dielectrophoresis: An Approach to Increase Sensitivity, Reduce Response Time and to Suppress Nonspecific Binding in Biosensors?

“…Recent work by Pethig and Hölzel [ 53 , 64 ] as well as Matyushov and Heyden [ 65 , 66 ] may give a more comprehensive explanation of protein DEP, however. Matyushov [ 65 ] suggested two reasons that contribute to the disagreement between theory and experimental observations: (i) a failure of Maxwell’s electrostatics to describe the cavity-field susceptibility, and (ii) the neglect of the protein permanent dipole by the Clausius–Mossotti equation.…”

“…In a series of papers, Hölzel and Pethig [ 53 , 64 , 67 ] propose a DEP force equation based on an empirical relationship between the macroscopic and microscopic forms of the Clausius–Mossotti factor. Like Matyushov, they also identified the intrinsic dipole moment of proteins as particularly relevant for DEP of globular proteins.…”