On the theory of dielectric spectroscopy of protein solutions

Abstract

We present a theory of the dielectric response of solutions containing large solutes, of the nanometer size, in a molecular solvent. It combines the molecular dipole moment of the solute with the polarization of a large subensemble of solvent molecules at the solute-solvent interface. The goal of the theory is two-fold: (i) to formulate the problem of the dielectric response avoiding the reliance on the cavity-field susceptibility of dielectric theories and (ii) to separate the non-additive polarization of the interface, jointly produced by the external field of the laboratory experiment and the solute, from specific solute-solvent interactions contributing to the dielectric signal. The theory is applied to experimentally reported frequency-dependent dielectric spectra of lysozyme in solution. The analysis of the data in the broad range of frequencies up to 700 GHz shows that the cavity-field susceptibility, critical for the theory formulation, is consistent with the prediction of Maxwell's electrostatics in the frequency range of 10-200 GHz, but deviates from it outside this range. In particular, it becomes much smaller than the Maxwell result, and shifts to negative values, at small frequencies. The latter observation implies a dia-electric response, or negative dielectrophoresis, of hydrated lysozyme. It also implies that the effective protein dipole recorded by dielectric spectroscopy is much smaller than the value calculated from the protein's charge distribution. We suggest an empirical equation that describes both the increment of the static dielectric constant and the decrement of the Debye water peak with increasing protein concentration. It gives fair agreement with broad-band dispersion and loss spectra of protein solutions, but misses the δ-dispersion region.

Limitations of the Clausius‐Mossotti function used in dielectrophoresis and electrical impedance studies of biomacromolecules

“…. Such an effect is consistent with numerical simulations and theory described by Matyushov for hydrated proteins . However, such analyses for rRNA are hampered by lack of relevant dielectric data–unlike the case for globular proteins for which numerous dielectric measurements have been reported and dipole moments checked using NMR and X‐ray databases .…”

Protein Dielectrophoresis and The Link to Dielectric Properties

“…From Figure 5, we can see that nDEP of lysozyme is expected at high frequencies from 10 MHz to 10 GHz, which agrees with DEP behavior modeled in Matyushov's report [119]. In the case of myoglobin, a change of the DEP behavior is expected from nDEP to pDEP in the high frequency range between 10 MHz and 10 GHz.…”

A Study of Dielectric Properties of Proteinuria between 0.2 GHz and 50 GHz

“…Boresch et al [10] and Matyushov [11] reported frequency dependence in simulated dielectric properties between the interaction of protein and water. The presence of protein causes the change in dielectric properties as it alters the mobility and linear conduction of a solution [6, 12].…”