On the Theory of Dielectric Spectroscopy of Protein Solutions

TL;DR

This paper develops a new theoretical framework for understanding the dielectric response of protein solutions, separating interface polarization effects from solute-solvent interactions, and applies it to experimental spectra of lysozyme.

Contribution

The theory avoids cavity-field concepts and introduces a method to distinguish interface polarization from specific solute-solvent interactions in dielectric spectra.

Findings

Cavity field susceptibility aligns with Maxwell's electrostatics between 10-200 GHz.

Susceptibility deviates outside this range, indicating complex dielectric behavior.

Hydrated lysozyme exhibits a dia-electric response, with a smaller effective dipole than expected.

Abstract

We present a theory of the dielectric response of a solution containing large solutes, of a 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 concepts 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 then 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 protein's charge distribution. We suggest an empirical equation that describes both the increment of the static dielectric constat 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 delta-dispersion region.