On the Theory of Dielectric Spectroscopy of Protein Solutions

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.