On the dielectric properties of cell suspensions at high volume fractions

Abstract

The dielectric increment Δϵ′ of the β-dispersion of biological cell suspensions is given (H.P. Schwan, Adv. Biol. Med. Phys., 5 (1957) 147) by the equation Δϵ′ = 9 PrC m/4ϵ 0, where cells of radius r and of a membrane capacitance C m farads per unit area are suspended at a volume fraction P. This equation predicts that Δϵ′ is proportional to P at all values of P, a prediction which is not borne out at high values of P. To deal with this problem, it has been suggested (but never adequately checked) that a better fit is obtained from the equation Δϵ′= (9 rCn m/4ϵ 0) P/[1+( P/2)] 2, in which the term 1/[1 + ( P/2)] 2 models the loss of linearity as the volume fraction increases. This term depends only on P and is independent of the cell radius r. By making careful and independent measurements of P, r and Δϵ′ for a number of bacterial and yeast cell suspensions, we show herein that this equation holds true over a wide range of volume fractions and cell sizes. Thus, the correction factor for the non-linear relationship between Δϵ′ and P is indeed independent of the cell radius. This has the important and useful consequence that a simple calibration curve of dielectric increment vs. dry weight or cell numbers permits one to determine the specific enclosed volume of the strain of interest, i.e. the volume enclosed by the cytoplasmic membranes of the cells per unit biomass. Finally, we show that the dielectric increment per unit biomass is directly proportional to the cell radius.