Some calculations on the turbidity of mitochondria and bacteria

Abstract

The calculation of the intensity of light scattered from objects of arbitrary size, shape, and index of refraction is, at the present time, impossible. For the case of spheres, the solution of Mie applies, the tables of the necessary function have been prepared with modern computing machines. Since mitochondria and bacteria have a low index of refraction compared with the suspending medium, the applicability of the Rayleigh-Gans approximation was investigated. It is found that for objects of this size, little error was introduced into the calculation of turbidity, although the intensity of light scattered in a particular direction might be grossly in error. It is shown that variations in shape, from spherical to an ellipsoid of revolution with a major to minor axis ratio of 4, would cause a decrease in turbidity of about 15% under typical conditions. Likewise, redistribution of material in the form of a shell decreased the turbidity to a small but significant degree. The influence of growth and of osmotic swelling on turbidity is discussed. The consideration were based on the Jöbst equation which is a limiting from of the Rayleigh-Gans approximation for large spherical particles. It is found that for osmotic swelling of spheroplasts or mitrochondria, the absorbancy varies nearly inversely with the volume $\text{(}\text{proportional}\text{V}{}^{\mathrm{<mtext>-</mtext><mtext>2</mtext><mtext>3</mtext>}}\text{)}$. On the other hand, for variations in size at constant concentration, the absorbancy varies directly as the four-thirds power of the volume of the particle. This implies that absorbancy measurements employed routinely in bacteriological studies are more nearly a measure of bacterial mass than of bacterial numbers.