Concentration Dependence of the Self-Diffusion of Human and Lumbricus terrestris Hemoglobin

The self-diffusion coefficient of the extracellular hemoglobin of Lumbricus terrestris (mol wt 3.7×106 daltons) has been measured at protein concentrations ranging from 2 to 25 g/100 ml. The self-diffusion coefficient of human hemoglobin has been measured at concentrations between 10 and 43 g/100 ml. For these measurements, 14C-labeled hemoglobin was made to diffuse from one Millipore filter into three consecutively arranged Millipore filters containing unlabeled hemoglobin. After a suitable time the filters were separated, and the protein diffusion coefficient was determined from the distribution of radioactivity in the four filters with a table given by Kawalki (1894, Ann. Phys. Chem. 52:166–190.). The following results were obtained. The diffusion coefficient of Lumbricus hemoglobin is 1.2×10-7 cm2s-1 at a protein concentration of 2.1 g/100 ml, and is reduced to about 1/10 of this value when the concentration is 25 g/100 ml (T = 21°C). Between 0 and 16 g/100 ml the logarithm of the diffusion coefficient of Lumbricus hemoglobin falls linearly with concentration. Above 16 g/100 ml a marked increase in the concentration dependence of the diffusion coefficient is observed. Extrapolation of the data to zero hemoglobin concentration yields a limiting value of the diffusion coefficient of Lumbricus hemoglobin of 1.3×10-7 cm2s-1. The diffusion coefficient of human hemoglobin is 4.5×10-7 cm2s-1 at a hemoglobin concentration of 9.7 g/100 ml, and falls to 0.14×10-7 cm2s-1 at a hemoglobin concentration of 43.0 g/100 ml. In addition to diffusivities, the viscosities of human and Lumbricus hemoglobin solutions were measured in a wide range of protein concentrations.The concentration dependence of the diffusivity of Lumbricus hemoglobin is compared to that of myoglobin, ovalbumin, and tetrameric hemoglobin. Proportionality between the diffusion coefficient and the reciprocal of the viscosity of the protein solution is found for all these proteins. It is also shown that an equation proposed by Anderson (1973) gives an excellent description of the diffusivity of the various proteins up to moderate protein concentrations. Above concentrations of 16 g/100 ml for Lumbricus hemoglobin, and 30 g/100 ml for tetrameric hemoglobin, however, protein diffusivity falls much more rapidly with increasing concentration than is predicted by this equation