On the Diffusion of Gases in Protein Solutions
The theory for diffusion in heterogenous media, also known a s obstruction theory, is utilized to analyze data on the diffusion of dissolved gases in protein solutions. It is suggested that the structure of t h e water molecules around t h e protein molecules has an imDortant effect on the diffusion coefficients of the gases
The diffusion of‘ dissolved gases in biological systems is an important problem in science and engineering. The uptake of oxygen in the lungs and transport to the tissues is an obvious example where molecular diffusion plays an important role. In the field of biochemical engineering the transport of oxygen into fermentation media requires the knowledge of the diffusion coefficient in order to make rational designs of fermentation equipment. Diffusion coefficients for a few gas-protein solution systems are available (Kreuzer, 1950; Pircher, 1952; Longmuir and Roughton, 1952: Keller and Friedlander, 1966; Goldstick and Fatt, 1970). The data to date deal with the diffusion of various gases in either albumin or (met)hemoglobin solutions. Most of the data reported in the literature have been measured over a limited protein concentration range. Goldstick and Fatt (1970), however, have reported oxygen diffusion coefficients in hemoglobin (saturated with oxygen) and bovine serum albumin solutions over a wide concentration range. The molecular weight of hemoglobin and serum albumin is 67,000 and 69,000. respectively, and is several orders of magnitude larger than that of the oxygen molecule. As a consequence the protein molecules in solution present an obstruction effect to the diffusion of oxygen, since the mobility of the protein molecules is much smaller than that of the oxygen molecule. The diffusivity of hemoglobin and serum albumin is about two orders of magnitude smaller than the diffusivity of oxygen (Kreuzer, 1970; Keller et al., 1971). In this note the data of Goldstick and Fatt are compared with available obstruction theory and some conclusions are made about the effect of water around the protein molecules. Obstruction Theory Prager (1960) derived an expression for the effective diffusion coefficient, D,of a small species in a medium containing a volume fraction f of immobile obstructions. The obstructions effectively block part of the area of diffusion for the small molecules and therefore decrease their mobility. Maxwell (1881) derived a relationship for a suspension of spherical obstructions in which the diffusing species has a finite permeability in the obstructions. The effective permeability was given by
where P,. and Pd are the permeabilities of the species in the continuous phase and the obstructions. Permeability is defined here as the product of diffusivity times the gas solubility. When P d
