This proposal is an experimental study of adsorption and diffusion of proteins within the interstitial spaces of a chromatographic resin. The primary focus of this study is the measurement of the diffusion coefficients and adsorption rate constants in resins by an NMR technique. This technique was first pioneered by the PIs using the protein hen egg white lysozyme. This enzyme was labelled with a fluorine spin label, dissolved in a medium without adsorbing boundaries, and subject to an rf pulse. Equations are written for the evolution of the transverse and longitudinal magnetization imparted by the pulse. From these equations, the magnitudes of the refocussable magnetization can be obtained as a function of the tracer diffusion coefficient; comparisons with the measured values of the magnetization allows for the computation of the diffusion coefficient. The proposal presents a novel idea for the measurement of adsorption. The PIs argue that when the decay rate of the transverse magnetization of the protein in the fluid is much smaller than that for the protein on the surface, and the characteristic time for adsorption is much longer than the time for relaxation of the transverse magnetization of adsorbed species, the equation which governs the refocussable magnetization is identical to that for relaxation in a nonadsorbing medium, with adsorption renormalizing a coefficient. They suggest first using this technique to obtain the diffusion coefficient, and then using a simulated echo, in which longitudinal relaxation governs much of the response, to measure the adsorption coefficient. Adsorption is not lumped in the dynamic equations for the longitudinal decay because the scale for longitudinal relaxation decay on the surface is of the order of that in the bulk. The proposed research will examine experimentally adsorption and diffusion in new adsorbent materials, particularly size excluded resins with small pores in order to determine the effects of hindered diffusion, and then in ion exchange, hydrophobic interaction and reversed phase systems. These materials will be studied with a view towards end-use applications in perfusion chromatography. In a second part of the study, protein molecules will be tagged with paramagnetic ions by means of chelators in order to render the aqueous protons dependent on the local protein concentration. The PIs intend to calibrate this effect, and use it to measure concentration profiles in the interstitial space. In a third and final part of the study, modeling efforts will be directed at prediction of diffusion and adsorption including the effects of pore size distribution, adsorption kinetics, and high loading. Separate theoretical efforts will focus on instabilities at miscible displacement fronts.
