Protein Protein Interaction (PPI) dictates the function of proteins and stability of protein formulations. Therapeutic formulations are optimized to maintain or enhance the efficacy while lengthening the stability window. Optimization includes the reduction in viscosity for better injectability and pain control for injections.
Viscosity is a strong function of PPI as well and PPI contributes to viscosity more than the media viscosity. As attractive PPI increases, viscosity increases accordingly. As attractive PPI decreases, so does the viscosity. If PPI is repulsive, viscosity also increases with increase of the repulsive interaction. Therefore, viscosity increases if strength of PPI increases whether it is repulsive or attractive.
PPI of antibody at high concentration was characterized with viscosity measurement. Viscosity of bovine gamma globulin solutions at 250 mg/mL in pH 7.2 near isoelectric point are measured as added salt types and concentrations are varied. Note that the bovine gamma globulin is not soluble in pH 7.2 (low ionic strength) without additional amount of salt. Addition of salt roughly above 30 mM "salts in" the protein. Addition of salts initially decreases the viscosity as its addition weakens the attractive interaction. Further addition of salts will increase viscosity, suggesting the attractive PPI strengthens.
All of the formulations presented in the graph exhibit shear thinning behavior regardless of magnitude of viscosity: viscosity decreases with increase in shear rate above the critical shear rate as viscosity curves of two formulations are shown in the graph. These results suggest that PPI created a structure every formulation, which is responsible for the shear thinning behavior. The structure is called clusters.
Common legacy practice is to measure viscosity at 1,000 or 2,000 1/s. Viscosity measured at the fixed shear rate does not tell if viscosity is in the plateau or shear thinning zone. Measuring viscosity at a wide shear rate range is better practice to extract every information regarding the formulation and PPI. In fact, viscosity measured at 1,000 1/s alone does not provide accurate estimation of injectability since injection shear rate ranges from 50,000 to 500,000 1.s. Its error can be higher than 34% (new injectability application note link).
Protein molecules are known to form clusters as attractive PPI increases or concentration of protein increases. The detection of the clusters can be made with viscosity rate sweep. Especially, the onset of the shear thinning correlates with the size of the cluster.
Well established in colloid science, Brownian motion keeps the structures close the equilibrium while the formulation is sheared. At low shear rates, this balance between shear flow and Brownian motion keeps the viscosity constant - plateau viscosity. As the shear rate is increased beyond a critical value, Brownian motion cannot keep up, which yields the shear thinning behavior. The relative time scale of Brownian motion and shear flow is determined by a dimensionless Peclet number. As the shear rate increases, Pe becomes greater than 1 and viscosity shear thins. Thus the relationship at the critical shear rate, providing estimation of the cluster size, L, as shown in the image. A larger value of L means that molecular interaction, PPI, is higher.
The following is quoted from Foss and Brady (J. Fluid Mech. (2000)). Shear thinning can be explained in the following manner: the Brownian stress arises from the flow-induced deformation of the equilibrium structure particles diffuse against the flow towards their unstressed configuration and the resultant stress is directly proportional to the deformation. As the peclet number increases the praticle motion cannot keep up with the flow and the structural deformation saturates. Hence the Brownian viscosity decreases as Pe increases.
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