High protein concentration formulation, in particular for antibody therapeutics, is preferred for cost-effective applications of antibodies. This strategy is however hampered by high viscosity, appearance of opalescence and phase separation, most likely caused by different mode and level of protein-protein interactions and aggregation/self-association of the proteins. As depicted in
Figure 4, the distance between protein molecules becomes less and less, which increase the probability of either repulsive or attractive molecular interactions. These molecular interactions may be transient, but sufficient to restrict molecular motions, leading to either high viscosity or opalescence. Local fluctuations of such transient interactions can cause fluctuation of protein concentration and hence refractive index and thereby opalescence or turbidity. To mitigate such high concentration-mediated viscosity or opalescence, various approaches are taken to suppress protein-protein interactions and arginine has been shown to be effective in suppressing viscosity, opalescence and phase separation and stated as a “winner” among various approaches for reducing these phenomena: note that 17 monoclonal antibody drugs out of total 20 protein therapeutics use arginine-containing formulations [
26].
3.1. Viscosity
More specifically, high viscosity occurs due to protein-protein interaction, especially with highly interactive multi-domain antibodies. This may be intuitively understood as depicted in
Figure 1 and
2, where movement of a protein molecule is controlled by surrounding (same) protein molecules through different mechanisms [
27]. High concentration of macromolecules inherently causes molecular crowding due to excluded volume effect (
Figure 1B), which interferes with the molecular motion of the solute by the surrounding macromolecules [
28]. The excluded volume effect is unrelated to the chemical nature of the macromolecules and simply occurs due to repulsive steric hindrance, which increases with the macromolecular concentration and size and therefore cannot be readily controlled by arginine or any other solution conditions. There are of course molecular interactions due to their chemical properties, i.e., attractive and repulsive interactions, as shown in
Figure 1 and
Figure 2. It can be easily speculated that a protein molecule would be difficult to move when there is attractive interaction between the protein molecules, which should lead to an increases in viscosity. Such attractive interaction is most likely mediated by electrostatic interactions, although hydrophobic interaction (
Figure 2B) or cross-linking (
Figure 2C and
D) cannot be excluded. Since the proteins involved in attractive interactions are within the same molecules, they have an identical net charge. For example, if one molecule is negatively charged, then all other protein molecules are also negatively charged, which would cause repulsive interactions. The electrostatic attractive interactions thus occur by uneven charge distribution and thereby resultant local negative or positive charges, dipole moment or charge fluctuation. In either case, charge shielding by ions can suppress these electrostatic interactions. When hydrophobic interactions, in addition to electrostatic interactions, are involved, arginine (which is ionic) is effective in suppressing both hydrophobic and electrostatic interactions.
There is second possible macromolecular interaction, which is repulsive. This is exactly the case when the protein molecules possess net charges that are not sufficiently screened by ions. In the presence of such a repulsive interactions, the molecular motion of a protein molecules is also restricted, resulting in increased viscosity. In such a case as well, ionic arginine can suppress the solution viscosity, although such repulsive interaction and resultant increased viscosity may be suppressed by salt, as involvement of hydrophobic interaction in repulsive interaction is unlikely [
29,
30].
Viscosity of solution is expressed in a simple manner by Einstein equation: η = η
0 (1 + 2.5 θ), where η is the viscosity of the protein solution, η
0 is the viscosity of water and θ is the volume fraction of the protein in water. The equation indicates that the viscosity of water increases with the added particles, in proportion to the volume fraction of the particle at dilute particle concentration, as the solution viscosity is related to friction between water molecules and particles and Brownian motion of the particles. Both the friction and Brownian motion are related to the size and shape of the particle. The constant 2.5 does not always apply for any particles. In
Figure 5 are depicted examples of three protein molecules to exist in dilute solution, where, the volume fraction is identical in three cases. However, the viscosity increases in the order of the particle size and shape (A < B < C). The constant is greater than 2.5 for aggregated particles. The Einstein equation only applies dilute dissociated particle solution. When the particles are electrically charged, however, the solution viscosity also deviates from Einstein relation due to the effects of charges on the surrounding ions and water molecules even at dilute particle concentration. This is not due to the electrostatic protein-protein interactions that dominate at high protein concentrations as depicted in
Figure 1 and
Figure 2. The charged particles bind water and ions, forming electrical double layer. When the solution moves, there is deformation or dragging of the electrical double layer, which causes increased viscosity [
31]. This effect of electric charges on solution viscosity is different from the molecular interactions at high protein concentrations, as shown in
Figure 1 and
Figure 2, which also lead to high viscosity. When the particle concentration increases, there is inter-particle interactions, which cause deviation from the linear relation to particle concentration. The viscosity increases much sharper than the linear relation predicted by Einstein relation or the modified relations. Such non-linear relation was expressed as a polynomial function of volume fraction or even more drastically by Mooney equation [
31]. Namely, as the concentration and particle number increase, there will be increased transient molecular interactions, leading to non-linear increase in solution viscosity.
Co-solvents and sequence modification have been used to reduce molecular interactions and thereby high viscosity [
32]. For example, mutation analysis showed that reduced hydrophobicity leads to lower viscosity. Such a lower viscosity was ascribed to reduced attractive protein-protein interaction and thereby faster diffusion coefficient of the mutant antibody than the wild-type antibody, whose diffusion is slowed by increasing protein concentration [
33]. More specifically, importance of Fv domains of the antibody was implicated for high viscosity [
34]. It was shown that increased hydrophobic patches or decreased isoelectric point (pI) in Fv domains correlated with high viscosity. The decrease in pI was responsible for decreased net charges and hence lower electrostatic repulsion at the formulation pH of ~5. This suggests that high viscosity occurs due to reduced repulsive electrostatic repulsion and increased hydrophobic interaction. Retention on hydrophobic interaction chromatography has been shown to correlate with the tendency of antibodies to suffer high viscosity, as protein binding to hydrophobic resin in hydrophobic chromatography (HIC) is related the hydrophobicity of native proteins [
35].
Poly-glutamine was found effective in reducing high viscosity of a mAb, perhaps masking the positively charged patches that may be responsible for electrostatic interactions [
36].
3.2. Opalescence
Another issue at a high antibody concentration is appearance of the solution. When antibody solu tion is concentrated at low temperature (e.g., in cold box), a gel-like structure is often observed. Such changes in high antibody concentration solution are observed without conformational changes and hence most likely due to self-association of antibody molecules. Upon visual inspection, a solution of antibody at high concentration often exhibits bluish color, which is called opalescence [
37]. Is this comparable to the phenomenon of a blue sky, where small particles in air effectively reflect shorter-wavelength light? The mechanism of opalescence has been investigated using light microscopy [
38]. Bovine γ-globulin solution showed transparent appearance below 50 mg/ml and white suspension at 50 mg/ml when stored at room temperature. This 50 mg/ml suspension was opaque, indicating that particulates were formed and caused light scattering of all visible wavelengths, resulting in a white appearance. Interestingly, further increase to 120 mg/ml resulted in opalescence with bluish appearance. It may be possible that increasing antibody concentration from 50 to 120 mg/ml resulted in conversion from large to small particles and hence wavelength dependence of light scattering. This conversion appears to be opposite to what is expected from increasing protein concentration. As expected, further increase to 230 mg/ml resulted in whitish suspension and resulted in opaque appearance again. Transmission electron microscopic observation of the 230 mg/ml γ-globulin solution showed net-work formation of the proteins due to extensive protein-protein interactions. This opalescence appearance can be suppressed by salts and more effectively by arginine [
39,
40].
Opalescence is a consequence of gradient of refractive index in solution, which causes reflection of low wavelength light (for blueish color appearance). Such differential light reflection may arise from small particles or fluctuation of refractive index but due to network formation of antibody molecules.