Supporting Information
Excluded volume effect- Modified Ross and Minton equation
Excluded volume is one of the factors contributing to viscosity of protein solutions at
high concentrations. Figure S1 represents modified Ross and Minton equation (Equation 9:
𝑘
𝜂𝑖𝑛ℎ = 𝜈 [𝜂]𝑙𝑛(𝜂𝑟𝑒𝑙 ) + [𝜂]) to determine the effect of macromolecular crowding on solution
viscosity at high concentration for DVD-IgTM protein compared to mAb. A linear plot of ηinh as a
function of ln(ηrel) means only excluded volume contributes to solution viscosity.(1, 2) The ratio
of slope over intercept provides effective crowding factor k/ν. From Figure S1, a higher slope for
DVD-IgTM protein than mAb indicates increased excluded volume contribution for the molecule,
which is in agreement with the intrinsic viscosity measurements from the main text (Figure 4b).
However, the equation does not give a linear fit to the viscosity data for both, mAb and DVDIgTM protein at near 0 and 15 mM ionic strengths. A curvature in the plot of ηinh vs. ln(ηrel)
indicates that attractive interactions start dominating in solution as concentration increases. At
near 0 mM ionic strength, similar trend is observed from light scattering measurements (Figure
2), where strong repulsive interactions are present in dilute solution (positive slope) and as the
concentration increases beyond 10 mg/mL, slope shows a curvature (further higher
concentrations were not measured in light scattering). In Figure S1, the slope for 15 mM ionic
strength solutions shows a downward curve, indicating that attractive interactions start
dominating beyond this concentration range which is in agreement with attractive interactions as
determined from Light scattering in Figure 2.
Figure S1: Inherent viscosity plotted against lnrel for mAb (■) and DVD-IgTM (▲) calculated
using Equation 9 in water or at near 0 mM ionic strength (solid line) and at pH 6.1 Histidine
buffer with ionic strength of 15 mM (dashed line). The lines are the polynomial fit to the data
points.
Change in Attractive interactions determined from Tcloud
Formulation factors (pH, ionic strength, salt-type, excipients) modulate the proteinprotein interactions significantly affecting protein properties such as charges, dipoles,
hydrophobic patches, etc., resulting in changes in physicochemical properties. Changing solution
conditions can positively impact one factor, while negatively affecting the other. For example,
increasing charges on the protein molecule can increase the repulsive interactions or decrease the
attractions between the molecules; however, they can still result in increased viscosity because of
the electroviscous effect. Determining the nature of these interactions in solution can provide a
better understanding of the solution conditions where viscosity is minimal. (1, 3, 4)
Liquid-liquid phase separation (LLPS) of a solution into a protein-rich and protein-poor
phase is another formulation challenge reported for proteins at high concentrations and is due to
attractive interactions in solution.(5-8) LLPS has thermodynamic basis to it, and hence in
addition to attractive interactions i.e. enthalpic effect, tendency to phase separate is higher as
temperature of the system is lowered to account for the entropic effect to lower the free energy of
the system.(9) In our previous studies (unpublished data), we have established a good correlation
between shifts in Tcloud (temperature that marks the onset of liquid-liquid phase separation in
solution)(10) and change in attractive interactions with change in solution conditions; low Tcloud
values indicate weak interactions in solution, while high Tcloud values indicate strong attractions
in solution. In the current study, in addition to light scattering, interactions in solutions were also
assessed by measuring Tcloud of the solution as a function of solution conditions and are plotted in
Figure S2a and S2b for 16 and 60 mg/mL protein concentrations, respectively. For Tcloud
measurements, percent transmittance for a sample is measured at 510 nm using UV-vis
spectrophotometer as the temperature of the solution is lowered. In the current study, for
comparative evaluation, temperature where percent transmittance reaches 70 is termed as
Tcloud.(8)
At pH 5.1, no phase separation was observed at any of the conditions at the temperatures
studied, indicating that weak repulsive interactions are present in the solution (data not plotted).
From Figure S2a and S2b, at pH 6.1, Tcloud shifts to higher temperatures on increasing the ionic
strength indicating increased attractive interactions in solution. Hydrophobic interactions are the
only short-range attractive interactions that become dominant as the ionic strength of the solution
is increased, thereby increasing the Tcloud at pH 6.1. Tcloud values and hence attractive interactions
decrease at pH 6.6 and 7.1, on increasing the ionic strength from 15 to 50 mM. The decrease is
more significant at pH 7.1 than at pH 6.6, possibly due to the presence of significant dipoles on
the molecule close to its pI (~7.5) which are shielded on increasing the ionic strength of the
solution. The change in Tcloud with change in pH and ionic strength is consistent at both 16 and
60 mg/mL protein concentration; Tcloud values at 60 mg/mL are slightly higher than at 16 mg/mL.
From our previous studies, (unpublished data) we have discussed that both hydrophobic
interactions and dipole-mediated interactions results in increased tendency of DVD-IgTM protein
to undergo phase separation (hence indicating shifts in Tcloud). These attractive interactions also
result in increased viscosity of DVD-IgTM protein solution and contribution of each type of
interaction was investigated further and presented in the main manuscript.
Figure S2: Tcloud (determined as temperature where percent transmittance is 70) for DVD-IgTM
protein at concentration of (a) 16 mg/mL and (b) 60 mg/mL, as a function of pH and at ionic
strengths of 15 mM (solid bar) and 50 mM (dashed bar). All solutions were analyzed in
duplicate. Error bars if not visible are smaller than the symbols used.
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