(228dz) Challenges in Predicting Protein-Protein Interactions from Measurements of Molecular Diffusivity

Dynamic light
scattering (DLS) can be used to measure the diffusivity of a protein within a
formulation.  The dependence of molecular diffusivity (D_m,2)
on protein concentration (traditionally expressed in terms of the interaction
parameter, k_D) is often measured to infer whether
protein-protein interactions are repulsive or attractive, resulting in
solutions that are colloidally stable or unstable, respectively.  In addition, the
infinite dilution diffusion coefficient D_0,2, calculated by
extrapolating DLS data to zero protein concentration, is a parameter often used
to measure changes in protein conformation.  Some problems can arise when using
diffusivity measurements from DLS to quantify colloidal stability as well as
conformational changes as proteins in solution are macroions whose Brownian
diffusion can be perturbed by the presence of other ions.  Multiple studies
have shown that when charged proteins undergo mutual diffusion with small,
mobile counter-ions such as Cl^-, charge separation is prevented
because diffusion-induced local electric fields slow the motions of the small
counter-ions and speed those of the protein macroions.  Thus, salt concentration
gradients with tunable amplitude can strongly amplify particle migrations not
representative of true colloidal forces between proteins.  In this study, we
hypothesize that electrostatic effects, unrelated to intermolecular forces can
impact protein diffusion, complicating the interpretation of both protein
colloidal stability as well as protein conformation from DLS data. 

In addition, k_Dcan be used to measure colloidal stability at high protein concentration,
a useful tool as many protein-based pharmaceuticals are prepared in highly
concentrated (100-200 mg mL^-1) solutions.  We postulate
that at high protein concentration, electrostatic effects as well as other
protein-protein interactions are small and that excluded volume effects account
for the majority of k_D which are not representative of colloidal
forces between proteins.

The dependence of
protein diffusion on electrolyte concentrations and local electric potential
gradients is studied using Maxwell-Stefan equations to predict the effects of
electrolytes on protein mutual diffusion coefficients.  These predictions are
then compared to experimental DLS results obtained using a DynaPro^TM
Dynamic Light Scattering Instrument from Wyatt Technology (Goleta, CA).  The two model
proteins used in this study are lysozyme and a mAb from 2 mM to 90 mM
KCl buffer at pH 6.0.  The
system contains three ionic and one neutral species, which are proteins,
counter-ions, co-ions, and the neutral solvent species, water.  Water
dissociation is neglected, whereas KCl completely dissociates into K⁺
and Cl^‑.  Inputs to the model are species mole fraction, net
charge, and intrinsic diffusion coefficient.  Since proteins are dialyzed at
25 mg mL^-1 into low ionic strength buffers, Donnan effects
are non-negligible and the concentration of K⁺ and Cl^-
ions present on the retentate side of the membrane after dialysis are
calculated using Donnan equations.  Far-UV CD is then used to look at protein
conformation as a function of ionic strength using a Chirascan-plus
spectrometer (Applied Photophysics, UK).  A
theoretical hard sphere (HS) model is made to determine the effect of
excluded volume on k_D(k_D^HS) as
a function of protein concentration.  To estimate this contribution,
we
use Mooney’s equation of viscosity to determine the dependence of protein
volume fraction on solution viscosity and use Stokes-Einstein equation to relate
viscosity to protein diffusion.

Good fits between
the multicomponent model and experimental DLS data are obtained, demonstrating
that large changes in protein diffusivity with protein concentration can result
even in the absence of protein-protein interactions (Fig. 1).  In addition, we
show that D_0,2 from DLS data is 40% higher for lysozyme and
10% higher for the mAb at 2 mM KCl compared to D_0,2 at the high
salt concentrations.  Comparing this data to far-UV CD, we show that DLS cannot
be reliably used to detect protein conformational changes as no conformational
changes in protein occur from 2 mM to 90 mM KCl.  Finally, even at
zero protein concentration, k_D^HSis -1.75
mL g^‑1 and it becomes increasingly negative as a function
of protein concentration although no protein-protein interactions are taken
into account.  We thus recommend comparing experimentally-determined k_D
values to theoretically predicted hard-sphere steric contributions for a more
accurate assessment of the effects of protein-protein interactions at higher
protein concentrations.  

In this study, we
demonstrate that the parameter k_D is impacted by the presence
of co-solute as well as high volume fraction of proteins so careful
interpretation of k_D is needed if it is used to understand
weak protein-protein interactions and colloidal stability of protein formulations.

FIGURE 1. DLS data
for lysozyme (A) and mAb (B) in 2 mM KCl (circle), 5 mM KCl
(diamond), 10 mM KCl (triangle), and 90 mM KCl (inverted triangle),
at pH 6.0.  Error bars represent the standard deviation of triplicate
measurements.  Most error bars are smaller than symbols.  Lines show the fit of
the model in 2 mM KCl (solid), 5 mM KCl (dash), 10 mM KCl
(dash-dot), and 90 mM KCl (dot), at pH 6.0. Insert in (B) shows a
zoomed-out version of the model to demonstrate curvature.