Comment pubs.acs.org/JPCB
Reply to “Comment on ‘Osmolyte Effects on Monoclonal Antibody Stability and Concentration-Dependent Protein Interactions with Water and Common Osmolytes’” Gregory V. Barnett,† Vladimir I. Razinkov,‡ Bruce A. Kerwin,‡ Steven Blake,§ Wei Qi,§ Robin A. Curtis,∥ and Christopher J. Roberts*,† †
Department of Chemical and Biomolecular Engineering, University of Delaware, Newark, Delaware 19716, United States Drug Product Development, Amgen Inc., Seattle, Washington 98119, United States § Malvern Biosciences Inc., Columbia, Maryland 21046, United States ∥ School of Chemical Engineering and Analytical Science, The University of Manchester, Manchester M13 9PL, U.K. ‡
do not find their argument compelling at lower concentrations where the data are effectively linear. Even examples where data eventually become nonlinear (e.g., sucrose and PEG in ref 1), there is still a low-concentration linear regime that cannot be overlooked even if one chooses to fit a parabola over the larger concentration range. Based on eq 1, it is clear that if G12 and G23 are reasonably independent of c3 at fixed T and p, then V̂ 2 versus c3 is linear, and three qualitatively different scenarios exist, depending on whether G12 − G23 is (i) positive, (ii) negative, or (iii) so small as to be effectively zero. Case (i) is equivalent to preferential exclusion of the osmolyte from the protein, whereas case (ii) is preferential accumulation of the osmolyte near the protein. Case (iii) is effectively that of an ideal mixture, in that the chemical potential of the protein is not significantly altered by the addition of osmolyte.2 When G12 and G23 are both strong functions of c3, the analysis of V̂ 2 versus c3 is more complex. Our analysis at high concentrations in ref 1 used a simple localslope approximation, but we agree with Rösgen and Auton that this is likely one of many reasonable approximations, and we include their illustrative alternative below. That notwithstanding, in the limit of sufficiently low c3 (mathematically, as c3 → 0), G12 and G23 are expected to be effectively constant. Therefore, the value of V̂ 2 at c3 = 0 is effectively G12, and the slope of V̂ 2 versus c3 in the low-c3 linear regime provides the difference between G12 and G23 (at fixed V̂ 3) for low osmolyte concentrations that are typical of conditions for stabilizing proteins in solution. Based on that, it was clear in ref 1 that sucrose was preferentially excluded at low sucrose concentrations, but surprisingly, trehalose and sorbitol showed no detectable preferential exclusion at all. In ref 1, the “low-c3” linear regime was between and 0 and ∼10 w/w % osmolyte in each case. The example Rösgen and Auton provide regarding sucrose is based on an additive peptide model3 (cf. Figure 1 of their Comment) and is one possible alternative when considering a wide range of osmolyte concentrations such that G12 and/or G23 may be c3-dependent. We question whether one should assume up front that such a model is accurate for predicting
T
he Comment by Rösgen and Auton focuses on analysis of experimental data in Barnett et al.1 for protein partial specific volume (V̂ 2) as a function of osmolyte concentration in ternary solutions of water (1), protein (2), and osmolyte (3) in order to deduce values of the water−protein Kirkwood−Buff (KB) integral (G12) and osmolyte−protein KB integral (G23) in the limit of near-zero protein concentration (c2). In that limit, V̂ 2 can be expressed as V2̂ = −G12 + c3V3̂ (G12 − G23)
(1)
for fixed temperature (T) and pressure (p).2 c3 denotes the concentration of osmolyte, and V̂ 3 is the partial specific volume of the osmolyte, and the small contribution from the ideal gas limit has been neglected. For all of the protein−osmolyte combinations tested by Barnett et al., the value of V̂ 3 was independent of c3, and therefore, c3 is effectively the independent experimental variable at fixed temperature and pressure.1 Rösgen and Auton argue that it is not possible to obtain values of G12 and G23 using just eq 1 and data for V̂ 2 without making some sort of assumption regarding how G12 and G23 depend on c3, unless both quantities are independent of c3. They first highlight that eq 1 provides one equation in two unknowns and argue that it not possible to obtain G12 and G23 as independent quantities without additional data and a second equation. While that would be correct for cases when one obtained V̂ 2 at a single value of c3, one can also consider cases when one has V̂ 2 as a function c3. Based on an earlier version of this Reply, Rösgen and Auton anticipate the argument below regarding V̂ 2 as a function c3 in their revised Comment and focus primarily on the question of whether one can uniquely interpret nonlinear behavior without additional data. They also argue that the same issues hold at low concentration, although we show below that the latter point is questionable. The crux of their argument regarding nonlinear behavior for V̂ 2 versus c3 is that G12 and G23 can depend on osmolyte concentration (c3), and therefore, there are multiple ways for one to obtain nonlinear V̂ 2 versus c3. Therefore, one cannot uniquely conclude whether there is preferential exclusion or accumulation from the data. If one focuses on the nonlinear regime, we agree with their argument unless one has a reliable model for the concentration dependence of KB integrals, and this applies for the highest osmolyte concentrations in ref 1. We © 2016 American Chemical Society
Received: July 8, 2016 Revised: October 2, 2016 Published: October 7, 2016 11350
DOI: 10.1021/acs.jpcb.6b06832 J. Phys. Chem. B 2016, 120, 11350−11351
Comment
The Journal of Physical Chemistry B G12 − G23 for a protein when it based solely on peptide data. Independent of that assumption, it is interesting that Rösgen and Auton argue that G12 and G23 can (or would) have strong dependences on osmolyte concentration even in the limit of low concentration. While we do not disagree such a scenario is mathematically possible, we are unaware of any physical basis for making that assumption instead of the thermodynamically and intuitively simpler assumption of reasonably constant G12 and G23 over the initial range of osmolyte concentration. We propose it is reasonable to use a simpler treatment, with G12 and G23 as approximately constant at low c3, until a more general theoretical or modeling treatment of proteins (not peptides) becomes available. In summary, we agree with a subset of arguments and analysis by Rösgen and Auton that show that V̂ 2 versus c3 data, on their own, are ambiguous for interpreting preferential interactions at high osmolyte concentration (c3) once V̂ 2 versus c3 is appreciably nonlinear. Extending that conclusion to low osmolyte concentrations is unnecessary when V̂ 2 is linear versus c3. In the absence of a compelling physical model for the c3 dependence of G12 and G23 at low c3, we suggest that the physically and intuitively simpler treatment for future analysis is to take the linear regime of V̂ 2 versus c3 and use that to deduce values for G12 and G23.
■
AUTHOR INFORMATION
Corresponding Author
*Tel.: 302-831-0838. Fax: 302-831-1048. E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
■
REFERENCES
(1) Barnett, G. V.; Razinkov, V. I.; Kerwin, B. A.; Blake, S.; Qi, W.; Curtis, R. A.; Roberts, C. J. Osmolyte Effects on Monoclonal Antibody Stability and Concentration-Dependent Protein Interactions with Water and Common Osmolytes. J. Phys. Chem. B 2016, 120 (13), 3318−3330. (2) Ben-Naim, A. Statistical Thermodynamics for Chemists and Biochemists; Springer-Verlag: New York, 1991. (3) Auton, M.; Bolen, D. W. Predicting the Energetics of OsmolyteInduced Protein Folding/Unfolding. Proc. Natl. Acad. Sci. U. S. A. 2005, 102 (42), 15065−15068.
11351
DOI: 10.1021/acs.jpcb.6b06832 J. Phys. Chem. B 2016, 120, 11350−11351
