Comment pubs.acs.org/JPCB
Comment on “Osmolyte Effects on Monoclonal Antibody Stability and Concentration-Dependent Protein Interactions with Water and Common Osmolytes” Jörg Rösgen*,† and Matthew Auton*,‡ †
College of Medicine, Penn State University, Hershey, Pennsylvania 17033, United States Mayo Clinic, Rochester, Minnesota 55905, United States
‡
I
n a recent publication, Barnett et al.1 attempted to use density data to derive the Kirkwood−Buff integrals of protein−osmolyte solvation and hydration, G23 and G12. The central equation in their paper to do this is v2̅ ≈ −G12 + c3v3̅ (G12 − G23)
solvation scenarios, and volume measurements alone cannot be used to distinguish between them. It may be tempting to try to resolve G23 at the limit of 0 M o smo lyte because, h ere, G 1 2 is alread y kno wn: 3 G12,0M ≈ − v2,0M ̅ . Equation 1 is then again tantalizing to use with (G12 − G23) as the slope for determining G23. However, one has to remember that G12 itself has an unknown slope, which contributes to the slope of v2̅ in eq 1 in addition to the (G12 − G23) term. So, still nothing can be said about G23 from eq 1 alone. It is, however, possible to combine the current volume data (eq 1) with model predictions of preferential solvation (eq 2) as reported in Figures 1 and 4 of Barnett et al.1 and solve for the solvation parameters G12 and G23. Equations 1 and 2 combine to4
(1)
where we omitted the negligibly small compressibility term. This is a single equation with two unknowns (G12 and G23), and solving for these requires a second equation. An ideal candidate is the first equation in the original paper (using the correct concentration scale, viz. molarity2): ⎛ ∂μ ⎞ ⎛ ∂μ ⎞ = c3(G12 − G23)⎜ 3 ⎟ ⎜ 2⎟ ⎝ ∂c3 ⎠T , p , c → 0 ⎝ ∂c3 ⎠T , p , c → 0 2
2
(2)
⎛ ∂μ ⎞ G12 = − v2̅ + v3̅ ⎜ 2 ⎟ ⎝ ∂m3 ⎠T , p , m
However, the authors did not measure chemical potential data for their protein, so they turn to an alternative that is valid only when the two unknowns are constant. Barnett et al.1 claim that the bracket term in eq 1 equals the slope, and the other term equals an intercept of a straight line. However, G12 and G23 are obviously not constant, as judged by the parabolic shape of v2̅ in two (sucrose and PEG) out of four osmolyte solutions (v2̅ is constant for sorbitol and trehalose). According to eq 1, constant Gij would lead to a linear v2̅ as a function of c3v3̅ . Consequently, Barnett et al.1 report only one set out of an infinite number of possible values for G12 and G23. As can be easily seen from eq 1, one has the liberty to choose any function of one’s own liking for G23 and then solve for G12 v + c3v3̅ G23 G12 = − 2̅ 1 − c3v3̅
(4)
2 →0
and ⎛ 1 ⎞⎛ ∂μ ⎞ G23 = − v2̅ + ⎜ v3̅ − ⎟⎜ 2 ⎟ c3 ⎠⎝ ∂m3 ⎠ ⎝ T ,p,m
2
⎛ ∂μ ⎞ /⎜ 3 ⎟ ⎝ ∂m3 ⎠T , p , m →0
2→0
(5)
Figure 1 shows the results for the case of sucrose, where according to Barnett et al.1 the experimental volumes are v2̅ [mL/g] = 070753 + 0.271c3v3̅ −1.593(c3v3̅ )2 and v3̅ [mL/g] = 0.6206, and the calculated transfer chemical potential is ∂μ2
( ) ≈ 29.12 kJ/molM
(3)
∂m3
(calculated by Barnett et al. 1
according to Auton et al.5). The derivative
to get solvation parameters that perfectly reproduce the empirical parabolic shape of v2̅ . There are two cases that Barnett et al.1 report: v2̅ is quadratic in osmolyte concentration or constant. Sucrose and trehalose are representative of these two cases. The experimental protein volumes, v2̅ [mL/g], are 0.70753 + 0.271 v3̅ c3 (sucrose) and 0.70915 (trehalose).1 Three examples for G23 are given each along with the G12 resulting from eq 3. The numbers in Table 1 show that the osmolyte solvation minus the hydration of the protein, G23 − G12, could be either positive (corresponding to preferential binding) or negative (preferential exclusion) or intersecting zero (switch between preferential binding and exclusion). The authors consider only the latter case, but the other two are possible, as well. In addition, there is an unlimited number of additional possible © 2016 American Chemical Society
2
⎛ ∂μ ⎞ /⎜ 3 ⎟ ⎝ ∂m3 ⎠T , p , m →0
∂μ3
( ) was taken ∂m3
from Rösgen et al.6 As can be clearly seen from the figure, no switch from preferential exclusion to binding remains. We show only the results for sucrose because this osmolyte is most likely to exhibit unusual behavior. Sucrose already has been shown to be atypical in its solvation of the peptide backbone where net preferential exclusion can also originate from positive solvation of both water and osmolyte.7 Whatever the hydration and osmolyte solvation details are, the net preferential exclusion of Received: June 3, 2016 Revised: August 30, 2016 Published: October 7, 2016 11331
DOI: 10.1021/acs.jpcb.6b05602 J. Phys. Chem. B 2016, 120, 11331−11332
Comment
The Journal of Physical Chemistry B
Table 1. Examples for Possible Solutions for the Solvation Parameters G12 and G23 for a Monoclonal Antibody1 in Sucrose and Trehalose G12 [mL/g] sucrose
trehalose
example example example example example example
1 2 3 1 2 3
−0.70753 −0.70753 −0.70753 −0.70915 −0.70915 −0.70915
− 1.61134v3̅ c3 + 1.61134v3̅ c3 − 1.63212v3̅ c3 + 1.63212v3̅ c3
G23 [mL/g] 0.632814 − 0.0183439v3̅ c3 −0.97835 + 1.593v3̅ c3 −2.58987 + 3.20434v3̅ c3 0.92297 − 1.63212v3̅ c3 −0.70915 −2.34127 + 1.63212v3̅ c3
(2) Rösgen, J. Synergy in Protein-Osmolyte Mixtures. J. Phys. Chem. B 2015, 119, 150−157. (3) Pjura, P. E.; Paulaitis, M. E.; Lenhoff, A. M. Molecular Thermodynamic Properties of Protein Solutions from Partial Specific Volumes. AIChE J. 1995, 41, 1005−1009. (4) Rösgen, J.; Pettitt, B. M.; Bolen, D. W. An analysis of the molecular origin of osmolyte-dependent protein stability. Protein Sci. 2007, 16, 733−743. (5) Auton, M.; Holthauzen, L.; Bolen, D. Anatomy of energetic changes accompanying urea-induced protein denaturation. Proc. Natl. Acad. Sci. U. S. A. 2007, 104, 15317−15322. (6) Rösgen, J.; Pettitt, B. M.; Bolen, D. W. Protein folding, stability, and solvation structure in osmolyte solutions. Biophys. J. 2005, 89, 2988−2997. (7) Auton, M.; Bolen, D.; Rösgen, J. Structural thermodynamics of protein preferential solvation: Osmolyte solvation of proteins, aminoacids, and peptides. Proteins: Struct., Funct., Genet. 2008, 73, 802−813. (8) Hesterberg, L.; Lee, J. Sedimentation study of a catalytically active form of rabbit muscle phosphofructokinase at pH 8.55. Biochemistry 1980, 19, 2030−2039. (9) Lee, J. C.; Timasheff, S. N. The Stabilization of Proteins by Sucrose. J. Biol. Chem. 1981, 256, 7193−7201. (10) Wills, P.; Winzor, D. Thermodynamic Analysis of Preferential Solvation in Protein Solutions. Biopolymers 1993, 33, 1627−1629. (11) Jacobsen, M.; Wills, P.; Winzor, D. Thermodynamic analysis of the effects of small inert cosolutes in the ultracentrifugation of noninteracting proteins. Biochemistry 1996, 35, 13173−13179.
Figure 1. Protein hydration G12 (dashed lines) and osmolation G23 (solid lines) reported1 (black lines) and recalculated here (colored lines). G12 > G23 corresponds to preferential exclusion.
sucrose has long been demonstrated by both sedimentation8 and equilibrium dialysis.9 It has also been pointed out that the preferential exclusion of sucrose from proteins is perfectly equivalent to its volume exclusion (i.e., two atoms cannot occupy the same space),10,11 which is quite the opposite of preferential accumulation of sucrose. Note that both sets of Gij in Figure 1 perfectly reproduce the parabolic equation for the experimental v2̅ .1 However, the set of Barnett et al.1 (black lines) is at variance with the generally found preferential exclusion of sucrose, while our revision (colored lines) properly accounts for sucrose exclusion. Since ∂μ2
( ) was not actually measured by anybody for the given ∂m3
protein, there may be slight deviations between reality and our analysis, which uses computed values for
∂μ2
( ). The analysis of ∂m3
Barnett et al.,1 in contrast, gives entirely uncertain solvation results, which are additionally implausible for the specific solution they chose.
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AUTHOR INFORMATION
Corresponding Authors
*E-mail:
[email protected]. Phone: +1-717-531-2026. *E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS Research reported in this publication was supported by NIH/ NIGMS GM049760. The content is solely the responsibility of the authors and does not necessarily represent the official views of the NIH.
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REFERENCES
(1) Barnett, G.; Razinkov, V.; Kerwin, B.; Blake, S.; Qi, W.; Curtis, R.; Roberts, C. Osmolyte Effects on Monoclonal Antibody Stability and Concentration-Dependent Protein Interactions with Water and Common Osmolytes. J. Phys. Chem. B 2016, 120, 3318−3330. 11332
DOI: 10.1021/acs.jpcb.6b05602 J. Phys. Chem. B 2016, 120, 11331−11332
