Critical examination of the colloidal particle model of globular proteins

Biophysical Journal

Volumn 108, Issue 3, 2015, Pages 724-737

  Sarangapani, Prasad S ^a   Hudson, Steven D ^b   Jones, Ronald L ^b   Douglas, Jack F ^b   Pathak, Jai A ^a  

^a MEDIMMUNE   (United States)

^b NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOVINAE;

BOVINE SERUM ALBUMIN; COLLOID;

ANIMAL; BOVINE; CHEMICAL STRUCTURE; CHEMISTRY; CIRCULAR DICHROISM; COLLOID; DIFFUSION; HYDRODYNAMICS; PH; STATIC ELECTRICITY; VISCOSITY;

ANIMALS; CATTLE; CIRCULAR DICHROISM; COLLOIDS; DIFFUSION; HYDRODYNAMICS; HYDROGEN-ION CONCENTRATION; MODELS, MOLECULAR; SERUM ALBUMIN, BOVINE; STATIC ELECTRICITY; VISCOSITY;

EID: 84947201513     PISSN: 00063495     EISSN: 15420086     Source Type: Journal    
DOI: 10.1016/j.bpj.2014.11.3483     Document Type: Article

References (145)

1. L.R. Barbosa, and M.G. Ortore R. Itri The importance of protein-protein interactions on the pH-induced conformational changes of bovine serum albumin: a small-angle x-ray scattering study Biophys. J. 98 2010 147 157
2. T.E. Creighton Proteins: Structures and Molecular Properties 1993 Macmillan New York
3. K.A. Dill Polymer principles and protein folding Protein Sci. 8 1999 1166 1180
4. A.V. Dobrynin, R.H. Colby, and M. Rubinstein Polyampholytes J. Polym. Sci. B Polym. Phys. 42 2004 3513 3538
5. J.E. Kohn, and I.S. Millett K.W. Plaxco Random-coil behavior and the dimensions of chemically unfolded proteins Proc. Natl. Acad. Sci. USA 101 2004 12491 12496
6. A.K. Jha, and A. Colubri T.R. Sosnick Statistical coil model of the unfolded state: resolving the reconciliation problem Proc. Natl. Acad. Sci. USA 102 2005 13099 13104
7. Y. Liu, and L. Porcar P. Baglioni Lysozyme protein solution with an intermediate range order structure J. Phys. Chem. B 115 2011 7238 7247
8. F. Zhang, and F. Roosen-Runge F. Schreiber Hydration and interactions in protein solutions containing concentrated electrolytes studied by small-angle scattering Phys. Chem. Chem. Phys. 14 2012 2483 2493
9. F. Zhang, and M.W.A. Skoda F. Schreiber Protein interactions studied by SAXS: effect of ionic strength and protein concentration for BSA in aqueous solutions J. Phys. Chem. B 111 2007 251 259
10. J.A. Pathak, R.R. Sologuren, and R. Narwal Do clustering monoclonal antibody solutions really have a concentration dependence of viscosity? Biophys. J. 104 2013 913 923
11. M.M. Castellanos, J.A. Pathak, and R.H. Colby Both protein adsorption and aggregation contribute to shear yielding and viscosity increase in protein solutions Soft Matter 10 2014 122 131
12. E.Y. Chi, and S. Krishnan J.F. Carpenter Physical stability of proteins in aqueous solution: mechanism and driving forces in nonnative protein aggregation Pharm. Res. 20 2003 1325 1336
13. L.R. De Young, A.L. Fink, and K.A. Dill Aggregation of globular proteins Acc. Chem. Res. 26 1993 614 620
14. K.A. Dill Theory for the folding and stability of globular proteins Biochemistry 24 1985 1501 1509
15. K.A. Dill Dominant forces in protein folding Biochemistry 29 1990 7133 7155
16. W.G. Lilyestrom, and S. Yadav T.M. Scherer Monoclonal antibody self-association, cluster formation, and rheology at high concentrations J. Phys. Chem. B 117 2013 6373 6384
17. A.P. Minton Models for excluded volume interaction between an unfolded protein and rigid macromolecular cosolutes: macromolecular crowding and protein stability revisited Biophys. J. 88 2005 971 985
18. S.J. Shire, Z. Shahrokh, and J. Liu Challenges in the development of high protein concentration formulations J. Pharm. Sci. 93 2004 1390 1402
19. M.E. Cromwell, E. Hilario, and F. Jacobson Protein aggregation and bioprocessing AAPS J. 8 2006 E572 E579
20. W. Wang, and C.J. Roberts Chapter 10: Aggregation and Immunogenicity of Therapeutic Proteins 2010 Wiley Online Library, John Wiley and Sons New York 10.1002/9780470769829.ch10
21. N. El Kadi, and N. Taulier M. Waks Unfolding and refolding of bovine serum albumin at acid pH: ultrasound and structural studies Biophys. J. 91 2006 3397 3404
22. A.H. Elcock, and J.A. McCammon Calculation of weak protein-protein interactions: the pH dependence of the second virial coefficient Biophys. J. 80 2001 613 625
23. Y. Li, and J. Lee Q. Huang Effects of pH on the interactions and conformation of bovine serum albumin: comparison between chemical force microscopy and small-angle neutron scattering J. Phys. Chem. B 112 2008 3797 3806
24. P.S. Sarangapani, and S.D. Hudson J.A. Pathak The limitations of an exclusively colloidal view of protein solution hydrodynamics and rheology Biophys. J. 105 2013 2418 2426
25. C. Tanford, and J.G. Buzzell The viscosity of aqueous solutions of bovine serum albumin between pH 4.3 and 10.5 J. Phys. Chem. 60 1956 225 231
26. S. Yadav, S.J. Shire, and D.S. Kalonia Factors affecting the viscosity in high concentration solutions of different monoclonal antibodies J. Pharm. Sci. 99 2010 4812 4829
27. S. Yadav, S.J. Shire, and D.S. Kalonia Viscosity analysis of high concentration bovine serum albumin aqueous solutions Pharm. Res. 28 2011 1973 1983
28. J.X. Zhou, and F. Solamo T. Tressel Viral clearance using disposable systems in monoclonal antibody commercial downstream processing Biotechnol. Bioeng. 100 2008 488 496
29. R. Nossal, C.J. Glinka, and S.H. Chen SANS studies of concentrated protein solutions. I. Bovine serum albumin Biopolymers 25 1986 1157 1175
30. C. Tanford, and J.G. Buzzell S.A. Swanson The reversible expansion of bovine serum albumin in acid solutions J. Am. Chem. Soc. 77 1955 6421 6428
31. J.T. Yang The viscosity of macromolecules in relation to molecular conformation Adv. Protein Chem. 16 1961 323 400
32. F. Booth The electroviscous effect for suspensions of solid spherical particles Proc. R. Soc. Lond. A Math. Phys. Sci. 203 1950 533 551
33. H. Liu, S. Garde, and S. Kumar Direct determination of phase behavior of square-well fluids J. Chem. Phys. 123 2005 174505
34. H. Liu, S.K. Kumar, and F. Sciortino Vapor-liquid coexistence of patchy models: relevance to protein phase behavior J. Chem. Phys. 127 2007 084902 084905
35. S. Ikeda, and K. Nishinari Intermolecular forces in bovine serum albumin solutions exhibiting solidlike mechanical behaviors Biomacromolecules 1 2000 757 763
36. H. Inoue, and T. Matsumoto Viscoelastic and SAXS studies of the structural transition in concentrated aqueous colloids of ovalbumin and serum albumins J. Rheol 38 1994 973 988
37. S. Kumar, V.K. Aswal, and J. Kohlbrecher SANS study of lysozyme vs. BSA protein adsorption on silica nanoparticles AIP Conf. Proc. 1447 2012 181 182
38. Y. Liu, and E. Fratini S.-H. Chen Effective long-range attraction between protein molecules in solutions studied by small angle neutron scattering Phys. Rev. Lett. 95 2005 118102 118105
39. T. Matsumoto, and H. Inoue Small angle x-ray scattering and viscoelastic studies of the molecular shape and colloidal structure of bovine and rat serum albumins in aqueous systems Chem. Phys. 178 1993 591 598
40. J.W. Mehl, J.L. Oncley, and R. Simha Viscosity and the shape of protein molecules Science 92 1940 132 133
41. H. Neurath, G.R. Cooper, and J.O. Erickson The shape of protein molecules. II. Viscosity and diffusion studies of native proteins J. Biol. Chem. 138 1941 411 436
42. K.M. Oates, and W.E. Krause R.H. Colby Rheopexy of synovial fluid and protein aggregation J. R. Soc. Interface 3 2006 167 174
43. O.D. Velev, E.W. Kaler, and A.M. Lenhoff Protein interactions in solution characterized by light and neutron scattering: comparison of lysozyme and chymotrypsinogen Biophys. J. 75 1998 2682 2697
44. E.J. Yearley, and I.E. Zarraga Y. Liu Small-angle neutron scattering characterization of monoclonal antibody conformations and interactions at high concentrations Biophys. J. 105 2013 720 731
45. V. Sharma, and A. Jaishankar G.H. McKinley Rheology of globular proteins: apparent yield stress, high shear rate viscosity and interfacial viscoelasticity of bovine serum albumin solutions Soft Matter 7 2011 5150 5160
46. J.T. Edsall The size and shape of protein molecules Progress in Chemical Research [Fortschritte der Chemischen Forschung] Vol. 1 1949 Springer Berlin, Germany 119 174
47. B. Lonetti, and E. Fratini P. Baglioni Viscoelastic and small angle neutron scattering studies of concentrated protein solutions Phys. Chem. Chem. Phys. 6 2004 1388 1395
48. H.D. Mertens, and D.I. Svergun Structural characterization of proteins and complexes using small-angle x-ray solution scattering J. Struct. Biol. 172 2010 128 141
49. Y. Minezaki, and N. Niimura T. Katsura Small angle neutron scattering from lysozyme solutions in unsaturated and supersaturated states (SANS from lysozyme solutions) Biophys. Chem. 58 1996 355 363
50. A.-J. Petrescu, and V. Receveur J.C. Smith Small-angle neutron scattering by a strongly denatured protein: analysis using random polymer theory Biophys. J. 72 1997 335 342
51. A. Shukla, and E. Mylonas D.I. Svergun Absence of equilibrium cluster phase in concentrated lysozyme solutions Proc. Natl. Acad. Sci. USA 105 2008 5075 5080
52. A. Stradner, and F. Cardinaux P. Schurtenberger Do equilibrium clusters exist in concentrated lysozyme solutions? Proc. Natl. Acad. Sci. USA 105 2008 E75 E76
53. A. Stradner, and H. Sedgwick P. Schurtenberger Equilibrium cluster formation in concentrated protein solutions and colloids Nature 432 2004 492 495
54. K.N. Toft, and B. Vestergaard J.P. Kutter High-throughput small angle x-ray scattering from proteins in solution using a microfluidic front-end Anal. Chem. 80 2008 3648 3654
55. C.F. Wu, and S.H. Chen Small angle neutron and x-ray scattering studies of concentrated protein solutions. II. Cytochrome c Biopolymers 27 1988 1065 1083
56. Y. Zhang, and J.F. Douglas E.J. Amis Influence of counterion valency on the scattering properties of highly charged polyelectrolyte solutions J. Chem. Phys. 114 2001 3299 3313
57. M. Boström, and F.W. Tavares J.M. Prausnitz Effect of salt identity on the phase diagram for a globular protein in aqueous electrolyte solution J. Phys. Chem. B 110 2006 24757 24760
58. E.R. Lima, and E.C. Biscaia J.M. Prausnitz Osmotic second virial coefficients and phase diagrams for aqueous proteins from a much-improved Poisson-Boltzmann equation J. Phys. Chem. C 111 2007 16055 16059
59. F.W. Tavares, and D. Bratko J.M. Prausnitz Ion-specific effects in the colloid-colloid or protein-protein potential of mean force: role of salt-macroion van der Waals interactions J. Phys. Chem. B 108 2004 9228 9235
60. F.W. Tavares, and J.M. Prausnitz Analytic calculation of phase diagrams for solutions containing colloids or globular proteins Colloid Polym. Sci. 282 2004 620 632
61. N. von Solms, and C.O. Anderson J.M. Prausnitz Molecular thermodynamics for fluid-phase equilibria in aqueous two-protein systems AIChE J. 48 2002 1292 1300
62. K.A. Dill, and S. Bromberg Molecular Driving Forces: Statistical Thermodynamics in Chemistry and Biology 2003 Taylor & Francis New York
63. C. Tanford Physical Chemistry of Macromolecules 1961 Wiley New York
64. S.E. Harding, and J.C. Horton Analytical Ultracentrifugation in Biochemistry and Polymer Science 1992 Royal Society of Chemistry Cambridge, UK
65. G.J. Howlett, A.P. Minton, and G. Rivas Analytical ultracentrifugation for the study of protein association and assembly Curr. Opin. Chem. Biol. 10 2006 430 436
66. P. Manavalan, and W.C. Johnson Sensitivity of circular dichroism to protein tertiary structure class Nature 305 1983 831 832
67. R. Pecora Dynamic Light Scattering: Applications of Photon Correlation Spectroscopy 1985 Springer New York
68. P. Schuck On the analysis of protein self-association by sedimentation velocity analytical ultracentrifugation Anal. Biochem. 320 2003 104 124
69. D.J. Scott, S.S.E. Harding, and A.J. Rowe Analytical Ultracentrifugation: Techniques and Methods 2005 Royal Society of Chemistry Cambridge, UK
70. D. Some, A. Hanlon, and K. Sockolov Characterizing protein-protein interactions via static light scattering: reversible heteroassociation Am. Biotechnol. Lab. 26 2008 18 22
71. J.J. Lee, and D.S. Berns Protein aggregation. The effect of deuterium oxide on large protein aggregates of C-phycocyanin Biochem. J. 110 1968 465 470
72. D. Arzenšek, D. Kuzman, and R. Podgornik Colloidal interactions between monoclonal antibodies in aqueous solutions J. Colloid Interface Sci. 384 2012 207 216
73. D. Roberts, and R. Keeling R. Curtis The role of electrostatics in protein-protein interactions of a monoclonal antibody Mol. Pharm. 11 2014 2475 2489
74. S.R. Kline Reduction and analysis of SANS and USANS data using IGOR PRO J. Appl. Cryst. 39 2006 895 900
75. J.S. Higgins, and H. Benoît Polymers and Neutron Scattering 1994 Clarendon Press Oxford, UK
76. J.-P. Hansen, and I.R. McDonald Theory of Simple Liquids 1990 Elsevier Amsterdam, The Netherlands
77. V. Kelkar, J. Narayanan, and C. Manohar Structure factor for colloidal dispersions. Use of exact potentials in random phase approximation Langmuir 8 1992 2210 2214
78. C. Manohar, and V. Kelkar Theory of colloidal systems: interactions and structure Langmuir 8 1992 18 22
79. S.V. Menon, V.K. Kelkar, and C. Manohar Application of Baxter's model to the theory of cloud points of nonionic surfactant solutions Phys. Rev. A 43 1991 1130 1133
80. J. Narayanan, and X.Y. Liu Protein interactions in undersaturated and supersaturated solutions: a study using light and x-ray scattering Biophys. J. 84 2003 523 532
81. J. Wu, and J.M. Prausnitz Osmotic pressures of aqueous bovine serum albumin solutions at high ionic strength Fluid Phase Equilib. 155 1999 139 154
82. D.I. Svergun, and M.H. Koch R.P. May Small Angle X-Ray and Neutron Scattering from Solutions of Biological Macromolecules 2013 Oxford University Press New York
83. A. Lomakin, N. Asherie, and G.B. Benedek Aeolotopic interactions of globular proteins Proc. Natl. Acad. Sci. USA 96 1999 9465 9468
84. M. Wertheim Fluids with highly directional attractive forces. I. Statistical thermodynamics J. Stat. Phys. 35 1984 19 34
85. M. Wertheim Fluids with highly directional attractive forces. II. Thermodynamic perturbation theory and integral equations J. Stat. Phys. 35 1984 35 47
86. M. Wertheim Fluids with highly directional attractive forces. III. Multiple attraction sites J. Stat. Phys. 42 1986 459 476
87. M. Wertheim Fluids with highly directional attractive forces. IV. Equilibrium polymerization J. Stat. Phys. 42 1986 477 492
88. R. Piazza Interactions and phase transitions in protein solutions Curr. Opin. Colloid Interface Sci. 5 2000 38 43
89. R. Piazza, V. Peyre, and V. Degiorgio "Sticky hard spheres" model of proteins near crystallization: a test based on the osmotic compressibility of lysozyme solutions Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 58 1998 R2733 R2743
90. R. Baxter Percus-Yevick equation for hard spheres with surface adhesion J. Chem. Phys. 49 1968 2770 2774
91. J.N. Israelachvili Intermolecular and Surface Forces 3rd Ed. 2011 Academic Press New York
92. E.E. Meyer, K.J. Rosenberg, and J. Israelachvili Recent progress in understanding hydrophobic interactions Proc. Natl. Acad. Sci. USA 103 2006 15739 15746
93. N.T. Southall, K.A. Dill, and A. Haymet A view of the hydrophobic effect J. Phys. Chem. B 106 2002 521 533
94. K. Baler, and O.A. Martin I. Szleifer Electrostatic unfolding and interactions of albumin driven by pH changes: a molecular dynamics study J. Phys. Chem. B 118 2014 921 930
95. C. De Kruif, and P. Rouw R. May Adhesive hard-sphere colloidal dispersions. A small-angle neutron-scattering study of stickiness and the structure factor Langmuir 5 1989 422 428
96. C. Regnaut, and J. Ravey Application of the adhesive sphere model to the structure of colloidal suspensions J. Chem. Phys. 91 1989 1211 1221
97. J.S. Pedersen Analysis of small-angle scattering data from colloids and polymer solutions: modeling and least-squares fitting Adv. Colloid Interface Sci. 70 1997 171 210
98. L. Mederos, and G. Navascues Phase diagram of the hard-sphere/attractive Yukawa system J. Chem. Phys. 101 1994 9841 9843
99. S.M. Kelly, T.J. Jess, and N.C. Price How to study proteins by circular dichroism Biochim. Biophys. Acta 1751 2005 119 139
100. R.W. Woody Circular dichroism Methods Enzymol. 246 1995 34 71
101. K. Yue, and K.A. Dill Forces of tertiary structural organization in globular proteins Proc. Natl. Acad. Sci. USA 92 1995 146 150
102. N.E. Price, and N.C. Price J.M. McDonnell The key role of protein flexibility in modulating IgE interactions J. Biol. Chem. 280 2005 2324 2330
103. R. Hemenger The effects of band shapes on circular dichroism spectra of chromophore aggregates J. Chem. Phys. 68 1978 1722 1728
104. S.M. Kelly, and N.C. Price The use of circular dichroism in the investigation of protein structure and function Curr. Protein Pept. Sci. 1 2000 349 384
105. C.J. Barrow, and A. Yasuda M.G. Zagorski Solution conformations and aggregational properties of synthetic amyloid β-peptides of Alzheimer's disease. Analysis of circular dichroism spectra J. Mol. Biol. 225 1992 1075 1093
106. O.B. Ptitsyn Molten globule and protein folding Adv. Protein Chem. 47 1995 83 229
107. K.A. Dill The meaning of hydrophobicity Science 250 1990 297 298
108. W. Essafi, and M.-N. Spiteri F. Boue Hydrophobic polyelectrolytes in better polar solvent. Structure and chain conformation as seen by SAXS and SANS Macromolecules 42 2009 9568 9580
109. M. Rubinstein, and R.H. Colby Polymer Physics 2003 Oxford University Press Oxford, UK
110. A.P. Minton, and H. Edelhoch Light scattering of bovine serum albumin solutions: extension of the hard particle model to allow for electrostatic repulsion Biopolymers 21 1982 451 458
111. A.P. Minton Effective hard particle model for the osmotic pressure of highly concentrated binary protein solutions Biophys. J. 94 2008 L57 L59
112. A.P. Minton The effective hard particle model provides a simple, robust, and broadly applicable description of nonideal behavior in concentrated solutions of bovine serum albumin and other nonassociating proteins J. Pharm. Sci. 96 2007 3466 3469
113. A.P. Minton A molecular model for the dependence of the osmotic pressure of bovine serum albumin upon concentration and pH Biophys. Chem. 57 1995 65 70
114. R.-J. Roe, and R. Roe Methods of X-Ray and Neutron Scattering in Polymer Science 2000 Oxford University Press New York
115. N. Ise Ordering of ionic solutes in dilute solutions through attraction of similarly charged solutes - a change of paradigm in colloid and polymer chemistry Angew. Chem. Int. Ed. Engl. 25 1986 323 334
116. N. Ise, and T. Okubo M. Fujimura Ordered structure in dilute solutions of poly-L-lysine as studied by small-angle x-ray scattering J. Chem. Phys. 78 1983 541 545
117. M.M. Castellanos, and J.A. Pathak R.H. Colby Explaining the non-Newtonian character of aggregating monoclonal antibody solutions using small-angle neutron scattering Biophys. J. 107 2014 469 476
118. E.J. Yearley, and P.D. Godfrin Y. Liu Observation of small cluster formation in concentrated monoclonal antibody solutions and its implications to solution viscosity Biophys. J. 106 2014 1763 1770
119. W. Essafi, and F. Lafuma C. Williams Anomalous counterion condensation in salt-free hydrophobic polyelectrolyte solutions: osmotic pressure measurements Europhys. Lett. 71 2005 938 942
120. W. Essafi, F. Lafuma, and C. Williams Structure of polyelectrolyte solutions at intermediate charge densities ACS Symposium Series 1994 ACS Publications Washington, DC 278
121. D. Leckband, and J. Israelachvili Intermolecular forces in biology Q. Rev. Biophys. 34 2001 105 267
122. E.E.J.W. Verwey, and J.T.G. Overbeek Theory of the Stability of Lyophobic Colloids 1999 Dover Publications Mineola, New York
123. J. Gao, and F.A. Gomez G.M. Whitesides Determination of the effective charge of a protein in solution by capillary electrophoresis Proc. Natl. Acad. Sci. USA 91 1994 12027 12030
124. Y.R. Gokarn, and E. Kras S. Hershenson Self-buffering antibody formulations J. Pharm. Sci. 97 2008 3051 3066
125. A.R. Karow, S. Bahrenburg, and P. Garidel Buffer capacity of biologics - from buffer salts to buffering by antibodies Biotechnol. Prog. 29 2013 480 492
126. V. Prabhu, and M. Muthukumar Y.B. Melnichenko Polyelectrolyte chain dimensions and concentration fluctuations near phase boundaries J. Chem. Phys. 119 2003 4085 4098
127. V.M. Prabhu Counterion structure and dynamics in polyelectrolyte solutions Curr. Opin. Colloid Interface Sci. 10 2005 2 8
128. M.S. Neergaard, and D.S. Kalonia M. van de Weert Viscosity of high concentration protein formulations of monoclonal antibodies of the IgG1 and IgG4 subclass - prediction of viscosity through protein-protein interaction measurements Eur. J. Pharm. Sci. 49 2013 400 410
129. B.D. Connolly, and C. Petry Y.R. Gokarn Weak interactions govern the viscosity of concentrated antibody solutions: high-throughput analysis using the diffusion interaction parameter Biophys. J. 103 2012 69 78
130. M. Heinen, and F. Zanini M. Antalík Viscosity and diffusion: crowding and salt effects in protein solutions Soft Matter 8 2012 1404 1419
131. D. Rosenbaum, and A. Kulkarni C. Zukoski Protein interactions and phase behavior: sensitivity to the form of the pair potential J. Chem. Phys. 111 1999 9882 9890
132. D. Rosenbaum, P.C. Zamora, and C.F. Zukoski Phase behavior of small attractive colloidal particles Phys. Rev. Lett. 76 1996 150 153
133. H.-X. Zhou, G. Rivas, and A.P. Minton Macromolecular crowding and confinement: biochemical, biophysical, and potential physiological consequences Annu. Rev. Biophys 37 2008 375 397
134. L. Skibinska, and J. Gapinski R. Pecora Effect of electrostatic interactions on the structure and dynamics of a model polyelectrolyte. II. Intermolecular correlations J. Chem. Phys. 110 1999 1794 1800
135. D. Bendedouch, and S.H. Chen J.S. Lin A method for determination of intra- and interparticle structure factors of macroions in solution from small angle neutron scattering J. Chem. Phys. 76 1982 5022 5026
136. V. Bloomfield The structure of bovine serum albumin at low pH Biochemistry 5 1966 684 689
137. N.J. Clark, and H. Zhang J.E. Curtis Small-angle neutron scattering study of a monoclonal antibody using free-energy constraints J. Phys. Chem. B 117 2013 14029 14038
138. M. Carbajal-Tinoco, and R. Ober C. Williams Structural changes and chain conformation of hydrophobic polyelectrolytes J. Phys. Chem. B 106 2002 12165 12169
139. B. Sjöberg, and K. Mortensen Structure and thermodynamics of nonideal solutions of colloidal particles: investigation of salt-free solutions of human serum albumin by using small-angle neutron scattering and Monte Carlo simulation Biophys. Chem. 65 1997 75 83
140. H.J. Angerman, and E. Shakhnovich Freezing in polyampholytes globules: influence of the long-range nature of the interaction J. Chem. Phys. 111 1999 772 785
141. S. Kanai, and M. Muthukumar Phase separation kinetics of polyelectrolyte solutions J. Chem. Phys. 127 2007 244908
142. Y. Kantor, and M. Kardar Excess charge in polyampholytes Europhys. Lett. 27 1994 643 647
143. V.V. Yamakov, and A. Milchev R. Everaers Conformations of random polyampholytes Phys. Rev. Lett. 85 2000 4305 4308
144. J.F. Douglas, and K.F. Freed Competition between hydrodynamic screening ("draining") and excluded volume interactions in an isolated polymer chain Macromolecules 27 1994 6088 6099
145. W.F. Stafford 3rd, and D.A. Yphantis Virial expansions for ideal self-associating systems Biophys. J. 12 1972 1359 1365