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Long- and Short-Range Electrostatic Interactions Affect the Rheology of Highly Concentrated Antibody Solutions

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To explain the differences in protein-protein interactions (PPI) of concentrated versus dilute formulations of a model antibody.


High frequency rheological measurements from pH 3.0 to 12.0 quantitated viscoelasticity and PPI at high concentrations. Dynamic light scattering (DLS) characterized PPI in dilute solutions.


For concentrated solutions at low ionic strength, the storage modulus, a viscosity component and a measure of PPI, is highest at the isoelectric point (pH 9.0) and lowest at pH 5.4. This profile flattens at higher ionic strength but not completely, indicating PPI consist of long-range electrostatics and other short-range attractions. At low concentrations, PPI are near zero at pI but become repulsive as the pH is shifted. Higher salt concentrations completely flatten this profile to zero, indicating that these PPI are mainly electrostatic.


This discrepancy occurs because long-range interactions are significant at low concentrations, whereas both long- and short-range interactions are significant at higher concentrations. Computer modeling was used to calculate antibody properties responsible for long- and short-range interactions, i.e. net charge and dipole moment. Charge-charge interactions are repulsive while dipole-dipole interactions are attractive. Their net effect correlated with the storage modulus profile. However, only charge-charge repulsions correlated with PPI determined by DLS.

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B 22 :

second osmotic virial coefficient

B′ 22 :

second osmotic virial coefficient multiplied by solute molecular weight


circular dichroism


dynamic light scattering

E B22 :

pairwise energetic interaction term

G′ :

storage modulus of complex viscosity

G″ :

loss modulus of complex viscosity


immunoglobulin G

k D :

interaction parameter from DLS


monoclonal antibody


magnitude of complex viscosity


Protein Databank


protein-protein interaction(s)

V B22 :

excluded volume term


  1. Fulton AB. How crowded is the cytoplasm? Cell. 1982;30:345–7.

    Article  CAS  PubMed  Google Scholar 

  2. Zimmerman SB, Minton AP. Macromolecular crowding: biochemical, biophysical, and physiological consequences. Annu Rev Biophys Biomol Struct. 1993;22:7–65.

    Article  Google Scholar 

  3. Minton AP. Influence of macromolecular crowding upon the stability and state of association of proteins: Predictions and observations. J Pharm Sci. 2005;94:1668–75.

    Article  CAS  PubMed  Google Scholar 

  4. Wang W, Singh S, Zeng DL, King K, Nema S. Antibody structure, instability, and formulation. J Pharm Sci. 2006;96:1–26.

    Article  Google Scholar 

  5. Shire SJ, Shahrokh Z, Liu J. Challenges in the development of high protein concentration formulations. J Pharm Sci. 2004;2004:1390–402.

    Article  Google Scholar 

  6. Liu J, Nguyen MD, Andya JD, Shire SJ. Reversible self-association increases the viscosity of a concentrated monoclonal antibody in aqueous solution. J Pharm Sci. 2005;94:1928–40.

    Article  CAS  PubMed  Google Scholar 

  7. Saluja A, Kalonia DS. Nature and consequences of protein-protein interactions in high protein concentration solutions. Int J Pharm. 2008;358:1–15.

    Article  CAS  PubMed  Google Scholar 

  8. Zhang J, Liu XY. Effect of protein–protein interactions on protein aggregation kinetics. J Chem Phys. 2003;119:10972–6.

    Article  CAS  Google Scholar 

  9. Kanai S, Liu J, Patapoff TW, Shire SJ. Reversible self-association of a concentrated monoclonal antibody solution mediated by Fab-Fab interaction that impacts solution viscosity. J Pharm Sci. 2008;97:4219–27.

    Article  CAS  PubMed  Google Scholar 

  10. Meehan S, Berry Y, Luisi B, Dobson CM, Carver JA, MacPhee CE. Amyloid fibril formation by lens crystallin proteins and its implications for cataract formation. J Biol Chem. 2004;279:3413–9.

    Article  CAS  PubMed  Google Scholar 

  11. Harper JD, Lansbury PT. Models of amyloid seeding in Alzheimer’s disease and scrapie: mechanistic truths and physiological consequences of the time-dependent solubility of amyloid proteins. Annu Rev Biochem. 1997;66:385–407.

    Article  CAS  PubMed  Google Scholar 

  12. Koo EH, Lansbury PT, Kelly JW. Amyloid diseases: abnormal protein aggregation in neurodegeneration. Proc Natl Acad Sci USA. 1999;96:9989–90.

    Article  CAS  PubMed  Google Scholar 

  13. Ganeval D, Noël LH, Preud’homme JL, Droz D, Grünfeld JP. Light-chain deposition disease: its relation with AL-type amyloidosis. Kidney Int. 1984;26:1–9.

    Article  CAS  PubMed  Google Scholar 

  14. Buxbaum JN, Chuba JV, Hellman GC, Solomon A, Gallo GR. Monoclonal immunoglobulin deposition disease: light chain and light and heavy chain deposition diseases and their relation to light chain amyloidosis. Clinical features, immunopathology, and molecular analysis. Ann Intern Med. 1990;112:455–64.

    CAS  PubMed  Google Scholar 

  15. Zimm BH. Applications of the methods of molecular distribution to solutions of large molecules. J Chem Phys. 1946;14:164–79.

    Article  CAS  Google Scholar 

  16. Teraoka I. Polymer solutions: an introduction to physical properties. New Jersey, USA: Wiley-IEEE; 2002.

    Google Scholar 

  17. George A, Chiang Y, Guo B, Arabshahi A, Cai Z, Wilson WW. Second virial coefficient as predictor in protein crystal growth. Methods Enzymol. 1997;276:100–10.

    Article  CAS  Google Scholar 

  18. Saluja A, Kalonia DS. Measurement of fluid viscosity at microliter volumes using quartz impedance analysis. AAPS PharmSciTech. 2004;5:e47.

    Article  PubMed  Google Scholar 

  19. Saluja A, Kalonia DS. Application of ultrasonic shear rheometer to characterize rheological properties of high protein concentration solutions at microliter volume. J Pharm Sci. 2005;94:1161–8.

    Article  CAS  PubMed  Google Scholar 

  20. Saluja A, Badkar AV, Zeng DL, Nema S, Kalonia DS. Application of high-frequency rheology measurements for analyzing protein-protein interactions in high protein concentration solutions using a model monoclonal antibody (IgG2). J Pharm Sci. 2006;95:1967–83.

    Article  CAS  PubMed  Google Scholar 

  21. Hackley VA, Ferraris CF. Guide to rheological nomenclature for liquid-based particle systems. Maryland, USA: NIST; 2001.

    Google Scholar 

  22. Saluja A, Badkar AV, Zeng DL, Nema S, Kalonia DS. Ultrasonic storage modulus as a novel parameter for analyzing protein-protein interactions in high protein concentration solutions: correlation with static and dynamic light scattering measurements. Biophys J. 2007;92:234–44.

    Article  CAS  PubMed  Google Scholar 

  23. Hiemenz PC, Rajagopalan R. Principles of colloid and surface chemistry. New York, USA: Marcel Dekker; 1997.

    Google Scholar 

  24. Curtis RA, Prausnitz JM, Blanch HW. Protein-protein and protein-salt interactions in aqueous protein solutions containing concentrated electrolytes. Biotechnol Bioeng. 1998;57:11–21.

    Article  CAS  PubMed  Google Scholar 

  25. Elcock AH, McCammon JA. Calculation of weak protein-protein interactions: the pH dependence of the second virial coefficient. Biophys J. 2001;80:613–25.

    Article  CAS  PubMed  Google Scholar 

  26. Torshin IY. Bioinformatics in the post-genomic era: the role of biophysics. New York, USA: Nova Science; 2006.

    Google Scholar 

  27. Al-Shakhshira RH, Regnierb FE, Whitec JL, Hema SL. Contribution of electrostatic and hydrophobic interactions to the adsorption of proteins by aluminium-containing adjuvants. Vaccine. 1995;13:41–4.

    Article  Google Scholar 

  28. Harris LJ, Larson SB, Hasel KW, McPherson A. Refined structure of an intact IgG2a monoclonal antibody. Biochem. 1997;36:1581–97.

    Article  CAS  Google Scholar 

  29. RCSB Protein Data Bank. (accessed December 2008).

  30. Hyperchem Professional 7.5.1 (Hypercube, Inc., Gainesville, Florida, USA).

  31. Discovery Studio 2.1 (Accelrys, Inc., San Diego, California, USA).

  32. Nezlin R. The immunoglobulins: structure and function. London, UK: Academic; 1998.

    Google Scholar 

  33. Li H, Robertson AD, Jensen JH. Very fast empirical prediction and interpretation of protein pKa values. Proteins. 2005;61:704–21.

    Article  CAS  PubMed  Google Scholar 

  34. Bas DC, Rogers DM, Jensen JH. Very fast prediction and rationalization of pKa values for protein-ligand complexes. Proteins. 2008;73:765–83.

    Article  CAS  PubMed  Google Scholar 

  35. Brooks BR, Bruccoleri RE, Olafson BD, States DJ, Swaminathan S, Karplus M. CHARMM: a program for macromolecular energy, minimization, and dynamics calculations. J Comp Chem. 1983;4:187–17.

    Article  CAS  Google Scholar 

  36. Gilson MK, Gilson HSR, Potter MJ. Fast assignment of accurate partial atomic charges. An electronegativity equalization method that accounts for alternate resonance forms. J Chem Inf Comput Sci. 2003;43:1982–97.

    CAS  PubMed  Google Scholar 

  37. Chen W, Huang J, Gilson MK. Identification of symmetries in molecules and complexes. J Chem Inf Comput Sci. 2004;44:1301–13.

    CAS  PubMed  Google Scholar 

  38. Felder CE, Prilusky J, Silman I, Sussman JL. A server and database for dipole moments of proteins. Nucleic Acids Res. 2007;35:W512–21.

    Article  PubMed  Google Scholar 

  39. Baker NA, Sept D, Joseph S, Holst MJ, McCammon JA. Electrostatics of nanosystems: Application to microtubules and the ribosome. Proc Natl Acad Sci USA. 2001;98:10037–41.

    Article  CAS  PubMed  Google Scholar 

  40. Dolinsky TJ, Nielsen JE, McCammon JA, Baker NA. PDB2PQR: an automated pipeline for the setup, execution, and analysis of Poisson-Boltzmann electrostatics calculations. Nuc Acids Res. 2004;32:W665–7.

    Article  CAS  Google Scholar 

  41. Humphrey W, Dalke A, Schulten K. VMD—visual molecular dynamics. J Molec Graphics. 1996;14:33–8.

    Article  CAS  Google Scholar 

  42. JAVA 1.4.2 programming language (Sun Microsystems, Inc., Santa Clara, California, USA).

  43. Shaw KL, Grimsley GR, Yakovlev GI, Makarov AA, Pace CN. The effect of net charge on the solubility, activity, and stability of ribonuclease Sa. Protein Sci. 2001;10:1206–15.

    Article  CAS  PubMed  Google Scholar 

  44. Neal BL, Asthagiri D, Lenhoff AM. Molecular origins of osmotic second virial coefficients of proteins. Biophys J. 1998;75:2469–77.

    Article  CAS  PubMed  Google Scholar 

  45. Papp E, Fricsovszky G, Meszéna G. Electrodichroism of purple membrane. Biophys J. 1986;49:1089–100.

    Article  CAS  PubMed  Google Scholar 

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The authors thank Pfizer Inc. for donating the mAb for this study and for partial financial support of this work.

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Correspondence to Devendra S. Kalonia.

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Chari, R., Jerath, K., Badkar, A.V. et al. Long- and Short-Range Electrostatic Interactions Affect the Rheology of Highly Concentrated Antibody Solutions. Pharm Res 26, 2607–2618 (2009).

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