Protein Structural Conformation and Not Second Virial Coefficient Relates to Long-Term Irreversible Aggregation of a Monoclonal Antibody and Ovalbumin in Solution

Purpose

The purpose of the study was to investigate the relationship of the second virial coefficient, B ₂₂, to the extent of irreversible protein aggregation upon storage.

Methods

A monoclonal antibody and ovalbumin were incubated at 37°C (3 months) under various solution conditions to monitor the extent of aggregation. The B ₂₂ values of these proteins were determined under similar solution conditions by a modified method of flow-mode static light scattering. The conformation of these proteins was studied using circular dichroism (CD) spectroscopy and second-derivative Fourier transform infrared spectroscopy.

Results

Both proteins readily aggregated at pH 4.0 (no aggregation observed at pH 7.4); the extent of aggregation varied with the ionic strength and the presence of cosolutes (sucrose, glycine, and Tween 80). Debye plots of the monoclonal antibody showed moderate attractive interactions at pH 7.4, whereas, at pH 4.0, nonlinear plots were obtained, indicating self-association. CD studies showed partially unfolded structure of antibody at pH 4.0 compared with that at pH 7.4. In the case of ovalbumin, similar B ₂₂ values were obtained in all solution conditions irrespective of whether the protein aggregated or not. CD studies of ovalbumin indicated the presence of a fraction of completely unfolded as well as partially unfolded species at pH 4.0 compared with that at pH 7.4.

Conclusions

The formation of a structurally altered state is a must for irreversible aggregation to proceed. Because this aggregation-prone species could be an unfolded species present in a small fraction compared with that of the native state or it could be a partially unfolded state whose net interactions are not significantly different compared with those of the native state, yet the structural changes are sufficient to lead to long-term aggregation, it is unlikely that B ₂₂ will correlate with long-term aggregation.

Appendix

Model for Self-Association and Data Analysis of Nonlinear Debye Plots

A monomer–dimer equilibrium is written as

$$ M + M{\mathop \Leftrightarrow \limits^{K_{{\dim }} } }D $$

(13)

where the association constant K _dim is defined as

$$ K_{{{\text{dim}}}} = \frac{{{\left[ {c_{{\text{d}}} } \right]}}} {{{\left[ {c_{{\text{m}}} } \right]}^{2} }} $$

(14)

where [c _d] is the molar concentration of the dimer and [c _m] is the molar concentration of the monomer. The total molar concentration [c _t] of the protein can be written in terms of the monomer concentration as

$$ {\left[ {c_{{\text{t}}} } \right]} = {\left[ {c_{{\text{m}}} } \right]} + 2{\left[ {c_{{\text{d}}} } \right]} $$

(15)

Combining Eqs. (13) and (14), solving the resulting quadratic equation for positive solution of [c _m] and [c _d], and converting molar concentration to grams per milliliter, the monomer and dimer concentrations can be written as

$$ c_{{{\text{monomer}}}} = \frac{{ - 1 + {\left( {1 + {8000K_{{{\text{dim}}}} c_{{\text{t}}} } \mathord{\left/ {\vphantom {{8000K_{{{\text{dim}}}} c_{{\text{t}}} } {M_{{\text{m}}} }}} \right. \kern-\nulldelimiterspace} {M_{{\text{m}}} }} \right)}^{{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 2}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{$2$}}} }} {{{4000K_{{{\text{dim}}}} } \mathord{\left/ {\vphantom {{4000K_{{{\text{dim}}}} } {M_{{\text{m}}} }}} \right. \kern-\nulldelimiterspace} {M_{{\text{m}}} }}} $$

(16)

$$ c_{{{\text{dimer}}}} = \frac{{1 + {4000K_{{{\text{dim}}}} c_{{\text{t}}} } \mathord{\left/ {\vphantom {{4000K_{{{\text{dim}}}} c_{{\text{t}}} } {M_{{\text{m}}} }}} \right. \kern-\nulldelimiterspace} {M_{{\text{m}}} } - {\left( {1 + {8000K_{{{\text{dim}}}} c_{{\text{t}}} } \mathord{\left/ {\vphantom {{8000K_{{{\text{dim}}}} c_{{\text{t}}} } {M_{{\text{m}}} }}} \right. \kern-\nulldelimiterspace} {M_{{\text{m}}} }} \right)}^{{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 2}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{$2$}}} }} {{{4000K_{{{\text{dim}}}} } \mathord{\left/ {\vphantom {{4000K_{{{\text{dim}}}} } {M_{{\text{m}}} }}} \right. \kern-\nulldelimiterspace} {M_{{\text{m}}} }}} $$

(17)

For an associating system, the Debye equation is written as

$$ \frac{{Kc_{{\text{t}}} }} {{R_{{90}} }} = {\left( {\frac{1} {{M_{{{\text{av}}}} }} + Bc_{{\text{t}}} } \right)} $$

(18)

where M _av is the weight average molecular weight of all the species present in the solution. Note that B ₂₂ has been substituted with the term B to represent the nonideality arising from monomer–monomer, monomer–dimer, and dimer–dimer interactions. For an associating system, the change in the chemical potential of the solvent with solute concentration is written as (50)

$$ \frac{{\partial \mu _{1} }} {{\partial c_{{\text{t}}} }} = \frac{{\partial c_{{\text{m}}} }} {{\partial c_{{\text{t}}} \cdot M_{{\text{m}}} }} + \frac{{\partial c_{{\text{d}}} }} {{\partial c_{{\text{t}}} \cdot 2M_{{\text{m}}} }} + \frac{{\partial {\left( {Bc_{{\text{t}}} ^{2} } \right)}}} {{\partial c_{{\text{t}}} }} $$

(19)

Substituting for c _m and c _d from Eqs. (16) and (17), taking partial derivatives, and using the result in the derivation of the Rayleigh's light scattering equation, the following Debye equation is obtained:

$$ \frac{{Kc_{t} }} {{R_{{90}} }} = \frac{{{\left( {1 + {8000K_{{\dim }} c_{t} } \mathord{\left/ {\vphantom {{8000K_{{\dim }} c_{t} } {M_{m} }}} \right. \kern-\nulldelimiterspace} {M_{m} }} \right)}^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} + 1}} {{2{\left( {{1 + 8000K_{{\dim }} c_{t} } \mathord{\left/ {\vphantom {{1 + 8000K_{{\dim }} c_{t} } {M_{m} }}} \right. \kern-\nulldelimiterspace} {M_{m} }} \right)}^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} M_{m} }} + Bc_{t} $$

(20)

Equation (20) was used to fit the curved Debye plots for the parameters K _dim, M _m, and B.