Introduction
By identifying the change in viscosity of a solution upon addition of a protein, a parameter known as the intrinsic viscosity
can be determined for that protein. The intrinsic viscosity of a protein is a value partially dependent on protein conformation.
From the intrinsic viscosity value, a viscosity increment value can be determined, which is a size-independent value dependent
solely upon the shape of a protein. The higher the viscosity increment, the more extended is the protein that it represents.
Antibody molecules are proteins, which play vital roles in the body's immune system. They can be split into five classes:
IgM, IgG, IgA, IgD and IgE which, although they each have unique structural and functional properties, all have the same basic
structure. Some of these classes of antibodies can be further sub-divided into subclasses. The IgG class, for example, consists
of four subclasses: IgG1, IgG2, IgG3 and IgG4.
The subclass IgG3 antibodies were investigated in this study because of their unusually long "hinge" region that gives this
antibody the extra flexibility that is vital for its function. 
Figure 1: Schematic diagram of (a) IgG3wt and (b) IgG3m15. Two 15 amino acid segments and one 17 amino acid segment, present
in the hinge of IgG3wt, are absent in the hinge of IgG3m15.
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The two chimeric IgG3 molecules investigated in this study were a wild type IgG3 with the full length 62 amino acid hinge
[Figure 1(a)], and a hinge-deleted mutant IgG3 with a 15 amino acid hinge [Figure 1(b)], developed by Michaelsen and coworkers.1These antibodies were developed to aid understanding of the functional significance of the extended IgG3 hinge. This study
aimed to identify the conformational differences caused by this hinge elongation, and relate these differences to their differing
abilities to activate the complement cascade.
High-resolution techniques such as x-ray crystallography and nuclear magnetic resonance (NMR) are commonly used for protein
structure determination. Studies of the solution conformations of antibodies have proved complicated, however, with NMR having
an upper molecular weight cut off of ~50000 Da, whilst IgG3 has a molecular weight of ~160000 Da. Additionally, crystallographic
structures of intact IgG molecules tend to have poorly characterized diffraction patterns around the hinge and Fc region of
the molecule because of the flexibility of the molecules.
An alternative approach to studying antibody conformation is to look at hydrodynamic parameters. The intrinsic viscosity parameter
was chosen to investigate the solution conformations of IgG3 molecules in this study. It was hoped that by obtaining the intrinsic
viscosity values of the two antibodies and subsequently creating models based on this shape information, conclusions could
be drawn on the differences in their solution conformations. An advantage of using a solution technique is that models represent
the structure of the protein in a dilute solution, which is more likely to relate to its conformation in vivo.
Background
Combining size exclusion chromatography (SEC) with light-scattering (LS), viscometer and refractive index (RI) detectors is
a powerful tool for protein characterization. This approach provides not only molecular weights (M) and the intrinsic viscosity ([η]) but also quantifies aggregates, determines hydrodynamic radii (Rh) and provides conformation information from a single SEC run. The advantage of this combination of detectors is that the
sample properties can be derived directly from the detector signals. The signals of the individual detectors correspond to
[η] = intrinsic viscosity
c = concentration
dn/dc = refractive index increment, kRI, Visc, LS = detector constants
The refractive index detector determines the refractive index increment, which is necessary for the calculation of the molecular
weight from the LS signal. The intrinsic viscosity is obtained from the viscometer signal after the concentration is appropriately
taken into consideration.2
The intrinsic viscosity of a protein is a function of shape, hydration and flexibility. If it is assumed that the hydration
of an antibody is known, the shape information that can be derived from an intrinsic viscosity value can be used to model
the solution conformation of a protein. The partial specific volume is the anhydrous volume per unit mass of a molecule dissolved in a solution. The viscosity increment
is a "universal shape parameter",4,5 meaning its value is dependent solely on shape.
Additionally from molecular weight and intrinsic viscosity, the hydrodynamic radius Rh of the protein can be obtained. This parameter is determined using Einstein's equation for hard spheres,6,7 which states that hydrodynamic volume (Vh) is proportional to the product of molecular weight and intrinsic viscosity (Equation 5). The hydrodynamic radius is obtained
from a combination of Vh and Equation 5, as shown in Equation 6.9
NA= Avogadro's number
Rh depends strongly on shape and this parameter can be used to differentiate between spherical or compact proteins and more
elongated proteins.
Modelling of Antibody Structure
Universal shape parameters such as the viscosity increment can be used to model the conformation parameters. Previous studies8, 9 have determined solution conformations of antibodies using a universal shape parameter obtained from the sedimentation coefficient
— the Perrin function. By representing the Fab and Fc domains as ellipsoids and altering the antibody inter-domain angles,
agreement was found between the experimental Perrin functions of the proteins and the theoretical Perrin functions from the
models.
The same approach can be applied to modelling based on the viscosity increment, to find the solution conformations of the
two IgG3 antibodies.
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