Solution Properties of
antibodies:
 Purity
 Conformation
Text book representation
of antibody structure:
Main tool: Analytical Ultracentrifuge
2 types of AUC Experiment:
Sedimentation Velocity
Sedimentation Equilibrium
Centrifugal force

Air
Centrifugal force 
Diffusion
Solvent
Solution
conc, c
conc, c
of movement of
 Rate
boundary  sed. coeff
distance, r
so20,w
1S=10-13sec
STATE
 STEADY
PATTERN
distance, r
FUNCTION ONLY OF
MOL. WEIGHT
PARAMETERS
2 types of AUC Experiment:
Sedimentation Velocity
Sedimentation Equilibrium
Centrifugal force

Air
Centrifugal force 
Diffusion
Solvent
Solution
conc, c
conc, c
of movement of
 Rate
boundary  sed. coeff
distance, r
so20,w
1S=10-13sec
STATE
 STEADY
PATTERN
distance, r
FUNCTION ONLY OF
MOL. WEIGHT
PARAMETERS
Solution Properties of
antibodies:
 Purity
Ultracentrifuge Analysis: IgG4 preparation
Ultracentrifuge Analysis: IgG4 preparation
Solution Properties of
antibodies:
 Conformation –
“Crystallohydrodynamics”
Single Ellipsoids won’t do…
So use the bead model approximation …
Developed by J. Garcia de la Torre and co-workers in Murcia Spain
2 computer programmes: HYDRO & SOLPRO
(please refer to D2DBT7 notes – see the example for lactoglobulin
octamers)
Conventional Bead
model
Bead-shell
model
1st
demonstration
that IgE is cusp
shaped
Bead model, s=7.26 Svedbergs, Rg=
6.8nm
Davies, Harding,
Glennie & Burton, 1990
…by comparing hydrodynamic properties
with those of hingeless mutant IgGMcg
Consistent with function….
Bead model, s=7.26 Svedbergs, Rg= 6.8nm
High Affinity
Receptor
Consistent with function….
High Affinity
Receptor
Better approach is is to use shell models!
Conventional Bead
model
Bead-shell
model
We call this approach “Crystallohydrodynamics”
Crystal structure of
domains
+ solution data for
domains
+ solution data for
intact antibody
= solution structure for
intact antibody
Bead-shell model: Human IgG1
Take Fab' domain crystal structure, and fit a surface
ellipsoid….
PDB File: 1bbj 3.1Å
Fitting algorithm:
ELLIPSE
(J.Thornton, S. Jones
& coworkers)
Ellipsoid semi-axes (a,b,c) = 56.7, 35.6, 23.1.
Ellipsoid axial ratios (a/b, b/c) = (1.60, 1.42)
Hydrodynamic P function = 1.045: see d2dbt8 notes
Now take Fc domain crystal structure, and fit a
surface ellipsoid….
Do the same for Fc
PDB File: 1fc1 2.9Å
Now fit bead model to the ellipsoidal surface
Fab’
P(ellipsoid)=1.045
P(bead) = 1.023
Fc
P(ellipsoid)=1.039
P(bead) = 1.039
Use SOLPRO computer programme: Garcia de la Torre,
Carrasco & Harding, Eur. Biophys. J. 1997
Check the P values are OK
The TRANSLATIONAL FRICTIONAL
RATIO f/fo (see d2dbt8 notes)
f/fo =conformation parameter x hydration term
f/fo =
P
x (1 + d/rovbar)1/3
Can be measured from the diffusion coefficient or from
the sedimentation coefficient
f/fo = constant x {1/vbar1/3} x {1/ M1/3} x {1/Do20,w}
f/fo = constant x {1/vbar1/3} x (1-vbar.ro) x M2/3 x {1/so20,w}
Experimental measurement of f/fo for IgGFab
Experimental measurement of f/fo for IgGFab
Estimation of time-averaged hydration, dapp
for the domains+whole antibody
dapp = {[(f/fo)/P]3 - 1}rovbar
Fab' domain
P(bead model) = 1.023
f/fo (calculated from so20,w and M) = 1.22+0.01
dapp = 0.51 g/g
Fc domain
P(bead model) = 1.039
f/fo (calculated from so20,w and M) = 1.29+0.02
dapp = 0.70 g/g
Intact antibody = 2 Fab's + 1 Fc.
Consensus hydration dapp ~ 0.59 g/g
we can now estimate P(experimental)
for the intact antibody
P(experimental)
=
f/fo x (1 + dapp/rovbar)-1/3
IgG’s: all these compact models give P’s lower than experimental
P=1.107
P=1.112
P=1.118
P=1.121
P=1.122
P=1.143
…so we rule them out!
Models for IgG2 & IgG4. Experimental P=1.22+0.03 (IgG2)
=1.23+0.02 (IgG4)
P = 1.230
P = 1.217
Carrasco, Garcia de la Torre, Davis, Jones, Athwal, Walters
Burton & Harding, Biophys. Chem. 2001
(Fab)2 : P(experimental) = 1.23+0.02
(Fab)2
P=1.208
“Open” models for IgG1 (with hinge)
P(experimental) = 1.26+0.03
P = 1.263
P = 1.264
P=1.215
A P=1.194
P=1.172
C
B
These are coplanar models
for a mutant hingeless
antibody, IgGMcg.
P(experimental) = 1.23+0.03
UNIQUENESS PROBLEM:
Although a particular model may give conformation
parameter P in good agreement with the
ultracentrifuge data, there may be other models
which also give good agreement.
This is the uniqueness or “degeneracy” problem.
To deal with this we need other hydrodynamic data:
Intrinsic viscosity [h] – viscosity increment n
Radius of gyration Rg – Mittelbach factor G
And work is ongoing in the NCMH in conjunction with
other laboratories