1.3.2 Non-interacting
System Analysis
When s-values are invariant with concentration, the sample may be
considered as composed of non-interacting species, a peak in the c
(s) representing a species. The non-interacting species analysis then
allows the determination of independent values for s and D, thus
M and R H , if the system consists of a limited number of species
(typically one or two).
1.3.3 Example of a
Non-interacting Protein
Species
Bovine serum albumin (BSA) will be used as an example of
non-interacting protein species. BSA is a 66-kDa protein, wellknown to form irreversible oligomers. The distribution of monomeric, dimeric, and trimeric species is commonly studied in AUC to
determine the instrument performance [16]. The SV data of two
BSA samples taken before or after a gel filtration step will be
analyzed to illustrate the behavior of heterogeneous versus homogeneous samples.
1.4 Characterization
of Protein
Hetero-association
Using SV
SV offers two significant advantages for the study of interacting
macromolecules: a relatively high hydrodynamic size-dependent
resolution allowing the separation of free and bound species and
the fact that during the experiment, the complexes will remain in a
bath of the free species. Thereby, dissociating complexes can
re-associate during the sedimentation process in a way that will
reflect their equilibrium and kinetic properties [17]. The standard
methods of analyzing SV data to obtain association constants
between interacting macromolecules are Lamm equation fitting
and c(s)-based isotherm analysis. Practically, the determination of
equilibrium and kinetic binding constants requires to run multiple
experiments at concentrations that cover a range of about 1/10 to
10 K d . It is advisable to make dilution or titration series to prepare
samples. In this way, these values can be refined with added constraints linking the concentrations of different experiments. In
dilution series of stock mixtures, the molar ratio is constant and
can be fixed or refined as a single global parameter. In titration
series, one protein is kept at low constant concentration in each
sample while the concentration of the binding partner varies in a
wide range.
1.4.1 Lamm Equation
Fitting to Characterize
Protein Hetero-association
Current computational strategies allow for direct boundary modeling of SV data for reacting systems with a set of coupled Lamm
equations describing all the species participating in the interaction
combined with information on the equilibrium association constant and reaction kinetics [18, 19]. It is noteworthy that only
this approach allows to estimate the kinetic off-rate constant k off
of interactions (see Note 2). This direct boundary fitting method
has been implemented in SEDPHAT with different binding models
available. Compared to the SV isotherm analysis, this analysis can be
conducted when only a few SV data sets are available (minimum
Heterogeneity and Affinity Interaction Analysis by Sedimentation Velocity
159
System Analysis
When s-values are invariant with concentration, the sample may be
considered as composed of non-interacting species, a peak in the c
(s) representing a species. The non-interacting species analysis then
allows the determination of independent values for s and D, thus
M and R H , if the system consists of a limited number of species
(typically one or two).
1.3.3 Example of a
Non-interacting Protein
Species
Bovine serum albumin (BSA) will be used as an example of
non-interacting protein species. BSA is a 66-kDa protein, wellknown to form irreversible oligomers. The distribution of monomeric, dimeric, and trimeric species is commonly studied in AUC to
determine the instrument performance [16]. The SV data of two
BSA samples taken before or after a gel filtration step will be
analyzed to illustrate the behavior of heterogeneous versus homogeneous samples.
1.4 Characterization
of Protein
Hetero-association
Using SV
SV offers two significant advantages for the study of interacting
macromolecules: a relatively high hydrodynamic size-dependent
resolution allowing the separation of free and bound species and
the fact that during the experiment, the complexes will remain in a
bath of the free species. Thereby, dissociating complexes can
re-associate during the sedimentation process in a way that will
reflect their equilibrium and kinetic properties [17]. The standard
methods of analyzing SV data to obtain association constants
between interacting macromolecules are Lamm equation fitting
and c(s)-based isotherm analysis. Practically, the determination of
equilibrium and kinetic binding constants requires to run multiple
experiments at concentrations that cover a range of about 1/10 to
10 K d . It is advisable to make dilution or titration series to prepare
samples. In this way, these values can be refined with added constraints linking the concentrations of different experiments. In
dilution series of stock mixtures, the molar ratio is constant and
can be fixed or refined as a single global parameter. In titration
series, one protein is kept at low constant concentration in each
sample while the concentration of the binding partner varies in a
wide range.
1.4.1 Lamm Equation
Fitting to Characterize
Protein Hetero-association
Current computational strategies allow for direct boundary modeling of SV data for reacting systems with a set of coupled Lamm
equations describing all the species participating in the interaction
combined with information on the equilibrium association constant and reaction kinetics [18, 19]. It is noteworthy that only
this approach allows to estimate the kinetic off-rate constant k off
of interactions (see Note 2). This direct boundary fitting method
has been implemented in SEDPHAT with different binding models
available. Compared to the SV isotherm analysis, this analysis can be
conducted when only a few SV data sets are available (minimum
Heterogeneity and Affinity Interaction Analysis by Sedimentation Velocity
159