Analytical
ultracentrifugation
Biomolecular interactions
Jan Komárek
S2004 Methods to study biomolecular interactions – classical versus modern
SELF-ASSOCIATION (oligomerization)
e.g. A + A A2
HETERO-ASSOCIATION
e.g. A + B AB
Interacting systems on AUC
What can be determined?
• stoichiometry (reaction scheme)
• affinity - Kd
• shape of the complex
- two or more different proteins
- protein-DNA
- protein-polysaccharide
- protein - small molecule
- two or more identical molecules
S2004 Methods to study biomolecular interactions – classical versus modern
Models in SEDPHAT
A + A A2
A + B AB
A + A + A A3
nA An
A A2 A4
A A4 A8
A + B + B ABB
A + B + B + B ABBB
A + B + C ABC
A + B + C …
competing B and C for A
(A+A) + (B+B) …
heterodimer of homodimers
(A+A) + B + B …
self-associating A with two sites for B
A + B + B + C + C …
A + B + B + C …
A + B + B ABB
2 non-symetrical sites
S2004 Methods to study biomolecular interactions – classical versus modern
Affinity range of biomolecular interactions studied by AUC
10-12 10-10 10-8 10-6 10-4 10-2
Kd [M]
very strong interactions
moderate-strength
interactions
weak/very weak
interactions
very low concentration,
dye-labeled proteins
proteins 0.1 - 5 mg/ml higher concentrations
necessary (≥ 5 mg/ml)
– complications due
to non-ideality effects
FDS IF
ABS
S2004 Methods to study biomolecular interactions – classical versus modern
Dissociation constant (Kd)
frequently x = y = 1:
AxBy xA + yB Kd =
[A]x·[B]y
[AxBy]
AB A + B Kd =
[A]·[B]
[AB]
• equilibrium constant that measures the propensity of a larger object to dissociate
reversibly to smaller components
• commonly used to describe the affinity between the molecules (lower Kd ~ higher affinity)
• inverse of association consant (1/Ka)
S2004 Methods to study biomolecular interactions – classical versus modern
Dissociation constant (Kd)
When [A] = Kd, then [B] = [AB] ! mass conservation:
[A]0 = [A] + [AB]
[B]0 = [B] + [AB]
AB A + B Kd =
[A]·[B]
[AB]
For a 2-component system, Kd has concentration units (M)
S2004 Methods to study biomolecular interactions – classical versus modern
Effect of concentration on species´ populations
total conc.
of A
% of A as
a monomer
% of A as
a dimer
0.1 uM 85 15
0.3 uM 70 30
1 uM 50 50
3 uM 33 67
10 uM 20 80
total conc.
of A
total conc.
of B
% of A in
a free form
% of A in
a complex
% of B in
a free form
% of B in
a complex
3 uM 0.1 uM 98 2 26 74
3 uM 0.3 uM 92 8 26 74
3 uM 1 uM 77 23 30 70
3 uM 3 uM 43 57 43 57
3 uM 10 uM 12 88 74 26
Self-association
A + A A2
Kd = 1 uM
Hetero-association
A + B AB
Kd = 1 uM
Populations changing in the concentration-dependent manner…
Below Kd, equilibrium shifted towards smaller oligomer (self-assoc.) /free species (hetero-assoc.)
Above Kd, equilibrium shifted towards higher oligomer (self-assoc.) /complex (hetero-assoc.)
S2004 Methods to study biomolecular interactions – classical versus modern
Determination of Kd
total conc.
of A
% of A as
a monomer
% of A as
a dimer
0.1 uM 85 15
0.3 uM 70 30
1 uM 50 50
3 uM 33 67
10 uM 20 80
total conc.
of A
total conc.
of B
% of A in
a free form
% of A in
a complex
% of B in
a free form
% of B in
a complex
3 uM 0.1 uM 98 2 26 74
3 uM 0.3 uM 92 8 26 74
3 uM 1 uM 77 23 30 70
3 uM 3 uM 43 57 43 57
3 uM 10 uM 12 88 74 26
Self-association
A + A A2
Kd = 1 uM
Hetero-association
A + B AB
Kd = 1 uM
→ Dilution series
Using a broad concentration range (one order above and below Kd) for accurate Kd
determination!
→ Titration series (A with B and/or B with A)
Dilution series of a purified complex
10x
10x
S2004 Methods to study biomolecular interactions – classical versus modern
Question: Any idea on Kd of BSA?
raw SV data:
48,000 rpm, 20 °C
IF detection
BSA, 1 mg/ml
PBS buffer, pH 7.5
monomer
78 %
dimer
13 %
trimer
5 %
c(s) distribution of 16 uM BSA:
S2004 Methods to study biomolecular interactions – classical versus modern
Question: Any idea on Kd of BSA?
raw SV data:
48,000 rpm, 20 °C
IF detection
BSA, 1 mg/ml
PBS buffer, pH 7.5
monomer
78 %
dimer
13 %
trimer
5 %
c(s) distribution of 16 uM BSA:
BSA IS NOT REVERSIBLE
SELF-ASSOCIATING SYSTEM
ALWAYS MEASURE MULTIPLE
CONCENTRATIONS!!!
S2004 Methods to study biomolecular interactions – classical versus modern
General workflow
STEP 1: Performing SV experiment at different loading concentration/ molar ratios
+ comparing c(s) distributions
Is there a reversible interaction?
- emerging of new peaks in c(s) distribution?
- shifts in peak position with protein concentration?
- changes in peak areas with protein concentration?
BSA His kinase
x
S2004 Methods to study biomolecular interactions – classical versus modern
General workflow
STEP 1: Performing SV experiment at different loading concentration/ molar ratios
+ comparing c(s) distributions
Fast or slow interaction?
SLOW INTERACTIONS FAST INTERACTIONS
(kd < 10-3-10-4 s-1) (kd > 10-3 s-1)
2 A A2 2 A A2
Rapid interconversion between
complex and free species, peak
position change with increasing
concentration
Sedimenting species stable, peak
positions constant, relative peak areas
change with increasing concentration
0.1 uM
0.3 uM
1 uM
3 uM
10 uM
Kd = 1 uM
kd = 5·10-5 s-1
0.1 uM
0.3 uM
1 uM
3 uM
10 uM
Kd = 1 uM
Brown, 2008
Self-association(monomer-dimer)
S2004 Methods to study biomolecular interactions – classical versus modern
General workflow
STEP 1: Performing SV experiment at different loading concentration/ molar ratios
+ comparing c(s) distributions
Fast kinetics system:
Sedimentation of A, B and complex AB
A =
B =
AB =
Schuck, 2010
S2004 Methods to study biomolecular interactions – classical versus modern
General workflow
STEP 1: Performing SV experiment at different loading concentration/ molar ratios
+ comparing c(s) distributions
Fast or slow interaction?
SLOW INTERACTIONS FAST INTERACTIONS
(kd < 10-3-10-4 s-1) (kd > 10-3 s-1)
A + B AB A + B AB
Rapid interconversion between
complex and free species, peak
position change with increasing
concentration
Sedimenting species stable, peak
positions constant, relative peak areas
change with increasing concentration
Hetero-association(A+B→AB)
0.1 uM
0.3 uM
1 uM
3 uM
10 uM
Kd = 1 uM
Brown, 2008
0.1 uM
0.3 uM
1 uM
3 uM
10 uM
Kd = 1 uM
kd = 5·10-5 s-1
S2004 Methods to study biomolecular interactions – classical versus modern
General workflow
STEP 2: Analyzing the interaction, determination of Kd
SEDIMENTATION VELOCITY
- direct fitting of sedimentation boundaries
- analysis with binding isotherms
- multi-signal SV (MSSV technique) – hetero-associations only
SEDIMENTATION EQUILIBRIUM
Direct fitting approach
Lamm equation for interacting system (1:1 hetero-association):
q – chemical flux, 1 and 2 are free species, 3 is a complex
Balbo, 2006
• necessary to globally fit the data obtained
at different concentrations/molar ratios
• difficult to apply in practice
• high requirements on sample purity
Analysis with binding isotherms
ISOTHERM – „dependence of a physical property of a mixture of interacting components
on the loading concentrations (keeping all other parameters constant, including temperature)“
Some macroscopis observations of a mixture are dependent on the relative
concentration of free and complex species, and a set of measurements in a
concentration series generate an isotherm that can be analyzed to determine
reaction scheme and Kd
sw – weight-averaged s-value of the whole system as a function of loading concentration of
sample (integration of distribution over all species participating in interaction)
sw,fast – weight-averaged s-value of the reaction boundary as a function of loading
concentration (fast kinetics only)
pop – concentration-dependent shift of peak areas (populations)
Analysis with binding isotherms:
• most frequently used approach, more tolerant to impurities
• information extracted from the c(s) distributions
Analysis with binding isotherms
Example of analysis – A + B AB with slow kinetics
sw
sw isotherm
pop isotherms
popA popB popAB
fitting of data to A+B AB
model for binding isotherms
Kd = 3.4 μM
Different concentrations of proteins – dilution serie, A and B in equimolar concentrations
Analysis with binding isotherms
Example of analysis – A + B AB with fast kinetics
sw
sw and sw,fast isotherm
pop isothermspopslow popreac
Kd = 12.2 μM
sw, fast
Different concentrations of proteins – dilution serie, A and B in equimolar concentrations
fitting of data to A+B AB
model for binding isotherms
Real example – Kd determination
His kinase
Oligomerization of histidine kinase:
Example of analysis of an interacting system
Sedimentation velocity AUC:
20º C, 48000 rpm, ABS detection (230 nm or 280 nm)
20 mM Tris/HCl, 100 mM NaCl, pH 7.4
0.05 mg/ml SV experiment performed at
different loading concentrations of
protein.
The distributions do not overlay,
there is a shift to higher s with
increasing concentration.
= sign of reversible interactions
0.15 mg/ml
Oligomerization of histidine kinase:
Example of analysis of an interacting system
Sedimentation velocity AUC:
20º C, 48000 rpm, ABS detection (230 nm or 280 nm)
20 mM Tris/HCl, 100 mM NaCl, pH 7.4
SV experiment performed at
different loading concentrations of
protein.
The distributions do not overlay,
there is a shift to higher s with
increasing concentration.
= sign of reversible interactions
0.45 mg/ml
Oligomerization of histidine kinase:
Example of analysis of an interacting system
Sedimentation velocity AUC:
20º C, 48000 rpm, ABS detection (230 nm or 280 nm)
20 mM Tris/HCl, 100 mM NaCl, pH 7.4
SV experiment performed at
different loading concentrations of
protein.
The distributions do not overlay,
there is a shift to higher s with
increasing concentration.
= sign of reversible interactions
0.80 mg/ml
Oligomerization of histidine kinase:
Example of analysis of an interacting system
Sedimentation velocity AUC:
20º C, 48000 rpm, ABS detection (230 nm or 280 nm)
20 mM Tris/HCl, 100 mM NaCl, pH 7.4
SV experiment performed at
different loading concentrations of
protein.
The distributions do not overlay,
there is a shift to higher s with
increasing concentration.
= sign of reversible interactions
1.40 mg/ml
Oligomerization of histidine kinase:
Example of analysis of an interacting system
Sedimentation velocity AUC:
20º C, 48000 rpm, ABS detection (230 nm or 280 nm)
20 mM Tris/HCl, 100 mM NaCl, pH 7.4
SV experiment performed at
different loading concentrations of
protein.
The distributions do not overlay,
there is a shift to higher s with
increasing concentration.
= sign of reversible interactions
2.00 mg/ml
Oligomerization of histidine kinase:
Example of analysis of an interacting system
Sedimentation velocity AUC:
20º C, 48000 rpm, ABS detection (230 nm or 280 nm)
20 mM Tris/HCl, 100 mM NaCl, pH 7.4
SV experiment performed at
different loading concentrations of
protein.
The distributions do not overlay,
there is a shift to higher s with
increasing concentration.
= sign of reversible interactions
REVERSIBLE DIMERTETRAMER
EQUILIBRIUM
Oligomerization of histidine kinase:
Example of analysis of an interacting system
Sedimentation velocity AUC:
20º C, 48000 rpm, ABS detection (230 nm or 280 nm)
20 mM Tris/HCl, 100 mM NaCl, pH 7.4
SV experiment performed at
different loading concentrations of
protein.
The distributions do not overlay,
there is a shift to higher s with
increasing concentration.
= sign of reversible interactions
sw isotherm analysis:
0.05 mg/ml:
sw = 3.425 S
sw
Oligomerization of histidine kinase:
Example of analysis of an interacting system
Sedimentation velocity AUC:
20º C, 48000 rpm, ABS detection (230 nm or 280 nm)
20 mM Tris/HCl, 100 mM NaCl, pH 7.4
sw isotherm analysis:
0.15 mg/ml:
sw = 3.589 S
sw
Oligomerization of histidine kinase:
Example of analysis of an interacting system
Sedimentation velocity AUC:
20º C, 48000 rpm, ABS detection (230 nm or 280 nm)
20 mM Tris/HCl, 100 mM NaCl, pH 7.4
sw isotherm analysis:
0.45 mg/ml:
sw = 3.850 S
sw
Oligomerization of histidine kinase:
Example of analysis of an interacting system
Sedimentation velocity AUC:
20º C, 48000 rpm, ABS detection (230 nm or 280 nm)
20 mM Tris/HCl, 100 mM NaCl, pH 7.4
sw isotherm analysis:
0.80 mg/ml:
sw = 4.079 S
sw
Oligomerization of histidine kinase:
Example of analysis of an interacting system
Sedimentation velocity AUC:
20º C, 48000 rpm, ABS detection (230 nm or 280 nm)
20 mM Tris/HCl, 100 mM NaCl, pH 7.4
sw isotherm analysis:
1.40 mg/ml:
sw = 4.307 S
sw
Oligomerization of histidine kinase:
Example of analysis of an interacting system
Sedimentation velocity AUC:
20º C, 48000 rpm, ABS detection (230 nm or 280 nm)
20 mM Tris/HCl, 100 mM NaCl, pH 7.4
sw isotherm analysis:
2.00 mg/ml:
sw = 4.476 S
sw
Oligomerization of histidine kinase:
Example of analysis of an interacting system
Sedimentation velocity AUC:
20º C, 48000 rpm, ABS detection (230 nm or 280 nm)
20 mM Tris/HCl, 100 mM NaCl, pH 7.4
sw isotherm analysis:
2.00 mg/ml:
sw = 4.476 S
sw
Oligomerization of histidine kinase:
Example of analysis of an interacting system
Sedimentation velocity AUC:
20º C, 48000 rpm, ABS detection (230 nm or 280 nm)
20 mM Tris/HCl, 100 mM NaCl, pH 7.4
Kd ~ 95 uM
s20,w
(tetramer)
s20,w
(dimer)
MSSV analysis of triple protein mixture of viral
glycoprotein, its cognate receptor and antigenrecognition
receptor fragment, ck(s) of mixture
shown as solid lines, ck(s) of each protein alone
dotted (Brown, 2008)
1:1:1
1:1
1:1
• determination of complex stoichiometry in heterogeneous
interactions of species with significantly different spectral
properties (ε280/ ε250, ε280/εIF)
• acquisition of multiple signals (wavelengths) necessary
• useful even for impure samples, multi-step associations,
or in cases the correct reaction model is unknown
Multi-signal sedimentation velocity (MSSV)
Sedimentation equilibrium
• sedimentation + diffusion + physical association - all
in equilibrium
• high sample purity crucial
• global fitting of data obtained for different loading
concentration/molar ratios needed for accurate Kd
determination
A A2
2A A2
M* - buoyant molar mass
A + B AB
AB
A B
c(r) – concentration of molecule at
radial distance r, c(r0) – concentration
of molecule at reference position r0,
K12 and KAB – association equilibrium
constant [M-1]
Collected SE data are fitted with the appropriate model to obtain Kd
Sedimentation equilibrium
Example of stoichiometry + Kd determination
20º C, 10500 rpm, 17500 rpm, 30000 rpm, ABS detection (230 nm and 280 nm)
20 mM Tris/HCl, 100 mM NaCl, pH 7.4
global analysis of SE data collected at three rotor speeds, 6 different protein concentrations
(detection at 280 and 230 nm)
dimer-tetramer
model fitting
the data well
Kd = 35.3 uM
Concentrations used:
0.06 mg/ml
0.12 mg/ml
0.24 mg/ml
0.35 mg/ml
0.71 mg/ml
1.30 mg/ml
Thank you for your attention
Contact:
Jan Komárek
Biomolecular Interactions and Crystallization CF
CEITEC
jan.komarek@ceitec.cz
S2004 Methods to study biomolecular interactions – classical versus modern