Application of Light Scattering for Analysis of
Protein-Protein Interaction and Aggregation
Ewa Folta-Stogniew
Yale University
•
•
•
Light Scattering Technologies
–
Static and dynamic light scattering
–
Parameters derived from SLS and DLS measurements
Flow Mode Light Scattering Applications
–
Molar mass distributions and differences in populations
–
Determination of an oligomeric state of modified proteins from SEC-LS/UV/RI
measurement
–
Determination of dimerization constant from SEC-LS measurements
Capabilities and limitation of LS measurements
Light Scattering Experiments
Monochromatic
Laser Light
Io
sample
cell
I
Θ1
Θ2
IΘ1
Computer
IΘ2
detector at angle Θ2
Light Scattering Experiments
•
Static (classical)
•
Dynamic (quasielastic)
fluctuation of intensity of scattered
light with time
time-averaged intensity of scattered
light
Measurements:
•
batch mode derived:
Parameters
• • “in-line”
mode(weight-average)
combined with a accuracy
fractionation
step,
Molar Mass
~5%
Parameters derived:
•
DT
translation diffusion coefficient
mainly Size Exclusion Chromatography,
Field Fractionation
2 chromatography,
1/2
hydrodynamic
radius (Stokes radius)
• (<ri.e.
•
RFlow
g > ) root mean square radii
h
for (<rg2>1/2)> (λ/ 20) ~ 15 nm
Uncertainty of ~10% for monodisperse sample
• A2 second virial coefficient
Rayleigh-Debye-Zimm formalism
Stokes-Einstein
K *c
1
=
+ 2A2c
R(θ ) MwP(θ )
R(Θ)
c
Mw
A2
P(Θ)
K
Rayleigh ratio (excess scattered light)
sample concentration (g/ml)
weight-average molecular weight (molar mass)
second virial coefficient (ml-mol/g2)
form factor (angular dependence)
optical constant [4π2n2 (dn/dc)2 /(λo4NA)]
DT =
DT
k
T
Rh
η
kT
6πηRh
translational diffusion coefficient
Boltzmann constant
temperature
radius
solvent viscosity
Typical SEC-MALLS system
SEC
sa m p le
w aste o r
colum n
collec tio n
H P LC
UV
LS
RI
syste m
d e te cto r
d e te cto r
d e te cto r
D L S + S LS
0.1 μ m p re-filte re d bu ffe r
0.1 μ m “in -lin e ” filte r
C o m p u te r
Three Detector monitoring
2.0
Peak ID - Ova_071305a_01_P_N
LS #11
AUX1
AUX2
LS #11, AUX1, AUX2
1.5
1.0
0.5
0.0
-0.5
4.0
8.0
12.0
16.0
20.0
Volume (mL)
UV at 280 nm
RI
LS at 90°
Molar mass distribution for multiple analyses
Ovalbumin 43 kDa
automated template processing of five data sets
Molar Mass vs. Volume
1.0x109
OVA_e_UV
OVA_200_a_P_N_UV_templat...
OVA_b_UV
OVA_c_UV
OVA_d_UV
Molar Mass (g/mol)
1.0x108
1.0x107
1.0x106
1.0x105
1.0x104
6.0
8.0
10.0
12.0
Volume (mL)
14.0
16.0
Determination of Weight Fractions
Cumulative Molar Mass
Cumulative Weight Fraction W
1.0
0.8
Oligomeric state
Average
Mw ± SD
[kDa]
OVA_e_UV
(3 analyses)
Fraction of Mass
[% of total]
(3 analyses)
OVA_200_a_P_N_UV_templat...
85.23 ± 0.06
42.80 ± 0.02
OVA_b_UV
9.4 ± 0.0
(50-96 kDa)
84.1± 0.2
OVA_c_UV
1.9 ± 0.0
(96-130 kDa) OVA_d_UV
121.8 ± 0.7
Mono (20-50 kDa)
0.6
Di
Tri
0.4
Agg. (0.13 –1 MDa)
284 ± 2
2.87± 0.06
Agg. (1 –100 MDa)
10.9±0.4 x103
0.6 ± 0.0
0.2
0.0
1.0x104
1.0x105
1.0x106
1.0x107
Molar Mass (g/mol)
1.0x108
1.0x109
Differences in population based on molar mass distribution
Molar Mass vs. Volume
1.0x10
9
Ovalbumin (5 runs)
OVA_e_UV
OVA_a_UV
OVA_b_UV
OVA_c_UV
OVA_d_UV
Ova_071305c
Ova_071305a
Ova_071305b
Molar Mass (g/mol)
1.0x10 8
1.0x10 7
Mw = 108 ± 17 kDa
Polydispersity Mw/Mn
2.3 ± 0.4
1.0x10 6
Ovalbumin
1.0x10 5
1.0x10 4
6.0
(3 runs)
Mw = 141 ± 3 kDa
Polydispersity Mw/Mn
8.0
10.0
12.0
Volume (mL)
14.0
16.0
2.92 ± 0.06
Differences in population based on molar mass distribution
Ovalbumin 43 kDa
Cumulative Molar Mass
OVA_e_UV
OVA_a_UV
OVA_b_UV
OVA_c_UV
OVA_d_UV
Ova_071305c
Ova_071305a
Ova_071305b
Cumulative Weight Fraction W
1.00
0.95
Average
Mw ± SD
[kDa]
(5 analyses)
Oligomeric state
Average
Mw ± SD
[kDa]
(3 analyses)
Fraction of
Mass
[% of total]
(5 analyses)
Fraction of
Mass
[% of total]
(3 analyses)
Mw = 141 ± 3
Mw = 108 ± 17
Mw = 141 ± 3
0.90
Mw = 108 ± 17
Ovalbumin
(5 runs) 43.0 ± 0.1
Mono (20-50 kDa)
0.85
4
1.0x10
(3 runs)
88.1 ± 0.1
85.23 ± 0.06
MMw
= 108
Di
(50-96
kDa) ± 17 kDa82.7 ± 0.4
MMw
± 3±kDa
84.1± 0.2= 141 7.68
0.04
9.4 ± 0.0
Tri (96-130 kDa)
Polydispersity
Mw/Mn114 ± 4
121.8
± 0.7
1.54 Mw/Mn
± 0.05
Polydispersity
1.9 ± 0.0
Agg. (0.13 –1 MDa)
270 ±10
284 ± 2
Agg. (1 –100 MDa)
10±1 x103
10.9±0.4 x103
2.3 ± 0.4
0.80
1.0x10
Ovalbumin
42.80 ± 0.02
5
1.0x10 6
1.0x10
Molar Mass (g/mol)
7
2.18 ± 0.08
2.87± 0.06
0.4 ± 0.0
0.6 ± 0.0
2.92 ± 0.06
1.0x10
8
1.0x10
9
Determination of the oligomeric state of modified proteins
from SEC-LS/UV/RI analysis
1. Glycosylated proteins
2. Proteins conjugated with polyethylene glycol
3. Membrane protein present as a complex with lipids and detergents
Input:
Results:
•
Polypeptide sequence
•
Oligomeric state of the polypeptide
•
Chemical nature of the modifier
•
Extend of modification (grams of
modifier /gram of polypeptide)
“three detector method”
Yutaro Hayashi, Hideo Matsui and Toshio Takagi (1989) Methods Enzymol,172:514-28
Jie Wen, Tsutomu Arakawa and John S. Philo (1996) Anal Biochem, 240:155-66
Ewa Folta-Stogniew (2006) Methods in Molecular Biology: New and Emerging Proteomics Techniques, pp. 97–112
Three Detector Method
k *(LS)(UV)
=
p
ε (RI)2
MW
MWp
Molecular Weight (polypeptide)
ε
extinction coefficient
LS
light scattering intensity
UV
absorbance (ε)
RI
refractive index change
k
calibration constant
Yutaro Hayashi, Hideo Matsui and Toshio Takagi (1989) Methods Enzymol,172:514-28
Jie Wen, Tsutomu Arakawa and John S. Philo (1996) Anal Biochem, 240:155-66
Ewa Folta-Stogniew (2006) Methods in Molecular Biology: New and Emerging Proteomics Techniques, pp. 97–112
Modified proteins: PEG-ylated and Glycoproteins
PEG-ylated protein:
75 kDa
36 kDa polypeptide + 39 kDa PEG
Polypeptide: 146 kDa
(tetramer: 144 kDa)
Molar Mass vs. Volume
3.0x10
5
Full protein: 291 kDa
Molar Mass (g/mol)
2.5x105
PEG-P_full
PEG-P_pp
2.0x105
1.5x105
1.0x105
5.0x104
0.0
8.0
10.0
12.0
14.0
Volume (mL)
16.0
18.0
(tetramer: 300 kDa)
PEG-ylated protein:
75 kDa
36 kDa polypeptide + 39 kDa PEG
475
66 kDa
Polypeptide: 146 kDa
(tetramer: 144 kDa)
Molar Mass vs. Volume
5.0x10
5
Full protein: 291 kDa
Molar Mass (g/mol)
4.0x105
BSA
APO
PEG-P_full
PEG-P_pp
3.0x105
2.0x105
1.0x105
0.0
8.0
10.0
12.0
14.0
Volume (mL)
16.0
18.0
(tetramer: 300 kDa)
Glycoprotein
44.1 kDa polypeptide; unknown level of glycosylation
1
0.20
2 3
Peak ID - Glycoprotein_Aggregates_RI_UV_LS
LS #11
AUX1
AUX2
peak
UV/RI
MMpp
(kDa)
1
0.54
90
0.4
122
2
0.52
45
0.4
63
3
0.37
23
1.1
48
0.10
0.05
0.00
-0.05
4.0
6.0
8.0
10.0
Volume (mL)
12.0
14.0
Grams of
sugar/gram of
polypeptide
Full
Glycoprotein
(kDa)
16.0
Molar Mass vs. Volume
polypeptide
glycoprotein
2.0x105
220 kDa
Full glycoprotein
66 kDa
1.5x105
Polypeptide
Molar Mass (g/mol)
LS #11, AUX1, AUX2
0.15
1.0x105
5.0x104
0.0
6.0
8.0
10.0
12.0
Volume (mL)
14.0
16.0
Glycosylated peptide: 9.13 kDa; 350 μg
Molar Mass vs. Volume
Alfa-Lactalbumin
Glyco_peptide
Glyco_peptide
2.0x104
Peak ID - Glyco_peptide
0.08
LS #11
AUX1
AUX2
0.06
LS #11, AUX1, AUX2
1.0x104
5.0x103
0.0
16.0
0.04
0.02
0.00
18.0
20.0
22.0
24.0
-0.02
16.0
26.0
18.0
20.0
22.0
Volume (mL)
Volume (mL)
24.0
26.0
Alfa-lactalbumin 14 kDa; 20 μg
0.020
Peak ID - Alfa-Lactalbumin
LS #11
AUX1
AUX2
0.015
LS #11, AUX1, AUX2
Molar Mass (g/mol)
1.5x104
0.010
0.005
0.000
-0.005
20.0
21.0
22.0
Volume (mL)
23.0
Alfa-lactalbumin 14 kDa; 20 μg
24.0
Determination of the oligomeric state of a complex of
glycosylated protein+peptide
protein
58 kDa extracellular ANP-binding domain (ECD) of
cell-surface receptor 16% of mass is sugar
dn/dct = 0.179 g/mL
48 kDa
ligand
polypeptide portion
2.7 kDa atrial natriuretic peptide (ANP)
Injected sample complex
(ECD : ANP)
2:1
0.07
0.06
156
75
43 kDa
0.05
0.04
0.03
0.02
0.01
0.00
8
9
10
ECD dimer = 2 x 58 = 116 kDa (polypeptide 96 kDa)
11
12
ANP = 2.7 kDa
Injected sample complex
(ECD : ANP)
2:1
Molar Mass vs. Volume
ECD1103A
1.6x105
Molar Mass (g/mol)
156
75
43 kDa
1.2x105
8.0x104
4.0x104
0.0
8.0
9.0
10.0
11.0
12.0
Volume (mL)
ECD dimer = 2 x 58 = 116 kDa (polypeptide 96 kDa)
ANP = 2.7 kDa
ECD-ANP complex; ~3 μg
ECD; ~2 μg
MWglycoprotein = 103 ± 10 kDa
MWglycoprotein = 54 ± 6 kDa
MWpolypeptide = 96 ± 7 kDa
MWpolypeptide = 44 ± 5 kDa
Molar Mass vs. Volume
ECD1103A
1.6x105
Molar Mass (g/mol)
156
75
43 kDa
1.2x105
8.0x104
4.0x104
0.0
8.0
9.0
10.0
11.0
12.0
Volume (mL)
ECD dimer = 2 x 58 = 116 kDa (polypeptide 96 kDa)
ANP = 2.7 kDa
Hydrophobic proteins
Determination of the oligomeric state of detergent solubilized proteins:
polypeptide+lipids+detergent complexes of unknown detergent+lipids content
47 kDa
Proteins:
33 kDa
porin LamB
hemolysin α-HL
detergent
dodecyl maltoside (C12M) MW = 511 g/mol
0.5g/L
i.e. 0.05%
CMC = 0.008%
micelle size 50-70 kDa
trimer = 141 kDa
heptamer = 231 kDa
porin
A280
220 kDa
heptamer = 215±20 kDa
66 kDa
43 kDa
1.2
A280 LamB
MMpp LamB
MMpp α-HL
300
0.8
A280 αHL
200
0.4
100
0.0
0
12
14
16
(141 kDa)
trimer = 141±3 kDa
hemolysin α-HL
33 kDa
475 kDa
LamB
18
elution volume [mL]
20
22
MMpp [kDa]
47 kDa
Proteins:
(231 kDa)
Three Detector Method
Yutaro Hayashi, Hideo Matsui and Toshio Takagi
Methods Enzymol 1989;172:514-28
allows determination of mass of detergent/lipids bound to a polypeptide
( RI )
⎛ dn ⎞
=
k
A
⎜ ⎟
2
dc
(UV )
⎝ ⎠ app
⎛ dn⎞
⎜ ⎟ =
⎝ dc ⎠app
⎛ dn⎞
⎜ ⎟ +
⎝ dc ⎠ pp
⎞
δ ⎛⎜ dn
⎟
dc
⎝
⎠d +l
= K'
(RI)
ε (UV)
δ is mass of detergent and/or lipids per 1 gram of polypeptide
Assumption : detergent does not produce any signal in UV
= 285 kDa
MWcomplex
= 271 kDa
MWpolypeptide = 141 kDa
MWpolypeptide = 215 kDa
δ = 1.02
δ = 0.26 lipids per 1 gram of polypeptide
lipids per 1 gram of polypeptide
475 kDa
220 kDa
66 kDa
A 280 LamB
1.2
δ = 1.02
A280
43 kDa
300
MM complex LamB
MM complex α-HL
A 280 αHL
0.8
200
δ = 0.26
0.4
100
MMcomplex [kDa]
MWcomplex
0
0.0
12
14
16
18
20
22
elution volume [mL]
Yernool D, Boudker O., Folta-Stogniew E., and Gouaux E. (2003) Trimeric subunit stoichiometry of the glutamate transporters from Bacillus caldotenax and Bacillus
stearothermophilus. Biochemistry 42: 12981-12988
Determination of dimerization constant from SEC-LS measurements
SecA protein
WT
monomer = 102 kDa
DS8 deletion mutant
monomer = 101 kDa
D11 deletion mutant
monomer = 100 kDa
SecA protein
WT
102 kDa
DS8 deletion mutant
101 kDa
D11 deletion mutant
100 kDa
Low salt buffer:
High salt buffer:
10 mM Tris pH 7.5, 5 mM Mg2+, 100 mM KCl
10 mM Tris pH 7.5, 5 mM Mg2+, 300 mM KCl
Molar Mass vs. Volume
Molar Mass vs. Volume
DS8_120407e_01_P_N
D11_062507a_01_P_N_temp
WT_062507a_01_P_N
2.5x105
2.0x105
Mola r Mass (g/mo l)
Molar Mass (g/mol)
2.0x105
1.5x105
1.0x105
5.0x104
0.0
12.0
D11_120607e_01_P_N
W T _120607e_01_P_N
DS8_120607e_01_P_N
2.5x105
1.5x105
1.0x105
5.0x104
14.0
16.0
Volume (mL)
18.0
0.0
12.0
14.0
16.0
Volume (mL)
18.0
D11 deletion mutant mono= 101 kDa
High salt buffer:
10 mM Tris pH 7.5, 5 mM Mg2+, 300
Molar Mass vs. Volume
2.5x10
5
mM KCl,
0.71 mg/mlD11_120607c_01_P_N
7.0 μM
Mw=106 kDa
D11_120607b_01_P_N
0.085 mg/ml
0.83
μM
Mw=103 kDa
D11_120607a_01_P_N
0.045 mg/ml 0.44 μM
Mw=103 kDa
0.019 mg/ml 0.18 μM
Mw=102 kDa
1.5x105
1.0x105
5.0x104
MW changes w ith concentration
0.0
12.0
14.0
16.0
Volume (mL)
18.0
220
MW weight average (kDa)
Molar Mass (g/mol)
2.0x105
D11 high salt
160
D11 high salt
D11 high salt
D11 high salt
100
40
0.01
0.1
1
[protein] (uM)
10
100
D11 deletion mutant mono= 101 kDa
Low salt buffer:
10 mM Tris pH 7.5, 5 mM Mg2+, 100
2.5x10
5
Molar Mass vs. Volume 0.69 mg/ml
0.17 mg/ml
0.083 mg/ml
0.037 mg/ml
0.014 mg/ml
Molar Mass (g/mol)
2.0x10 5
mM KCl,
D11_062507b_01_P_N
6.8 μM
Mw=163
D11_062507e_01_P_N
1.7 μM
Mw=137
D11_062507d_01_P_N
kDa
kDa
Mw=129 kDa
Mw=115 kDa
Mw=105 kDa
0.81 μM
0.36 μM
0.14 μM
1.5x10 5
1.0x10 5
5.0x10 4
14.0
16.0
Volume (mL)
Mw = f m M m + f d M d = M m (2 − f m )
2M = D
(1 − f m )
[ D]
Ka =
=
[ M ]2 2( f m ) 2 ct
fm =
− 1 + 1 + 8 K a ct
4 K a ct
18.0
220
MW weight average (kDa)
0.0
12.0
MW changes w ith concentration
D11 low salt
160
D11 low salt
D11 low salt
D11 low salt
D11 low salt
100
40
0.01
0.1
1
[protein] (uM)
10
100
WT
monomer = 102 kDa
DS8 deletion mutant monomer = 101 kDa
D11 deletion mutant
Low salt buffer:
monomer = 100 kDa
100 mM KCl
High salt buffer:
Molar Mass vs. Volume
Molar Mass vs. Volume
DS8_120407e_01_P_N
D11_062507a_01_P_N_temp
WT_062507a_01_P_N
2.5x10 5
2.0x105
Molar Mass (g/mol)
1.5x10 5
1.0x10 5
1.5x105
1.0x105
5.0x104
5.0x10 4
0.0
12.0
14.0
16.0
18.0
0.0
12.0
14.0
WT
DS8
D11
WT
DS8
D11
Kd= <1e-9
Kd=7±1e-8 M
Kd=3.5±0.2e-6 M
18.0
Kd= 2.2±0.2e-6 M
Kd= 2.41±0.05e-5 M
Kd> 2.4e-4 M
240
weight-average MW (kDa)
240
220
200
180
160
140
120
100
80
1e-9
16.0
Volume (mL)
Volume (mL)
weight-average MW (kDa)
D11_120607e_01_P _N
W T _120607e_01_P _N
DS 8_120607e_01_P _N
2.5x105
2.0x10 5
Molar Mass (g/mol)
300 mM KCl
1e-8
1e-7
1e-6
1e-5
[protein]
1e-4
(M)
1e-3
1e-2
220
200
180
160
140
120
100
80
1e-9
1e-8
1e-7
1e-6
1e-5
[protein]
1e-4
(M)
1e-3
1e-2
Thermodynamic linkage for SecA dimerization
Low Salt
100 mM KCl
Protein
Kd [M]
High Salt
300 mM KCl
ΔG dimer
(kcal/mol)
Kd [M]
ΔG dimer
(kcal/mol)
WT
<1x10-9
-12.3
2.2±0.2x10-6
-7.7
DS8
7±1x10-8
-9.7
2.41±0.05x10-5
-6.3
D11
3.5±0.2x10-6
-7.4
>2.4x10-4
-4.9
D11 high ΔG = -4.9 kcal/mol
-2.5 kcal/mol
DS8 high ΔG = -6.3 kcal/mol
-2.8 kcal/mol
D11 low ΔG = -7.4 kcal/mol
WT high ΔG = -7.7 kcal/mol
-1.4 kcal/mol
-3.4 kcal/mol
WT high ΔG = -7.7 kcal/mol
-7.4 kcal/mol
-6.0 kcal/mol
DS8 low ΔG = -9.7 kcal/mol
-4.9 kcal/mol
-4.6 kcal/mol
-4.6 kcal/mol
-2.6 kcal/mol
WT low ΔG = -12.3 kcal/mol
WT low ΔG = -12.3 kcal/mol
Capabilities
Static LS
•
fast and accurate determination of molar masses (weight average)
– glycosylated protein, conjugated with PEG, protein-lipids-detergent complexes, proteinnucleic acid complexes
•
accuracy of ± 5% in molar mass determination
•
easy to implement, fully automated (data collection and data analysis)
•
highly reproducible (no operator’s bias)
•
SEC/MALS excellent in detecting and quantifying population with various oligomeric state in
protein
•
excellent approach for determination of oligomeric state of modified proteins and peptides
•
can be used to determine association constant (concentration gradient measurements)
Limitations
Static LS
•
measures weight average molar mass – needs fractionation to resolve
different oligomeric states
•
possible losses of sample during filtration and fractionation
•
limitation on solvent choices (related to a fractionation step)
•
SEC/MALS dilution during experiment
Ken Williams
Director of W.M. Keck Biotechnology Resource Laboratory at Yale
University School of Medicine
NIH
Users of SEC/LS Service
http://info.med.yale.edu/wmkeck/biophysics
[email protected]
http://info.med.yale.edu/wmkeck/biophysics/publications_biophysics_resource.pdf
Ovalbumin 43 kDa
Aggregates
Lower order oligomers
angular dependence of scattered light
no angular dependence of scattered
light
3D Plot - OVA_e_RI
12
18
17
16
15
14
163°
11
10
9
8
7
90°
6
5
4
3
14°
Morphology of aggregates from angular dependence of LS signal;
size determination- Rg
3D Plot - OVA_e_RI
Determination of radius of gyration,
Rg, (root mean square radius,
R.M.S.,) from angular dependence
of scattered light
12
K *c 1
= (1+ (16π 2/ 3 λ2 ) < Rg 2 > sin2 (θ2 ) )
R(θ) Mw
Zimm Plot
18
17
16
15
11
14
10
9
8
7
6
5
90°
163°
Debye Plot - Ova_b_H_aggregates
6.50x10-8
RMS Radius vs. Volume
6.00x10-8
5.50x10-8
5.00x10-8
4.50x10-8
4.00x10-8
0.0
0.2
0.4
0.6
0.8
sin²(theta/2)
Peak, Slice : 1, 944
Volume
: 7.867 mL
Fit degree
: 1
Conc.
: (1.915 ± 0.020)e-6 g/mL
Mw
: (2.277 ± 0.024)e+7 g/mol
Radius
: 46.8 ± 0.2 nm
1.0
R.M.S. Radius (nm)
K*c/R(theta)
Ova_122105a_Rg-Rh
1000.0
100.0
10.0
6.0
Radius: 46.8±0.2 nm
7.0
8.0
Volume (mL)
90° & AUX detector
9.0
4
3
14°
Inferring conformational information from the relationship between
molecular size (Rg) and molecular weight (Molar Mass)
Rg ~ M ν
RMS Radius vs. Molar Mass
log(Rg) versus log(MM)
ν
ν
For
Sphere
0.33
Coil
0.5
Rod
1
Rollings, J.E. (1992) in “Laser Light Scattering in
Biochemistry”, Eds. S.E. Harding, D. B. Sattelle and V.
A. Bloomfield; p. 275-293
R.M.S. Radius (nm)
Ova_122105a_Rg-Rh
0.38 ± 0.00
log(Rg)
Slope =
1000.0
100.0
10.0
1.0x106
ν = 0.4
1.0x107
1.0x108
Molar Mass (g/mol)
log (MM)
1.0x109
Shape analysis: log(Rg) versus log(MM)
Aggregates of Ovalbumin vs. “amyloid-type” fibers
Molar Mass vs. Volume
RMS Radius vs. Molar Mass
1000.0
Molar Mass (g/mol)
1.0x108
Ova_Rg-Rh
Amyloids_peak
1.0x107
1.0x10
6
1.0x105
6.0
R.M.S. Radius (nm)
1.0x109
Amyloids_peak
0.75 ± 0.01
Ova_Rg-Rh
0.38 ± 0.00
100.0
ν = 0.8
ν = 0.4
7.0
8.0
9.0
10.0
10.0
1.0x105
1.0x106
Volume (mL)
For
Sphere
ν
0.33
Coil
0.5
Rod
1
1.0x107
1.0x108
Molar Mass (g/mol)
1.0x109
Ova_aggr
ν = 0.4
Sphere/Coil
Amyloids
ν = 0.8
Coil/Rod
Shape analysis: shape factor ρ = Rg/Rh
Aggregates of Ovalbumin vs. amyloid fibers
ρ = Rg/Rh
Shape factor:
Combination of MALS (Rg) and DLS (Rh)
Ovalbumin
Amyloids
120
1.4
100
1.2
1
0.6
0.8
Rh
0.6
40
6.5
7
7.5
8
8.5
20
15
Rg
Rh
5
0
0
6
9
RI
10
0.2
0
6
25
0.4
20
0
30
Rg
0.4
0.2
1.4
1
RI
60
35
1.2
80
0.8
1.6
7
8
9
10
volume [mL]
volume [mL]
Rg/Rh = 0.91
Rg/Rh = 1.84
B
Rizos, A. K., Spandidos, D. A., and Krambovitis, E., (2003) Int. J. Med., 12, 559-563
Shape analysis: shape factor ρ = Rg/Rh
Aggregates of Ovalbumin vs. amyloid fibers
ρ = Rg/Rh
Shape factor:
Combination of MALS (Rg) and DLS (Rh)
Ovalbumin
1.4
100
1
0.6
7
7.5
8
8.5
25
20
15
Rg
Rh
5
0.2
0
0
6
9
RI
10
0.4
7
8
9
10
volume [mL]
volume [mL]
Rg/Rh = 0.91
1.732
30
0.6
0
6.5
Rod
1.4
Rh
20
6
0.816
35
0.8
40
0
Coil
1.6
Rg
0.4
0.2
0.774
1
RI
60
Sphere
1.2
80
0.8
ρ = Rg/Rh
Amyloids
120
1.2
For
Coil
Rg/Rh = 1.84
B
Rod
Rizos, A. K., Spandidos, D. A., and Krambovitis, E., (2003) Int. J. Med., 12, 559-563
Shape analysis:
Rg ~ M ν
ρ = Rg/Rh
ν
For
Sphere
Coil
Rod
0.33
0.5
1
Ovalbumin
1.4
100
1
0.6
7
7.5
8
8.5
1.732
30
0.6
0
6.5
Rod
1.4
Rh
20
6
0.816
35
0.8
40
0
Coil
1.6
Rg
0.4
0.2
0.774
25
1
RI
60
Sphere
1.2
80
0.8
ρ = Rg/Rh
Amyloids
120
1.2
For
9
20
15
Ova_aggr
ν = 0.4
Rg
Rh
10
0.4
5
0.2
0
0
6
7
8
9
10
volume [mL]
volume [mL]
Rg/Rh = 0.91
RI
Coil
Sphere/Coil
Rg/Rh = 1.84
Amyloids
ν = 0.8
Rod
Coil/Rod
Shape analysis:
shape factor ρ = Rg/Rh
ρ = Rg/Rh = 1.84
log(Rg) versus log(MM)
Slope = ν
Amyloids
TABLE 1 Summary of scaling exponents and average -ratio values
c
aCgn
c
Avg
Rod
ν = 0.8 Coil/Rod
a
ρ−ratio
m
(ν)
m
–0.3 ± 0.1
–0.27 ± 0.07
1.65 ± 0.1
0.74 ± 0.16
0.64 ± 0.12
–1.13 ± 0.34
–1.25 ± 0.34
1.76 ± 0.13
0.74 ± 0.15
0.8 ± 0.4
( -chymotrypsinogen A)
bG-CSF
(bovine granulocyte-colony
stimulating factor)
a
Weiss W F, IV, Hodgdon T. K., Kaler E. W., Lenhoff A. M., and Roberts C. J. (2007) Nonnative Protein Polymers: Structure,
Morphology, and Relation to Nucleation and Growth. Biophysical Journal 93: 4392-4403
Cryo-TEM micrograph of aCgn samples (c0 = 1 mg/mL) at m = 0.05
Weiss W F, IV, Hodgdon T. K., Kaler E. W., Lenhoff A. M., and Roberts C. J. (2007) Nonnative
Protein Polymers: Structure, Morphology, and Relation to Nucleation and Growth. Biophysical
Journal 93: 4392-4403
Molar Mass Distribution Plot
BSA 66 kDa
Shape information from light scattering measurements
156 kDa
40.3 kDa
43 kDa
Protein “F”
Molar Mass vs. Volume
Ald0624a_01_P
FLK06245b_01_P
OVA0624a_01_P
Molar Mass (g/mol)
1.6x10 5
1.2x10 5
8.0x10 4
4.0x10 4
0.0
10.0
12.0
14.0
Volume (mL)
16.0
Protein “F” frictional ratio Rh/Rs = 1.85
40.3 kDa
Rh = 4.2 nm
non-spherical shape
156 kDa
Rh = 4.2 nm
43 kDa
Rh = 2.9 nm
Shape Effects
Hydrodynamic Radius vs. Volume
Hydrodynamic Radius (nm)
10.0
8.0
FLK06245b_01_P
Ald0624a_01_P
OVA0624a_01_P
4 fold difference in
mass – same
hydrodynamic size
6.0
4.0
2.0
0.0
10.0
12.0
14.0
Volume (mL)
16.0
• Batch Mode Light Scattering Applications
– Detection of aggregates in DLS and SLS
measurement
Batch Mode Static MALLS experiment
Monomer 14 kDa
Strip Chart - Sample1_2_aggregates
0.5
-5
8.50x10
Sample 1
Detector: 11
0.4
-5
8.00x10
-5
7.50x10
Sample 2
0.3
-5
7.00x10
0.2
-5
6.50x10
0.1
-5
6.00x10
0.0
0.2
0.4
0.0
5.0
0.8
1.0
0.8
1.0
sin²(Θ/2)
-6
7.00x10
4.0
Detector: AUX1
0.6
3.0
-6
6.00x10
2.0
-6
5.00x10
1.0
-6
4.00x10
0.0
-1.0
0.0
4.0
8.0
12.0
-6
3.00x10
0.0
0.2
0.4
sin²(Θ/2)
Volume (mL)
Sample
0.6
Weight Average MM, Mw ± SD*
[kDa]
RMS
[nm]
1
15 ± 1
0
2
126 ± 8
56 ± 10
Angular dependence of scattered light clearly indicates presence of aggregates
Determination of hydrodynamic radius, Rh, from a Dynamic LS experiment
Ovalbumin; monomer:
43 kDa; Rh=3.0 nm
Rh = 8±7 nm from Cumulant Fit (Polydispersity 93%)
Regularization Fit:
Peak
Rh (nm)
Polydispersity (%)
MW (R) kDa
% Intensity
% Mass
1
3.1
12.8
46
54
99.9
2
24
17.8
>1MDa
23
0.1
3
86
13.4
>1MDa
23
<0.1
Dissociation of aggregates upon dilution; time course
Protein H 23 kDa; Rh=2.3 nm
Rh=94 nm
Rh=2.8 nm
Rh=23 nm
Rh=2.3 nm;
Pd=42%
88% monomer
Ovalbumin 43 kDa
8% dimer
1.5% trimer
3% aggregates < 1MDa
Strip Chart - OVA_b_UV_traces
2.0
0.4% 1-100 MDa
Detector: AUX1
1.5
1.0
UV at 280 nm
?
0.5
0.0
-0.5
1.0
0.4% 1-100 MDa
Detector: 11
0.8
0.6
LS at 90 deg
0.4
0.2
0
10
20
Volume (mL)
30
Intensity of scattered light
~ Mw*c
due to their high Mw aggregates scatter very strongly
A monomeric protein
43 kDa and aggregates 10 MDa at 2 mg/mL:
Intensity of LS signal
Changes in intensity of scattered light due to aggregates
presence
3
intensity monomer
2
intentisty aggregates
1
0
0.0%
total intensity
0.5%
% (w /w ) aggregates
1.0%
Why Light Scattering?
•LS measurements are non-invasive and non-destructive
•small sample volumes
•great dynamic range for sizing: hydrodynamic radii ~ 2nm to 500 nm
•great dynamic range for Mw determination: < 1kDa to >10 MDa
•wide range of concentrations (non-ideality can be addressed through the
determination of second virial coefficient)
•perfectly suited for determination of oligomeric state of modified proteins
without prior knowledge of extend of modification (glycosylated proteins,
proteins modified by polyethylene glycol, or membrane proteins present
as complexes with lipids and detergents)
•LS measurements are perfect tools for detection and characterization of aggregates
•Scattering Intensity, R(Θ)~ Mw*c
because of their big Mw, aggregates scatter strongly even when present at
low concentrations; easily detectable
•Angular variation of the scattered light is related to the size and shape of the molecule
the light scattering signal from aggregates will show angular
dependence, while LS signal produces by lower order oligomers
like dimers, trimers, tetramers, et c. will not
Various uses of Light Scattering for assessing protein aggregates
Experiment
Detects
Aggregates
Information
about
population
(distribution)
Challenge
in use
Sample
dilution
Speed
DLS
Yes
No
Low
No
Fast
Micro-batch
MALS
Yes
No
High
No
Medium
Yes
Medium
Yes
Medium
SEC/MALLS/DLS Yes
Determination of hydrodynamic radius, Rh, from a Dynamic LS experiment
Ovalbumin; monomer:
43 kDa; Rh=3.0 nm
Rh = 8±7 nm from Cumulant Fit (Polydispersity 93%)
Regularization Fit:
Peak
Rh (nm)
Polydispersity (%)
MW (R) kDa
% Intensity
% Mass
1
3.1
12.8
46
54
99.9
2
24
17.8
>1MDa
23
0.1
3
86
13.4
>1MDa
23
<0.1
Results from a batch mode Dynamic LS experiment:
Ovalbumin 43 kDa; Rh=3.0 nm
Rh = 3.2±0.6 nm from Cumulant Fit (Polydispersity 19%)
Regularization Fit:
Peak
Rh (nm)
Polydispersity (%)
MW (R) kDa
% Intensity
% Mass
1
3.1
12.9
46
96
100
2
32
0
>1MDa
2
0
3
2423
0
>1MDa
2
0
)
MW p = k * ( LS )(UV
2
ε ( RI )
y = 92.383x - 3.4044
Three-detector calibration
10-17-01
MW
(kDa)
Ova
43
BSA(1)
66
BSA(2)
132
Ald
156
Apo-Fer
475
500
400
MW [kDa]
Protein
2
R = 0.9996
300
experimental MWp
200
Linear (theoretical MWp)
100
0
0
2
4
ratio (LS)*(UV)/(A*(RI^2))
6
Flow Mode Light Scattering Applications
– Molar mass distributions and differences in populations
– Determination of an oligomeric state of modified proteins and oligos
from SEC-LS/UV/RI measurement
– Determination of dimerization constant from SEC-LS measurements
LS @ 90 degree
RI
UV @ 280 nm
0.8
Peak ID - PRNC__DC
90°
AUX1
AUX2
AUX, 90° Detector
0.6
0.4
0.2
0.0
-0.2
10.0
12.0
14.0
16.0
Volume (mL)
18.0
20.0
Protein “F”
frictional ratio P= Rh/Rs = 1.85
non-spherical shape
Axial ratio a/b (prolate) = 16.6
(oblate) = 22.9
40.3 kDa
156 kDa
43 kDa
Rh = 4.2 nm
Rh = 4.2 nm
Rh = 2.9 nm
Hydrodynamic Radius vs. Volume
FLK06245b_01_P
Ald0624a_01_P
OVA0624a_01_P
Hydrodynamic Radius (nm)
10.0
8.0
4 fold difference in mass –
same hydrodynamic size
6.0
4.0
2.0
0.0
10.0
12.0
14.0
Volume (mL)
Harding S E, Longman E., Carrasco B., Ortega A., and de la Torre J. G. (2004) Studying antibody conformations by
ultracentrifugation and hydrodynamic modeling. Methods Mol Biol 248: 93-113
16.0
Determination of Mw and second virial coefficient from Zimm
plot analysis of light scattering data.
Baselines - BSA_A2_H
10.0
8.0
Zimm Plot - BSA_A2_H
1.72x10-5
K*c/R(theta)
K*c/R(theta)
LS signal at 90º
Detector: 11
1.76x10-5
6.0
1.68x10-5
4.0
1.64x10-5
2.0
0.0
0.0
2.0
4.0
6.0
Volume (mL)
1.60x10-5
0.0
8.0
RMS : 4.8 ± 1.4
nm
MM
: (6.180 ± 0.014)e+4 g/mol
A2
: (5.226 ± 0.316)e-4
mol mL/g²
0.5
1.0
1.5
2.0
sin²(theta/2) + 1085*c
BSA solutions at concentrations: 0.22, 0.44, 0.75 and 1.1 mg/mL and the data were analyzed using Zimm
formalism
Mw
B
65
(5.226 ± 0.316)e-4 mol mL/g²
• Batch Mode Light Scattering Applications
– Detection of aggregates in DLS and SLS
measurement
Determination of Molar Mass and second virial coefficient from a
batch static LS experiment
BSA 66 kDa
10.0
Baselines - BSA_A2_H
K *c
1
=
+ 2 A2c
R (θ ) MwP (θ )
K*c/R(theta)
1.72x10-5
6.0
1.68x10-5
4.0
A2
1.64x10-5
2.0
0.0
0.0
Zimm Plot - BSA_A2_H
R(Θ)
LS signal
at 90º
8.0
Detector: 11
-5
1.76x10
K*c
2.0
4.0
Volume (mL)
6.0
1.60x10-5
0.0
8.0
0.5
RMS : 4.8 ± 1.4
nm
MM
: (6.180 ± 0.014)e+4 g/mol
A2
: (5.226 ± 0.316)e-4
mol mL/g²
1.0
1.5
2.0
and Rh from DLS
sin²(theta/2) + 1085*c
1.30
Zimm plot analysis of static light
scattering data
1.20
Temperature : 27.831 °C
Rh
: 3.4 nm
1.10
Mw = 62 kDa
A2 = (5.226 ± 0.316)e-4 mol mL/g²
1.00
0.90
-7
1.0x10
B. H. Zimm, (1948) J. Chem. Phys., 16, 1099
-6
1.0x10
-5
1.0x10
-4
1.0x10
-3
1.0x10
-2
1.0x10
Delay time (sec.)
-1
1.0x10
0
1.0x10
1
1.0x10
Batch Mode Static MALLS experiment
Monomer 14 kDa
Strip Chart - Sample1_2_aggregates
0.5
-5
8.50x10
Sample 1
Detector: 11
0.4
-5
8.00x10
-5
7.50x10
Sample 2
0.3
-5
7.00x10
0.2
-5
6.50x10
0.1
-5
6.00x10
0.0
0.2
0.4
0.0
5.0
0.8
1.0
0.8
1.0
sin²(Θ/2)
-6
7.00x10
4.0
Detector: AUX1
0.6
3.0
-6
6.00x10
2.0
-6
5.00x10
1.0
-6
4.00x10
0.0
-1.0
0.0
4.0
8.0
12.0
-6
3.00x10
0.0
0.2
0.4
sin²(Θ/2)
Volume (mL)
Sample
0.6
Weight Average MM, Mw ± SD*
[kDa]
RMS
[nm]
1
15 ± 1
0
2
126 ± 8
56 ± 10
Angular dependence of scattered light clearly indicates presence of aggregates
Determination of hydrodynamic radius, Rh, from a Dynamic LS experiment
Ovalbumin; monomer:
43 kDa; Rh=3.0 nm
Rh = 8±7 nm from Cumulant Fit (Polydispersity 93%)
Regularization Fit:
Peak
Rh (nm)
Polydispersity (%)
MW (R) kDa
% Intensity
% Mass
1
3.1
12.8
46
54
99.9
2
24
17.8
>1MDa
23
0.1
3
86
13.4
>1MDa
23
<0.1
Dissociation of aggregates upon dilution; time course
Protein H 23 kDa; Rh=2.3 nm
Rh=94 nm
Rh=2.8 nm
Rh=23 nm
Rh=2.3 nm;
Pd=42%
Feature detected in a batch mode LS measurements
for sample containing aggregates
•
Static (classical)
•
Dynamic (quasielastic)
Aggregates present:
Aggregates present:
• elevated weight average Molar Mass
• autocorrelation function cannot be
described by single exponential (cumulant fit)
(Mw weight average)
• angular dependence in scattered light
• polydispersity from cumulant fit >15%
Missing information: how much and what size?
Solutions
• Sample fractionation followed by batch measurements
• Column separation with simultaneous LS characterization
PEG-ylated oligo
Molar Mass vs. Volume
PEG40_TSK4000_112905b_02...
S2_112905a_P_N_full
5.6x10 4
PEG (40K)
Molar Mass (g/mol)
5.2x10 4
(80 μg total)
Polydispersity= 1.001
4.8x10 4
40K PEG + 12.9 kDa oligo
4.4x10 4
PEG-oligo
4.0x10 4
3.6x10 4
6.0
MM = 41.0 kDa
7.0
8.0
(73 μg total)
MM = 52.1 kDa
9.0
Volume (mL)
BSA 66 kDa
Molar Mass vs. Volume
5.2x104
DNA_S1_280nm_11290
PEG40_112905b
Molar Mass (g/mol)
4.8x104
PEG (40K)
(40 μg total)
Polydispersity= 1.001
4.4x104
40K PEG + 8.3 kDa oligo
4.0x104
PEG-oligo
3.6x104
6.0
MM = 41.0 kDa
7.0
8.0
Volume (mL)
9.0
MM = 48.5 kDa
(70 μg total)