Post on 10-Mar-2020
Applications of
Dynamic Light Scattering
to Polydisperse Systems
Onofrio AnnunziataDepartment of ChemistryTexas Christian University
Fort Worth, TX, USA
Horned Frog
The horned lizard is the state reptile of Texas and, as the "horned frog", is the mascot of Texas Christian University (TCU).
Wikipedia
Field autocorrelation function
0
0.2
0.4
0.6
0.8
1
0 2 4 6 8 10
q 2 D τ
g(1
) ( τ
) ( )(1) 2( , ) expg q q Dτ τ= −
Strong correlationτ = 0, g(1) =1
No correlationτ → ∞, g(1) = 0
Shortτ
Longτ
(1) ( ) (0) ( )S Sg E Eτ τ< ⋅ >∼
(1) ( ) 1g τ ≈ (1) ( ) 0g τ ≈
6b
h
k TDRπ η
=
Polydisperse particles ( )(1) 2( , ) expj jj
g q W q Dτ τ= −∑
Polydisperse systems
Example 1 Example 2
jj jW c M∼
1(1) 2 3
321 1ln ( , ) ...2 6
kg q kkτ τ τ τ= − + − +
Cumulant Analysis of Polydisperse Systems
12/z kD q< > =
z j jj
D W D< > =∑
( )22 42 /z zD D k q< > − < > =
22z j j
jD W D< > =∑
MEAN
VARIANCE
Determination of the moments of the distribution
Huntington's disease (HD) is caused by a CAG/poly-L-glutamine (polyGln) repeat expansion in the first exon of a gene encoding a large protein of unknown function, so-called huntingtin.
1. Protein aggregation
Protein aggregation: GST-HD fusion proteins (Huntington's disease)
Q = polyglutamineP = polyprolineT = cleavage sites for trypsin
Pathological
Normal
Georgalis et al. PNAS (1998), 95, p. 6118.
Georgalis et al. PNAS (1998), 95, p. 6118.
GST-HD20
GST-HD51
GST-HD20
GST-HD51
GST-HD20 and GST-HD51 aggregationAfter mild treatment with trypsin
GST-H20 aggregation give rise to large polyspersity
Cumulant Analysis
(1)1 2
21ln ( , ) ...2
kg q kτ τ τ= − + +
12/z kD q< > =
2
21
22
2z z
z
kD DD k
< > − < > =< >
Determination of W(D) distribution using regularization
( )(1) 2( ) expj jj
g W q Dτ τ= −∑The determination of W(D) is a ill-posed problem:
a small change in g(1) (τ) produces large changes in W(D)
W
D
Both curves yield virtually the same (1)( )g τ
W(D) is non-negative
W(D) is smooth
Problem Solution
Smoothness preclude spikes in the distribution (smoothness parameter)
Available algorithms: CONTIN, PrecisionDeconvolve, Dynals
W
D0
How to choose the correct smoothness
No smoothness
Weak smoothness
Strong smoothness
Smoothness should just be enough to provide reproducible results
6b
h
k TDRπ η
=
W
Lomakin et al., Methods in Molecular Biology, 299, p. 153 (2005).
Lomakin et al., Methods in Molecular Biology, 299, p. 153 (2005).
Inte
nsity
Dis
tribu
tion
Mas
sD
istri
butio
nIn
tens
ityD
istri
butio
nW
W
/W M
Intensity distribution vs mass distribution
Preparation of Surfactant Peptides
Rh
A6D
V6D
2. Self-assembly of surfactants
A6D
V6D
V6D2
L6D2
Each peptide is 2-3 nm in length, similar to biological phospholipids.
Vauthey et al. PNAS 2002, 99, p. 5355
3. Effect of solvent on protein self-assembly
Supramolecular Assembly of Amelogenin nanospheres
Du et al., Science, 307, p. 1450 (2005)
Self-assembly of Amelogenin is a key factor in controlling the formation of carbonated apatite crystals during dental enamel biomineralization.
TEM image of amelogenin self-assemby into chains
Supramolecular Assembly of Amelogenin nanospheres in different solvents
Aqueous Acetate buffer, pH = 4.5 Aqueous Acetonitrile 60%
Du et al., Science, 307, p. 1450 (2005)
Proteinmonomer
Proteinnanosphere
Insulin aggregation upon shaking
4. Characterization of protein-based pharmaceutical formulations
Initial conditions 3 weeks, no shaking
One hour shakingOne day shaking
Sluzky et al. PNAS (1991), 88, p. 9377.
TEM image
(scale bar: 100 nm)
Fibrils
Protofibrils
5. Kinetics of Aβ amyloids fibrillogenesis
H-Asp-Ala-Glu-Phe-Arg-His-Asp-Ser-Gly-Tyr-Glu-Val-His-His-Gln-Lys-Leu-Val-Phe-Phe-Ala-Glu-Asp-Val-Gly-Ser-Asn-Lys-Gly-Ala-Ile-Ile-Gly-Leu-Met-Val-Gly-Gly-Val-Val-OH
Aβ(1−40)
Walsh et al., J. Biol. Chem. 274, p. 25945 (1999)
HPLC a good alternative to filters for DLS measurements
Protofibrils
Aβ oligomers
Take oligomers from the HPLC outlet and RUN to the DLS apparatus!
1 hr
1.5 hr
2 hr
3 hr
4 hr
6 hr
Kinetic evolution of Aβ amyloids fibrillogenesis
oligomers
protofibrils
concentration 150 μMHCl 0.1 M
Temporal evolutions of mean hydrodynamic radius of protofibrils
concentration 150 μMHCl 0.1 M
4 οC
24 οC
Kusumoto et al. PNAS 95 (1998), p. 12277
NucleatingFiber
4nmhR =
Hydrodynamic radius for cylinders2
2
12 1 1ln
hL xR
xx
−=+ −
0.37( )1d L dxL L
−⎡ ⎤= +⎢ ⎥⎣ ⎦
Protofibril growth
L
d=
calculate L
Protofibril growth
Kinetic model First order kinetics
fe
dNk c
dt=
Linear density: 11.6nmλ −=
fN Lλ=
edL k cdt
λ =
(Tomski et al. Arch. Biochem. Biophys. 294 (1992) p. 630)
fN Number of monomers in fibril
c Monomer concentration
ek Kinetic constant for elongation
Arrhenius plot
exp( / )e Ak A E RT= −
23 1 kcal/molAE = ±
Kusumoto et al. PNAS 95 (1998), p. 12277
The Activation energy for unfolding for peptides of similar size is 10-30 kcal/mol
186 10 L/(mol s)A = × ⋅
Pautot et al., Langmuir, 19, 2870 (2003)
Synthesis of Vesicles from an inverted emulsion
A) Water is emulsified in oil with lipids, forming a stable inverted emulsion.
B) The water that will receive the final vesicles is located below the emulsion. A lipid monolayer is formed at the oil-water interface.
C) The inverted emulsion droplets are heavier and than the oil and sediment into the water phase. At the interface, the final vesicles are formed.
A C
B
water water
vesicle
6. Vesicle/emulsion Characterization
( )(1) ( , ) exp jj
jWg q τ τ= −Γ∑ 2j jq DΓ =
vesicles
emulsion
W
1/h jR Γ∼
Characterization of Vesicles from the inverted emulsion
The distribution for the inverted emulsion is slightly broader perhaps due to presence of lipid aggregates.
The mean radius of the two distribution is comparable:
Vesicles: 170 nm
Emulsion: 220 nm
Pautot et al., Langmuir, 19, 2870 (2003)
Crosslinker (CL): Glutaraldehyde OHC-CH2-CH2-CH2-CHO
….. …..= = =→ → → → →….. …..….. …..= = =→ → → → →
No chemical equilibrium Polydisperse system
7. Formation of crosslinked protein microspheres
Irreversible oligomerization
Generally protein oligomerization yields soluble oligomers or amorphous aggregates
Liquid-Liquid Phase Separation (LLPS)of Protein-Buffer Systems
LLPS (light microscope)
EXAMPLE: γD-crystallin-phosphate buffer 0.1M, pH 7.1
266
270
274
278
282
286
0 200 400 600
c 1 (mg/ml)
T (K
)
CRITICALPOINT
LPPS
TEM
PER
ATU
RE
(K)
CONCENTRATION (mg/ml)
tie-line
266
270
274
278
282
286
0 200 400 600
c 1 (mg/ml)
T (K
)
CRITICALPOINT
LPPS266
270
274
278
282
286
0 200 400 600
c 1 (mg/ml)
T (K
)
CRITICALPOINT
LPPS
TEM
PER
ATU
RE
(K)
CONCENTRATION (mg/ml)
tie-line
The critical temperature is proportional to protein-protein net attraction energy
Lomakin et al., J. Chem. Phys. (1996), 104, p. 1645
(only few examples are known!)
Physicochemical Properties of protein LLPS
LLPS is difficult to observe because
presence of solution freezing pointmetastable with respect to protein crystals protein aggregation may occur firstweak protein-protein attraction for water-soluble proteins
The range of Protein-protein interactions is short
The second liquid phase is highly concentrated in protein droplet
LLPS may be used as a pathway for protein nano/microparticles and crystallization (Mild conditions: protein structure is preserved)
Interest:
Macromolecular Crowding(Depletion forces due to polymer coils)
free volume
depletion layer polymer coil
overlap
protein volume
Maximize free volume accessible to the center of the polymer coil for entropic reasons
Protein-protein Attraction is increased
Asakura & Osawa, J. Chem. Phys. (1954), p. 1255Ilett et al., Phys Rev. E (1995), p. 1344
• PEG is a hydrophilic nonionic polymer used in many biochemical and industrial applications (e.g. two-phase partitioning, pharmaceutical products, cosmetics).
• PEG is the most successful protein crystallizing agent.
HO-(CH2CH2O)n-H
Polyethylene Glycol (PEG)
PEG can be used to induce LLPS in protein aqueous systems
Wang & Annunziata, J. Phys Chem. B (2007), 111, 1222
c1c2
T ph
( K )
(Protein-buffer system)
LLPS surface of the protein-PEG-buffer system
Annunziata et al., PNAS (2002), 99, p.14165.Annunziata et al., PNAS (2003), 100, p.970.
1
2
ph
= protein concentration= PEG concentration= LLPS temperature
ccT
PEG -->
Wang & Annunziata, J. Phys Chem. B (2007), 111, 1222
-15
-10
-5
0
5
10
15
20
2 3 4 5Average Hydrodinamic Radius (nm)
Tph (
o C)
C1
proteinoligomerization
LLPS BOUNDARY (monomer)
supersaturation
T
0phT
LLPS BOUNDARY
(oligomers)oligT
Protein sample concentration
sample
Oligomerization-induced liquid-liquid phase separation
Lysozyme 10 mg/mL
Wang and Annunziata, Manuscript in prep.
Bar length = 10 μmCL = cross-linker = glutaraldehyde
CL 0.2%
CL 0.075%
CL 0.15%
CL 0.3%
Oligomerization-induced microsphere formation(lysozyme, albumin, invertase)
0
0.20.4
0.6
0.8
11.2
1.4
0 0.2 0.4 0.6Crosslinker Concentration (%)
1/ D
iam
eter
( μm
-1)
0123456789
0 0.2 0.4 0.6Crosslinker Concentration (%)
Dia
met
er ( μ
m)
Diameter ~ CCL-1
C1
proteinoligomerization
LLPS BOUNDARY (monomer)
supersaturation
T
0phT
LLPS BOUNDARY
(oligomers)oligT
Protein sample concentration
sample
Oligomerization-induced microsphere formation
1 10 100 1000
Hydrodynamic Radius (nm)
Scat
tere
d in
tens
ity
dist
ribut
ion
time 0 hr
1 10 100 1000
Hydrodynamic Radius (nm)
Scat
tere
d in
tens
ity
dist
ribut
ion
time 24 hr
1 10 100 1000
Hydrodynamic Radius (nm)
Scat
tere
d in
tens
ity
dist
ribut
ion
time 20 hr
1 10 100 1000
Hydrodynamic Radius (nm)
Scat
tere
d in
tens
ity
dist
ribut
ion
time 21 hr
Wang and Annunziata, Manuscript in prep.
( Lysozyme 10 mg/mL, NaCl 0.5 M, pH 4.5)(glutaraldehyde 0.07%, T = 25 °C)
Oligomerization kinetics
oligomersclusters
Oligomerization kinetics and microsphere nucleation
1
10
100
1000
1 10 100
time (hours)
Hyd
rody
nam
ic R
adiu
s (n
m)
CL 0.09%CL 0.07%CL 0.05%
120 nm180 nm
250 nm
5.7 nm 5.7 nm 5.7 nm
Onset of LLPS nucleation at the same oligomer radius
( Lysozyme 10 mg/mL, NaCl 0.5 M, pH 4.5, T = 25 °C)
The radius of protein nanoclusters decreases as crosslinker concentration increases
0
0.002
0.004
0.006
0.008
0.01
0 0.02 0.04 0.06 0.08 0.1
Crosslinker W%
1/R
h (nm
-1)
The radius of protein clusters is inversely proportional to crosslinker concentration.