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.