Pursuing the initial stages of crystal growth

using dynamic light scattering (DLS) and

fluorescence correlation spectroscopy (FCS)

Takashi SugiyamaMiyasaka laboratory

Introduction

Many studies have been done for decades to clarify the mechanism of crystallization. It is, however, its dynamics are too complicated to be understood in detail.

Direct measurement of nucleation process requires a detection method of individual molecules moving freely in solution. It is still difficult even now.

Solution Nano/micro crystal Bulk crystalNucleationNucleation

Initial stage

NsNc0

ΔGcΔG

Thermodynamic background of crystal growth

Aggregation size becomelarger than critical size. Crystal growth

<Supersaturated solution>

Critical size

G 4

3 R3ns 4R2

Crystallization of colloidal particles

Atomic force microscope

•High sensitivity•High temporal resolution•High spatial resolution

Previous approaches for pursuing nucleation of crystals

Laser scanning microscope

molecular ordering dynamics of proteins at single molecule level on substrates

・・

High-sensitive photo detection methods have been developed recently, motivating researchers to pursue the crystal growth using them.

Dynamic light scattering (DLS)Dynamic light scattering (DLS)Fluorescence correlation spectroscopy (FCS)Fluorescence correlation spectroscopy (FCS)

CONTENTS

Principle of DLS and FCS Confocal setup Autocorrelation function (ACF)

Pursuing crystal growth of naphthalene using DLS

Pursuing protein nucleation using FCS

Summary

Experimental setup for DLS and FCS

Confocal optical setup

Objective

High spatial resolution (in particular, z-axis) can be achieved.

Only fluorescent light from probe molecules or scattered lightfrom crystals on the focal plane is detected.

•DLS: Scattering light from particles•FCS: Fluorescent light from dyes

Image plane Molecles/nanoparticles

Laser light

Pinhole

High sensitive Photodetector(Single photon counting module)

Sample solution

Autocorrelation function (ACF)

ACF can be used to analyze many kinds of fluctuations.

g(τ) : autocorrelation function (ACF)I(t) : signal intensity

τ : delay timeδ : fluctuations of intensity

g() I(t ) I(t)

I(t) 2

2)(

)()(1

tI

tItI

Fast fluctuationSlow fluctuation

Slow decay of ACF Fast decay of ACF

g()

g()

“Kinetics of the formation of organic molecular nanocrystals”

Jack Adrian et al., Nanoletters, 1,141-143 (2001)

Pursuing crystal growth of naphthalene using DLS

Sample

Ternary system: naphthalene/acetone/water

Naphthalene/acetone solution

Water

Easy to control the solubility of naphthalene to the mixture solvent

Obtained ACF was fitted with Siegert relation

)2exp(1)( 2)2( Dqg : 0~1, experimental constant

q : scattering vector magnitude

)()2( g : ACF

Diffusion coefficient is determined.

Stokes-Einstein equation

a

kTD

6

η: viscosityT : temperaturek : Boltzmann constant

a : hydrodynamic radius

Hydrodynamic radius can be calculated.

: diffusion coeffcientD

Result

The diffusion coefficient of the naphthalene nanocrystal decreased with time.

Particle is monodisperse during each measurement.

Sample (1) Naphthalene/Acttone/Water = 0.040/0.637/0.323

Sample (2) Naphthalene/Acttone/Water = 0.013/0.523/0.464

(1)

(2)

Sample (1)

Growing process of naphthalene nanocrystals is pursued

Incident beam:He-Ne laser(633 nm)

Time(sec)

Other method is needed to pursue nucleationsteps.

Using DLS, time-evolution of the naphthalene crystal sizes (~100nm) under supersaturation could be pursued.

In the DLS measurement, nucleation steps of the crystal cannot be observed because nucleation occurs faster than measurement time.

NsNc

ΔGcΔG

0

Summary and assignment

“Screening crystallization conditions using fluorescence correlation spectroscopy”

Maxim E. Kuil et al., Acta Cryst., D58, 1536-1541 (2002)

Pursuing protein nucleation using FCS

It is impossible to apply the FCS under high concentration of fluorescent probe, where fluctuation of fluorescent light is too small.

Small amount of fluorescent labeled proteins are added to the solutions of unlabeled ones

Possible to pursue nucleus (clusters) using FCS

Labeled protein

Unlabeled protein

Supersaturated solution ・・・ High molecular concentration

Free diffusion Cluster

Sample

: LysozymeProtein

Dye for labelling : Cy5 succinimidyl ester

Cy5 labelled proteins were prepared.

(Label ratio : 0.3~1.6 per protein)

<Lysozyme crystal>

Cy5-labelled protein is homogeneously incorporated, suggesting labeled proteins affect their crystallization little.

Concentration of labelled protein : ~5nM

Solubility change of proteins in adding electrolyte

Effect of salting out Salting out constant :Ks

sK Ωσ:salting out term Λ :salting in term

Ωσ depends on hydrophobic part of the surfaceand increasing rate of surface tension.Λ is independent of types of electrolyte and their concentration under high electrolyte concentration.

In case of increase in electrolyte concentration…

Ks becomes large.Ωσ large

Λ not change

Model used for fitting:

M

i

DD

i

t

ii

t

Stt

fe

T

T

NtG

121

1

111

11)(

G(t): fluorescence intensity ACFN: number of particlesT: fraction of fluorophores in triplet state

τt: triplet lifetimeM: number of fluorescent component

fi: fraction in i componentS: structural parameter

ACF Diffusion coefficient can be calculated.

D

wxyD 4

2

Relationship τD (the average residence time) and D (diffusion coefficient) Wxy is the radius of detection volume.

Diffusion rate became slow with increase in protein

concentration

correlation time t/μs

Excitation light : He-Ne laser (633 nm)

•Viscosity rise of the solution due to an increase in the concentration of the protein•Cluster formation of the protein

Results

crystallizing

0.31M1M

no NaClHard sphere

model

Diffusion rate became slow and crystallizing occurred with increasing electrolyte concentration.

Electrolyte concentration dependence (1)

NaCl

When NaCl was added, diffusion rate became slow andcrystallization occurred.

Decrease of the volume for the proteins to move freely

Protein cluster and/or nucleus formation

The thickness change of electrical double layer

From the experimental results

Diffusion rate became slow although protein concentration was constant.No NaCl concentration dependence was observed on diffusion coefficient of lysozyme at low protein concentration.

Protein cluster and/or nucleus formation was observed

Diffusion coefficient change of labeled lysozyme due to nucleation and/or association of the protein was pursued using FCS.

The result suggests

NsNc

ΔGcΔG

0

Calculation volume ratio (no NaCl : 1M NaCl ) 1 : 2.1E

xist

ing

prob

abil

ity

no NaCl

0.31 M NaCl

1 M NaCl

Criticalnucleus

Equilibrium shifts to the critical nucleus

0.2Mno (NH4)2SO4

1M

Hard sphere model

・ Diffusion rate is independent of electrolyte concentration.

・ Crystallizing didn’t occur.

(NH4)2SO4

Electrolyte concentration dependence (2) [Control experiment]

Summary

Using FCS, the change of diffusion coefficient wasobserved when nucleation and/or association of the protein was occurred.

The number of molecules inside critical nucleus has not been determined yet.

Direct measurement of molecular motion will pave the way to further understandings of molecular nucleation.