Pursuing the initial stages of crystal growth using dynamic light scattering (DLS) and fluorescence correlation spectroscopy (FCS) Takashi Sugiyama Miyasaka 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. Initial stage Solution Nucleation Nano/micro crystal Bulk crystal Direct measurement of nucleation process requires a detection method of individual molecules moving freely in solution. It is still difficult even now. Thermodynamic background of crystal growth ΔGc ΔG <Supersaturated solution> Critical size 4 G R3ns 4R2 3 0 Nc Aggregation size become larger than critical size. Ns Crystal growth Previous approaches for pursuing nucleation of crystals Laser scanning microscope Crystallization of colloidal particles Atomic force microscope ・ ・ ・ molecular ordering dynamics of proteins at single molecule level on substrates • High sensitivity • High temporal resolution • High spatial resolution High-sensitive photo detection methods have been developed recently, motivating researchers to pursue the crystal growth using them. Dynamic light scattering (DLS) 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 Image plane Molecles/nanoparticles Pinhole Sample solution Objective Laser light High sensitive Photodetector (Single photon counting module) • DLS: Scattering light from particles • FCS: Fluorescent light from dyes High spatial resolution (in particular, z-axis) can be achieved. Only fluorescent light from probe molecules or scattered light from crystals on the focal plane is detected. Autocorrelation function (ACF) ACF can be used to analyze many kinds of fluctuations. I(t ) I(t) g( ) I(t) 2 g(τ) : autocorrelation function (ACF) I(t) : signal intensity τ : delay time δ : fluctuations of intensity I (t ) I (t ) 1 I (t ) 2 g( ) g( ) Slow fluctuation Slow decay of ACF Fast fluctuation Fast decay of ACF Pursuing crystal growth of naphthalene using DLS “Kinetics of the formation of organic molecular nanocrystals” Jack Adrian et al., Nanoletters, 1,141-143 (2001) 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 g( 2) ( ) : ACF g( 2) ( ) 1 exp(2Dq2 ) : 0~1, experimental constant D : diffusion coeffcient q : scattering vector magnitude Diffusion coefficient is determined. Stokes-Einstein equation D kT 6a k : Boltzmann constant T : temperature η: viscosity a : hydrodynamic radius Hydrodynamic radius can be calculated. Result Incident beam:He-Ne laser(633 nm) Sample (1) Naphthalene/Acttone/Water = 0.040/0.637/0.323 Sample (2) Naphthalene/Acttone/Water = 0.013/0.523/0.464 Sample (1) (1) (2) Time(sec) Particle is monodisperse during each measurement. The diffusion coefficient of the naphthalene nanocrystal decreased with time. Growing process of naphthalene nanocrystals is pursued ΔGc ΔG Summary and assignment 0 Using DLS, time-evolution of the naphthalene crystal sizes (~100nm) under supersaturation could be pursued. Nc Ns In the DLS measurement, nucleation steps of the crystal cannot be observed because nucleation occurs faster than measurement time. Other method is needed to pursue nucleation steps. Pursuing protein nucleation using FCS “Screening crystallization conditions using fluorescence correlation spectroscopy” Maxim E. Kuil et al., Acta Cryst., D58, 1536-1541 (2002) Supersaturated solution ・・・ High molecular concentration 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 Free diffusion Cluster Sample Protein : Lysozyme Dye for labelling : Cy5 succinimidyl ester Cy5 labelled proteins were prepared. (Label ratio : 0.3~1.6 per protein) Concentration of labelled protein : ~5nM <Lysozyme crystal> Cy5-labelled protein is homogeneously incorporated, suggesting labeled proteins affect their crystallization little. Solubility change of proteins in adding electrolyte Effect of salting out Salting out constant :Ks Ks Ωσ:salting out term Λ :salting in term Ωσ depends on hydrophobic part of the surface and 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… Ωσ Λ large not change Ks becomes large. Model used for fitting: t fi 1 T t M G(t ) 1 1 e i 1 1 t N 1 T Di 1 1 t S 2 Di G(t): fluorescence intensity ACF τt: triplet lifetime N: number of particles M: number of fluorescent component S: structural parameter T: fraction of fluorophores in triplet state fi: fraction in i component Relationship τD (the average residence time) and D (diffusion coefficient) Wxy is the radius of detection volume. ACF D 2 wxy 4D Diffusion coefficient can be calculated. Results Excitation light : He-Ne laser (633 nm) Diffusion rate became slow with increase in protein concentration correlation time t/μs • Viscosity rise of the solution due to an increase in the concentration of the protein • Cluster formation of the protein Electrolyte concentration dependence (1) NaCl crystallizing 1M 0.31M no NaCl Hard sphere model Diffusion rate became slow and crystallizing occurred with increasing electrolyte concentration. When NaCl was added, diffusion rate became slow and crystallization occurred. Decrease of the volume for the proteins to move freely The thickness change of electrical double layer Protein cluster and/or nucleus formation 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 Calculation volume ratio (no NaCl : 1M NaCl ) 1 : 2.1 Existing probability no NaCl 0.31 M NaCl 1 M NaCl Critical nucleus The result suggests Diffusion coefficient change of labeled lysozyme due to nucleation and/or association of the protein was pursued using FCS. ΔGcΔG Equilibrium shifts to the critical nucleus 0 Nc Ns Electrolyte concentration dependence (2) [Control experiment] (NH4)2SO4 1M 0.2M no (NH4)2SO4 Hard sphere model ・ Crystallizing didn’t occur. ・ Diffusion rate is independent of electrolyte concentration. Summary Using FCS, the change of diffusion coefficient was observed 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.
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