Time Correlation Function Of Intensity Research Articles

Inferring Diffusion Dynamics from FCS in Heterogeneous Nuclear Environments

Fluorescence correlation spectroscopy (FCS) is a noninvasive technique that probes the diffusion dynamics of proteins down to single-molecule sensitivity in living cells. Critical mechanistic insight is often drawn from FCS experiments by fitting the resulting time-intensity correlation function, G(t), to known diffusion models. When simple models fail, the complex diffusion dynamics of proteins within heterogeneous cellular environments can be fit to anomalous diffusion models with adjustable anomalous exponents. Here, we take a different approach. We use the maximum entropy method to show—first using synthetic data—that a model for proteins diffusing while stochastically binding/unbinding to various affinity sites in living cells gives rise to a G(t) that could otherwise be equally well fit using anomalous diffusion models. We explain the mechanistic insight derived from our method. In particular, using real FCS data, we describe how the effects of cell crowding and binding to affinity sites manifest themselves in the behavior of G(t). Our focus is on the diffusive behavior of an engineered protein in 1) the heterochromatin region of the cell’s nucleus as well as 2) in the cell’s cytoplasm and 3) in solution. The protein consists of the basic region-leucine zipper (BZip) domain of the CCAAT/enhancer-binding protein (C/EBP) fused to fluorescent proteins.

Conformational Fluctuations of Chromosomal DNA in E-Coli

We measured the conformational fluctuations of DNA in E. Coli in vivo using fluorescence correlation spectroscopy (FCS). The chromosomal DNA was randomly decorated with a cell-permeable intercalating dye. Conformational fluctuations of the DNA move the fluorophores stochastically into the diffraction-limited excitation volume of a focused laser beam. The time correlation function of the fluorescence intensity reflects the underlying dynamics of the DNA on length scales down to ∼200 nm. A comparison between live cells and dead yet structurally intact cells shows identical fluctuation spectra for short time scales, yet substantial differences for frequencies below 100 Hz. Live cells show much stronger fluctuations in this regime. This observation points to the crucial importance of active molecular motor action, as opposed to passive thermal noise, in driving larger conformational fluctuations in the chromosomal DNA, in particular on length scales exceeding ∼500 nm.

A study of alcohol-induced gelation of β-lactoglobulin with small-angle neutron scattering, neutron spin echo, and dynamic light scattering measurements

Gelation of beta-lactoglobulin (beta-Lg) in various alcohol-water mixtures with 0.1 M (M = mol L(-1)) hydrochloric acid was investigated with small-angle neutron scattering (SANS), neutron spin echo (NSE), and time-resolved dynamic light scattering (TRDLS) measurements. The beta-Lg in alcohol-water solutions undergoes gelation at specific alcohol concentrations where the alcohol-induced alpha-helical structure of beta-Lg is stabilized. The SANS profiles showed that beta-Lg exists as a single molecule at a low alcohol concentration. With increasing alcohol concentration, the profiles indicate a power law behavior of approximately 1.7 when the samples gelate. These behaviors were observed in all alcohol-water mixtures used, but the alcohol concentrations where the SANS profiles change shift to a lower alcohol concentration region with an increase in the size of the hydrophobic group of the alcohols. Apparent diffusion constants, obtained from the intermediate scattering function (ISF) of NSE and the intensity time correlation function (ITCF) of TRDLS, mainly depend on the viscosity of alcohol-water mixtures before gelation. After gelation, on the other hand, the ISFs of gels do not change appreciably in the range of the NSE time scale, indicating the microscopically rigid structure of beta-Lg gel. The ITCF functions obtained from TRDLS follow a double exponential decay type before gelation, but a logarithmic one (exponent alpha = 0.7) after gelation. It is most likely that the alcohol-induced gelation undergoes a similar mechanism to that for the heat-induced one at pH = 7 where beta-Lg aggregates stick together to form a fractal network, although the gelation time is faster in the former than in the latter.

DYNAMIC LIGHT SCATTERING STUDIES OF SOL-GEL TRANSITION IN AQUEOUS ALGINATE SOLUTION INDUCED BY CALCIUM CATIONS

The sol-gel transition of aqueous alginate solutions induced by calcium cations has been studied by using dynamic light scattering.A critical relaxation was observed near the gel point,which was characterized by the power law of the time-intensity correlation function g~((2))(t)-1∝t~(-μ).The comparison of this critical exponent μ with the critical exponent n for mechanical relaxation obtained with dynamic rheology measurements shows μ=2n for the Ca-alginate sol-gel transition.The critical exponent μ was found to be proportional to q~2,q is the scattering vector,and the proportional coefficient almost equaled to the correlation length of the critical gel.

Comparison of heat- and pressure-induced gelation of β-lactoglobulin aqueous solutions studied by small-angle neutron and dynamic light scattering

The gelation mechanism of β-lactoglobulin (bLG) aqueous solutions was investigated by dynamic light scattering (DLS) and small-angle neutron scattering (SANS). Temperature- and pressure-jump experiments, respectively, abbreviated as T-jump (from 20 to 75°C; T-jump) and P-jump (from 0.1 to 315MPa) were carried out and the time evolution of gel structure was monitored by DLS and SANS as a function of time. The gelation threshold was determined by DLS as the point when nonergodicity appeared. In the case of T-jump, a rapid increase of the time-average scattered intensity, 〈I〉T, and a steep decrease of the initial amplitude of the intensity–intensity time correlation function, σI2, were observed at the gelation threshold. On the other hand, P-jump showed a gradual increase of the 〈I〉T and a continuous decrease of the σI2. It was revealed by SANS that bLG underwent thermal denaturation, resulting in a formation of gels consisting of densely aggregated unfolded bLG oligomers. On the other hand, the pressure-induced gels were found to be a fractal aggregates consisting of primary particles of bLG monomers. The difference in the gel structure as well as gelation mechanism between bLGs treated by T-jump and P-jump is discussed in comparison with T-induced and P-induced microphase separation of amphiphilic block copolymers in water [Osaka N, Shibayama M. Phys Rev Lett 2006;96:048303].

Comparison of Critical Exponents Determined by Rheology and Dynamic Light Scattering on Irreversible and Reversible Gelling Systems

AbstractSummary: The sol‐gel transition of a radical chain cross‐linking copoly‐merization system [N‐vinylcaprolactam/2‐hydroxylethyl methacrylate/allyl‐methacrylate] and various thermoreversible gelling systems (mixtures made of xanthan gum and locust bean gum as well as gelatin) have been studied using in‐situ time‐resolved dynamic light scattering (DLS) and in‐situ rheology. A critical dynamical behavior was observed near the sol‐gel transition, which is characterized by the presence of a power‐law spectra in the time‐intensity correlation function g2(t)−1 ∝ t−µ and in the low‐amplitude oscillatory shear experiment G′(ω) ∝ G″(ω) ∝ ωn. A comparison of the obtained critical dynamical exponents µ and n were made according to the theory by Doi and Onuki. This theory predicts a relation between these exponents, but up to now no detailed experimental comparison was done in the past. It was found that for all investigated systems n > µ.

Dynamics of thermoresponsive PNIPAM- g-PEO copolymer chains in semi-dilute solution

The effects of concentration and temperature on dynamics of poly( N-isopropylacrylamide)- graft-poly(ethylene oxide) (PNIPAM- g-PEO) chains in semi-dilute aqueous solution were studied by static and dynamic laser light scattering. The intensity–intensity time correlation function shows a fast and a slow relaxation mode, with line widths Γ f and Γ s, respectively. Γ f is scaled to the scattering vector ( q) as Γ f ∝ q 2, revealing that it is due to the cooperative diffusion of the subchains between two neighboring entangled points. As the concentration increases, the slow relaxation becomes slower and contributes more to the total scattered light intensity, indicating that the slow relaxation is related to the chain entanglement. On the other hand, when the solution temperature increases, the PNIPAM chain backbone shrinks, but the fast relaxation remains and the slow mode slows down with a minimum rate at ∼33 °C. It indicates that the slow mode arises from inter-chain clustering, which is gradually suppressed by the intra-chain shrinking. The sample position independence of the time-averaged scattered light intensity 〈 I〉 T reveals that the solution is homogeneous and the clustering is transient.

“Spreading” of a biphoton in a group-velocity-dispersion medium and two-photon interference

It is shown that two-photon Bell states can be prepared by “spreading” of a two-photon wave packet (biphoton) in a dispersive medium without compensating for group delays between photons with orthogonal polarizations or using narrow-band filters but by selecting the time correlation function. This is possible because two-photon interference effects are manifested in the shape of the time correlation function of intensity due to its spreading.

Laser Light-Scattering Study of Solution Dynamics of Water/Cycloether Mixtures

The complexation of tetrahydrofuran as well as 1,4-dioxane with water has been investigated by laser light scattering (LLS). The complexation of cycloethers with water molecules makes the diffusion of water clusters visible in LLS. The intensity−intensity time correlation function of a simple mixture of water and tetrahydrofuran (THF) or 1,4-dioxane has two diffusive relaxation modes. The fast mode with a diffusion coefficient in the range 2−8 × 10-6 cm2 s-1 is related to mutual diffusion of the complexes formed between small water clusters and THF or 1,4-dioxane. The slow mode with a dynamic correlation length of 200−600 nm can be removed by filtration, indicating that the mixing of water and cycloethers is microscopically incomplete. Further, using a trace amount of spherical poly(N-isopropyl acryamide) microgels as probes, we indirectly investigated the water/THF interaction. Our results showed that PNIPAM swell in ether pure water or pure THF but fully collapse when [THF]:[water] = 0.05−0.15, in which the water/THF complexes are nonsolvent for PNIPAM. When [cycloether]:[water] > ∼0.16, water is not able to further complex with cycloethers added so that extra cycloethers exist as individual molecules to reswell the microgels, indicating that it is small water clusters, such as the pentamer and hexagon, that solvate PNIPAM.

Mesoscopic physics of photons

We review the general features of coherent multiple scattering of electromagnetic waves in random media. In particular, coherent backscattering and angular correlation functions of speckle patterns are studied in some detail. We present a general formalism based on a physically intuitive description that also permits us to derive quantitative expressions. Then, the notion of phase boxes describing the quantum crossings of diffusons is discussed. This notion permits us to understand the long-range correlations that are at the origin of most of the mesoscopic effects either for electrons or photons. Then, we turn to the problem of decoherence, namely, the washing out of interference effects. We use as an example the effect of a nondeterministic motion of the scatterers. We discuss some applications of these ideas to diffusive wave spectroscopy, including calculations of the intensity–time correlation function in the presence of quantum crossings.

Gel Formation Analyses by Dynamic Light Scattering

Abstract A novel methodology for non-destructive and real-time determination of the gelation threshold for both chemical and physical systems has been proposed. This method i.e., a time-resolved dynamic light scattering (TRDLS) measurement, allows one not only to determine the gelation threshold but also to investigate critical dynamics near gelation threshold, mechanism of gelation, and architecture of gelling cluster. The gelation threshold was found to be characterized by (1) the appearance of a speckle pattern in the scattering intensity, (2) a power-law in the intensity–time correlation function (ICF), (3) a specific broadening of the distribution function, and (4) a noticeable suppression of the initial amplitude of ICF. All of these features originate from some unique aspects of gels: nonergodicity, frozen inhomogeneities, and divergence of connectivity correlation. As an application of these concepts, we propose four methods for determination of gelation threshold and examine their validity and usefulness for various types of gels; these include chemical gels of N-isopropylacrylamide, a gelling system of silica gel in a reaction batch, thermoreversible physical gels of poly(vinyl alcohol)–Congo Red complex, and biological gels of gelatin and globular protein.

Dynamic light scattering study on gelatin aqueous solutions and gels

The sol–gel transition of gelatin aqueous solutions has been investigated by dynamic light scattering as a function of gelatin concentration, C, at 10 °C, by taking account of the nonergodic nature of gels. The sol–gel transition concentration, Cgel, was determined to be around 0.35 wt % in this particular case. The scattered intensity exhibited a speckle pattern for C>Cgel. The dynamic component of the scattered intensity, 〈IF〉T, was successfully extracted from the time-average scattered intensity, 〈I〉T. 〈IF〉T diverged at Cgel and decreased by further increasing C. The time-intensity correlation function exhibited a power-law behavior exclusively at C≈Cgel. The exponent was found to be independent of the scattering vector, as it should be as a critical exponent of connectivity.

Dynamic light‐scattering characterization of the molecular weight distribution of unfractionated polyimide

AbstractUsing a developed laser light‐scattering (LLS) procedure, we accomplished the characterization of an unfractionated polyimide (UPI) in CHCl3 at 25°C. The Laplace inversion of precisely measured intensity–intensity time correlation function from dynamic LLS leads us first to an estimate of the characteristic line‐width distribution G(Γ), and then to the translational diffusion coefficient distribution G(D). By using a previously established calibration of D (cm2/s) = 3.53 × 10−4 M−0.579, we were able to convert G(D) into a molecular weight distribution. The weight‐average molecular weight Mw, calculated from the molecular weight distribution, agrees well with that directly measured in static LLS. Our results indicate that both the calibration and LLS procedure used in this study are ready to be applied as a routine method for the characterization of the molecular weight distribution of polyimide. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 81: 1670–1674, 2001

Heat-Induced Gelation of β-Lactoglobulin. 1. Time-Resolved Dynamic Light Scattering

The time evolution of the dynamics of globular protein during the gelation process via aggregation has been studied by time-resolved dynamic light scattering (DLS) for β-lactoglobulin (β-LG) in aqueous solutions at pH 2 and 7. The following facts were disclosed: (1) The scattered intensity, 〈I〉T, started to fluctuate, and the intensity−time correlation function (ITCF) exhibited a power-law behavior (g(2)(τ) − 1 ∼ τα-1) at the gelation threshold, tth. (2) The variations of 〈I〉T's were different between the two pHs, a gradual increase for pH 2 and a stepwise increase followed by a plateau for pH 7. (3) The exponent α was found to be strongly dependent on pH. The values of α were 0.51 ± 0.05 for pH 2 and 0.74 ± 0.05 for pH 7. (4) A strong concentration and pH dependence of tth was also observed in both cases. These findings indicate that β-LG gels formed at pH 2 and pH 7 have different architectures, i.e., loosely tied networks (for pH 2) and fractal aggregates (for pH 7) of protein molecules.

Self-diffusion and interaction of the polystyrene–polyisoprene blend in chloroform probed by quasielastic light scattering

Solutions of an incompatible polystyrene (PS)–polyisoprene (PIP) blend dissolved in CHCl3 are investigated by light scattering as a function of total polymer concentration at a fixed composition in the semidilute regime. Two diffusive modes are observed in the intensity–intensity time-correlation function. As the total polymer concentration increases, it is found that the rate constant of the fast mode increases and that of the slow mode as well as the relative amplitude of the fast mode decrease. With the help of a theory developed in this laboratory, we deduce from the light scattering data the self-diffusion coefficients and the Flory–Huggins interaction parameter χF of the two polymers. The self-diffusion coefficients of both polymers decrease as the total polymer concentration increase. Meanwhile, the Flory–Huggins interaction parameter χF between PS and PIP in CHCl3 (equal to 0.017) is nearly independent of polymer concentration. After making corrections for the excluded volume effect between unlike polymer using polymer solution theory, we obtain from χF a net segment–segment interaction parameter χF0, which is rather close to that obtained from the solvent free dry blend.

Scalings of fluorine-containing polyimides in cyclopentanone

Eight 2,29-bis(3,4-dicarboxyphenyl) hexafluoropropane dianhydride-4,49- diamino-3,39-dimethylbiphenyl (6FDA-OTOL) fractions and seven 2,29-bis(4-(3,4-dicar- boxyphenoxy) phenyl) propane dianhydride-4,49-diamino-3,39-dimethylbiphenyl (BISADA-OTOL) fractions in cyclopentanone at 30 °C were characterized by a combi- nation of viscometry and static and dynamic laser light scattering (LLS). In static LLS, the angular dependence of the absolute scattered intensity led to the weight-average molar mass (Mw), the z-average root mean square radius of gyration, and the second virial coefficient. In dynamic LLS, the Laplace inversion of each measured intensity- intensity time correlation function resulted in a corresponding translational diffusion coefficient distribution (G(D)). The scalings of ^D& (cm 2 /s) 5 8.13 3 10 25 Mw 20.47 and (h) (dL/g) 5 2.36 3 10 23 Mw 0.54 for 6FDA-OTOL and ^D& (cm 2 /s) 5 3.02 3 10 24 Mw 20.60 and (h) (dL/g) 5 2.32 3 10 23 Mw 0.53 for BISADA-OTOL were established. With these scalings, we successfully converted each G(D) value into a corresponding molar mass distribution. At 30 °C, cyclopentanone is a good solvent for BISADA-OTOL but a poor solvent for 6FDA-OTOL; this can be attributed to an ether linkage in BISADA-OTOL. Therefore, BISADA-OTOL has a more extended chain conformation than 6FDA-OTOL in cyclopentanone. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 2077-2080,

Convection and thermodiffusion of colloidal gold tracers by laser light scattering.

In a dynamic light scattering experiment, we have investigated the time intensity correlation function and the profile of the transmitted laser beam for organic dispersions of light absorbing colloidal particles containing tiny gold clusters. The correlation functions have been found to show a superposition of an exponential decay, corresponding to Brownian motion of the tracers, and well-defined oscillations. These oscillations are caused by convection due to local heating of the sample by the incident laser beam, which has been confirmed independently via measurements of the local temperature within the sample. It will be shown how the particle convection velocity, which is the order of 1 mm/s, can be obtained quantitatively from the oscillating correlation functions. The profile of the transmitted beam allowed us to determine the Soret coefficient, which is a measure for the thermal diffusion of the particles. This article shows how tracer diffusion, convection, and thermal diffusion can be determined simultaneously by one single experiment, laser light scattering of light absorbing colloidal particles in dispersion.

Statistical properties of focal plane speckle

The second order statistical properties of coherent radiation scattered from a rough surface in the focal plane of an optical system are analysed. Two types of motion of the scattering surface are considered: arbitrary movement in his own plane without velocity gradients across the illuminating laser spot and secondly for a rotational target movement. The expressions for the space–time intensity correlation function and the corresponding power spectrum are derived and the characteristics of speckle motion are analysed. It is shown that for rotational motion of the target the speckle pattern will rotate in the focal plane about a displaced axis. It is shown also that the statistical properties of the scattered radiation on the axis of the incident beam under rotational movement conditions are identical to those under uniform motion of the scattering surface. An experiment carried out with a He–Ne laser has confirmed the mathematical model suggested.

Dynamic light scattering in polymer-dispersed liquid crystals

A polymer dispersed liquid crystal was studied by dynamic light scattering. In the experiments, where no electric field is applied, the system exhibits additional slow dynamics to the ones observed in bulk nematic liquid crystals. This slow dynamics gradually disappears with an increasing electric field. While the measured time intensity correlation function does not depend on the scattering vector in the system where no field is applied due to the multiple scattering, its dependence on the electric field shows expected size effects. In confined systems, with typical size $d$, there are no eigenmodes of the orientational fluctuations in droplets with the wave vectors less than the minimal wave vector ${q}_{\mathrm{min}}\ensuremath{\sim}\ensuremath{\pi}/d$. We observed a quadratic dependence of the inverse relaxation time on the scattering vector down to a certain scattering vector, below which the relaxation time remains constant. The size calculated from this minimal scattering vector is in agreement with the average droplet size obtained from scanning electron microscope photographs and the atomic force microscope images of our sample. The electric field changes the temperature behavior of the inverse relaxation time near the nematic-isotropic phase transition, which increases with the temperature when the electric field is applied, but decreases when the field is absent.

Light‐scattering Characterization of the Molecular Weight Distributions of Some Intractable Polymers

Recent developments of using laser light scattering (LLS) to characterize the molecular weight distribution f(M) of special polymers such as Kevlar, Tefzel, Teflon, branched epoxy clusters, gelatin, dextran, segment copolymers and polymer mixtures, are reviewed. The basic principle of combining static (classic) and dynamic LLS results is outlined. In dynamic LLS, the line-width (or the translational diffusion coefficient) distribution G(Γ) can be obtained from the precisely measured intensity–intensity time correlation function. The key problem is transforming G(Γ) to a corresponding molecular weight distribution f(M) is to establish a calibration between D (the translational diffusion coefficient) and M. Typical examples were used to illustrate different calibration methods, including the methods of using a series of narrowly distributed polymer standards with different molecular weights, using two or more broadly distributed polymer samples, and one broadly distributed polymer samples plus an additional experimental method (e.g. viscometry or size exclusion chromatography). The advantages and disadvantages of the LLS method are discussed by comparison with size exclusion chromatography. © 1997 John Wiley & Sons, Ltd.