Mean Square Displacement Distribution Research Articles

Microrheology imaging of fiber suspensions - a case study for lyophilized collagen I in HCl solutions.

In fiber suspensions with low optical contrast, the in situ characterization of structural properties with conventional microscopy methods fails. However, overlaying subsequent images of multiple particle tracking (MPT) videos including short trajectories usually discarded in MPT analysis allowed for direct visualization of individual fibers and the network structure of lyophilized collagen I (Coll) distributed in hydrochloric acid solutions. MPT yielded a broad distribution of mean square displacements (MSDs). Freely diffusing tracer particles yielded viscosities indicating that, irrespective of concentration, a constant amount of Coll is dissolved in the aqueous phase. Particles found elastically trapped within fibrous Coll structures exhibited a broad range of time-independent MSDs and we propose a structure comprising multiple fiber bundles with dense regions inaccessible to tracers and elastic regions of different stiffness in between. Bulky aggregates inaccessible to the 0.2 μm tracers exist even at low Coll concentrations, a network of slender fibers evolves above the sol-gel transition and these fibers densify with increasing Coll concentration. This novel MPT-based imaging technique possesses great potential to characterize the fiber distribution in and structural properties of a broad range of biological and technical suspensions showing low contrast when imaged with conventional techniques. Thus, MPT imaging and microrheology will help to better understand the effect of fiber distribution and network structure on the viscoelastic properties of complex suspensions.

(Invited) Elucidating the Micro Phase-Separation of Mixed Kappa and Iota Carrageenan Gels Using Multiple Particle Tracking

Carrageenan is a family of linear sulfated polysaccharides extracted from seaweeds. Among the different types of carrageenan, kappa carrageenan (KC) and iota carrageenan (IC) are widely used in industries due to its gelling behavior. Because of its importance in industries, KC and IC as well as its mixtures have been extensively studied using different methods. However, it is still unclear whether mixed KC:IC undergo a phase separated network structure of IC-rich and KC-rich or interpenetrated network structure. In this report, the network structure and gelation mechanism of KC, IC and its mixture were elucidated using multiple particle tracking. Sodium-type κ- and ι- carrageenan powder was purchased from Tokyo Chemical Industry Co., Ltd. (Tokyo, Japan). All samples were dialyzed against NaCl solution and subsequently against deionized water, to obtain Na+ type carrageenan solutions. Samples were prepared by diluting carrageenan and KCl solutions and heated for 30 min at 70 °C under vigorous stirring. The prepared solutions were mixed using vortex to obtain 1.5% w/w carrageenan with 10 mM KCl and heated at 90 °C for 20 min. Fluorescently labelled 0.1 μm particles (Green, ThermoScientific) were added at a concentration of ~0.01% (v/w) at 90 °C and stirred for another 5 min to assure homogenous dispersion. Mixture of KC and IC was prepared at different volume fraction of IC. Movies of the diffusing particles were recorded at a frame rate of 7.5 frames per second for 110 seconds. In cooling experiments, particle tracking was performed at different sample temperatures from 50 °C to 10 °C. In storage experiments, hot solutions of carrageenan were cooled down from 50 °C to 5 °C at a rate of 1 °C/min in a temperature-controlled incubator to form a gel. The gelled sample was stored at 5 °C prior to experiment and particle tracking was performed at 5 °C. Particle tacking was implemented in Mathematica 10 (Wolfram Research, Inc., USA). The temperature dependence of the mean square displacement (MSD) of particles in KC, IC and mixed KC:IC gels were carried out to quantify the dynamics of the evolving network structure on cooling as shown in Figure 1. In mixed KC:IC, a two-step decrease in MSD was observed. The onset of the observed decrease is close to the decrease in pure KC and IC gels. This trend is consistent with the observed increase in the viscoelastic modulus in dynamic viscoelasticity measurements. The decrease in the MSD with decreasing temperature is due to the steric hindrance created by the formation of clusters of IC and KC chain aggregates. This suggests that KC and IC chains formed aggregates independently on cooling. In pure carrageenan, IC gels formed weak entanglement among clusters of IC chain that allowed diffusion of particles through crevices of the entangled clusters while KC gels rapidly formed thick aggregates of interconnected clusters that confined the particles. On the other hand, in mixed KC:IC, the presence of IC clusters decreased the mobility of KC chains at low temperature thus slowed the formation of stable clusters of KC. With storage time, a broad distribution of MSD was observed for the mixed gels. This suggests that an inhomogeneous solution was formed as KC and IC clusters continue to rearrange to form a stable network. The degree of heterogeneity in the mixed gels is reflected in the corresponding van Hove distribution of particle displacement and the distribution of MSD as a function of slope. In the van Hove distribution, a bimodal Gaussian form with a broad and narrow Gaussian width fit well on the distribution suggests a mobile and immobile fraction of particle at each mixing ratios. In the distribution of MSD as a function of slope, the mobile and immobile particles were identified and clustered accordingly. This suggests that the presence of mobile particles was due to the existence of IC-rich domains that allowed diffusion of particles and the immobile particles was due to the confinement of particles in KC-rich domains as shown in the graphical representation in Figure 1. This is consistent with the proposed gelation mechanism of a local phase separation into IC-rich and KC-rich domains. As the volume fraction of IC was increased, the number of mobile particles increased consequently and suggests a phase transition from a sea-island (80%KC:20%IC) to a bi-continuous (50%KC:50%IC) to an island-sea (30%KC:70%IC) network structure is likely to occur. Figure 1

Exact solution and invariant for fractional Cattaneo anomalous diffusion of cells in two-dimensional comb framework

This paper presents an investigation on anomalous diffusion of cells in a two-dimensional comb framework with effects of fractional Cattaneo flux. Formulated governing equation is an evolution equation with the coexisting characteristics of parabolic (diffusion) and hyperbolic (wave) for $$\alpha $$ in (0, 1). Exact solution is obtained by the special fractional integral transformations, and a novel invariant is established, i.e., $$\left\langle {x^{2}\left( t \right) } \right\rangle \cdot \left\langle P \right\rangle = 0.5$$ (the mean square displacement multiplied by the total number of cells along the x-axis = 0.5). Moreover, the characteristics of cells distribution, the total number and the mean square displacement of cells along the x-axis with different involved parameters, especially with the fractional parameter evolution, are shown graphically and analyzed in detail. For the cells distribution versus x, it turns from parabolic and hyperbolic with the decrease in t or the increase in $$\alpha $$ or $$\xi $$ . It is monotonically decreasing for the cells distribution versus $$\alpha $$ with different x, t and $$\xi $$ . For the distribution versus t with different $$\alpha $$ and $$\xi $$ or versus $$\alpha $$ with different t, it is monotonically decreasing for the distribution of total number while monotonically increasing for the distribution of mean square displacement. It is remarkable that the anomalous subdiffusion happens along the x-axis for arbitrary parameters which is different from the classical Cattaneo diffusion.

Microrheology, microstructure, and aging of physically cross-linked poly(vinyl alcohol)/poly(ethylene glycol) blends

Physically cross-linked blends of concentrated poly(vinyl alcohol) (PVA) and poly(ethylene glycol) (PEG) undergo microphase separation and gel as they age. We investigate the microrheology and microstructure of these materials by using particle tracking and dynamic light scattering to measure the thermal motion of small polystyrene spheres suspended in the blends. Dynamic light scattering probes the ensemble-averaged motion of all the probe particles over a wide range of time scales, while video-based particle tracking follows the motion of many individual tracer particles. Dynamic light scattering shows that the tracer particles move diffusively at short and long time scales, while their motion is restricted by material elasticity at intermediate time scales. The particle tracking experiments show a wide distribution of mean square displacements at a given lag time, indicating spatial heterogeneity on the micron length scale. We separate the particles into three populations according to their behavior. We extract information about the local microrheological environments probed by each population and study their dependence on PEG concentration and aging time. We find that addition of PEG to the PVA solutions influences the microrheological environment significantly, and that phase separation occurs prior to gelation as the blends age. The gelation time determined from the microrheological measurements is later than the bulk gel time, indicating that the different phase-separated regions age differently. Our results are consistent with a model in which the PVA/PEG blends consist of PVA-poor pores within a continuous PVA-rich domain.

Micro-heterogeneity of cellulosic fiber biopolymer prepared from corn hulls

Z-trim is a zero calorie cellulosic fiber biopolymer produced from corn hulls. The micro-structural heterogeneities of Z-trim biopolymer were investigated by monitoring the thermally driven displacements of well-dispersed micro-spheres via video fluorescence microscopy named multiple-particle tracking (MPT). By comparing the distribution of the time-dependent mean-square displacement (MSD) of polystyrene micro-spheres embedded in three concentrations of Z-trim, we found that the degree of heterogeneity of the suspensions increased dramatically within a narrow range of concentrations. The ensemble-averaged MSD of 0.5 g/100 g Z-trim biopolymer exhibited a power-law behavior that scaled log-linearly with time lag. This behavior was similar to that of homogeneous aqueous glycerol solution. But the MSD distribution for Z-trim was wider and more asymmetric than for glycerol. Increasing Z-trim concentration caused more deviation of micro-spheres colloidal dispersion from homogeneity as detected by the MPT.

Microrheological studies of regenerated silk fibroin solution by video microscopy

AbstractWe have carried out studies on the rheological properties of regenerated silk fibroin (RSF) solution using video microscopy. The degummed silk from the Bombyx mori silkworm was used to prepare RSF solution by dissolving it in calcium nitrate tetrahydrate‐methanol solvent. Measurements were carried out by tracking the position of an embedded micron‐sized polystyrene bead within the RSF solution through video imaging. The time dependent mean squared displacement (MSD) of the bead in solution and hence the complex shear modulus of this solution was calculated from the bead's position information. We present here the results of rheological measurements of the silk polymer network in solution over a frequency range, whose upper limit is the frame capture rate of our camera at full resolution. By examining the distribution of MSD of beads at different locations within the sample volume, we demonstrate that this probe technique enables us to detect local inhomogeneities at nanometre length scales, not detectable either by a rheometer or from diffusing wave spectroscopy. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 2555–2562, 2007

Multiple‐Particle Tracking Study of Microheterogeneity of Nutrim‐10 Suspensions

ABSTRACTNutrim is a newly developed food product containing dietary soluble fiber β‐glucan. The microstructural heterogeneities of Nutrim‐10 suspensions were investigated by monitoring the thermally driven displacements of well‐dispersed microspheres through video fluorescence microscopy. By comparing the distribution of the time‐dependent mean‐square displacement (MSD) of polystyrene microspheres embedded in three concentrations of Nutrim‐10 suspensions, we found that the degree of heterogeneity of suspensions increased dramatically within a narrow range of Nutrim‐10 concentrations. The ensemble‐averaged MSD of 5.5% Nutrim‐10 suspension exhibited a power‐law behavior scaling linearly with time, which was similar to the behavior for a homogeneous aqueous glycerol solution. But the MSD distribution was wider and more asymmetric than for glycerol. Increasing Nutrim‐10 concentration rendered the MSD distribution much more asymmetric and skewed. This study provided a quantitative method to characterize the organization of Nutrim‐10 in suspension.

Use of computer simulation in the interpretation of elastic neutron scattering in complex molecular systems: a small protein in various environments

Abstract Elastic and quasielastic neutron scattering experiments on complex systems are often difficult to interpret unambiguously directly using analytical dynamical models. In such cases computer simulations can be used to provide information at atomic detail. Here we report on the use of normal mode analysis (NMA) and molecular dynamics (MD) simulations of a small protein, bovine pancreatic trypsin inhibitor (BPTI) in vacuum and in various solvents. The simulations were performed over a range of temperatures (80–300 K). The vacuum simulation data are used to investigate neutron scattering properties. Effects are determined of instrumental energy resolution and of approximations commonly used to extract mean-square displacement data from elastic scattering experiments. Both the presence of a distribution of mean-square displacements in the protein and the use of the Gaussian approximation to the dynamic structure factor lead to quantified underestimation of the mean-square displacement obtained. Variation of the environment of the protein shows that the dry protein has higher fluctuations at lower temperatures than in the solvated protein, in agreement with recent experiments [1] , [2] , that the dynamical transition is solvent-independent on short timescales (also in agreement with experiment [3] ), and that at longer timescales it is strongly activated by water.

Temperature Dependence of Protein Dynamics: Computer Simulation Analysis of Neutron Scattering Properties

The temperature dependence of the internal dynamics of an isolated protein, bovine pancreatic trypsin inhibitor, is examined using normal mode analysis and molecular dynamics (MD) simulation. It is found that the protein exhibits marked anharmonic dynamics at temperatures of ∼100–120 K, as evidenced by departure of the MD-derived average mean square displacement from that of the harmonic model. This activation of anharmonic dynamics is at lower temperatures than previously detected in proteins and is found in the absence of solvent molecules. The simulation data are also used to investigate neutron scattering properties. The effects are determined of instrumental energy resolution and of approximations commonly used to extract mean square displacement data from elastic scattering experiments. Both the presence of a distribution of mean square displacements in the protein and the use of the Gaussian approximation to the dynamic structure factor lead to quantified underestimation of the mean square displacement obtained.

Microheterogeneity and microrheology of wheat gliadin suspensions studied by multiple-particle tracking.

By monitoring the thermally driven displacements of imbedded polystyrene microspheres via video fluorescence microscopy, we quantified the microstructural and micromechanical heterogeneities of wheat gliadin suspensions. We found that the degree of heterogeneity of the suspensions, as measured by the width and skewness of the microspheres' mean squared displacement (MSD) distribution, increased dramatically over a narrow range of gliadin concentrations. The ensemble-averaged MSD of a 250 mg/mL gliadin suspension exhibited a power-law behavior scaling linearly with time, a behavior similar to that observed for a homogeneous aqueous glycerol solution. However, the MSD distribution was wider and more asymmetric than for glycerol. With increasing concentration of gliadin, the ensemble-averaged MSD rapidly displayed a plateau at small time scales, the MSD distribution became wider and more asymmetric, and the local viscoelastic moduli extracted from multiple-particle-tracking measurements showed an increasingly wide range.

Multiple-Particle Tracking Measurements of Heterogeneities in Solutions of Actin Filaments and Actin Bundles

One of the central functions of actin cytoskeleton is to provide the mechanical support required for the establishment and maintenance of cell morphology. The mechanical properties of actin filament assemblies are a consequence of both the available polymer concentration and the actin regulatory proteins that direct the formation of higher order structures. By monitoring the displacement of well-dispersed microspheres via fluorescence microscopy, we probe the degree of spatial heterogeneity of F-actin gels and networks in vitro. We compare the distribution of the time-dependent mean-square displacement (MSD) of polystyrene microspheres imbedded in low- and high-concentration F-actin solutions, in the presence and absence of the F-actin-bundling protein fascin. The MSD distribution of a 2.6- μM F-actin solution is symmetric and its standard deviation is similar to that of a homogeneous solution of glycerol of similar zero-shear viscosity. However, increasing actin concentration renders the MSD distribution wide and asymmetric, an effect enhanced by fascin. Quantitative changes in the shape of the MSD distribution correlate qualitatively with the presence of large heterogeneities in F-actin solutions produced by increased filament concentration and the presence of actin bundles, as detected by confocal microscopy. Multiple-particle tracking offers a new, quantitative method to characterize the organization of biopolymers in solution.