Investigating the microenvironments of inhomogeneous soft materials with multiple particle tracking

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Original entry: Ian Burgess, Fall 2009

Reference

M. T. Valentine, P. D. Kaplan, D. Thota, J. C. Crocker, T. Gisler, R. K. Prud'homme, M. Beck, D. A. Weitz, "Investigating the microenvironments of inhomogeneous soft materials with multiple particle tracking," Phys. Rev. E, 64, 061506(9) (2001).

Keyworks

Microrheology, mean-square displacement, Brownian motion, diffusion coefficient.

Summary

This article describes a new particle tracking technique that allows localized probing of individual microenvironments in inhomogeneous soft materials. Their technique applies passive microrheology to a large ensemble (~100) of fluorescent-labeled particles. They simultaneously track the motion of each particle using video microscopy. The parallelism of this technique allows them to collect much data about several different types of microenvironments in the system in a short amount of time. The limitation of this technique is that the measured particle trajectories are too short to make statistically meaningful comparisons between individual particles, due to the fixed field of view. To overcome this obstacle, the authors group particles whose mean-square displacements are statistically indistinguishable and then combine the data within each group to gain more accurate statistics about each environment. To demonstrate the effectiveness of their technique, the authors apply it to three different types of media. First, a glycerol/water mixture, which should behave as a homogeneous viscous fluid, is used as a standard. The other media studies are agarose, which is an inhomogeneous and porous gel, and F actin, a component of cellular cytoplasm.


Results

Wk1fig1.jpg

Shown above is the authors' comparison of van Hove correlation functions for the mean displacement of particles moving in Glycerol (top) and agarose (bottom). Ensemble averages for each are shown on the left (a) and individual particles are compared on the right. For glycerol, the ensemble average is fit well by a Gaussian distribution, whose variance increases with the time-window of the sample, and individual particles obey the same statistics, what is expected for a simple viscous fluid with a homogeneous diffusion coefficient. In the agarose sample, the ensemble average is not well fit by a Gaussian, however individual particles fit well to Gaussians with different variances. Thus, the different diffusion coefficients of the different microenvironments in the gel can be identified.


Using this type of analysis, the authors were able to generate a spatial map of the different microenvironments within the inhomogeneous agarose sample. They were able to identify individual microenvironments in which particle statistics correlated very well, by found no spatial correlation between microenvironments. In the F actin sample, they found that the ensemble-average statistics were non-normal (as with agarose) indicating inhomogeneity in the sample, but, unlike in agarose, they were unable to identify individual environments from distinguishable single-particle statistics. They concluded that this indicates that there is temporal and/or very short range spatial variation in the sample and that individual particles are experienceing multiple environments during the course of one experiment.

Investigating the microenvironments of inhomogeneous soft materials with multiple particle tracking

Second entry: Anna Wang, Fall 2010

Background

Although rheological measurements can provide much information about the bulk properties of a material, the study of inhomogeneous materials is not complete without probing microenvironments. By using tracking particles which are smaller than the characteristic features of the inhomogeneous material, passive and active microrheology can not only provide information about the local rheology but also the steric constraints of the environment.

Overview

The authors demonstrated how passive microrheology using video microscopy and higher order statistics could be used to study the microenvironments in inhomogeneous soft matter. The Brownian motion (in one dimension) of ~100 fluorescently tagged particles was tracked with video microscopy, providing massive amounts of information in a short amount of time. In theory the differences in the mean-squared displacements of the particles would reflect the particles’ different microenvironments; however, the finite imaging volume of the technique intrinsically limits the accuracy of the mean-squared displacements. Other statistical tools were hence developed to provide statistically viable information about the microenvironments, whilst keeping the advantage of short imaging time.

The efficacy of these statistical tools was demonstrated through the probing of three soft media: glycerol/water (homogeneous), agarose (heterogeneous, porous) and F-actin (heterogeneous, dynamic).

Results

The van Hove correlation functions at two different lag times (0.033s and 0.1s) for the ensemble (left) and individual particles (right) are shown below.

Wk1 glycerol.png

In glycerol/water, the ensemble-averaged data (above, left) fitted a Gaussian distribution well, as expected for a homogeneous viscous fluid. The individual particles (above, right) also displayed Gaussian statistics and were all fit by the same Gaussian, indicating that they experienced the same local diffusion coefficient (which can be determined from the variance of the Gaussian). The F-test was used to cluster the data, forming statistically meaningful groups which data can be averaged over. Only one cluster was produced ie all particles measured the same viscosity.

Wk1 agaorse.png Wk1 ftest agarose.png

In agarose, the ensemble data (above left) did not fit a Gaussian distribution. The individual particles did (above, centre), however, but with different variances. This indicated that the particles experienced different local diffusion coefficients. Using clusters from the F-test (above right), the average mean-squared displacements were determined for each cluster and their time dependence revealed that the mean-squared displacement plateaued for long times. This indicated constraint on the particle by the material, and hence could provide either a measure of either local elasticity, or steric constraint (eg pore). Analysis revealed that the plateau can provide information on pore size.

Wk1 factin.png

In F-actin, neither the ensemble (above, left) nor individual data (above, right) fit a Gaussian distribution. The F-test failed to produce distinguishable clusters, suggesting that the F-actin sample may have been temporally inhomogeneous. The authors suggested that the particles may move through various microenvironments during the course of the experiment, and the F-actin network is also dynamic over the same time scale.