Reply to the 'Comment on "A symmetrical method to obtain shear moduli from microrheology"' by M. Tassieri, Soft Matter, 2018, 14, DOI.

The Comment on our paper introducing "a symmetric method to obtain shear moduli from microrheology" proposes an interpolation method to generate oversampled data from an original time series that are then used to approximate shear moduli at frequencies "beyond the Nyquist frequency." The author states that this can be done without the use of "preconceived fitting functions," implying that the results are unique and reliable. We disagree with these assertions. While it is possible to generate reasonable looking transforms at frequencies above the Nyquist limit by interpolation, any results obtained above the Nyquist limit will be questionable at best. Moreover, while the cubic spline interpolation the author uses may be standard, it constitutes a particular "preconceived" fit and produces oversampled data that are not unique.

A symmetrical method to obtain shear moduli from microrheology.

Passive microrheology typically deduces shear elastic loss and storage moduli from displacement time series or mean-squared displacements (MSD) of thermally fluctuating probe particles in equilibrium materials. Common data analysis methods use either Kramers-Kronig (KK) transformation or functional fitting to calculate frequency-dependent loss and storage moduli. We propose a new analysis method for passive microrheology that avoids the limitations of both of these approaches. In this method, we determine both real and imaginary components of the complex, frequency-dependent response function χ(ω) = χ'(ω) + iχ''(ω) as direct integral transforms of the MSD of thermal particle motion. This procedure significantly improves the high-frequency fidelity of χ(ω) relative to the use of KK transformation, which has been shown to lead to artifacts in χ'(ω). We test our method on both model and experimental data. Experiments were performed on solutions of worm-like micelles and dilute collagen solutions. While the present method agrees well with established KK-based methods at low frequencies, we demonstrate significant improvement at high frequencies using our symmetric analysis method, up to almost the fundamental Nyquist limit.

Ligand-directed delivery of fluorophores to track native calcium-permeable AMPA receptors in neuronal cultures.

Subcellular trafficking of neuronal receptors is known to play a key role in synaptic development, homeostasis, and plasticity. We have developed a ligand-targeted and photo-cleavable probe for delivering a synthetic fluorophore to AMPA receptors natively expressed in neurons. After a receptor is bound to the ligand portion of the probe molecule, a proteinaceous nucleophile reacts with an electrophile on the probe, covalently bonding the two species. The ligand may then be removed by photolysis, returning the receptor to its non-liganded state while leaving intact the new covalent bond between the receptor and the fluorophore. This strategy was used to label polyamine-sensitive receptors, including calcium-permeable AMPA receptors, in live hippocampal neurons from rats. Here, we describe experiments where we examined specificity, competition, and concentration on labeling efficacy as well as quantified receptor trafficking. Pharmacological competition during the labeling step with either a competitive or non-competitive glutamate receptor antagonist prevented the majority of labeling observed without a blocker. In other experiments, labeled receptors were observed to alter their locations and we were able to track and quantify their movements. We used a small molecule, ligand-directed probe to deliver synthetic fluorophores to endogenously expressed glutamate receptors for the purpose of tracking these receptors on live, hippocampal neurons. We found that clusters of receptors appear to move at similar rates to previous studies. We also found that the polyamine toxin pharmacophore likely binds to receptors in addition to calcium-permeable AMPA receptors.

Nonthermal fluctuations of the mitotic spindle.

We present direct measurements of fluctuations in the nucleus of yeast cells. While prior work has shown these fluctuations to be active and non-thermal in character, their origin and time dependence are not understood. We show that the nuclear fluctuations we observe are quantitatively consistent with uncorrelated, active force fluctuations driving a nuclear medium that is dominated by an uncondensed DNA solution, for which we perform rheological measurements on an in vitro model system under similar conditions to what is expected in the nucleus.

Accurate detection and complete tracking of large populations of features in three dimensions.

Localization and tracking of colloidal particles in microscopy images generates the raw data necessary to understand both the dynamics and the mechanical properties of colloidal model systems. Yet, despite the obvious importance of analyzing particle movement in three dimensions (3D), accurate sub-pixel localization of the particles in 3D has received little attention so far. Tracking has been limited by the choice of whether to track all particles in a low-density system, or whether to neglect the most mobile fraction of particles in a dense system. Moreover, assertions are frequently made on the accuracies of methods for locating particles in colloid physics and in biology, and the field of particle locating and tracking can be well-served by quantitative comparison of relative performances. We show that by iterating sub-pixel localization in three dimensions, the centers of particles can be more accurately located in three-dimensions (3D) than with all previous methods by at least half an order of magnitude. In addition, we show that implementing a multi-pass deflation approach, greater fidelity can be achieved in reconstruction of trajectories, once particle positions are known. In general, all future work must defend the accuracy of the particle tracks to be considered reliable. Specifically, other researchers must use the methods presented here (or an alternative whose accuracy can be substantianted) in order for the entire investigation to be considered legitimate, if the basis of the physical argument (in colloids, biology, or any other application) depends on quantitative accuracy of particle positions. We compare our algorithms to other recent and related advances in location/tracking in colloids and in biology, and discuss the relative strengths and weaknesses of all the algorithms in various situations. We carry out performance tests directly comparing the accuracy of our and other 3D methods with simulated data for both location and tracking, and in providing relative performance data, we assess just how accurately software can locate particles. We discuss how our methods, now applied to colloids, could improve the location and tracking of features such as quantum dots in cells.

Intermittent and spatially heterogeneous single-particle dynamics close to colloidal gelation.

Dynamical heterogeneities exist ubiquitously in materials near a dynamical arrest transition, such as glass formation or gelation. Among the readily discernible features of heterogeneous dynamics is a non-Gaussian exponential component in the distribution of the constituent particle displacements that is not understood at the single-particle level. We present an experimental study of particle dynamics and self-van Hove functions G_{s}(r,t) in a colloid-polymer system approaching gelation. We show experimental evidence, in the special case of a gelation transition, for exponentially distributed times for anomalously large displacements, and confirm that an exponential tail in G_{s} arises from rare events with associated Poisson statistics. We focus on the role of the anomalous large displacements and analyze their time scales, relating them to other time scales typically used to describe structural relaxation in gels and glasses: the time to cage breakup and the time for re-emergence of Fickian behavior at long times. Furthermore, we search for a structural origin of the dynamical heterogeneity. Various quantities characterizing local structure are examined. We found evidence of a strong correlation between local structure and local dynamics, in contrast to what has been found in supercooled liquids.

Imaging cellulose synthase motility during primary cell wall synthesis in the grass Brachypodium distachyon.

The mechanism of cellulose synthesis has been studied by characterizing the motility of cellulose synthase complexes tagged with a fluorescent protein; however, this approach has been used exclusively on the hypocotyl of Arabidopsis thaliana. Here we characterize cellulose synthase motility in the model grass, Brachypodium distachyon. We generated lines in which mEGFP is fused N-terminal to BdCESA3 or BdCESA6 and which grew indistinguishably from the wild type (Bd21-3) and had dense fluorescent puncta at or near the plasma membrane. Measured with a particle tracking algorithm, the average speed of GFP-BdCESA3 particles in the mesocotyl was 164 ± 78 nm min-1 (error gives standard deviation [SD], n = 1451 particles). Mean speed in the root appeared similar. For comparison, average speed in the A. thaliana hypocotyl expressing GFP-AtCESA6 was 184 ± 86 nm min-1 (n = 2755). For B. distachyon, we quantified root diameter and elongation rate in response to inhibitors of cellulose (dichlorobenylnitrile; DCB), microtubules (oryzalin), or actin (latrunculin B). Neither oryzalin nor latrunculin affected the speed of CESA complexes; whereas, DCB reduced average speed by about 50% in B. distachyon and by about 35% in A. thaliana. Evidently, between these species, CESA motility is well conserved.

Stochastic variation: from single cells to superorganisms.

Observed phenotype often fails to correspond with genotype. Although it is well established that uncontrolled genetic modifier effects and environmental variability can affect phenotype, stochastic variation in gene expression can also contribute to phenotypic differences. Here we examine recent work that has provided insights into how fundamental physical properties of living cells, and the probabilistic nature of the chemical reactions that underlie gene expression, introduce noise. We focus on instances in which a stochastic decision initiates an event in the development of a multicellular organism and how that decision can be subsequently fixed. We present an example indicating that a similar interplay between an initial stochastic decision and subsequent fixation may underlie the regulation of reproduction in social insects. We argue, therefore, that stochasticity affects biological processes from the single-gene scale through to the complex organization of an ant colony, and represents a largely neglected component of phenotypic variation and evolution.

Microrheology of microtubule solutions and actin-microtubule composite networks.

We perform local or microrheological measurements on microtubule solutions, as well as composite networks. The viscoelastic properties of microtubules as reported from two-point microrheology agree with the macroscopic measurement at high frequencies, but appear to show a discrepancy at low frequencies, at time scales on the order of a second. A composite of filamentous actin (F-actin) and microtubules has viscoelastic behavior between that of F-actin and pure microtubules. We further show that the Poisson ratio of the composite, measured by the length-scale dependent two-point microrheology, is robustly smaller than that of the F-actin network at time scales tau>1 s, suggesting that a local compressibility is conferred by the addition of microtubules to the F-actin network.

Dynamics of weakly aggregated colloidal particles.

We discuss the behaviour of the dynamics of colloidal particles with a weak attractive interparticle interaction that is induced through the addition of polymer to the solvent. We briefly review the description of their behaviour in terms of the jamming phase diagram, which parametrized the fluid-to-solid transition due to changes in volume fraction, attractive energy or applied stress. We focus on a discussion of ageing of the solid gels formed by these colloid-polymer mixtures. They exhibit a delayed collapse induced by gravity. The time evolution of the height of the sediment exhibits an unexpected scaling behaviour, suggesting a universal nature to this delayed collapse. We complement these measurements of the scaling of the collapse with microscopic investigations of the evolution of the structure of the network using confocal microscopy. These results provide new insight into the origin of this ageing behaviour.