Soft and fragile matter


A Microfluidic Technique to Probe Cell Deformability
Amy C. Rowat et al, J. Vis. Exp. (91), e51474, doi:10.3791/51474 (2014).
Here we detail the design, fabrication, and use of a microfluidic device to evaluate the deformability of a large number of individual cells in an efficient manner. Typically, data for ~102 cells can be acquired within a 1 hr experiment. An automated image analysis program enables efficient post-experiment analysis of image data, enabling processing to be complete within a few hours. Our device geometry is unique in that cells must deform through a series of micron-scale constrictions, thereby enabling the initial deformation and time-dependent relaxation of individual cells to be assayed. The applicability of this method to human promyelocytic leukemia (HL-60) cells is demonstrated. Driving cells to deform through micron-scale constrictions using pressure-driven flow, we observe that human promyelocytic (HL-60) cells momentarily occlude the first constriction for a median time of 9.3 msec before passaging more quickly through the subsequent constrictions with a median transit time of 4.0 msec per constriction. By contrast, all-trans retinoic acid-treated (neutrophil-type) HL-60 cells occlude the first constriction for only 4.3 msec before passaging through the subsequent constrictions with a median transit time of 3.3 msec. This method can provide insight into the viscoelastic nature of cells, and ultimately reveal the molecular origins of this behavior.
Link to online video publication.

The kitchen as a physics classroom
Amy C Rowat et al, 2014 Phys. Educ. 49 512.
Cooking is a tangible, familiar, and delicious tool for teaching physics, which is easy to implement in a university setting. Through our courses at Harvard and UCLA, each year we are engaging hundreds of undergraduate students, primarily non-science majors, in science concepts and the scientific research process. We find that weekly lectures by chefs and professors, paired with edible lab experiments, generate enthusiasm and provide strong motivation for students to learn physics. By the end of the
course, students are able to conduct independent scientific research and present their results in a final science fair. Given the considerable broad appeal of food and cooking, the topic could be adapted to other postsecondary as well as secondary-level courses.
Paper is online here

Entropic crystal–crystal transitions of Brownian squares
Kun Zhao, Robijn Bruinsma, and Thomas G. Mason
When a monolayer of hard microscale square platelets, produced lithographically, is osmotically concentrated in a flat plane to raise the particle area fraction ϕA, an order–order transition occurs between a hexagonal rotator crystal and a rhombic crystal. Strikingly, phases having fourfold symmetry are not observed at any ϕA. The rhombic lattice angle α increases continuously with ϕA, as the system maximizes its total rotational and translational entropy. A cage model, based on packing rotationally swept squares, or “squaroids,” reasonably predicts the measured αðϕAÞ, indicating that rotational entropy and the square particle shape combine to produce the rhombic unit cell.
JPEGs: Entropic crystal–crystal transitions.jpg (1,017.85 KB)
PDFs: PNAS-2011-Zhao-1014942108.pdf (9.03 MB)
Research categories: Soft and fragile matter

The Science of Chocolate: Interactive Activities on Phase Transitions, Emulsification, and Nucleation
Amy C. Rowat, Kathryn A. Hollar, Howard A. Stone, Daniel Rosenberg, J. Chem. Educ., 2011, 88 (1), pp 29–33.
Nearly everyone loves chocolate, which makes this an excellent topic for communicating scientific concepts to the general public and to students in the classroom. Here we present the outline and activities for an interactive presentation on the science of chocolate for nonspecialists and their children ages 6 and up. We design the presentation around three major questions related to observable properties of chocolate: Why does chocolate melt in your mouth, not in your hand? Why does chocolate feel smooth in your mouth? Why does chocolate look glossy and snap when you break it? To address these questions, we lead the audience through a series of taste experiments, and use a combination of live demonstrations and interactive activities with children. The general approach can be adapted to a variety of informal and classroom settings focused on sharing the excitement of scientific understanding with students and the public.
JPEGs: Chocolate.jpg (162.16 KB)
PDFs: ed100503p.pdf (15.49 MB)

The folded protein as a viscoelastic solid
Y. Wang and G. Zocchi, “The folded protein as a visco-elastic solid”, Europhys. Lett. 96, 18003 (2011).
Yong Wang and Giovanni Zocchi
We apply a nanorheology technique to explore the mechanical properties of a globular protein in the frequency range 10 Hz–10 kHz and find that the folded state of the protein behaves like a viscoelastic solid. For increasing amplitude of the forcing, we observe three different regimes: linear elasticity, then a regime of viscoelastic but reversible deformations, and finally an irreversible regime. The second regime, which has the signature of a viscoelastic solid, gives access to the internal dissipation coefficient of the folded state, for which we find γ ≈ 4 × 10−5 kg/s, corresponding to an internal viscosity η ∼ 104 Pa · s for frequencies below ∼ 10 Hz. We propose that the large discrepancy between this value, which agrees with previous AFM indentation experiments, and the value of the internal viscosity extracted from refolding experiments is a consequence of the viscoelastic nature of the protein’s mechanics. Thus the present method yields detailed measurements of the mechanics of the folded state.
JPEGs: Nano_rheology.jpg (2.39 MB)
PDFs: Yong_4_reprint.pdf (4.74 MB)
Research categories: Biological Macromolecules, Soft and fragile matter

Hydrodynamics in curved membranes: The effect of geometry on particulate mobility
Mark L. Henle and Alex J. Levine
We determine the particulate transport properties of fluid membranes with nontrivial geometries that are surrounded by viscous Newtonian solvents. Previously, this problem in membrane hydrodynamics was discussed for the case of flat membranes by Saffman and Delbrück, P. G. Saffman and M. Delbrück, Proc. Natl. Acad. Sci. U.S.A. 72, 3111 1975. We review and develop the formalism necessary to consider the hydrodynamics of membranes with arbitrary curvature and show that the effect of local geometry is twofold. First, local Gaussian curvature introduces in-plane viscous stresses even for situations in which the velocity field is coordinate-independent. Secondly, even in the absence of Gaussian curvature, the geometry of the membrane modifies the momentum transport between the bulk fluids and the membrane. We illustrate these effects by examining in detail the mobilities of particles bound to spherical and cylindrical membranes. These two examples provide experimentally testable predictions for particulate mobilities and membrane velocity fields on giant unilamellar vesicles and membrane tethers. Finally, we use the examples of spherical and cylindrical membranes to demonstrate how the global geometry and topology of the membrane influences the membrane velocities and the particle mobilities.
JPEGs: Hydrodynamics in curved membranes.jpg (1.75 MB)
PDFs: Phys. Rev. E 2010 Henle.pdf (5.48 MB)
Research categories: Nonequilibrium physics, Soft and fragile matter

Stochastic self-assembly of incommensurate clusters
D'Orsogna, Lakatos, Chou, Stochastic self-assembly of incommensurate clusters, Journal of Chemical Physics, 136, 084110, (2012).
M. R. D’Orsogna, G. Lakatos, T. Chou
Nucleation and molecular aggregation are important processes in numerous physical and biological systems. In many applications, these processes often take place in confined spaces, involving a finite number of particles. We examine the classic problem of homogeneous nucleation and self-assembly by deriving and analyzing a fully discrete stochastic master equation, enumerating the highest probability steady-states, and deriving exact analytical formulae for quenched and equilibrium mean cluster size distributions. We find striking differences between the our results and those derived from mass-action equations that depend primarily on the divisibility of the total available mass by the maximum allowed cluster size, and the remainder. When such mass "incommensurability" arises, a single remainder particle can ``emulsify'' the system by significantly broadening the equilibrium mean cluster size distribution. This discreteness-induced broadening effect is periodic in the total mass of the system but arises even when the system size is asymptotically large, provided the ratio of the total mass to the maximum cluster size is finite. Our findings define a new scaling regime in which results from classic mass-action theories are qualitatively inaccurate, even in the limit of large total system size.
PDFs: JCP_final.pdf (8.73 MB)
PNGs: Stochastic self-assembly of.png (725.98 KB)
Research categories: Nonequilibrium physics, Soft and fragile matter

Morphological Phase Diagram for Lipid Membrane Domains with Entropic Tension
Rim, J.E., Ursell, T.S., Phillips, R., and Klug, W.S., “Morphological Phase Diagram for Lipid Mem- brane Domains with Entropic Tension”, Phys. Rev. Lett., 106(5):057801 (2011)
Circular domains in phase-separated lipid vesicles with symmetric leaflet composition commonly exhibit three stable morphologies: flat, dimpled, and budded. However, stable dimples (i.e., partially budded domains) present a puzzle since simple elastic theories of domain shape predict that only flat and spherical budded domains are mechanically stable in the absence of spontaneous curvature. We argue that this inconsistency arises from the failure of the constant surface tension ensemble to properly account for the effect of entropic bending fluctuations. Formulating membrane elasticity within an entropic tension ensemble, wherein tension represents the free energy cost of extracting membrane area from thermal bending of the membrane, we calculate a morphological phase diagram that contains regions of mechanical stability for each of the flat, dimpled, and budded domain morphologies.
PDFs: Rim-PRL-2011.pdf (4.59 MB)
PNGs: Morphological Phase Diagram for Lipid Membrane Domains with Entropic Tension.png (984.66 KB)
Research categories: Cellular mechanics, Soft and fragile matter

The Mechanics and Affine-Nonaffine Transition in Polydisperse Semi-flexible Networks
Bai, M., Missel, A.R., Klug, W.S., and Levine, A.J., “The Mechanics and Affine-Nonaffine Transition in Polydisperse Semi-flexible Networks”, Soft Matter, 7(3):907–914 (2011)
Semiflexible gels are composed of a crosslinked network of filaments that can support both bending and extensional forces. We study numerically the mechanical effect of adding a low density of highly incompliant semiflexible filaments to a random network of softer semiflexible filaments. Such heterogeneous networks form simple models of the mechanics of cytoskeletal networks composed primarily of F-actin but containing a low density of significantly stiffer microtubules. Networks composed solely of these two filament types were recently studied in the in vitro experiments of Lin et al. Here we determine the effect of the stiffer impurity filaments generally on the collective mechanics of the heterogeneous filament network and, more specifically, on the affine to non-affine (A/NA) crossover in the softer filament matrix, which occurs in semiflexible networks as a function of their network density. We show that the addition of a small fraction of longer and stiffer filaments to a nonaffine network leads to a significant increase in its collective elastic moduli, even though the stiff filaments do not themselves form a stress bearing network. We also determine the relationship between the density of the stiff filaments and the geometric measure of nonaffinity for the network. Here the effect of the stiffer impurity filaments is complex: their addition makes affine networks slightly more affine, but highly nonaffine networks even more nonaffine. Moreover, there is a strong negative spatial correlation between density of the stiff filaments and local geometric measure of nonaffinity. Taken together, these two observations show that the stiffer filaments serve to locally suppress nonaffine deformation but redistribute it to regions of the network where the stiffer filaments are sparse.
PDFs: Bai-SoftMatter-2011.pdf (4.67 MB)
PNGs: The Mechanics and Affine-Nonaffine Transition in Polydisperse Semi-flexible Networks.png (7.64 MB)
Research categories: Cellular mechanics, Soft and fragile matter

Affine to Nonaffine Transition in Networks of Nematically Ordered Semiflexible Polymers
Missel A.R., Bai M., Klug W.S., and Levine A.J., “Affine to Nonaffine Transition in Networks of Nematically Ordered Semiflexible Polymers”, Phys. Rev. E, 82:041907 (2010)
We study the mechanics of nematically ordered semiflexible networks showing that they, like isotropic networks, undergo an affine to nonaffine crossover controlled by the ratio of the filament length to the nonaffinity length. Deep in the nonaffine regime, however, these anisotropic networks exhibit a much more complex mechanical response characterized by a vanishing linear-response regime for highly ordered networks and a dependence of the shear modulus on shear direction at both small ͑linear͒ and finite ͑nonlinear͒ strains that is different from the affine prediction of orthotropic continuum linear elasticity. We show that these features can be understood in terms of a generalized floppy modes analysis of the nonaffine mechanics and a type of cooperative Euler buckling.
PDFs: Missel-PRE-2010.pdf (4.17 MB)
PNGs: Cooperative Euler buckling.png (2.86 MB)
Research categories: Cellular mechanics, Soft and fragile matter

On the Role of the Filament Length Distribution in the Mechanics of Semiflexible Networks
Bai, M., Missel, A.R., Levine, A.J., and Klug, W.S.,“On the Role of the Filament Length Distribution in the Mechanics of Semiflexible Networks”, Acta Biomaterialia, 7(5):2109–2118 (2011)
This paper explores the effects of filament length polydispersity on the mechanical properties of semiflexible crosslinked polymer networks. Extending previous studies on monodisperse networks, we compute numerically the response of crosslinked networks of elastic filaments of bimodal and exponential length distributions. These polydisperse networks are subject to the same affine to nonaffine (A/NA) transition observed previously for monodisperse networks, wherein the decreases in either crosslink density or bending stiffness lead to a shift from affine, stretching-dominated deformations to nonaffine, bendingdominated deformations. We find that the onset of this transition is generally more sensitive to changes in the density of longer filaments than shorter filaments, meaning that longer filaments have greater mechanical efficiency. Moreover, in polydisperse networks, mixtures of long and short filaments interact cooperatively to generally produce a nonaffine mechanical response closer to the affine prediction than comparable monodisperse networks of either long or short filaments. Accordingly, the mechanical affinity of polydisperse networks is dependent on the filament length composition. Overall, length polydispersity has the effect of sharpening and shifting the A/NA transition to lower network densities. We discuss the implications of these results on experimental observation of the A/NA transition, and on the design of advanced materials.
PDFs: Filament Length Distribution.pdf
PNGs: Filament Length Distribution in the Mechanics of Semiflexible Networks.png (13.04 MB)
Research categories: Cellular mechanics, Soft and fragile matter

The physics of retinal detachments
Tom Chou, Michael Siegel
We develop mathematical model describing the mechanical and fluid forces associated with ex- udative retinal detachments. We assume that the retina adheres to the underlying retinal pigment epitelium (RPE) cells layer via an attractive interaction potential that can be irreversibly destroyed. By computing the total water flow arising from transretinal, vascular, and retinal pigment epithe- lium (RPE) pump currents, we determine the conditions under which the subretinal fluid pressure exceeds the maximum yield stress holding the retina and RPE together, giving rise to an extended retinal delamination. We also investigate localized, blister-like retinal detachments by balancing mechanical tension in the retina with both the chorioretinal adhesion energy and the pressure jump across the retina. For detachments formed by traction, we find a critical radius beyond which the blister is unstable to unbounded growth. On the other hand, if growth of the detached blister is further driven by inflamed choroidal tissue (in which e.g., the RPE pumps do not function), we find in certain cases the blister size depends simply on two parameters, the normal-tissue, dimensionless RPE pump flux, and a dimensionless combination comprising the retinal stretching elasticity, the retina-RPE adhesion energy, and the area of the inflamed lesion. We find parameter regimes which lead to either a finite or infinite blister radii, and to the corresponding blister shape. Our model provides a mathematical description of the physical mechanisms involved in exudative retinal de- tachments and macular edema and can guide further development of retinal reattachment protocols or preventative procedures.
JPEGs: csr-oct.jpg (3.01 MB)
Research categories: Cellular mechanics, Tissues and Organisms, Nonequilibrium physics, Soft and fragile matter