We develop a model for gels and entangled solutions of semiflexible biopolymers such as F-actin. Such networks play a crucial structural role in the cytoskeleton of cells. We show that the rheologic properties of these networks can result from nonclassical rubber elasticity. This model can explain a number of elastic properties of such networks {\em in vitro}, including the concentration dependence of the storage modulus and yield strain.Comment: Uses RevTeX, full postscript with figures available at http://www.umich.edu/~fcm/preprints/agel/agel.htm

The relationship between the mechanical properties of cells and their molecular architecture has been the focus of extensive research for decades. The cytoskeleton, an internal polymer network, in particular determines a cell's mechanical strength and morphology. This cytoskeleton evolves during the normal differentiation of cells, is involved in many cellular functions, and is characteristically altered in many diseases, including cancer. Here we examine this hypothesized link between function and elasticity, enabling the distinction between different cells, by using a microfluidic optical stretcher, a two-beam laser trap optimized to serially deform single suspended cells by optically induced surface forces. In contrast to previous cell elasticity measurement techniques, statistically relevant numbers of single cells can be measured in rapid succession through microfluidic delivery, without any modification or contact. We find that optical deformability is sensitive enough to monitor the subtle changes during the progression of mouse fibroblasts and human breast epithelial cells from normal to cancerous and even metastatic state. The surprisingly low numbers of cells required for this distinction reflect the tight regulation of the cytoskeleton by the cell. This suggests using optical deformability as an inherent cell marker for basic cell biological investigation and diagnosis of disease.

When a dielectric object is placed between two opposed, nonfocused laser beams, the total force acting on the object is zero but the surface forces are additive, thus leading to a stretching of the object along the axis of the beams. Using this principle, we have constructed a device, called an optical stretcher, that can be used to measure the viscoelastic properties of dielectric materials, including biologic materials such as cells, with the sensitivity necessary to distinguish even between different individual cytoskeletal phenotypes. We have successfully used the optical stretcher to deform human erythrocytes and mouse fibroblasts. In the optical stretcher, no focusing is required, thus radiation damage is minimized and the surface forces are not limited by the light power. The magnitude of the deforming forces in the optical stretcher thus bridges the gap between optical tweezers and atomic force microscopy for the study of biologic materials.

One hundred fifty years ago glial cells were discovered as a second, non-neuronal, cell type in the central nervous system. To ascribe a function to these new, enigmatic cells, it was suggested that they either glue the neurons together (the Greek word ''␥␣'' means ''glue'') or provide a robust scaffold for them (''support cells''). Although both speculations are still widely accepted, they would actually require quite different mechanical cell properties, and neither one has ever been confirmed experimentally. We investigated the biomechanics of CNS tissue and acutely isolated individual neurons and glial cells from mammalian brain (hippocampus) and retina. Scanning force microscopy, bulk rheology, and optically induced deformation were used to determine their viscoelastic characteristics. We found that (i) in all CNS cells the elastic behavior dominates over the viscous behavior, (ii) in distinct cell compartments, such as soma and cell processes, the mechanical properties differ, most likely because of the unequal local distribution of cell organelles, (iii) in comparison to most other eukaryotic cells, both neurons and glial cells are very soft (''rubber elastic''), and (iv) intriguingly, glial cells are even softer than their neighboring neurons. Our results indicate that glial cells can neither serve as structural support cells (as they are too soft) nor as glue (because restoring forces are dominant) for neurons. Nevertheless, from a structural perspective they might act as soft, compliant embedding for neurons, protecting them in case of mechanical trauma, and also as a soft substrate required for neurite growth and facilitating neuronal plasticity.biomechanics ͉ elasticity ͉ viscosity ͉ retina ͉ hippocampus

A new scanning probe-based microrheology approach is used to quantify the frequency-dependent viscoelastic behavior of both fibroblast cells and polymer gels. The scanning probe shape was modified using polystyrene beads for a defined surface area nondestructively deforming the sample. An extended Hertz model is introduced to measure the frequency-dependent storage and loss moduli even for thin cell samples. Control measurements of the polyacrylamide gels compare well with conventional rheological data. The cells show a viscoelastic signature similar to in vitro actin gels.

Viscoelasticity of the leading edge, i.e., the lamellipodium, of a cell is the key property for a deeper understanding of the active extension of a cell's leading edge. The fact that the lamellipodium of a cell is very thin (<1000 nm) imparts special challenges for accurate measurements of its viscoelastic behavior. It requires addressing strong substrate effects and comparatively high stresses (>1 kPa) on thin samples. We present the method for an atomic force microscopy-based microrheology that allows us to fully quantify the viscoelastic constants (elastic storage modulus, viscous loss modulus, and the Poisson ratio) of thin areas of a cell (<1000 nm) as well as those of thick areas. We account for substrate effects by applying two different models-a model for well-adhered regions (Chen model) and a model for nonadhered regions (Tu model). This method also provides detailed information about the adhered regions of a cell. The very thin regions relatively near the edge of NIH 3T3 fibroblasts can be identified by the Chen model as strongly adherent with an elastic strength of approximately 1.6 +/- 0.2 kPa and with an experimentally determined Poisson ratio of approximately 0.4 to 0.5. Further from the edge of these cells, the adherence decreases, and the Tu model is effective in evaluating its elastic strength ( approximately 0.6 +/- 0.1 kPa). Thus, our AFM-based microrheology allows us to correlate two key parameters of cell motility by relating elastic strength and the Poisson ratio to the adhesive state of a cell. This frequency-dependent measurement allows for the decomposition of the elastic modulus into loss and storage modulus. Applying this decomposition and Tu's and Chen's finite depth models allow us to obtain viscoelastic signatures in a frequency range from 50 to 300 Hz, showing a rubber plateau-like behavior.

Subdiffusion and its causes in both in vivo and in vitro lipid membranes have become the focus of recent research. We report apparent subdiffusion, observed via single particle tracking (SPT), in a homogeneous system that only allows normal diffusion (a DMPC monolayer in the fluid state). The apparent subdiffusion arises from slight errors in finding the actual particle position due to noise inherent in all experimental SPT systems. A model is presented that corrects this artifact, and predicts the time scales after which the effect becomes negligible. The techniques and results presented in this paper should be of use in all SPT experiments studying normal and anomalous diffusion.

Plasticity of cancer invasion and metastasis depends on the ability of cancer cells to switch between collective and single cell dissemination, controlled by cadherinmediated cell-cell junctions. In clinical samples, E-cadherin expressing and deficient tumors both invade collectively and metastasize equally, implicating additional mechanisms controlling cell-cell cooperation and individualization. Using spatially defined organotypic culture, intravital microscopy of mammary tumors in mice and in silico modeling, we here identify cell density regulation by 3D tissue boundaries to physically control collective movement irrespective of the composition and stability of cell-cell junctions. Deregulation of adherens junctions, including E-cadherin and p120-catenin, resulted in a transition from coordinated to uncoordinated collective movement along extracellular boundaries, whereas singlecell escape depended on locally free tissue space. These data indicate that cadherins and ECM confinement cooperate to determine unjamming transitions towards step-wise epithelial fluidization and, ultimately, cell individualization.