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Blebs are pressure-driven cell protrusions implicated in cellular functions such as cell division, apoptosis, and cell motility, including motility of protease-inhibited cancer cells. Because of their mechanical nature, blebs inform us about general cell-surface mechanics, including membrane dynamics, pressure propagation throughout the cytoplasm, and the architecture and dynamics of the actin cortex. Mathematical models including detailed fluid dynamics have previously been used to understand bleb expansion. Here, we develop mathematical models in two and three dimensions on longer timescales that recapitulate the full bleb life cycle, including both expansion and healing by cortex reformation, in terms of experimentally accessible biophysical parameters such as myosin contractility, osmotic pressure, and turnover of actin and ezrin. The model provides conditions under which blebbing occurs, and naturally gives rise to traveling blebs. The model predicts conditions under which blebs travel or remain stationary, as well as the bleb traveling velocity, a quantity that has remained elusive in previous models. As previous studies have used blebs as reporters of membrane tension and pressure dynamics within the cell, we have used our system to investigate various pressure equilibration models and dynamic, nonuniform membrane tension to account for the shape of a traveling bleb. We also find that traveling blebs tend to expand in all directions unless otherwise constrained. One possible constraint could be provided by spatial heterogeneity in, for example, adhesion density.

Blebs are pressure-driven protrusions that play an important role in cell migration, particularly in three-dimensional environments. A bleb is initiated when the cytoskeleton detaches from the cell membrane, resulting in the pressure-driven flow of cytosol toward the area of detachment and local expansion of the cell membrane. Recent experiments involving blebbing cells have led to conflicting hypotheses regarding the timescale of intracellular pressure propagation. The interpretation of one set of experiments supports a poroelastic model of the cytoplasm that leads to slow pressure equilibration when compared to the timescale of bleb expansion. A different study concludes that pressure equilibrates faster than the timescale of bleb expansion. To address this discrepancy, a dynamic computational model of the cell was developed that includes mechanics of and the interactions among the cytoplasm, the actin cortex, the cell membrane, and the cytoskeleton. The model results quantify the relationship among cytoplasmic rheology, pressure, and bleb expansion dynamics, and provide a more detailed picture of intracellular pressure dynamics. This study shows the elastic response of the cytoplasm relieves pressure and limits bleb size, and that both permeability and elasticity of the cytoplasm determine bleb expansion time. Our model with a poroelastic cytoplasm shows that pressure disturbances from bleb initiation propagate faster than the timescale of bleb expansion and that pressure equilibrates slower than the timescale of bleb expansion. The multiple timescales in intracellular pressure dynamics explain the apparent discrepancy in the interpretation of experimental results.

I-BAR proteins are well-known actin-cytoskeleton adaptors and have been observed to be involved in the formation of plasma membrane protrusions (filopodia). I-BAR proteins contain an all-helical, crescent-shaped IRSp53-MIM domain (IMD) dimer that is believed to be able to couple with a membrane shape. This coupling could involve the sensing and even the generation of negative plasma membrane curvature. Indeed, the in vitro studies have shown that IMDs can induce inward tubulation of liposomes. While N-BAR domains, which generate positive membrane curvature, have received a considerable amount of attention from both theory and experiments, the mechanisms of curvature coupling through IMDs are comparatively less studied and understood. Here we used a membrane-shape stability assay developed recently in our lab to quantitatively characterize IMD-induced membrane-shape transitions. We determined a membrane-shape stability diagram for IMDs that reveals how membrane tension and protein density can comodulate the generation of IMD-induced membrane protrusions. From comparison to analytical theory, we determine three key parameters that characterize the curvature coupling of IMD. We find that the curvature generation capacity of IMDs is significantly stronger compared to that of endophilin, an N-BAR protein known to be involved in plasma membrane shape transitions. Contrary to N-BAR domains, where amphipathic helix insertion is known to promote its membrane curvature generation, for IMDs we find that amphipathic helices inhibit membrane shape transitions, consistent with the inverse curvature that IMDs generate. Importantly, in both of these types of BAR domains, electrostatic interactions affect membrane-binding capacity, but do not appear to affect the curvature generation capacity of the protein. These two types of BAR domain proteins show qualitatively similar membrane shape stability diagrams, suggesting an underlying ubiquitous mechanism by which peripheral proteins regulate membrane curvature.

Here we investigated the question whether cells, being highly heterogeneous objects, could be described with the elastic modulus (effective Young’s modulus) in a self-consistent way. We performed a comparative analysis of the elastic modulus derived from the indentation data obtained with atomic force microscopy (AFM) on human cervical epithelial cells (both normal and cancerous). Both sharp (cone) and dull (2500-nm radius sphere) AFM probes were used. The indentation data were processed through different elastic models. The cell was approximated as a homogeneous elastic medium that had either 1), smooth hemispherical boundary (Hertz/Sneddon models) or 2), the boundary covered with a layer of glycocalyx and membrane protrusions (“brush” models). Consistency of these approximations was investigated. Specifically, we tested the independence of the elastic modulus of the indentation depth, which is assumed in these models. We demonstrated that only one model showed consistency in treating cells as a homogeneous elastic medium, namely, the brush model, when processing the indentation data collected with the dull AFM probe. The elastic modulus demonstrated strong depth dependence in all models: Hertz/Sneddon models (no brush taken into account), and when the brush model was applied to the data collected with sharp conical probes. We conclude that it is possible to describe the elastic properties of the cell body by means of an effective elastic modulus, used in a self-consistent way, when using the brush model to analyze data collected with a dull AFM probe. The nature of these results is discussed.

Circular dorsal ruffles (CDRs) are transient actin-rich ring-like structures which form on the dorsal surface of growth-factor stimulated cells. However, the dynamics and mechanism of formation of CDRs are still unknown. It has been observed that CDR formation leads to stress fibers disappearing near the CDRs. Since stress fiber formation can be modified by substrate stiffness, we examined the effect of substrate stiffness on CDR formation by seeding NIH 3T3 fibroblasts on glass and polydimethylsiloxane (PDMS) substrates of varying stiffnesses from 20 kPa to 1800 kPa. We found that increasing substrate stiffness increased the lifetime of the CDRs. We developed a mathematical model of the signaling pathways involved in CDR formation to provide insight into this lifetime and size dependence which is linked to substrate stiffness via Rac-Rho antagonism. From the model, increasing stiffness raised mDia1-nucleated stress fiber formation due to Rho activation. The increased stress fibers present increased replenishment of the G-actin pool, therefore prolonging Arp2/3-nucleated CDR formation due to Rac activation. Negative feedback by WAVE-related RacGAP on Rac explained how CDR actin propagates as an excitable wave, much like wave propagation in other excitable medium, e.g., nerve signal transmission. Accepted version

Focal adhesions (FAs) are the predominant mechanism by which cells mechanically couple to and exert traction forces on their extracellular matrix (ECM). It is widely presumed that FA size is modulated by force to mediate changes in adhesion strength at different levels of cellular tension. However, previous studies seeking correlations between force and FA morphology have yielded variable and often conflicting results. Here we show that a strong correlation between adhesion size and traction force exists only during the initial stages of myosin-mediated adhesion maturation and growth. For mature adhesions, no correlation between traction stress and size is observed. Rather, the tension that is sustained at mature adhesions is more strongly influenced by proximity to the cell edge, with peripheral adhesions transmitting higher tension than adhesions near the cell center. Finally, we show that mature adhesions can withstand sixfold increases in tension without changes in size. Thus, although a strong correlation between adhesion size and mechanical tension is observed during the initial stages of myosin-mediated adhesion maturation, no correlation is observed in mature, elongated adhesions. This work places spatiotemporal constraints on the force-dependent growth of adhesions and provides insight into the mechanical regulation of cell-ECM adhesion.

Low pulling forces applied locally to cell surface membranes produce viscoelastic cell surface protrusions. As the force increases, the membrane can locally separate from the cytoskeleton and a tether forms. Tethers can grow to great lengths exceeding the cell diameter. The protrusion-to-tether transition is known as the crossover. Here we propose a unified approach to protrusions and tethers providing, to our knowledge, new insights into their biomechanics. We derive a necessary and sufficient condition for a crossover to occur, a formula for predicting the crossover time, conditions for a tether to establish a dynamic equilibrium (characterized by constant nonzero pulling force and tether extension rate), a general formula for the tether material after crossover, and a general modeling method for tether pulling experiments. We introduce two general protrusion parameters, the spring constant and effective viscosity, valid before and after crossover. Their first estimates for neutrophils are 50 pN μm−1 and 9 pN s μm−1, respectively. The tether elongation after crossover is described as elongation of a viscoelastic-like material with a nonlinearly decaying spring (NLDs-viscoelastic material). Our model correctly describes the results of the published protrusion and tether pulling experiments, suggesting that it is universally applicable to such experiments.

Cells remodel their plasma membrane and cytoskeleton during numerous physiological processes, including spreading and motility. Morphological changes require the cell to adjust its membrane tension on different timescales. While it is known that endo- and exocytosis regulate the cell membrane area in a timescale of 1 h, faster processes, such as abrupt cell detachment, require faster regulation of the plasma membrane tension. In this article, we demonstrate that cell blebbing plays a critical role in the global mechanical homeostasis of the cell through regulation of membrane tension. Abrupt cell detachment leads to pronounced blebbing (which slow detachment does not), and blebbing decreases with time in a dynamin-dependent fashion. Cells only start spreading after a lag period whose duration depends on the cell's blebbing activity. Our model quantitatively reproduces the monotonic decay of the blebbing activity and accounts for the lag phase in the spreading of blebbing cells.

Communication between cells is crucial for proper functioning of multicellular organisms. The recently discovered membranous tubes, named tunneling nanotubes, that directly bridge neighboring cells may offer a very specific and effective way of intercellular communication. Our experiments on RT4 and T24 urothelial cell lines show that nanotubes that bridge neighboring cells can be divided into two types. The nanotubes of type I are shorter and more dynamic than those of type II, and they contain actin filaments. They are formed when cells explore their surroundings to make contact with another cell. The nanotubes of type II are longer and more stable than type I, and they have cytokeratin filaments. They are formed when two already connected cells start to move apart. On the nanotubes of both types, small vesicles were found as an integral part of the nanotubes (that is, dilatations of the nanotubes). The dilatations of type II nanotubes do not move along the nanotubes, whereas the nanotubes of type I frequently have dilatations (gondolas) that move along the nanotubes in both directions. A possible model of formation and mechanical stability of nanotubes that bridge two neighboring cells is discussed.

Mesenchymal cell migration through a three-dimensional (3D) matrix typically involves major matrix remodeling. The direction of matrix deformation occurs locally in all three dimensions, which cannot be measured by current techniques. To probe the local, 3D, real-time deformation of a collagen matrix during tumor cell migration, we developed an assay whereby matrix-embedded beads are tracked simultaneously in all three directions with high resolution. To establish a proof of principle, we investigated patterns of collagen I matrix deformation near fibrosarcoma cells in the absence and presence of inhibitors of matrix metalloproteinases and acto-myosin contractility. Our results indicate that migrating cells show patterns of local matrix deformation toward the cell that are symmetric in magnitude with respect to the axis of cell movement. In contrast, patterns of matrix release from the cell are asymmetric: the matrix is typically relaxed first at the back of the cell, allowing forward motion, and then at the cell's leading edge. Matrix deformation in regions of the matrix near the cell's leading edge is elastic and mostly reversible, but induces irreversible matrix rupture events near the trailing edge. Our results also indicate that matrix remodeling spatially correlates with protrusive activity. This correlation is mediated by myosin II and Rac1, and eliminated after inhibition of pericellular proteolysis or ROCK. We have developed an assay based on high-resolution 3D multiple-particle tracking that allows us to probe local matrix remodeling during mesenchymal cell migration through a 3D matrix and simultaneously monitor protrusion dynamics.

It has been hypothesized, from earlier studies on single-tether extraction from individual leukocytes and human umbilical vein endothelial cells, that during rolling of leukocytes on the endothelium, simultaneous extraction of membrane nanotubes (tethers) occurs, resulting in enhancement of the force decrease on the adhesive bond. In this study, using the micropipette aspiration technique and fluorescence microscopy, we show that tethers are indeed extracted simultaneously when an endothelial cell and a leukocyte are separated after brief contact and adhesion, and the endothelial cell contributes much more to the composite tether length. In addition, the constitutive relationship for simultaneous tether extraction is determined with neutrophils and T-lymphocytes as force transducers, and cytokine-stimulated human umbilical vein and dermal microvascular endothelial cells as substrates, respectively. This relationship is consistent with that derived theoretically from the constitutive equations for single-tether extraction from either cell alone. Moreover, we show that simultaneous tether extraction was likely terminated by receptor-ligand bond dissociation. With a biomechanical model of leukocyte rolling, we predict the force history of the adhesive receptor-ligand bond and show that it is remarkably similar for different leukocyte-endothelial cell pairs. Simultaneous tether extraction therefore represents a generic mechanism for stabilizing leukocyte rolling on the endothelium.

Tethers were created between a living Escherichia coli bacterium and a bead by unspecifically attaching the bead to the outer membrane and pulling it away using optical tweezers. Upon release, the bead returned to the bacterium, thus showing the existence of an elastic tether between the bead and the bacterium. These tethers can be tens of microns long, several times the bacterial length. Using mutants expressing different parts of the outer membrane structure, we have shown that an intact core lipopolysaccharide is a necessary condition for tether formation, regardless of whether the beads were uncoated polystyrene or beads coated with lectin. A physical characterization of the tethers has been performed yielding visco-elastic tether force-extension relationships: for first pull tethers, a spring constant of 10–12pN/μm describes the tether visco-elasticity, for subsequent pulls the spring constant decreases to 6–7pN/μm, and typical relaxation timescales of hundreds of seconds are observed. Studies of tether stability in the presence of proteases, lipases, and amylases lead us to propose that the extracted tether is primarily composed of the asymmetric lipopolysaccharide containing bilayer of the outer membrane. This unspecific tethered attachment mechanism could be important in the initiation of bacterial adhesion.

Fluorescence resonance energy transfer (FRET) between matched carbocyanine lipid analogs in the plasma membrane outer leaflet of RBL mast cells was used to investigate lateral distributions of lipids and to develop a general method for quantitative measurements of lipid heterogeneity in live cell membranes. FRET measured as fluorescence quenching of long-chain donor probes such as DiO-C18 is greater with long-chain, saturated acceptor probes such as DiI-C16 than with unsaturated or shorter-chain acceptors with the same chromophoric headgroup compared at identical concentrations. FRET measurements between these lipid probes in model membranes support the conclusion that differential donor quenching is not caused by nonideal mixing or spectroscopic differences. Sucrose gradient analysis of plasma membrane-labeled, Triton X-100-lysed cells shows that proximity measured by FRET correlates with the extent of lipid probe partitioning into detergent-resistant membranes. FRET between DiO-C16 and DiI-C16 is sensitive to cholesterol depletion and disruption of liquid order (Lo) by short-chain ceramides, and it is enhanced by cross linking of Lo-associated proteins. Consistent results are obtained when homo-FRET is measured by decreased fluorescence anisotropy of DiI-C16. These results support the existence of nanometer-scale Lo/liquid disorder heterogeneity of lipids in the outer leaflet of the plasma membrane in live cells.

Ligands mounted to surfaces via extensible tethers are present in nature and represent a growing class of molecules used to engineer adhesion in drug targeting, biosensing, self-assembling nanostructures, and in other biophysical research. Using a continuum approach with geometric and thermodynamic arguments, we derive a number of analytical expressions that relate key properties of single-tethered ligand-receptor interactions to multiple bond formation between curved surfaces. The theoretical predictions are in good agreement with measurements made with the surface forces apparatus. We establish that, when ligated, many tethers commonly used in biophysical research exhibit a discrete binding range that can be accurately measured with force spectroscopy. The distribution of bound ligated tethers is independent of the surfaces’ interaction radius, R. The bridging force scales linearly with R, the tether’s effective spring constant and grafting density, and with the ligand-receptor bond energy when the surfaces are in direct contact. These results are contrasted to bridging forces that evolve between plane-parallel geometries. Last, we show how our simple analytical reductions can be used to predict adhesive forces for STEALTH liposomes and other targeted and self-assembled nanoparticles.

One of the earliest lipid intermediates forming in the course of membrane fusion is the lipid stalk. Although many aspects of the stalk hypothesis were elaborated theoretically and confirmed by experiments it remained unresolved whether stalk formation is always an energy consuming process or if there are conditions where the stalks are energetically favorable and form spontaneously resulting in an equilibrium stalk phase. Motivated by a recent breakthrough experiments we analyze the physical factors determining the spontaneous stalk formation. We show that this process can be driven by interplay between two factors: the elastic energy of lipid monolayers including a contribution of the saddle splay deformation and the energy of hydration repulsion acting between apposing membranes. We analyze the dependence of stalk formation on the saddle splay (Gaussian) modulus of the lipid monolayers and estimate the values of this modulus based on the experimentally established phase boundary between the lamellar and the stalk phases. We suggest that fusion proteins can induce stalk formation just by bringing the membranes into close contact, and accumulating, at least locally, a sufficiently large energy of the hydration repulsion.

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.

Membrane budding-fission is a fundamental process generating intracellular carriers of proteins. Earlier works were focused only on formation of coated buds connected to the initial membrane by narrow membrane necks. We present the theoretical analysis of the whole pathway of budding-fission, including the crucial stage where the membrane neck undergoes fission and the carrier separates from the donor membrane. We consider two successive intermediates of the reaction: 1), a constricted membrane neck coming out of aperture of the assembling protein coat, and 2), hemifission intermediate resulting from self-fusion of the inner monolayer of the neck, while its outer monolayer remains continuous. Transformation of the constricted neck into the hemifission intermediate is driven by the membrane stress produced in the neck by the protein coat. Although apparently similar to hemifusion, the fission is predicted to have an opposite dependence on the monolayer spontaneous curvature. Analysis of the further stages of the process demonstrates that in all practically important cases the hemifission intermediate decays spontaneously into two separate membranes, thereby completing the fission process. We formulate the “job description” for fission proteins by calculating the energy they have to deliver and the radii of the protein coat aperture which have to be reached to drive the fission process.

The transverse tubular system (t-system) is a major site for signaling in mammalian ventricular cardiomyocytes including electrical signaling and excitation-contraction coupling. It consists of membrane invaginations, which are decorated with various proteins including mechanosensitive ion channels. Here, we investigated mechanical modulation of the t-system. By applying fluorescent markers, three-dimensional scanning confocal microscopy, and methods of digital image analysis, we studied isolated ventricular cardiomyocytes under different strains. We demonstrate that strain at the cellular level is transmitted to the t-system, reducing the length and volume of tubules and altering their cross-sectional shape. Our data suggest that a cellular strain of as little as 5% affects the shape of transverse tubules, which has important implications for the function of mechanosensitive ion channels found in them. Furthermore, our study supports a prior hypothesis that strain can cause fluid exchange between the t-system and extracellular space.

The recent discovery of electrically conductive bacterial appendages has significant physiological, ecological, and biotechnological implications, but the mechanism of electron transport in these nanostructures remains unclear. We here report quantitative measurements of transport across bacterial nanowires produced by the dissimilatory metal-reducing bacterium, Shewanella oneidensis MR-1, whose electron transport system is being investigated for renewable energy recovery in microbial fuel cells and bioremediation of heavy metals and radionuclides. The Shewanella nanowires display a surprising nonlinear electrical transport behavior, where the voltage dependence of the conductance reveals peaks indicating discrete energy levels with higher electronic density of states. Our results indicate that the molecular constituents along the Shewanella nanowires possess an intricate electronic structure that plays a role in mediating transport.

A new mechanism of cell-cell communication was recently proposed after the discovery of tunneling nanotubes (TNTs) between cells. TNTs are membrane protrusions with lengths of tens of microns and diameters of a few hundred nanometers that permit the exchange of membrane and cytoplasmic constituents between neighboring cells. TNTs have been reported to mediate intercellular Ca(2+) signaling; however, our simulations indicate that passive diffusion of Ca(2+) ions alone would be inadequate for efficient transmission between cells. Instead, we observed spontaneous and inositol trisphosphate (IP(3))-evoked Ca(2+) signals within TNTs between cultured mammalian cells, which sometimes remained localized and in other instances propagated as saltatory waves to evoke Ca(2+) signals in a connected cell. Consistent with this, immunostaining showed the presence of both endoplasmic reticulum and IP(3) receptors along the TNT. We propose that IP(3) receptors may actively propagate intercellular Ca(2+) signals along TNTs via Ca(2+)-induced Ca(2+) release, acting as amplification sites to overcome the limitations of passive diffusion in a chemical analog of electrical transmission of action potentials.

Cell movement biased by a chemical gradient, or chemotaxis, coordinates the recruitment of cells and collective migration of cell populations. During wound healing, chemotaxis of fibroblasts is stimulated by platelet-derived growth factor (PDGF) and certain other chemoattractants. Whereas the immediate PDGF gradient sensing response has been characterized previously at the level of phosphoinositide 3-kinase (PI3K) signaling, the sensitivity of the response at the level of cell migration bias has not yet been studied quantitatively. In this work, we used live-cell total internal reflection fluorescence microscopy to monitor PI3K signaling dynamics and cell movements for extended periods. We show that persistent and properly aligned (i.e., high-fidelity) fibroblast migration does indeed correlate with polarized PI3K signaling; accordingly, this behavior is seen only under conditions of high gradient steepness (>10% across a typical cell length of 50 μm) and a certain range of PDGF concentrations. Under suboptimal conditions, cells execute a random or biased random walk, but nonetheless move in a predictable fashion according to the changing pattern of PI3K signaling. Inhibition of PI3K during chemotaxis is accompanied by loss of both cell-substratum contact and morphological polarity, but after a recovery period, PI3K-inhibited fibroblasts often regain the ability to orient toward the PDGF gradient.

Invadopodia are subcellular organelles thought to be critical for extracellular matrix (ECM) degradation and the movement of cells through tissues. Here we examine invadopodia generation, turnover, and function in relation to two structural aspects of the ECM substrates they degrade: cross-linking and fiber density. We set up a cellular automaton computational model that simulates ECM penetration and degradation by invadopodia. Experiments with denatured collagen (gelatin) were used to calibrate the model and demonstrate the inhibitory effect of ECM cross-linking on invadopodia degradation and penetration. Incorporation of dynamic invadopodia behavior into the model amplified the effect of cross-linking on ECM degradation, and was used to model feedback from the ECM. When the model was parameterized with spatial fibrillar dimensions that closely matched the organization, in real life, of native ECM collagen into triple-helical monomers, microfibrils, and macrofibrils, little or no inhibition of invadopodia penetration was observed in simulations of sparse collagen gels, no matter how high the degree of cross-linking. Experimental validation, using live-cell imaging of invadopodia in cells plated on cross-linked gelatin, was consistent with simulations in which ECM cross-linking led to higher rates of both invadopodia retraction and formation. Analyses of invadopodia function from cells plated on cross-linked gelatin and collagen gels under standard concentrations were consistent with simulation results in which sparse collagen gels provided a weak barrier to invadopodia. These results suggest that the organization of collagen, as it may occur in stroma or in vitro collagen gels, forms gaps large enough so as to have little impact on invadopodia penetration/degradation. By contrast, dense ECM, such as gelatin or possibly basement membranes, is an effective obstacle to invadopodia penetration and degradation, particularly when cross-linked. These results provide a novel framework for further studies on ECM structure and modifications that affect invadopodia and tissue invasion by cells.

Cell adhesion mechanically couples cells to surfaces. The durability of individual bonds between the adhesive receptors and their ligands in the presence of forces determines the cellular adhesion strength. For adhesive receptors such as integrins, it is a common paradigm that the cell regulates its adhesion strength by altering the affinity state of the receptors. However, the probability distribution of rupture forces is dependent not only on the affinity of individual receptor-ligand bonds but also on the mechanical compliance of the cellular anchorage of the receptor. Hence, by altering the anchorage, the cell can regulate its adhesion strength without changing the affinity of the receptor. Here, we analyze the anchorage of the integrin VLA-4 with its ligand VCAM-1. For this purpose, we develop a model based on the Kelvin body, which allows one to quantify the mechanical properties of the adhesive receptor's anchorage using atomic force microscopy on living cells. As we demonstrate, the measured force curves give valuable insight into the mechanics of the cellular anchorage of the receptor, which is described by the tether stiffness, the membrane rigidity, and the membrane viscosity. The measurements relate to a tether stiffness of k(t) = 1.6 microN/m, an initial membrane rigidity of k(i) = 260 microN/m, and a viscosity of mu = 5.9 microN x s/m. Integrins exist in different activation states. When activating the integrin with Mg(2+), we observe altered viscoelastic parameters of k(t) = 0.9 microN/m, k(i) = 190 microN/m, and mu = 6.0 microN x s/m. Based on our model, we postulate that anchorage-related effects are common regulating mechanisms for cellular adhesion beyond affinity regulation.

Multiple tethers are very likely extracted when leukocytes roll on the endothelium under high shear stress. Endothelial cells have been predicted to contribute more significantly to simultaneous tethers and thus to the overall rolling stabilization. We therefore extracted and quantified double tethers from endothelial cells with the micropipette aspiration technique. We show that the constitutive parameters (threshold force (F0) and effective viscosity (etaeff)) for double-tether extraction are twice those for single-tether extraction and are remarkably similar for human neonatal (F0=105+/-5 pN; etaeff=1.0+/-0.1 pN.s/microm) and adult (F0=118+/-13 pN; etaeff=1.3+/-0.2 pN.s/microm) dermal microvascular, and human umbilical vein (F0=99+/-3 pN; etaeff=1.0+/-0.1 pN.s/microm) endothelial cells. Additionally, these parameters are also independent of surface receptor type, cytokine stimulation, and attachment state of the endothelial cell. We also introduce a novel correlation between the cell-substrate contact stress and gap width, with which we can predict the apparent cell-substrate separation range to be 0.01-0.1 microm during leukocyte rolling. With a biomechanical model of leukocyte rolling, we calculate the force history on the receptor-ligand bond during tether extraction and predict maximum stabilization for the double simultaneous tether extraction case.

The aquatic bacterium Caulobacter crescentus divides asymmetrically to a flagellated swarmer cell and a cell with a stalk. At the end of the stalk is an adhesive organelle known as the holdfast, which the stalked cell uses to attach to a solid surface. Often there are two or more cells with their stalks attached to the same holdfast. By analyzing the fluctuations in the stalk angle for a pair of cells attached to a single holdfast, we determine the elastic stiffness of the holdfast. We model the holdfast as three torsional springs in series and find that the effective torsional spring constant for the holdfast is of the order of (10−17–10−18) Nm, with unequal spring constants. The asymmetry suggests the sequence in which the cells attach to each other, and in some cases suggests that strong crosslinks form between the stalks as they make a shared holdfast.

We propose a framework for tracking arbitrary complex cell boundary movements, relying on a unique definition of protrusion and retraction as the pathlength a virtual edge marker traverses when moving continuously perpendicular to the cell boundary. We introduce the level set method as a numerical scheme to reconstruct continuous boundary movement in time-lapse image sequences with finite time sampling. For moderately complex movements, we describe a numerically less expensive method that satisfactorily approximates the definition. Densely sampled protrusion and retraction rates were accumulated in space-time charts revealing distinct morphodynamic states. Applying this technique to the profiling of epithelial cell protrusion we identified three different states. In the I-state, long cell edge sectors are synchronized in cycles of protrusion and retraction. In the V-state random bursts of protrusion initiate protrusion waves propagating transversally in both directions. Cells switch between both states dependent on the Rac1 activation level. Furthermore, the persistence of transversal waves in the V-state depends on Arp2/3 concentration. Inhibition of PAK shifts cells into a λ-state where continuous protrusion is occasionally interrupted by self-propagating ruffles. Our data support a model where activation of Rac1 mediates the propagation of protrusion waves, whose persistence depends on the relative abundance of activated Arp2/3 and polymerizable G-actin.

Actin dynamics is important in determining cell shape, tension, and migration. Methods such as fluorescent speckle microscopy and spatial temporal image correlation spectroscopy have been used to capture high-resolution actin turnover dynamics within cells in two dimensions. However, these methods are not directly applicable in 3D due to lower resolution and poor contrast. Here, we propose to capture actin flow in 3D with high spatial-temporal resolution by combining nanoscale precise imaging by rapid beam oscillation and fluctuation spectroscopy techniques. To measure the actin flow along cell protrusions in cell expressing actin-eGFP cultured in a type I collagen matrix, the laser was orbited around the protrusion and its trajectory was modulated in a clover-shaped pattern perpendicularly to the protrusion. Orbits were also alternated at two positions closely spaced along the protrusion axis. The pair cross-correlation function was applied to the fluorescence fluctuation from these two positions to capture the flow of actin. Measurements done on nonmoving cellular protrusion tips showed no pair-correlation at two orbital positions indicating a lack of flow of F-actin bundles. However, in some protrusions, the pair-correlation approach revealed directional flow of F-actin bundles near the protrusion surface with flow rates in the range of ∼1 μm/min, comparable to results in two dimensions using fluorescent speckle microscopy. Furthermore, we found that the actin flow rate is related to the distance to the protrusion tip. We also observed collagen deformation by concomitantly detecting collagen fibers with reflectance detection during these actin motions. The implementation of the nanoscale precise imaging by rapid beam oscillation method with a cloverleaf-shaped trajectory in conjunction with the pair cross-correlation function method provides a quantitative way of capturing dynamic flows and organization of proteins during cell migration in 3D in conditions of poor contrast. © 2013 The Authors.

We present a physical model that describes the active localization of actin-regulating proteins inside stereocilia during steady-state conditions. The mechanism of localization is through the interplay of free diffusion and directed motion, which is driven by coupling to the treadmilling actin filaments and to myosin motors that move along the actin filaments. The resulting localization of both the molecular motors and their cargo is calculated, and is found to have an exponential (or steeper) profile. This localization can be at the base (driven by actin retrograde flow and minus-end myosin motors), or at the stereocilia tip (driven by plus-end myosin motors). The localization of proteins that influence the actin depolymerization and polymerization rates allow us to describe the narrow shape of the stereocilia base, and the observed increase of the actin polymerization rate with the stereocilia height.

Actin-based cellular protrusions are a ubiquitous feature of cell morphology, e.g., filopodia and microvilli, serving a huge variety of functions. Despite this, there is still no comprehensive model for the mechanisms that determine the geometry of these protrusions. We present here a detailed computational model that addresses a combination of multiple biochemical and physical processes involved in the dynamic regulation of the shape of these protrusions. We specifically explore the role of actin polymerization in determining both the height and width of the protrusions. Furthermore, we show that our generalized model can explain multiple morphological features of these systems, and account for the effects of specific proteins and mutations.

Many physiological phenomena involve directional cell migration. It is usually attributed to chemical gradients in vivo. Recently, other cues have been shown to guide cells in vitro, including stiffness/adhesion gradients or micro-patterned adhesive motifs. However, the cellular mechanism leading to these biased migrations remains unknown, and, often, even the direction of motion is unpredictable. In this study, we show the key role of fluctuating protrusions on ratchet-like structures in driving NIH3T3 cell migration. We identified the concept of efficient protrusion and an associated direction index. Our analysis of the protrusion statistics facilitated the quantitative prediction of cell trajectories in all investigated conditions. We varied the external cues by changing the adhesive patterns. We also modified the internal cues using drug treatments, which modified the protrusion activity. Stochasticity affects the short- and long-term steps. We developed a theoretical model showing that an asymmetry in the protrusion fluctuations is sufficient for predicting all measures associated with the long-term motion, which can be described as a biased persistent random walk., Comment: Supplementary movies available upon request

Membrane tethers are extracted when neutrophils roll on the endothelium to initiate their transendothelial migration. Tether extraction from both neutrophils and endothelial cells stabilizes neutrophil rolling, so it has been studied extensively and the force-velocity relationship for tether extraction is of great interest. Due to limitations of the techniques used in previous studies, this relationship has been obtained only from tethers perpendicular to the cell surface. Here, with the microcantilever technique, where latex beads affixed on silicon cantilevers were used as the force transducer, we extracted tethers either perpendicular or tangential to the neutrophil surface. We found that the force-velocity relationship was not sensitive to tether pulling direction. Little movement of the tether-cell junction was observed during tangential tether extraction, and no coalescence was observed during multiple tether extraction. Following adhesion rupture, spontaneous tether retraction was visualized by membrane staining, which revealed two phases: one was fast and exponential, whereas the other was slow and linear. Both phases can be reproduced with a mechanical model. These results show for the first time, to our knowledge, how neutrophil tethers shorten upon instantaneous force removal, and furthermore, they illustrate how membrane tethers contribute to neutrophil rolling stability during the inflammatory response.