Table of contents

One of the most striking achievements of evolution is the ability to build cellular systems that are both robust and dynamic. Taken by themselves, both properties are obvious requirements: robustness reflects the fact that cells are there to survive, and dynamics is required to adapt to changing environments. However, it is by no means trivial to understand how these two requirements can be implemented simultaneously in a physical system. The long and difficult quest to build adaptive materials is testimony to the inherent difficulty of this goal. Here materials science can learn a lot from nature, because cellular systems show that robustness and dynamics can be achieved in a synergetic fashion. For example, the capabilities of tissues to repair and regenerate are still unsurpassed in the world of synthetic materials.

One of the most important aspects of the way biological cells adapt to their environment is their adhesive interaction with the substrate. Numerous aspects of the physiology of metazoan cells, including survival, proliferation, differentiation and migration, require the formation of adhesions to the cell substrate, typically an extracellular matrix protein. Adhesions guide these diverse processes both by mediating force transmission from the cell to the substrate and by controlling biochemical signaling pathways. While the study of cell–substrate adhesions is a mature field in cell biology, a quantitative biophysical understanding of how the interactions of the individual molecular components give rise to the rich dynamics and mechanical behaviors observed for cell–substrate adhesions has started to emerge only over the last decade or so.

The recent growth of research activities on cell–substrate interactions was strongly driven by the introduction of new physical techniques for surface engineering into traditional cell biological work with cell culture. For example, microcontact printing of adhesive patterns was used to show that cell fate depends not on the amount of ligand for adhesion receptors, but on its spatial distribution [1]. New protocols for the preparation of soft elastic substrates were essential to show that adhesion structures and cytoskeleton of adherent cells strongly adapt to substrate stiffness [2], with dramatic effects for cellular decision making. For example, it has been shown recently that differentiation of mesenchymal stem cells is strongly influenced by substrate stiffness [3]. Thus, physical factors appear to be equally important as biochemical ones in determining the cellular response to its substrate [4].

The introduction of novel physical techniques not only opened up completely new perspectives regarding biological function, it also introduced a new quantitative element into this field. For example, the availability of soft elastic substrates with controlled stiffness allows us to reconstruct cellular traction forces and to correlate them with other cellular features. This development enables modeling approaches to work in close contact with experimental data, thus opening up the perspective that the field of cell–substrate interactions will become a quantitative and predictive science in the future.

Because physical research into cell–substrate interactions has become one of the fastest growing research areas in cellular biophysics and materials science, we believe that it is very timely that this special issue gathers some of the on-going research effort in this field. In contrast to the non-living world, cellular systems usually interact with their environment through specific adhesion, mainly based on adhesion receptors from the integrin family. During recent years, force spectroscopy has emerged as one of the main methods to study the physics of specific adhesion. In this special issue, single cell force spectroscopy is used by Boettiger and Wehrle-Haller to characterize the strength of cell-matrix adhesion and how it is modulated by the glycocalyx [5], while Chirasatitsin and Engler use force spectroscopy mapping to characterize the spatial distribution of adhesive sites on the substrate [6]. Scrimgeour et al describe a new method to adhesively pattern self-assembled monolayers for cell adhesion by a simple photobleaching setup [7] and Stricker et al demonstrate how elastic substrates can be combined with microcontact printing to improve the reconstruction of traction forces [8]. The work by Metzner et al shows that meaningful results on the cell–substrate interactions can be extracted also from experiments in which cells interact with biofunctionalized beads [9].

If cells start to adhere to a substrate, the main rate-limiting step is establishment of close contact between the plasma membrane and the substrate. This process can be followed with high spatial and temporal resolution with reflection interference microscopy, as demonstrated by Ryzhkov et al for mouse embryonic fibroblasts [10] and by Cretel et al for T lymphocytes [11]. Once mature adhesion has been achieved, the integrin-based focal adhesions providing anchorage to the substrate are strongly connected to the actin cytoskeleton, the main determinant of cell shape and structure. Heil and Spatz use microfabricated pillars to perturb the mechanical balance and quantitatively characterize the fast response of the focal adhesions [12]. A similar approach is used by Kirchenbüchler et al, who use deformation of an elastic substrate to demonstrate that the weak link in the mechanical system of substrate, adhesions and actin cytoskeleton is most likely located at the adhesion-cytoskeleton interface [13]. Rather than using external perturbations, Zemel et al quantify and model how cells spontaneously polarize their cytoskeleton in response to the physical properties of the substrate [14].

Quantitative analysis of cellular data has become standard in the field of cell–substrate interactions. Moreover, theoretical models for cell–substrate interactions help us to identify and understand the mechanisms underlying the observed phenomena in these complex systems. Recently, a large effort has been invested into understanding how force transmitted by the actin cytoskeleton changes the state of focal adhesions. In the contribution by Biton and Safran, this issue is addressed for the case that force arises from shear flow over an adhering cell [15]. Another important source for force on focal adhesions is actin retrograde flow, which has been demonstrated before to show variable coupling to the underlying layer of adhesion receptors. Two contributions discuss how stochastic bond dynamics at the cell–substrate interface is modulated by physical factors. The model by Sabass and Schwarz suggests that dissipation in the actin cytoskeleton stabilizes bond dynamics [16] and the model by Li et al suggests that catch bonding and multiple layers are important elements of the way focal adhesions function [17].

If interacting with an elastic environment, the combined system of focal adhesions and actin cytoskeleton can be used by cells to sense its rigidity and to make decisions on its response. Moshayedi et al show that great care has to be taken when preparing soft elastic substrates for cell culture studies and then use their protocols to quantitatively evaluate the mechanosensitive response of astrocytes from the brain [18]. The cellular system used by Lee et al is pericytes from the microvasculature, for which the authors show that they exert sufficient forces to stimulate vascular endothelial cells [19]. Buxboim et al use the technology of soft elastic substrates to measure how far mesenchymal stem cells can mechanically sense into their substrate [20].

The mechanical activity of cells observed in two-dimensional cell culture has significant consequences for both physiological and disease-related situations, including cell migration, tissue maintenance and tumor growth. Jannat et al show that chemotaxis of neutrophils, that is the first line of the immune system, is strongly modulated by mechanosensing on substrates of varying stiffness [21]. Mogilner and Rubinstein present a theoretical systems analysis for the shape of rapidly migrating keratocytes [22]. Saez et al show, with microfabricated pillar assays, how force is distributed within a layer of epithelial cells [23]. For three-dimensional tissue models, new techniques have to be developed to characterize the complex mechanics of hydrogels. Levental et al [24] and Kotlarchyk et al [25] approach this challenge with mechanical and optical methods, respectively. Narayanan et al combine experiments and continuum models to explore how chemo-mechanical interactions influence tumor growth [26].

References

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[2] Pelham R J Jr and Wang Y-L 1997 Cell locomotion and focal adhesions are regulated by substrate flexibility Proc. Natl. Acad. Sci. USA94 13661

[3] Engler A J, Sen S, Sweeney H L and Discher D E 2006 Matrix elasticity directs stem cell lineage specification Cell126 677–89

[4] Geiger B, Spatz J P and Bershadsky A D 2009 Environmental sensing through focal adhesions Nat. Rev. Mol. Cell Biol.10 21

[5] Boettiger D and Wehrle-Haller B 2010 Integrin and glycocalyx mediated contributions to cell adhesion identified by single cell force spectroscopy J. Phys.: Condens. Matter22 194101

[6] Chirasatitsin S and Engler A J 2010 Detecting cell-adhesive sites in extracellular matrix using force spectroscopy mapping J. Phys.: Condens. Matter22 194102

[7] Scrimgeour J, Kodali V K, Kovari D T and Curtis J E 2010 Photobleaching-activated micropatterning on self-assembled monolayers J. Phys.: Condens. Matter22 194103

[8] Stricker J, Sabass B, Schwarz U S and Gardel M L 2010 Optimization of traction force microscopy for micron-sized focal adhesions J. Phys.: Condens. Matter22 194104

[9] Metzner C, Raupach C, Mierke C T and Fabry B 2010 Fluctuations of cytoskeleton-bound microbeads—the effect of bead–receptor binding dynamics J. Phys.: Condens. Matter22 194105

[10] Ryzhkov P, Prass M, Gummich M, Kühn J-S, Oettmeier C and Döbereiner H-G 2010 Adhesion patterns in early cell spreading J. Phys.: Condens. Matter22 194106

[11] Cretel E, Touchard D, Benoliel A M, Bongrand P and Pierres A 2010 Early contacts between T lymphocytes and activating surfaces J. Phys.: Condens. Matter22 194107

[12] Heil P and Spatz J P 2010 Lateral shear forces applied to cells with single elastic micropillars to influence focal adhesion dynamics J. Phys.: Condens. Matter22 194108

[13] Kirchenbüchler D, Born S, Kirchgeßner N, Houben S, Hoffmann B and Merkel R 2010 Substrate, focal adhesions, and actin filaments: a mechanical unit with a weak spot for mechanosensitive proteins J. Phys.: Condens. Matter22 194109

[14] Zemel A, Rehfeldt F, Brown A E X, Discher D E and Safran S A 2010 Cell shape, spreading symmetry, and the polarization of stress-fibers in cells J. Phys.: Condens. Matter22 194110

[15] Biton Y Y and Safran S A 2010 Theory of the mechanical response of focal adhesions to shear flow J. Phys.: Condens. Matter22 194111

[16] Sabass B and Schwarz U S 2010 Modeling cytoskeletal flow over adhesion sites: competition between stochastic bond dynamics and intracellular relaxation J. Phys.: Condens. Matter22 194112

[17] Li Y, Bhimalapuram P and Dinner A R 2010 Model for how retrograde actin flow regulates adhesion traction stresses J. Phys.: Condens. Matter22 194113

[18] Moshayedi P, da F Costa L, Christ A, Lacour S P, Fawcett J, Guck J and Franze K 2010 Mechanosensitivity of astrocytes on optimized polyacrylamide gels analyzed by quantitative morphometry J. Phys.: Condens. Matter22 194114

[19] Lee S, Zeiger A, Maloney J M, Kotecki M, Van Vliet K J and Herman I M 2010 Pericyte contraction at the cell-material interface can modulate the microvascular niche J. Phys.: Condens. Matter22 194115

[20] Buxboim A, Rajagopal K, Brown A E X and Discher D E 2010 How deeply cells feel: methods for thin gels J. Phys.: Condens. Matter22 194116

[21] Jannat R A, Robbins G P, Ricart B G, Dembo M and Hammer D A 2010 Neutrophil adhesion and chemotaxis depend on substrate mechanics J. Phys.: Condens. Matter22 194117

[22] Mogilner A and Rubinstein B 2010 Actin disassembly 'clock' and membrane tension determine cell shape and turning: a mathematical method J. Phys.: Condens. Matter22 194118

[23] Saez A, Anon E, Ghibaudo M, du Roure O, Di Meglio J-M, Hersen P, Silberzan P, Buguin A, Ladoux B 2010 Traction forces exerted by epithelial cell sheets J. Phys.: Condens. Matter22 194119

[24] Levental I, Levental K R, Klein E A, Assoian R, Miller R T, Wells R G and Janmey P A 2010 A simple indentation device for measuring micrometer-scale tissue stiffness J. Phys.: Condens. Matter22 194120

[25] Kotlarchyk M A, Botvinick E L and Putnam A J 2010 Characterization of hydrogel microstructure using laser tweezers particle tracking and confocal reflection imaging J. Phys.: Condens. Matter22 194121

[26] Narayanan H, Verner S N, Mills K L, Kemkemer R and Garikipati K 2010 In silico estimates of the free energy rates in growing tumor spheroids J. Phys.: Condens. Matter22 194122

The measurement of cell adhesion using single cell force spectroscopy methods was compared with earlier methods for measuring cell adhesion. This comparison provided a means and rationale for separating components of the measurement retract curve that were due to interactions between the substrate and the glycocalyx, and interactions that were due to cell surface integrins binding to a substrate-bound ligand. The glycocalyx adhesion was characterized by multiple jumps with dispersed jump sizes that extended from 5 to 30 µm from the origin. The integrin mediated adhesion was represented by the F_max (maximum detachment force), was generally within the first 5 µm and commonly detached with a single rupture cascade. The integrin peak (F_max) increases with time and the rate of increase shows large cell to cell variability with a peak ∼ 50 nN s ^{− 1} and an average rate of increase of 75 pN s ^{− 1}. This is a measure of the rate of increase in the number of adhesive integrin–ligand bonds/cell as a function of contact time.

The cell microenvironment is composed of extracellular matrix (ECM), which contains specific binding sites that allow the cell to adhere to its surroundings. Cells employ focal adhesion proteins, which must be able to resist a variety of forces to bind to ECM. Current techniques for detecting the spatial arrangement of these adhesions, however, have limited resolution and those that detect adhesive forces lack sufficient spatial characterization or resolution. Using a unique application of force spectroscopy, we demonstrate here the ability to determine local changes in the adhesive property of a fibronectin substrate down to the resolution of the fibronectin antibody-functionalized tip diameter, ∼ 20 nm. To verify the detection capabilities of force spectroscopy mapping (FSM), changes in loading rate and temperature were used to alter the bond dynamics and change the adhesion force. Microcontact printing was also used to pattern fluorescein isothiocyanate-conjugated fibronectin in order to mimic the discontinuous adhesion domains of native ECM. Fluorescent detection was used to identify the pattern while FSM was used to map cell adhesion sites in registry with the initial fluorescent image. The results show that FSM can be used to detect the adhesion domains at high resolution and may subsequently be applied to native ECM with randomly distributed cell adhesion sites.

Functional chemical micropatterns were fabricated by exploiting the photobleaching of dye-coupled species near methacrylate self-assembled monolayers. Using this approach we have demonstrated that multiple chemistries can be coupled to the monolayer using a standard fluorescence microscope. The surface bound functional groups remain active and patterns with feature sizes down to 3 µm can be readily achieved with excellent signal-to-noise ratio. Control over the ligand binding density was demonstrated to illustrate the convenient route provided by this platform for fabricating complex spatial gradients in ligand density.

To understand how adherent cells regulate traction forces on their surrounding extracellular matrix (ECM), quantitative techniques are needed to measure forces at the cell–ECM interface. Microcontact printing is used to create a substrate of 1 µm diameter circles of ECM ligand to experimentally study the reconstruction of traction stresses at constrained, point-like focal adhesions. Traction reconstruction with point forces (TRPF) and Fourier transform traction cytometry (FTTC) are used to calculate the traction forces and stress field, respectively, at isolated adhesions. We find that the stress field calculated with FTTC peaks near the center of individual adhesions but propagates several microns beyond the adhesion location. We find the optimal set of FTTC parameters that yield the highest stress magnitude, minimizing information lost from over-smoothing and sampling of the displacement or stress field. A positive correlation between the TRPF and FTTC measurements exists, but integrating the FTTC stress field over the adhesion area yields only a small fraction of the force calculated by TRPF. An effective area similar to that defined by the width of the stress distribution measured with FTTC is required to reconcile these measurements. These measurements set bounds on the spatial resolution and precision of FTTC measurements on micron-sized adhesions.

The cytoskeleton (CSK) of living cells is a crosslinked fiber network, subject to ongoing biochemical remodeling processes that can be visualized by tracking the spontaneous motion of CSK-bound microbeads. The bead motion is characterized by anomalous diffusion with a power-law time evolution of the mean square displacement (MSD), and can be described as a stochastic transport process with apparent diffusivity D and power-law exponent β: MSD ∼ D (t/t₀)^β. Here we studied whether D and β change with the time that has passed after the initial bead–cell contact, and whether they are sensitive to bead coating (fibronectin, integrin antibodies, poly-L-lysine, albumin) and bead size (0.5–4.5 µm). The measurements are interpreted in the framework of a simple model that describes the bead as an overdamped particle coupled to the fluctuating CSK network by an elastic spring. The viscous damping coefficient characterizes the degree of bead internalization into the cell, and the spring constant characterizes the strength of the binding of the bead to the CSK. The model predicts distinctive signatures of the MSD that change with time as the bead couples more tightly to the CSK and becomes internalized. Experimental data show that the transition from the unbound to the tightly bound state occurs in an all-or-nothing manner. The time point of this transition shows considerable variability between individual cells (2–30 min) and depends on the bead size and bead coating. On average, this transition occurs later for smaller beads and beads coated with ligands that trigger the formation of adhesion complexes (fibronectin, integrin antibodies). Once the bead is linked to the CSK, however, the ligand type and bead size have little effect on the MSD. On longer timescales of several hours after bead addition, smaller beads are internalized into the cell more readily, leading to characteristic changes in the MSD that are consistent with increased viscous damping by the cytoplasm and reduced binding strength.

Mouse embryonic fibroblasts explore the chemical suitability before spreading on a given substrate. We find this early phase of cell spreading to be characterized by transient adhesion patches with a typical mean size of (1.0 ± 0.4) µm and a lifetime of (33 ± 12) s. Eventually, these patches fuse to initiate extensive spreading of the cell. We monitor cell adhesion using reflection interference contrast and total internal reflection fluorescence microscopy. Digital time lapse movies are analysed employing spatio-temporal correlation functions of adhesion patterns. Correlation length and time can be scaled to obtain a master curve at the fusion point.

Cells continually probe their environment to adapt their behaviour. A current challenge is to determine how they analyse nearby surfaces and how they process information to take decisions. We addressed this problem by monitoring human T lymphocyte attachment to surfaces coated with activating anti-CD3 or control anti-HLA antibodies. Interference reflection microscopy allowed us to monitor cell-to-surface apposition with a few nanometre vertical resolution during the first minutes following contact. We found that (i) when a cell fell on a surface, contact extension was preceded by a lag of several tens of seconds. (ii) During this lag, vertical membrane undulations seemed to generate transient contacts with underlying surfaces. (iii) After the lag period, the contact area started increasing linearly with a rate of about 1.5  µm² s ^{− 1} on activating surfaces and about 0.2 µm² s ^{− 1} on control surfaces. (iv) Concomitantly with lateral surface extension, the apparent distance between cell membranes and surfaces steadily decreased. These results are consistent with the hypothesis that the cell decision to spread rapidly on activating surfaces resulted from the integration of information yielded by transient contacts with these surfaces generated by membrane undulations during a period of about 1 min.

Focal adhesions (FAs) are important adhesion sites between eukaryotic cells and the extracellular matrix, their size depending on the locally applied force. To quantitatively study the mechanosensitivity of FAs, we induce their growth and disassembly by varying the distribution of intracellular stress. We present a novel method for micromanipulation of living cells to explore the dynamics of focal adhesion (FA) assembly under force. Fibroblasts are sheared laterally to their adhesion surface with single PDMS micropillars in order to apply laterally stretch or compression to focal adhesions. This allows for measuring the shear force exerted by the micropillar and correlates it with FA length and growth velocity. Furthermore, we analyze the resulting dynamics of FA molecules (paxillin) and compare intensity profiles along FAs before and after the application of external force. The responses of stretched and relaxed FAs differ fundamentally: relaxed and compressed FAs disassemble isotropically and show no length variation while stretched FAs grow unisotropically in the direction of the applied force and show protein influx only at their front.

Mechanosensing is a vital prerequisite for dynamic remodeling of focal adhesions and cytoskeletal structures upon substrate deformation. For example, tissue formation, directed cell orientation or cell differentiation are regulated by such mechanosensing processes. Focal adhesions and the actin cytoskeleton are believed to be involved in these processes, but where mechanosensing molecules are located and how elastic substrate, focal adhesions and the cytoskeleton couple with each other upon substrate deformation still remains obscure. To approach these questions we have developed a sensitive method to apply defined spatially decaying deformation fields to cells cultivated on ultrasoft elastic substrates and to accurately quantify the resulting displacements of the actin cytoskeleton, focal adhesions, as well as the substrate. Displacement fields were recorded in live cell microscopy by tracking either signals from fluorescent proteins or marker particles in the substrate. As model cell type we used myofibroblasts. These cells are characterized by highly stable adhesion and force generating structures but are still able to detect mechanical signals with high sensitivity. We found a rigid connection between substrate and focal adhesions. Furthermore, stress fibers were found to be barely extendable almost over their whole lengths. Plastic deformation took place only at the very ends of actin filaments close to focal adhesions. As a result, this area became elongated without extension of existing actin filaments by polymerization. Both ends of the stress fibers were mechanically coupled with detectable plastic deformations on either site. Interestingly, traction force dependent substrate deformation fields remained mostly unaffected even when stress fiber elongations were released. These data argue for a location of mechanosensing proteins at the ends of actin stress fibers and describe, except for these domains, the whole system to be relatively rigid for tensile strain with a mechanical coupling between the front and rear end of a cell.

The active regulation of cellular forces during cell adhesion plays an important role in the determination of cell size, shape, and internal structure. While on flat, homogeneous and isotropic substrates some cells spread isotropically, others spread anisotropically and assume elongated structures. In addition, in their native environment as well as in vitro experiments, the cell shape and spreading asymmetry can be modulated by the local distribution of adhesive molecules and topography of the environment. We present a simple elastic model and experiments on stem cells to explain the variation of cell size with the matrix rigidity. In addition, we predict the experimental consequences of two mechanisms of acto-myosin polarization and focus here on the effect of the cell spreading asymmetry on the regulation of the stress-fiber alignment in the cytoskeleton. We show that when cell spreading is sufficiently asymmetric the alignment of acto-myosin forces in the cell increases monotonically with the matrix rigidity; however, in general this alignment is non-monotonic, as shown previously. These results highlight the importance of the symmetry characteristics of cell spreading in the regulation of cytoskeleton structure and suggest a mechanism by which different cell types may acquire different morphologies and internal structures in different mechanical environments.

The response of cells to shear flow is primarily determined by the asymmetry of the external forces and moments that are sensed by each member of a focal adhesion pair connected by a contractile stress fiber. In the theory presented here, we suggest a physical model in which each member of such a pair of focal adhesions is treated as an elastic body subject to both a myosin-activated contractile force and the shear stress induced by the external flow. The elastic response of a focal adhesion complex is much faster than the active cellular processes that determine the size of the associated focal adhesions and the direction of the complex relative to the imposed flow. Therefore, the complex attains its mechanical equilibrium configuration which may change because of the cellular activity. Our theory is based on the experimental observation that focal adhesions modulate their cross-sectional area in order to attain an optimal shear. Using this assumption, our elastic model shows that such a complex can passively change its orientation to align parallel to the direction of the flow.

In migrating cells, retrograde flow of the actin cytoskeleton is related to traction at adhesion sites located at the base of the lamellipodium. The coupling between the moving cytoskeleton and the stationary adhesions is mediated by the continuous association and dissociation of molecular bonds. We introduce a simple model for the competition between the stochastic dynamics of elastic bonds at the moving interface and relaxation within the moving actin cytoskeleton represented by an internal viscous friction coefficient. Using exact stochastic simulations and an analytical mean field theory, we show that the stochastic bond dynamics lead to biphasic friction laws as observed experimentally. At low internal dissipation, stochastic bond dynamics lead to a regime of irregular stick-and-slip motion. High internal dissipation effectively suppresses cooperative effects among bonds and hence stabilizes the adhesion.

Cells from animals adhere to and exert mechanical forces on their surroundings. Cells must control these forces for many biological processes, and dysfunction can lead to pathologies. How the actions of molecules within a cell are coordinated to regulate the adhesive interaction with the extracellular matrix remains poorly understood. It has been observed that cytoplasmic proteins that link integrin cell-surface receptors with the actin cytoskeleton flow with varying rates from the leading edge toward the center of a cell. Here, we explore theoretically how measurable subcellular traction stresses depend on the local speed of retrograde actin flow. In the model, forces result from the stretching of molecular complexes in response to the drag from the flow; because these complexes break with extension-dependent kinetics, the flow results in a decrease in their number when sufficiently large. Competition between these two effects naturally gives rise to a clutch-like behavior and a nonmonotonic trend in the measured stresses, consistent with recent data for epithelial cells. We use this basic framework to evaluate slip and catch bond mechanisms for integrins; better fits of experimental data are obtained with a catch bond representation. Extension of the model to one comprising multiple molecular interfaces shifts the peak stress to higher speeds. Connections to other models and cell movement are discussed.

Cells are able to detect and respond to mechanical cues from their environment. Previous studies have investigated this mechanosensitivity on various cell types, including neural cells such as astrocytes. In this study, we have carefully optimized polyacrylamide gels, commonly used as compliant growth substrates, considering their homogeneity in surface topography, mechanical properties, and coating density, and identified several potential pitfalls for the purpose of mechanosensitivity studies. The resulting astrocyte response to growth on substrates with shear storage moduli of G' = 100 Pa and G' = 10 kPa was then evaluated as a function of coating density of poly-D-lysine using quantitative morphometric analysis. Astrocytes cultured on stiff substrates showed significantly increased perimeter, area, diameter, elongation, number of extremities and overall complexity if compared to those cultured on compliant substrates. A statistically significant difference in the overall morphological score was confirmed with an artificial intelligence-based shape analysis. The dependence of the cells' morphology on PDL coating density seemed to be weak compared to the effect of the substrate stiffness and was slightly biphasic, with a maximum at 10–100  µg ml ^{− 1} PDL concentration. Our finding suggests that the compliance of the surrounding tissue in vivo may influence astrocyte morphology and behavior.

Pericytes physically surround the capillary endothelium, contacting and communicating with associated vascular endothelial cells via cell–cell and cell–matrix contacts. Pericyte–endothelial cell interactions thus have the potential to modulate growth and function of the microvasculature. Here we employ the experimental finding that pericytes can buckle a freestanding, underlying membrane via actin-mediated contraction. Pericytes were cultured on deformable silicone substrata, and pericyte-generated wrinkles were imaged via both optical and atomic force microscopy (AFM). The local stiffness of subcellular domains both near and far from these wrinkles was investigated by using AFM-enabled nanoindentation to quantify effective elastic moduli. Substratum buckling contraction was quantified by the normalized change in length of initially flat regions of the substrata (corresponding to wrinkle contour lengths), and a model was used to relate local strain energies to pericyte contractile forces. The nature of pericyte-generated wrinkling and contractile protein-generated force transduction was further explored by the addition of pharmacological cytoskeletal inhibitors that affected contractile forces and the effective elastic moduli of pericyte domains. Actin-mediated forces are sufficient for pericytes to exert an average buckling contraction of 38% on the elastomeric substrata employed in these in vitro studies. Actomyosin-mediated contractile forces also act in vivo on the compliant environment of the microvasculature, including the basement membrane and other cells. Pericyte-generated substratum deformation can thus serve as a direct mechanical stimulus to adjacent vascular endothelial cells, and potentially alter the effective mechanical stiffness of nonlinear elastic extracellular matrices, to modulate pericyte–endothelial cell interactions that directly influence both physiologic and pathologic angiogenesis.

Tissue cells lack the ability to see or hear but have evolved mechanisms to feel into their surroundings and sense a collective stiffness. A cell can even sense the effective stiffness of rigid objects that are not in direct cellular contact—like the proverbial princess who feels a pea placed beneath soft mattresses. How deeply a cell feels into a matrix can be measured by assessing cell responses on a controlled series of thin and elastic gels that are affixed to a rigid substrate. Gel elasticity E is readily varied with polymer concentrations of now-standard polyacrylamide hydrogels, but to eliminate wrinkling and detachment of thin gels from an underlying glass coverslip, vinyl groups are bonded to the glass before polymerization. Gel thickness is nominally specified using micron-scale beads that act as spacers, but gels swell after polymerization as measured by z-section, confocal microscopy of fluorescent gels. Atomic force microscopy is used to measure E at gel surfaces, employing stresses and strains that are typically generated by cells and yielding values for E that span a broad range of tissue microenvironments. To illustrate cell sensitivities to a series of thin-to-thick gels, the adhesive spreading of mesenchymal stem cells was measured on gel mimics of a very soft tissue (e.g. brain, E ∼ 1 kPa). Initial results show that cells increasingly respond to the rigidity of an underlying 'hidden' surface starting at about 10–20  µm gel thickness with a characteristic tactile length of less than about 5  µm.

Neutrophil adhesion to the vasculature and chemotaxis within tissues play critical roles in the inflammatory response to injury and pathogens. Unregulated neutrophil activity has been implicated in the progression of numerous chronic and acute diseases such as rheumatoid arthritis, asthma and sepsis. Cell migration of anchorage-dependent cells is known to depend on both chemical and mechanical interactions. Although neutrophil responses to chemical cues have been well characterized, little is known about the effect of underlying tissue mechanics on neutrophil adhesion and migration. To address this question, we quantified neutrophil migration and traction stresses on compliant hydrogel substrates with varying elasticity in a micromachined gradient chamber in which we could apply either a uniform concentration or a precise gradient of the bacterial chemoattractant fMLP. Neutrophils spread more extensively on substrates of greater stiffness. In addition, increasing the stiffness of the substrate leads to a significant increase in the chemotactic index for each fMLP gradient tested. As the substrate becomes stiffer, neutrophils generate higher traction forces without significant changes in cell speed. These forces are often displayed in pairs and focused in the uropod. Increases in the mean fMLP concentration beyond the K_D of the receptor lead to a decrease in chemotactic index on all surfaces. Blocking with an antibody against β₂-integrins leads to a significant reduction, but not an elimination, of directed motility on stiff materials, but no change in motility on soft materials, suggesting neutrophils can display both integrin-dependent and integrin-independent motility. These findings are critical for understanding how neutrophil migration may change in different mechanical environments in vivo and can be used to guide the design of migration inhibitors that more efficiently target inflammation.

Motile cells regulate their shape and movements largely by remodeling the actin cytoskeleton. Principles of this regulation are becoming clear for simple-shaped steadily crawling cells, such as fish keratocytes. In particular, the shape of the leading edge and sides of the lamellipodium—cell motile appendage—is determined by graded actin distribution at the cell boundary, so that the denser actin network at the front grows, while sparser actin filaments at the sides are stalled by membrane tension. Shaping of the cell rear is less understood. Here we theoretically examine the hypothesis that the cell rear is shaped by the disassembly clock: the front-to-rear lamellipodial width is defined by the time needed for the actin-adhesion network to disassemble to the point at which the membrane tension can crush this network. We demonstrate that the theory predicts the observed cell shapes. Furthermore, turning of the cells can be explained by biases in the actin distribution. We discuss experimental implications of this hypothesis.

Whereas the adhesion and migration of individual cells have been well described in terms of physical forces, the mechanics of multicellular assemblies is still poorly understood. Here, we study the behavior of epithelial cells cultured on microfabricated substrates designed to measure cell-to-substrate interactions. These substrates are covered by a dense array of flexible micropillars whose deflection enables us to measure traction forces. They are obtained by lithography and soft replica molding. The pillar deflection is measured by video microscopy and images are analyzed with home-made multiple particle tracking software. First, we have characterized the temporal and spatial distributions of traction forces of cellular assemblies of various sizes. The mechanical force balance within epithelial cell sheets shows that the forces exerted by neighboring cells strongly depend on their relative position in the monolayer: the largest deformations are always localized at the edge of the islands of cells in the active areas of cell protrusions. The average traction stress rapidly decreases from its maximum value at the edge but remains much larger than the inherent noise due to the force resolution of our pillar tracking software, indicating an important mechanical activity inside epithelial cell islands. Moreover, these traction forces vary linearly with the rigidity of the substrate over about two decades, suggesting that cells exert a given amount of deformation rather than a force. Finally, we engineer micropatterned substrates supporting pillars with anisotropic stiffness. On such substrates cellular growth is aligned with respect to the stiffest direction in correlation with the magnitude of the applied traction forces.

Mechanical properties of cells and extracellular matrices are critical determinants of function in contexts including oncogenic transformation, neuronal synapse formation, hepatic fibrosis and stem cell differentiation. The size and heterogeneity of biological specimens and the importance of measuring their mechanical properties under conditions that resemble their environments in vivo present a challenge for quantitative measurement. Centimeter-scale tissue samples can be measured by commercial instruments, whereas properties at the subcellular (nm) scale are accessible by atomic force microscopy, optical trapping, or magnetic bead microrheometry; however many tissues are heterogeneous on a length scale between micrometers and millimeters which is not accessible to most current instrumentation. The device described here combines two commercially available technologies, a micronewton resolution force probe and a micromanipulator for probing soft biological samples at sub-millimeter spatial resolution. Several applications of the device are described. These include the first measurement of the stiffness of an intact, isolated mouse glomerulus, quantification of the inner wall stiffness of healthy and diseased mouse aortas, and evaluation of the lateral heterogeneity in the stiffness of mouse mammary glands and rat livers with correlation of this heterogeneity with malignant or fibrotic pathology as evaluated by histology.

Hydrogels are commonly used as extracellular matrix mimetics for applications in tissue engineering and increasingly as cell culture platforms with which to study the influence of biophysical and biochemical cues on cell function in 3D. In recent years, a significant number of studies have focused on linking substrate mechanical properties to cell function using standard methodologies to characterize the bulk mechanical properties of the hydrogel substrates. However, current understanding of the correlations between the microstructural mechanical properties of hydrogels and cell function in 3D is poor, in part because of a lack of appropriate techniques. Here we have utilized a laser tracking system, based on passive optical microrheology instrumentation, to characterize the microstructure of viscoelastic fibrin clots. Trajectories and mean square displacements were observed as bioinert PEGylated (PEG: polyethylene glycol) microspheres (1, 2 or 4.7  µm in diameter) diffused within confined pores created by the protein phase of fibrin hydrogels. Complementary confocal reflection imaging revealed microstructures comprised of a highly heterogeneous fibrin network with a wide range of pore sizes. As the protein concentration of fibrin gels was increased, our quantitative laser tracking measurements showed a corresponding decrease in particle mean square displacements with greater resolution and sensitivity than conventional imaging techniques. This platform-independent method will enable a more complete understanding of how changes in substrate mechanical properties simultaneously influence other microenvironmental parameters in 3D cultures.

The physics of solid tumor growth can be considered at three distinct size scales: the tumor scale, the cell–extracellular matrix (ECM) scale and the sub-cellular scale. In this paper we consider the tumor scale in the interest of eventually developing a system-level understanding of the progression of cancer. At this scale, cell populations and chemical species are best treated as concentration fields that vary with time and space. The cells have chemo-mechanical interactions with each other and with the ECM, consume glucose and oxygen that are transported through the tumor, and create chemical by-products. We present a continuum mathematical model for the biochemical dynamics and mechanics that govern tumor growth. The biochemical dynamics and mechanics also engender free energy changes that serve as universal measures for comparison of these processes. Within our mathematical framework we therefore consider the free energy inequality, which arises from the first and second laws of thermodynamics. With the model we compute preliminary estimates of the free energy rates of a growing tumor in its pre-vascular stage by using currently available data from single cells and multicellular tumor spheroids.

We review some recent advances in the rheology of two-dimensional liquid foams, which should have implications for three-dimensional foams, as well as other mechanical systems that have a yield stress. We focus primarily on shear localization under steady shear, an effect first highlighted in an experiment by Debrégeas et al. A continuum theory which incorporates wall drag has reproduced the effect. Its further refinements are successful in matching results of more extensive observations and making interesting predictions regarding experiments for low strain rates and non-steady shear. Despite these successes, puzzles remain, particularly in relation to quasistatic simulations. The continuum model is semi-empirical: the meaning of its parameters may be sought in comparison with more detailed simulations and other experiments. The question of the origin of the Herschel–Bulkley relation is particularly interesting.

Hybrid nanostructures are systems composed of two or more nanostructures designed for improving the performance over individual components. In this work we introduce the concept of bridging natural photosynthetic protein–pigment complexes with nanostructures fabricated in an artificial way, such as semiconductor nanocrystals, metallic nanoparticles or carbon nanotubes, with the purpose of enhancing the efficiency of light harvesting either via plasmon excitation in metals or absorption tunability characteristics of semiconductors. In addition to presenting basic features of inorganic nanostructures, we discuss recent advances in the field of hybrid nanostructures composed of photosynthetic pigment–protein complexes.

We present a novel study on the effect of a magnetic field applied on a binary mixture doped with magnetic nanoparticles close to its demixing transition. Turbidity measurements in the Faraday configuration show that the effect of applying an external field produces changes in the critical opalescence of the mixture that allow us to track an aggregation produced by critical Casimir forces and a reversible aggregation due to the formation of chain-like flocks in response to the external magnetic field. The observation of a crossover of the aggregation curves through optical signals is interpreted as the evolution from low to high power dispersion nuclei due to an increase in the radius of the condensation seed brought about by Casimir or magnetic interactions. Finally, evidence of an enhanced magnetocaloric effect due to the coupling between mixing and ordering phase transitions is presented which opens up a nonsolid state approach of designing refrigerating cycles and devices.

We have conducted x-ray diffraction, calorimetric and Brillouin-scattering experiments on n-butanol between 77 and 300 K, aiming to explore the physical nature of the so-called 'glacial state' previously found in n-butanol as well as in triphenyl phosphite. In addition to our structural and thermodynamic studies of the liquid–glass transition and of the stable crystal state in n-butanol, we have found that the metastable 'glacial state' that can be obtained in the temperature range 125–160 K is not a second amorphous state, but rather the result of a frustrated or aborted crystallization process that produces plenty of nanocrystallites embedded in a disordered matrix. The crystalline order of these nanocrystallites of the 'glacial phase' is exactly the same as that well observed in the fully ordered stable crystal into which it transforms by heating above 160 K.

Raman scattering and differential scanning calorimetry (DSC) measurements have been carried out on four mixed tellurium–zinc oxide (TeO₂)_{1 − x}(ZnO)_x (x = 0.1, 0.2, 0.3, 0.4) glasses under variable temperature, with particular attention being given to the respective glass transition region. From the DSC measurements, the glass transition temperature T_g has been determined for each glass, showing a monotonous decrease of T_g with increasing ZnO content. The Raman study is focused on the low-frequency band of the glasses, the so-called boson peak (BP), whose frequency undergoes an abrupt decrease at a temperature T_d very close to the respective T_g values obtained by DSC. These results show that the BP is highly sensitive to dynamical effects over the glass transition and provides a means for an equally reliable (to DSC) determination of T_g in tellurite glasses and other network glasses. The discontinuous temperature dependence of the BP frequency at the glass transition, along with the absence of such a behaviour by the high-frequency Raman bands (due to local atomic vibrations), indicates that marked changes of the medium range order (MRO) occur at T_g and confirms the correlation between the BP and the MRO of glasses.

The drift–diffusion equation on a finite interval with reflecting boundary conditions is solved by Laplace transformation. The Green function is obtained as a series in powers of e ^{− hu/D}, where u is the drift velocity, D the diffusion coefficient and h the width of the interval. In the drift-dominated regime , the first terms provide an exact solution in the limit of short and long times, and a good approximation in the intermediate regime. As a possible application, we discuss confined colloidal suspensions subjected to an external field.

We present an extended analysis of the wavevector dependent shear viscosity of monatomic and diatomic (liquid chlorine) fluids over a wide range of wavevectors and for a variety of state points. The analysis is based on equilibrium molecular dynamics simulations, which involve the evaluation of transverse momentum density and shear stress autocorrelation functions. For liquid chlorine we present the results in both atomic and molecular formalisms. We find that the viscosity kernel of chlorine in the atomic representation is statistically indistinguishable from that in the molecular representation. The results further suggest that the real space viscosity kernels of monatomic and diatomic fluids depend sensitively on the density, the potential energy function and the choice of fitting function in reciprocal space. It is also shown that the reciprocal space shear viscosity data can be fitted to two different simple functional forms over the entire density, temperature and wavevector range: a function composed of n-Gaussian terms and a Lorentzian-type function. Overall, the real space viscosity kernel has a width of 3–6 atomic diameters, which means that the generalized hydrodynamic constitutive relation is required for fluids with strain rates that vary nonlinearly over distances of the order of atomic dimensions.

We report the measurements of birefringence as a function of temperature of a binary system 4-cyanophenyl [4'(4''-n-heptylphenyl)]benzoate (7CPB) + 4-cyanophenyl 4-nonylbenzoate (9.CN) showing a nematic–smectic A_d-re-entrant nematic phase sequence by means of the optical transmission method. The temperature dependence of the birefringence has been determined from the transmitted intensity data and the orientational order parameters have been calculated. These observations indicate that re-entrant nematic to induced smectic A_d and induced smectic A_d to nematic phase transitions for all the mixtures are of second order. There is a continuous change in the Δn values at the nematic–smectic A_d and smectic A_d-re-entrant nematic phase transitions. However, for some mixtures a slight increase in birefringence on cooling in the vicinity of the smectic A_d-re-entrant nematic transition has been observed. We have also fitted our experimental results with those calculated from the modified McMillan theory as proposed by Luckhurst and Timimi.

Mesoscopic structural evolution under thermal annealing of yttrium aluminium garnet fractal aggregates has been investigated by small-angle neutron scattering. Fractal dimension remains invariant with sintering temperature but the extent of the fractal realm is narrowed down significantly. A Monte Carlo simulation, based on Ostwald-ripening type of relaxation of fractal aggregates for a mass conserved system, has been attempted in order to understand the aforementioned novel observation. A local group merge sintering model was adopted for the relaxation of the fractal aggregates. Diffusion driven mass transport over local branches of fractal clusters causes smoothening of branches but keeps the overall shape unaltered at lower resolution. Predictions of the model were found to be consistent, in terms of microstructural evolution, with experimental data. The present simulation was also successful in explaining the evolution of the particle size distribution of the aggregate. To the best of our knowledge this is the first reported experimental and theoretical investigation on the effect of annealing temperature on nano-ceramic fractal aggregates.

Nuclear spin relaxation and the Knight shift for ⁷¹Ga, ⁶⁹Ga, and ¹¹⁵In isotopes were studied by nuclear magnetic resonance (NMR) in liquid gallium–indium alloy confined to porous glass and alloy surface film and were compared with the bulk counterparts. Drastic spin relaxation acceleration under nanoconfinement was observed for the three isotopes. Quadrupole and magnetic contributions to spin relaxation were separated for gallium and indium isotopes using the experimental data obtained, which allowed, in particular, the evaluation of correlation times of atomic mobility. The strong decrease in the correlation time was found for confined alloy which evidenced a remarkable diffusion slowdown. The effect of changes in atomic mobility on NMR line broadening was also discussed.