Reply to the 'Comment on "Tensional homeostasis at different length scales" by J. Humphrey and C. Cyron, Soft Matter, 2022, 18, DOI: 10.1039/D1SM01151K'.

Drs Humphrey and Cyron wrote a commentary regarding our review article entitled "Tensional homeostasis at different length scales" that was published in Soft Matter, 2020, 16, 6946-6963. These authors brought up some valid concerns to which we would like to respond. Their first concern is related to our remark regarding equations that we used to describe homeostasis in blood vessels, where we stated that those equations were limited only to linearly elastic materials. We were wrong, and we agree with the authors that these equations hold for all cylindrical vessels regardless of their material properties. Their second concern is related to tensional homeostasis at the subcellular level. Drs Humphrey and Cyron disagree with our substantiated claim that tensional homeostasis breaks down at the level of focal adhesions (FAs) of a living cell. In our reply, we provided several pieces of evidence that demonstrate that tensional homeostasis depends upon FA size, FA maturity and FA force dynamics and thus, tensional homeostasis cannot hold in all FAs across a cell. In summary, we are grateful for the opportunity to reply to the commentary of Drs Humphrey and Cyron. Moreover, we are excited that this topic has become an important focus in the biomechanics and mechanobiology communities, and we feel strongly that critical feedback is necessary to move this field forward.

Integrin ß1 orchestrates the abnormal cell-matrix attachment and invasive behaviour of E-cadherin dysfunctional cells.

BACKGROUND: Tumour progression relies on the ability of cancer cells to penetrate and invade neighbouring tissues. E-cadherin loss is associated with increased cell invasion in gastric carcinoma, and germline mutations of the E-cadherin gene are causative of hereditary diffuse gastric cancer. Although E-cadherin dysfunction impacts cell-cell adhesion, cell dissemination also requires an imbalance of adhesion to the extracellular matrix (ECM). METHODS: To identify ECM components and receptors relevant for adhesion of E-cadherin dysfunctional cells, we implemented a novel ECM microarray platform coupled with molecular interaction networks. The functional role of putative candidates was determined by combining micropattern traction microscopy, protein modulation and in vivo approaches, as well as transcriptomic data of 262 gastric carcinoma samples, retrieved from the cancer genome atlas (TCGA). RESULTS: Here, we show that E-cadherin mutations induce an abnormal interplay of cells with specific components of the ECM, which encompasses increased traction forces and Integrin ß1 activation. Integrin ß1 synergizes with E-cadherin dysfunction, promoting cell scattering and invasion. The significance of the E-cadherin-Integrin ß1 crosstalk was validated in Drosophila models and found to be consistent with evidence from human gastric carcinomas, where increased tumour grade and poor survival are associated with low E-cadherin and high Integrin ß1 levels. CONCLUSIONS: Integrin ß1 is a key mediator of invasion in carcinomas with E-cadherin impairment and should be regarded as a biomarker of poor prognosis in gastric cancer.

Tensional homeostasis at different length scales.

Tensional homeostasis is a phenomenon of fundamental importance in mechanobiology. It refers to the ability of organs, tissues, and cells to respond to external disturbances by maintaining a homeostatic (set point) level of mechanical stress (tension). It is well documented that breakdown in tensional homeostasis is the hallmark of progression of diseases, including cancer and atherosclerosis. In this review, we surveyed quantitative studies of tensional homeostasis with the goal of providing characterization of this phenomenon across a broad range of length scales, from the organ level to the subcellular level. We considered both static and dynamics approaches that have been used in studies of this phenomenon. Results that we found in the literature and that we obtained from our own investigations suggest that tensional homeostasis is an emergent phenomenon driven by collective rheostatic mechanisms associated with focal adhesions, and by a collective action of cells in multicellular forms, whose impact on tensional homeostasis is cell type-dependent and cell microenvironment-dependent. Additionally, the finding that cadherins, adhesion molecules that are important for formation of cell-cell junctions, promote tensional homeostasis even in single cells, demonstrates their relevance as a signaling moiety.

Tensional homeostasis in endothelial cells is a multicellular phenomenon.

Mammalian cells of various types exhibit the remarkable ability to adapt to externally applied mechanical stresses and strains. Because of this adaptation, cells can maintain their endogenous mechanical tension at a preferred (homeostatic) level, which is essential for normal physiological functions of cells and tissues and provides protection against various diseases, including atherosclerosis and cancer. Conventional wisdom is that the cell possesses the ability to maintain tensional homeostasis on its own. Recent findings showed, however, that isolated cells cannot maintain tensional homeostasis. Here we studied the effect of multicellular interactions on tensional homeostasis by measuring traction forces in isolated bovine aortic endothelial cells and in confluent and nonconfluent cell clusters of different sizes. We found that, in isolated cells, the traction field exhibited a highly dynamic and erratic behavior. However, in cell clusters, dynamic fluctuations of the traction field became attenuated with increasing cluster size, at a rate that was faster in nonconfluent than confluent clusters. The driving mechanism of attenuation of traction field fluctuations was statistical averaging of the noise, and the impeding mechanism was nonuniform stress distribution in the clusters, which resulted from intercellular force transmission, known as a "global tug-of-war." These results show that isolated cells could not maintain tensional homeostasis, which confirms previous findings, and that tensional homeostasis is a multicellular phenomenon, which is a novel finding.

Tensegrity, cellular biophysics, and the mechanics of living systems.

The recent convergence between physics and biology has led many physicists to enter the fields of cell and developmental biology. One of the most exciting areas of interest has been the emerging field of mechanobiology that centers on how cells control their mechanical properties, and how physical forces regulate cellular biochemical responses, a process that is known as mechanotransduction. In this article, we review the central role that tensegrity (tensional integrity) architecture, which depends on tensile prestress for its mechanical stability, plays in biology. We describe how tensional prestress is a critical governor of cell mechanics and function, and how use of tensegrity by cells contributes to mechanotransduction. Theoretical tensegrity models are also described that predict both quantitative and qualitative behaviors of living cells, and these theoretical descriptions are placed in context of other physical models of the cell. In addition, we describe how tensegrity is used at multiple size scales in the hierarchy of life­from individual molecules to whole living organisms­to both stabilize three-dimensional form and to channel forces from the macroscale to the nanoscale, thereby facilitating mechanochemical conversion at the molecular level.

Fluidization, resolidification, and reorientation of the endothelial cell in response to slow tidal stretches.

Mechanical stretch plays an important role in regulating shape and orientation of the vascular endothelial cell. This morphological response to stretch is basic to angiogenesis, neovascularization, and vascular homeostasis, but mechanism remains unclear. To elucidate mechanisms, we used cell mapping rheometry to measure traction forces in primary human umbilical vein endothelial cells subjected to periodic uniaxial stretches. Onset of periodic stretch of 10% strain amplitude caused a fluidization response typified by attenuation of traction forces almost to zero. As periodic stretch continued, the prompt fluidization response was followed by a slow resolidification response typified by recovery of the traction forces, but now aligned along the axis perpendicular to the imposed stretch. Reorientation of the cell body lagged reorientation of the traction forces, however. Together, these observations demonstrate that cellular reorientation in response to periodic stretch is preceded by traction attenuation by means of cytoskeletal fluidization and subsequent traction recovery transverse to the stretch direction by means of cytoskeletal resolidification.

A zipper network model of the failure mechanics of extracellular matrices.

Mechanical failure of soft tissues is characteristic of life-threatening diseases, including capillary stress failure, pulmonary emphysema, and vessel wall aneurysms. Failure occurs when mechanical forces are sufficiently high to rupture the enzymatically weakened extracellular matrix (ECM). Elastin, an important structural ECM protein, is known to stretch beyond 200% strain before failing. However, ECM constructs and native vessel walls composed primarily of elastin and proteoglycans (PGs) have been found to fail at much lower strains. In this study, we hypothesized that PGs significantly contribute to tissue failure. To test this, we developed a zipper network model (ZNM), in which springs representing elastin are organized into long wavy fibers in a zipper-like formation and placed within a network of springs mimicking PGs. Elastin and PG springs possessed distinct mechanical and failure properties. Simulations using the ZNM showed that the failure of PGs alone reduces the global failure strain of the ECM well below that of elastin, and hence, digestion of elastin does not influence the failure strain. Network analysis suggested that whereas PGs drive the failure process and define the failure strain, elastin determines the peak and failure stresses. Predictions of the ZNM were experimentally confirmed by measuring the failure properties of engineered elastin-rich ECM constructs before and after digestion with trypsin, which cleaves the core protein of PGs without affecting elastin. This study reveals a role for PGs in the failure properties of engineered and native ECM with implications for the design of engineered tissues.

Pattern Generation for Micropattern Traction Microscopy.

Micropattern traction microscopy allows control of the shape of single cells and cell clusters. Furthermore, the ability to pattern at the micrometer length scale allows the use of these patterned contact zones for the measurement of traction forces, as each micropatterned dot allows for the formation of a single focal adhesion that then deforms the soft, underlying hydrogel. This approach has been used for a wide range of cell types, including endothelial cells, smooth muscle cells, fibroblasts, platelets, and epithelial cells. This review describes the evolution of techniques that allow the printing of extracellular matrix proteins onto polyacrylamide hydrogels in a regular array of dots of prespecified size and spacing. As micrometer-scale patterns are difficult to directly print onto soft substrates, patterns are first generated on rigid glass coverslips that are then used to transfer the pattern to the hydrogel during gelation. First, the original microcontact printing approach to generate arrays of small dots on the coverslip is described. A second step that removes most of the pattern to leave islands of small dots is required to control the shapes of cells and cell clusters on such arrays of patterned dots. Next, an evolution of this approach that allows for the generation of islands of dots using a single subtractive patterning step is described. This approach is greatly simplified for the user but has the disadvantage of a decreased lifetime for the master mold needed to make the patterns. Finally, the computational approaches that have been developed for the analysis of images of displaced dots and subsequent cell-generated traction fields are described, and updated versions of these analysis packages are provided.

Differential Impacts on Tensional Homeostasis of Gastric Cancer Cells Due to Distinct Domain Variants of E-Cadherin.

In epithelia, breakdown of tensional homeostasis is closely associated with E-cadherin dysfunction and disruption of tissue function and integrity. In this study, we investigated the effect of E-cadherin mutations affecting distinct protein domains on tensional homeostasis of gastric cancer cells. We used micropattern traction microscopy to measure temporal fluctuations of cellular traction forces in AGS cells transfected with the wild-type E-cadherin or with variants affecting the extracellular, the juxtamembrane, and the intracellular domains of the protein. We focused on the dynamic aspect of tensional homeostasis, namely the ability of cells to maintain a consistent level of tension, with low temporal variability around a set point. Cells were cultured on hydrogels micropatterned with different extracellular matrix (ECM) proteins to test whether the ECM adhesion impacts cell behavior. A combination of Fibronectin and Vitronectin was used as a substrate that promotes the adhesive ability of E-cadherin dysfunctional cells, whereas Collagen VI was used to test an unfavorable ECM condition. Our results showed that mutations affecting distinct E-cadherin domains influenced differently cell tensional homeostasis, and pinpointed the juxtamembrane and intracellular regions of E-cadherin as the key players in this process. Furthermore, Fibronectin and Vitronectin might modulate cancer cell behavior towards tensional homeostasis.

Inflation instability in the lung: an analytical model of a thick-walled alveolus with wavy fibres under large deformations.

Inflation of hollow elastic structures can become unstable and exhibit a runaway phenomenon if the tension in their walls does not rise rapidly enough with increasing volume. Biological systems avoid such inflation instability for reasons that remain poorly understood. This is best exemplified by the lung, which inflates over its functional volume range without instability. The goal of this study was to determine how the constituents of lung parenchyma determine tissue stresses that protect alveoli from instability-related overdistension during inflation. We present an analytical model of a thick-walled alveolus composed of wavy elastic fibres, and investigate its pressure-volume behaviour under large deformations. Using second-harmonic generation imaging, we found that collagen waviness follows a beta distribution. Using this distribution to fit human pressure-volume curves, we estimated collagen and elastin effective stiffnesses to be 1247 kPa and 18.3 kPa, respectively. Furthermore, we demonstrate that linearly elastic but wavy collagen fibres are sufficient to achieve inflation stability within the physiological pressure range if the alveolar thickness-to-radius ratio is greater than 0.05. Our model thus identifies the constraints on alveolar geometry and collagen waviness required for inflation stability and provides a multiscale link between alveolar pressure and stresses on fibres in healthy and diseased lungs.

As the endothelial cell reorients, its tensile forces stabilize.

When adherent cells are subjected to uniaxial sinusoidal stretch at frequencies close to physiological, their body and their contractile stress fibers realign nearly perpendicularly to the stretch axis. A common explanation for this phenomenon is that stress fibers reorient along the direction where they are unaffected by the applied cyclic stretch and thus can maintain optimal (homeostatic) tensile force. The ability of cells to achieve tensional homeostasis in response to external disturbances is important for normal physiological functions of cells and tissues and it provides protection against diseases, including cancer and atherosclerosis. However, quantitative experimental data that support the idea that stretch-induced reorientation is associated with tensional homeostasis are lacking. We observed previously that in response to uniaxial cyclic stretch of 10% strain amplitudes, traction forces of single endothelial cells reorient in the direction perpendicular to the stretch axis. Here we carried out a secondary analysis of those data to investigate whether this reorientation of traction forces is associated with tensional homeostasis. Our analysis showed that stretch-induced reorientation of traction forces was accompanied by attenuation of temporal variability of the traction field to the level that was observed in the absence of stretch. These findings represent a quantitative experimental evidence that stretch-induced reorientation of cellular traction forces is associated with the cell's tendency to achieve tensional homeostasis.

Effect of correlation between traction forces on tensional homeostasis in clusters of endothelial cells and fibroblasts.

The ability of cells to maintain a constant level of cytoskeletal tension in response to external and internal disturbances is referred to as tensional homeostasis. It is essential for the normal physiological function of cells and tissues, and for protection against disease progression, including atherosclerosis and cancer. In previous studies, we defined tensional homeostasis as the ability of cells to maintain a consistent level of cytoskeletal tension with low temporal fluctuations. In those studies, we measured temporal fluctuations of cell-substrate traction forces in clusters of endothelial cells and of fibroblasts. We observed those temporal fluctuations to decrease with increasing cluster size in endothelial cells, but not in fibroblasts. We quantified temporal fluctuation, and thus homeostasis, through the coefficient of variation (CV) of the traction field; the lower the value of CV, the closer the cell is to the state of tensional homeostasis. This metric depends on correlation between individual traction forces. In this study, we analyzed the contribution of correlation between traction forces on traction field CV in clusters of endothelial cells and fibroblasts using experimental data that we had obtained previously. Results of our analysis showed that positive correlation between traction forces was detrimental to homeostasis, and that it was cell type-dependent.

Focal adhesion displacement magnitude is a unifying feature of tensional homeostasis.

Tensional homeostasis is widely recognized to exist at the length scales of organs and tissues, but the cellular length scale mechanism for tension regulation is not known. In this study, we explored whether tensional homeostasis emerges from the behavior of the individual focal adhesion (FA), which is the subcellular structure that transmits cell stress to the surrounding extracellular matrix. Past studies have suggested that cell contractility builds up until a certain displacement is achieved, and we thus hypothesized that tensional homeostasis may require a threshold level of substrate displacement. Micropattern traction microscopy was used to study a wide range of FA traction forces generated by bovine vascular smooth muscle cells and bovine aortic endothelial cells cultured on substrates of stiffness of 3.6, 6.7, 13.6, and 30 kPa. The most striking feature of FA dynamics observed here is that the substrate displacement resulting from FA traction forces is a unifying feature that determines FA tensional stability. Beyond approximately 1 µm of substrate displacement, FAs, regardless of cell type or substrate stiffness, exhibit a precipitous drop in temporal fluctuations of traction forces. These findings lead us to the conclusion that traction force dynamics collectively determine whether cells or cell ensembles develop tensional homeostasis, and this insight is necessary to fully understand how matrix stiffness impacts cellular behavior in healthy conditions and, more important, in pathological conditions such as cancer or vascular aging, where environmental stiffness is altered. STATEMENT OF SIGNIFICANCE: Tensional homeostasis is widely recognized to exist at the length scales of organs and tissues, but the cellular length scale mechanism for tension regulation is not known. In this study, we explored whether tensional homeostasis emerges from the behavior of the individual focal adhesion (FA), which is the subcellular structure that transmits cell stress to the extracellular matrix. We utilized micropattern traction microscopy to measure time-lapses of FA forces in vascular smooth muscle cells and in endothelial cells. We discovered that the magnitude of the substrate displacement determines whether the FA has low temporal variability of traction forces. This finding is significant since it is the first known feature of tensional homeostasis that is broadly unifying across a range of environmental conditions and cell types.

Cytoskeletal mechanics in airway smooth muscle cells.

Mechanical properties and contractility of airway smooth muscle tissue are largely responsible for airway narrowing and airway hyperresponsiveness in asthma. To explain these pathological phenomena, investigators have studied the mechanical behaviour of airway smooth muscle cells and its relationship to the underlying cellular biophysical and biochemical mechanisms. During the past decade, a growing body of evidence has indicated that a deformable intracellular polymer network, known as the cytoskeleton, plays a major role in transmitting and distributing mechanical forces within the cell and in their conversion into biochemical responses. We review here evidence suggesting that the tensed and crosslinked cytoskeletal lattice, the contractile apparatus, and the cytoskeleton-extracellular matrix interactions are key determinants of mechanical properties and mechanosensing of airway smooth muscle cells, with the mechanical distending stress of the cytoskeleton playing the central role.

Durotaxis as an elastic stability phenomenon.

It is well documented that directed motion of cells is influenced by substrate stiffness. When cells are cultured on a substrate of graded stiffness, they tend to move from softer to stiffer regions--a process known as durotaxis. In this study, we propose a mathematical model of durotaxis described as an elastic stability phenomenon. We model the cytoskeleton (CSK) as a planar system of prestressed elastic line elements representing actin stress fibers (SFs), which are anchored via focal adhesions (FAs) at their end points to an elastic substrate of variable stiffness. The prestress in the SFs exerts a pulling force on FAs reducing thereby their chemical potential. Using Maxwell's global stability criterion, we obtain that the model stability increases as it is moved from a softer towards a stiffer region of the substrate. Numerical simulations reveal that elastic stability of SFs has a predominantly stabilizing effect, greater than the stabilizing effect of decreasing chemical potential of FAs. This is a novel finding which indicates that elasticity of the CSK plays an important role in cell migration and mechanosensing in general.

Power-law creep behavior of a semiflexible chain.

Rheological properties of adherent cells are essential for their physiological functions, and microrheological measurements on living cells have shown that their viscoelastic responses follow a weak power law over a wide range of time scales. This power law is also influenced by mechanical prestress borne by the cytoskeleton, suggesting that cytoskeletal prestress determines the cell's viscoelasticity, but the biophysical origins of this behavior are largely unknown. We have recently developed a stochastic two-dimensional model of an elastically joined chain that links the power-law rheology to the prestress. Here we use a similar approach to study the creep response of a prestressed three-dimensional elastically jointed chain as a viscoelastic model of semiflexible polymers that comprise the prestressed cytoskeletal lattice. Using a Monte Carlo based algorithm, we show that numerical simulations of the chain's creep behavior closely correspond to the behavior observed experimentally in living cells. The power-law creep behavior results from a finite-speed propagation of free energy from the chain's end points toward the center of the chain in response to an externally applied stretching force. The property that links the power law to the prestress is the chain's stiffening with increasing prestress, which originates from entropic and enthalpic contributions. These results indicate that the essential features of cellular rheology can be explained by the viscoelastic behaviors of individual semiflexible polymers of the cytoskeleton.

Dependence of Tensional Homeostasis on Cell Type and on Cell-Cell Interactions.

INTRODUCTION: The ability to maintain a homeostatic level of cell tension is essential for many physiological processes. Our group has recently reported that multicellularity is required for tensional homeostasis in endothelial cells. However, other studies have shown that isolated fibroblasts also maintain constant tension over short time scales without the need of cell-cell contacts. Therefore, in this study, our aim was to determine how different cell types regulate tension as isolated cells or in small clustered groupings and to investigate the role of cell-cell adhesion molecules, such as E-cadherin, in this system. METHODS: Micropattern traction force microscopy was used to determine how bovine aortic endothelial cells, bovine vascular smooth muscle cells, mouse embryonic fibroblasts, and human gastric adenocarcinoma cells, with or without cell-cell interactions due to E-cadherin, maintain tensional homeostasis over time. Tension temporal fluctuations in single cells and cell clusters were evaluated. RESULTS: We found that only endothelial cells require clustering for tensional homeostasis. The same was not verified in fibroblasts or vascular smooth muscle cells. Of relevance, in adenocarcinoma cells, we verified that tensional homeostasis was dependent on the competence of the adhesion molecule E-cadherin at both the single cells and multicellular levels. CONCLUSION: These findings indicate that cell-cell contacts may be critical for tensional homeostasis and, potentially, for barrier function of the endothelium. Furthermore, the cell-cell adhesion molecule E-cadherin is an important regulator of tensional homeostasis, even in the absence of cadherin engagement with neighboring cells, which demonstrates its relevance not only as a structural molecule but also as a signaling moiety.

Modeling tensional homeostasis in multicellular clusters.

Homeostasis of mechanical stress in cells, or tensional homeostasis, is essential for normal physiological function of tissues and organs and is protective against disease progression, including atherosclerosis and cancer. Recent experimental studies have shown that isolated cells are not capable of maintaining tensional homeostasis, whereas multicellular clusters are, with stability increasing with the size of the clusters. Here, we proposed simple mathematical models to interpret experimental results and to obtain insight into factors that determine homeostasis. Multicellular clusters were modeled as one-dimensional arrays of linearly elastic blocks that were either jointed or disjointed. Fluctuating forces that mimicked experimentally measured cell-substrate tractions were obtained from Monte Carlo simulations. These forces were applied to the cluster models, and the corresponding stress field in the cluster was calculated by solving the equilibrium equation. It was found that temporal fluctuations of the cluster stress field became attenuated with increasing cluster size, indicating that the cluster approached tensional homeostasis. These results were consistent with previously reported experimental data. Furthermore, the models revealed that key determinants of tensional homeostasis in multicellular clusters included the cluster size, the distribution of traction forces, and mechanical coupling between adjacent cells. Based on these findings, we concluded that tensional homeostasis was a multicellular phenomenon. Copyright © 2016 John Wiley & Sons, Ltd.

Biomechanics of the lung parenchyma: critical roles of collagen and mechanical forces.

The biomechanical properties of connective tissues play fundamental roles in how mechanical interactions of the body with its environment produce physical forces at the cellular level. It is now recognized that mechanical interactions between cells and the extracellular matrix (ECM) have major regulatory effects on cellular physiology and cell-cycle kinetics that can lead to the reorganization and remodeling of the ECM. The connective tissues are composed of cells and the ECM, which includes water and a variety of biological macromolecules. The macromolecules that are most important in determining the mechanical properties of these tissues are collagen, elastin, and proteoglycans. Among these macromolecules, the most abundant and perhaps most critical for structural integrity is collagen. In this review, we examine how mechanical forces affect the physiological functioning of the lung parenchyma, with special emphasis on the role of collagen. First, we overview the composition of the connective tissue of the lung and their complex structural organization. We then describe how mechanical properties of the parenchyma arise from its composition as well as from the architectural organization of the connective tissue. We argue that, because collagen is the most important load-bearing component of the parenchymal connective tissue, it is also critical in determining the homeostasis and cellular responses to injury. Finally, we overview the interactions between the parenchymal collagen network and cellular remodeling and speculate how mechanotransduction might contribute to disease propagation and the development of small- and large-scale heterogeneities with implications to impaired lung function in emphysema.

Microtubules may harden or soften cells, depending of the extent of cell distension.

Experimental data show that disruption of microtubules causes cells to either become stiffer or softer. Current understanding of these behaviors is based on several different mechanisms, each of which can account for only stiffening or softening. In this study we offer a model that can explain both these features. The model is based on the cellular tensegrity idea. Key premises of the model are that cell shape stability is secured through pre-existing mechanical stress (prestress) borne by the actin cytoskeletal network, and that this prestress is partly balanced by cytoskeletal microtubules and partly by the extracellular matrix. Thus, disturbance of this balance would affect cell deformability. The model predicts that disruption of microtubules causes an increase or a decrease in cell stiffness, depending on the extent to which microtubules participate in balancing the prestress which, in turn, depends on the extent of cell spreading. In highly spread cells microtubules have a minor and negative contribution to cell stiffness, whereas in less spread cells their contribution is positive and substantial. Since in their natural habitat cells seldom exhibit highly spread forms, the above results suggest that the contribution of microtubules to cell deformability cannot be overlooked.