A computational model of the response of adherent cells to stretch and changes in substrate stiffness

Stiffness sensing by smooth muscle cells: Continuum mechanics modeling of the acto-myosin role

Aortic smooth muscle cells (SMCs) play a vital role in maintaining homeostasis in the aorta by sensing and responding to mechanical stimuli. However, the mechanisms that underlie the ability of SMCs to sense and respond to stiffness change in their environment are still partially unclear. In this study, we focus on the role of acto-myosin contractility in stiffness sensing and introduce a novel continuum mechanics approach based on the principles of thermal strains. Each stress fiber satisfies a universal stress-strain relationship driven by a Young's modulus, a contraction coefficient scaling the fictitious thermal strain, a maximum contraction stress and a softening parameter describing the sliding effects between actin and myosin filaments. To account for the inherent variability of cellular responses, large populations of SMCs are modeled with the finite-element method, each cell having a random number and a random arrangement of stress fibers. Moreover, the level of myosin activation in each stress fiber satisfies a Weibull probability density function. Model predictions are compared to traction force measurements on different SMC lineages. It is demonstrated that the model not only predicts well the effects of substrate stiffness on cellular traction, but it can also successfully approximate the statistical variations of cellular tractions induced by intercellular variability. Finally, stresses in the nuclear envelope and in the nucleus are computed with the model, showing that the variations of cytoskeletal forces induced by substrate stiffness directly induce deformations of the nucleus which can potentially alter gene expression. The predictability of the model combined to its relative simplicity are promising assets for further investigation of stiffness sensing in 3D environments. Eventually, this could contribute to decipher the effects of mechanosensitivity impairment, which are known to be at the root of aortic aneurysms.

Biomechanics of cells and subcellular components: A comprehensive review of computational models and applications

Cells are a fundamental structural, functional and biological unit for all living organisms. Up till now, considerable efforts have been made to study the responses of single cells and subcellular components to an external load, and understand the biophysics underlying cell rheology, mechanotransduction and cell functions using experimental and in silico approaches. In the last decade, computational simulation has become increasingly attractive due to its critical role in interpreting experimental data, analysing complex cellular/subcellular structures, facilitating diagnostic designs and therapeutic techniques, and developing biomimetic materials. Despite the significant progress, developing comprehensive and accurate models of living cells remains a grand challenge in the 21st century. To understand current state of the art, this review summarises and classifies the vast array of computational biomechanical models for cells. The article covers the cellular components at multi-spatial levels, that is, protein polymers, subcellular components, whole cells and the systems with scale beyond a cell. In addition to the comprehensive review of the topic, this article also provides new insights into the future prospects of developing integrated, active and high-fidelity cell models that are multiscale, multi-physics and multi-disciplinary in nature. This review will be beneficial for the researchers in modelling the biomechanics of subcellular components, cells and multiple cell systems and understanding the cell functions and biological processes from the perspective of cell mechanics.

Stiffening of the extracellular matrix is a sufficient condition for airway hyperreactivity

The current therapeutic approach to asthma focuses exclusively on targeting inflammation and reducing airway smooth muscle force to prevent the recurrence of symptoms. However, even when inflammation is brought under control, airways in an asthmatic can still hyperconstrict when exposed to a low dose of agonist. This suggests that there are mechanisms at play that are likely triggered by inflammation and eventually become self-sustaining so that even when airway inflammation is brought back under control, these alternative mechanisms continue to drive airway hyperreactivity in asthmatics. In this study, we hypothesized that stiffening of the airway extracellular matrix is a core pathological change sufficient to support excessive bronchoconstriction even in the absence of inflammation. To test this hypothesis, we increased the stiffness of the airway extracellular matrix by photo-crosslinking collagen fibers within the airway wall of freshly dissected bovine rings using riboflavin (vitamin B2) and Ultraviolet-A radiation. In our experiments, collagen crosslinking led to a twofold increase in the stiffness of the airway extracellular matrix. This change was sufficient to cause airways to constrict to a greater degree, and at a faster rate when they were exposed to 10^-5 M acetylcholine for 5 min. Our results show that stiffening of the extracellular matrix is sufficient to drive excessive airway constriction even in the absence of inflammatory signals.NEW & NOTEWORTHY Targeting inflammation is the central dogma on which current asthma therapy is based. Here, we show that a healthy airway can be made to constrict excessively and at a faster rate in response to the same stimulus by increasing the stiffness of the extracellular matrix, without the use of inflammatory agents. Our results provide an independent mechanism by which airway remodeling in asthma can sustain airway hyperreactivity even in the absence of inflammatory signals.

Migration of the 3T3 Cell with a Lamellipodium on Various Stiffness Substrates—Tensegrity Model

Changes in mechanical stimuli and the physiological environment are sensed by the cell. Thesechanges influence the cell’s motility patterns. The cell’s directional migration is dependent on the substrate stiffness. To describe such behavior of a cell, a tensegrity model was used. Cells with an extended lamellipodium were modeled. The internal elastic strain energy of a cell attached to the substrates with different stiffnesses was evaluated. The obtained results show that on the stiffer substrate, the elastic strain energy of the cell adherent to this substrate decreases. Therefore, the substrate stiffness is one of the parameters that govern the cell’s directional movement.

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.

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.

Intercellular communication controls agonist-induced calcium oscillations independently of gap junctions in smooth muscle cells

In this study, we report the existence of a communication system among human smooth muscle cells that uses mechanical forces to frequency modulate long-range calcium waves. An important consequence of this mechanical signaling is that changes in stiffness of the underlying extracellular matrix can interfere with the frequency modulation of Ca²⁺ waves, causing smooth muscle cells from healthy human donors to falsely perceive a much higher agonist dose than they actually received. This aberrant sensing of contractile agonist dose on stiffer matrices is completely absent in isolated smooth muscle cells, although the isolated cells can sense matrix rigidity. We show that the intercellular communication that enables this collective Ca²⁺ response in smooth muscle cells does not involve transport across gap junctions or extracellular diffusion of signaling molecules. Instead, our data support a collective model in which mechanical signaling among smooth muscle cells regulates their response to contractile agonists.

Intercellular Adhesion Stiffness Moderates Cell Decoupling as a Function of Substrate Stiffness

The interplay between cell-cell and cell-substrate interactions is complex yet necessary for the formation and healthy functioning of tissues. The same mechanosensing mechanisms used by the cell to sense its extracellular matrix also play a role in intercellular interactions. We used the discrete element method to develop a computational model of a deformable cell that includes subcellular components responsible for mechanosensing. We modeled a three-dimensional cell pair on a patterned (two-dimensional) substrate, a simple laboratory setup to study intercellular interactions. We explicitly modeled focal adhesions and adherens junctions. These mechanosensing adhesions matured, becoming stabilized by force. We also modeled contractile stress fibers that bind the discrete adhesions. The mechanosensing fibers strengthened upon stalling. Traction exerted on the substrate was used to generate traction maps (along the cell-substrate interface). These simulated maps are compared to experimental maps obtained via traction force microscopy. The model recreates the dependence on substrate stiffness of the tractions' spatial distribution, contractile moment of the cell pair, intercellular force, and number of focal adhesions. It also recreates the phenomenon of cell decoupling, in which cells exert forces separately when substrate stiffness increases. More importantly, the model provides viable molecular explanations for decoupling: mechanosensing mechanisms are responsible for competition between different fiber-adhesion configurations present in the cell pair. The point at which an increasing substrate stiffness becomes as high as that of the cell-cell interface is the tipping point at which configurations that favor cell-substrate adhesion dominate over those favoring cell-cell adhesion. This competition is responsible for decoupling.

Modeling of Mechanosensing Mechanisms Reveals Distinct Cell Migration Modes to Emerge From Combinations of Substrate Stiffness and Adhesion Receptor-Ligand Affinity

Mesenchymal cell migration is an integral process in development and healing. The process is regulated by both mechanical and biochemical properties. Mechanical properties of the environment are sensed through mechanosensing, which consists of molecular responses mediated by mechanical signals. We developed a computational model of a deformable 3D cell on a flat substrate using discrete element modeling. The cell is polarized in a single direction and thus moves along the long axis of the substrate. By modeling discrete focal adhesions and stress fibers, we implement two mechanosensing mechanisms: focal adhesion stabilization by force and stress fiber strengthening upon contraction stalling. Two substrate-associated properties, substrate (ligand) stiffness and adhesion receptor–ligand affinity (in the form of focal adhesion disassembly rate), were varied for different model setups in which the mechanosensing mechanisms are set as active or inactive. Cell displacement, focal adhesion number, and cellular traction were quantified and tracked in time. We found that varying substrate stiffness (a mechanical property) and adhesion receptor–ligand affinity (a biochemical property) simultaneously dictate the mode in which cells migrate; cells either move in a smooth manner reminiscent of keratocytes or in a cyclical manner reminiscent of epithelial cells. Mechanosensing mechanisms are responsible for the range of conditions in which a cell adopts a particular migration mode. Stress fiber strengthening, specifically, is responsible for cyclical migration due to build-up of enough force to elicit rupture of focal adhesions and retraction of the cellular rear. Together, both mechanisms explain bimodal dependence of cell migration on substrate stiffness observed in the literature.

Cell focal adhesion clustering leads to decreased and homogenized basal strains

The subendothelial matrix of the artery is a complex mechanical environment where endothelial cells respond to and affect changes upon the underlying substrate. Our recent work has demonstrated that endothelial cell strain heterogeneity increases on a more heterogeneous underlying subendothelial matrix, and these cells display increased focal adhesion presence on stiffer substrate areas. However, the impact of these grouped focal adhesions on endothelial cell strains has not been explored. Here, we use finite element modeling to investigate the effects of microscale stiffness heterogeneities and focal adhesion location and stiffness on endothelial cell strains. Shear stress applied to the apical cell layer demonstrated a minimal effect on cell strain values, while substrate stretch had a greater effect on cell strain in the cell-substrate model. The addition of focal adhesions into the computational model (cell-FA-substrate model) predicted a decrease and homogenization of the cell strains. For simulations including focal adhesions, stiffer and more distributed adhesions caused increased and more heterogeneous endothelial cell strains. Overall, our data indicate that cells may group focal adhesions to minimize and homogenize their basal strains.

Modelling Cell Origami via a Tensegrity Model of the Cytoskeleton in Adherent Cells

Cell origami has been widely used in the field of three-dimensional (3D) cell-populated microstructures due to their multiple advantages, including high biocompatibility, the lack of special requirements for substrate materials, and the lack of damage to cells. A 3D finite element method (FEM) model of an adherent cell based on the tensegrity structure is constructed to describe cell origami by using the principle of the origami folding technique and cell traction forces. Adherent cell models contain a cytoskeleton (CSK), which is primarily composed of microtubules (MTs), microfilaments (MFs), intermediate filaments (IFs), and a nucleoskeleton (NSK), which is mainly made up of the nuclear lamina and chromatin. The microplate is assumed to be an isotropic linear-elastic solid material with a flexible joint that is connected to the cell tensegrity structure model by spring elements representing focal adhesion complexes (FACs). To investigate the effects of the degree of complexity of the tensegrity structure and NSK on the folding angle of the microplate, four models are established in the study. The results demonstrate that the inclusion of the NSK can increase the folding angle of the microplate, indicating that the cell is closer to its physiological environment, while increased complexity can reduce the folding angle of the microplate since the folding angle is depended on the cell types. The proposed adherent cell FEM models are validated by comparisons with reported results. These findings can provide theoretical guidance for the application of biotechnology and the analysis of 3D structures of cells and have profound implications for the self-assembly of cell-based microscale medical devices.

Extracellular matrix stiffness regulates human airway smooth muscle contraction by altering the cell-cell coupling

For an airway or a blood vessel to narrow, there must be a connected path that links the smooth muscle (SM) cells with each other, and transmits forces around the organ, causing it to constrict. Currently, we know very little about the mechanisms that regulate force transmission pathways in a multicellular SM ensemble. Here, we used extracellular matrix (ECM) micropatterning to study force transmission in a two-cell ensemble of SM cells. Using the two-SM cell ensemble, we demonstrate (a) that ECM stiffness acts as a switch that regulates whether SM force is transmitted through the ECM or through cell-cell connections. (b) Fluorescent imaging for adherens junctions and focal adhesions show the progressive loss of cell-cell borders and the appearance of focal adhesions with the increase in ECM stiffness (confirming our mechanical measurements). (c) At the same ECM stiffness, we show that the presence of a cell-cell border substantially decreases the overall contractility of the SM cell ensemble. Our results demonstrate that connectivity among SM cells is a critical factor to consider in the development of diseases such as asthma and hypertension.

The consequence of substrates of large-scale rigidity on actin network tension in adherent cells

There is compelling evidence that substrate stiffness affects cell adhesion as well as cytoskeleton organization and contractile activity. This work was designed to study the cytoskeletal contractile activity of single cells plated on micropost substrates of different stiffness using a numerical model simulating the intracellular tension of individual cells. We allowed cells to adhere onto micropost substrates of various rigidities and used experimental traction force data to infer cell contractility using a numerical model. The model shows that higher substrate stiffness leads to an increase in intracellular tension. The strength of this model is its ability to calculate the mechanical state of each cell in accordance to its individual cytoskeletal structure. This is achieved by regenerating a numerical cytoskeleton based on microscope images of the actin network of each cell. The resulting numerical structure consequently represents pulling characteristics on its environment similar to those generated by the cell in-vivo. From actin imaging we can calculate and better understand how forces are transmitted throughout the cell.

Integrated lung tissue mechanics one piece at a time: Computational modeling across the scales of biology

The lung is a delicately balanced and highly integrated mechanical system. Lung tissue is continuously exposed to the environment via the air we breathe, making it susceptible to damage. As a consequence, respiratory diseases present a huge burden on society and their prevalence continues to rise. Emergent function is produced not only by the sum of the function of its individual components but also by the complex feedback and interactions occurring across the biological scales - from genes to proteins, cells, tissue and whole organ - and back again. Computational modeling provides the necessary framework for pulling apart and putting back together the pieces of the body and organ systems so that we can fully understand how they function in both health and disease. In this review, we discuss models of lung tissue mechanics spanning from the protein level (the extracellular matrix) through to the level of cells, tissue and whole organ, many of which have been developed in isolation. This is a vital step in the process but to understand the emergent behavior of the lung, we must work towards integrating these component parts and accounting for feedback across the scales, such as mechanotransduction. These interactions will be key to unlocking the mechanisms occurring in disease and in seeking new pharmacological targets and improving personalized healthcare.

Transition From Phasic to Tonic Contractility in Airway Smooth Muscle After Birth: An Experimental and Computational Modeling Study

Fetal airway smooth muscle (ASM) exhibits phasic contractile behavior, which transitions to a more sustained "tonic" contraction after birth. The timing and underlying mechanisms of ASM transition from a phasic to a tonic contractile phenotype are yet to be established. We characterized phasic ASM contraction in preterm (128 day gestation), term (~150 day gestation), 1-4 month, 1 yr, and adult sheep (5yr). Spontaneous phasic activity was measured in bronchial segments as amplitude, frequency, and intensity. The mechanism of phasic ASM contraction was investigated further with a computational model of ASM force development and lumen narrowing. The computational model comprised a two-dimensional cylindrical geometry of a network of contractile units and the activation of neighboring cells was dependent on the strength of coupling between cells. As expected, phasic contractions were most prominent in fetal airways and decreased with advancing age, to a level similar to the level in the 1-4 month lambs. Computational predictions demonstrated phasic contraction through the generation of a wave of activation events, the magnitude of which is determined by the number of active cells and the strength of cell-cell interactions. Decreases in phasic contraction with advancing age were simulated by reducing cell-cell coupling. Results show that phasic activity is suppressed rapidly after birth, then sustained at a lower intensity from the preweaning phase until adulthood in an ovine developmental model. Cell-cell coupling is proposed as a key determinant of phasic ASM contraction and if reduced could explain the observed maturational changes.

Blood pressure-induced physiological strain variability modulates wall structure and function in aorta rings

Vascular smooth muscle cells respond to mechanical stretch by reorganizing their cytoskeletal and contractile elements. Recently, we showed that contractile forces in rat aorta rings were maintained when the rings were exposed to 4 h of physiological variability in cycle-by-cycle strain, called variable stretch (VS), mimicking beat-to-beat blood pressure variability. Contractility, however, was reduced when the aorta was exposed to monotonous stretch (MS) with an amplitude equal to the mean peak strain of VS.

OBJECTIVE

Here we reanalyzed the data to obtain wall stiffness as well as added new histologic and inhibitor studies to test the effects of VS on the extracellular matrix.

MAIN RESULTS

The results demonstrate that while the stiffness of the aorta did not change during 4 h MS or VS, nonlinearity in mechanical behavior was slightly stronger following MS. The inhibitor studies also showed that mitochondrial energy production and cytoskeletal organization were involved in this fluctuation-driven mechanotransduction. Reorganization of β-actin in the smooth muscle layer quantified from immunohistochemically labeled images correlated with contractile forces during contraction. Histologic analysis of wall structure provided evidence of reorganization of elastin and collagen fibers following MS but less so following VS. The results suggested that the loss of muscle contraction in MS was compensated by reorganization of fiber structure leading to similar wall stiffness as in VS.

SIGNIFICANCE

We conclude that muscle tone modulated by variability in stretch plays a role in maintaining aortic wall structural and mechanical homeostasis with implications for vascular conditions characterized by a loss or an increase in blood pressure variability.

Emergent mechanics of actomyosin drive punctuated contractions and shape network morphology in the cell cortex

Filamentous actin (F-actin) and non-muscle myosin II motors drive cell motility and cell shape changes that guide large scale tissue movements during embryonic morphogenesis. To gain a better understanding of the role of actomyosin in vivo, we have developed a two-dimensional (2D) computational model to study emergent phenomena of dynamic unbranched actomyosin arrays in the cell cortex. These phenomena include actomyosin punctuated contractions, or "actin asters" that form within quiescent F-actin networks. Punctuated contractions involve both formation of high intensity aster-like structures and disassembly of those same structures. Our 2D model allows us to explore the kinematics of filament polarity sorting, segregation of motors, and morphology of F-actin arrays that emerge as the model structure and biophysical properties are varied. Our model demonstrates the complex, emergent feedback between filament reorganization and motor transport that generate as well as disassemble actin asters. Since intracellular actomyosin dynamics are thought to be controlled by localization of scaffold proteins that bind F-actin or their myosin motors we also apply our 2D model to recapitulate in vitro studies that have revealed complex patterns of actomyosin that assemble from patterning filaments and motor complexes with microcontact printing. Although we use a minimal representation of filament, motor, and cross-linker biophysics, our model establishes a framework for investigating the role of other actin binding proteins, how they might alter actomyosin dynamics, and makes predictions that can be tested experimentally within live cells as well as within in vitro models.

Recent genetic and mechanical studies of embryonic development reveal a critical role for intracellular scaffolds in generating the shape of the embryo and constructing internal organs. In this paper we developed computer simulations of these scaffolds, composed of filamentous actin (F-actin), a rod-like protein polymer, and mini-thick filaments, composed of non-muscle myosin II, forming a two headed spring-like complex of motor proteins that can walk on, and remodel F-actin networks. Using simulations of these dynamic interactions, we can carry out virtual experiments where we change the physics and chemistry of F-actin polymers, their associated myosin motors, and cross-linkers and observe the changes in scaffolds that emerge. For example, by modulating the motor stiffness of the myosin motors in our model we can observe the formation or loss of large aster-like structures. Such fine-grained control over the physical properties of motors or filaments within simulations are not currently possible with biological experiments, even where mutant proteins or small molecule inhibitors can be targeted to specific sites on filaments or motors. Our approach reflects a growing adoption of simulation methods to investigate microscopic features that shape actomyosin arrays and the mesoscale effects of molecular scale processes. We expect predictions from these models will drive more refined experimental approaches to expose the many roles of actomyosin in development.

The Nuclear Option: Evidence Implicating the Cell Nucleus in Mechanotransduction

Biophysical stimuli presented to cells via microenvironmental properties (e.g., alignment and stiffness) or external forces have a significant impact on cell function and behavior. Recently, the cell nucleus has been identified as a mechanosensitive organelle that contributes to the perception and response to mechanical stimuli. However, the specific mechanotransduction mechanisms that mediate these effects have not been clearly established. Here, we offer a comprehensive review of the evidence supporting (and refuting) three hypothetical nuclear mechanotransduction mechanisms: physical reorganization of chromatin, signaling at the nuclear envelope, and altered cytoskeletal structure/tension due to nuclear remodeling. Our goal is to provide a reference detailing the progress that has been made and the areas that still require investigation regarding the role of nuclear mechanotransduction in cell biology. Additionally, we will briefly discuss the role that mathematical models of cell mechanics can play in testing these hypotheses and in elucidating how biophysical stimulation of the nucleus drives changes in cell behavior. While force-induced alterations in signaling pathways involving lamina-associated polypeptides (LAPs) (e.g., emerin and histone deacetylase 3 (HDAC3)) and transcription factors (TFs) located at the nuclear envelope currently appear to be the most clearly supported mechanism of nuclear mechanotransduction, additional work is required to examine this process in detail and to more fully test alternative mechanisms. The combination of sophisticated experimental techniques and advanced mathematical models is necessary to enhance our understanding of the role of the nucleus in the mechanotransduction processes driving numerous critical cell functions.

Regulation of Mitochondrial Structure and Dynamics by the Cytoskeleton and Mechanical Factors

Mitochondria supply cells with energy in the form of ATP, guide apoptosis, and contribute to calcium buffering and reactive oxygen species production. To support these diverse functions, mitochondria form an extensive network with smaller clusters that are able to move along microtubules aided by motor proteins. Mitochondria are also associated with the actin network, which is involved in cellular responses to various mechanical factors. In this review, we discuss mitochondrial structure and function in relation to the cytoskeleton and various mechanical factors influencing cell functions. We first summarize the morphological features of mitochondria with an emphasis on fission and fusion as well as how network properties govern function. We then review the relationship between the mitochondria and the cytoskeletal structures, including mechanical interactions. We also discuss how stretch and its dynamic pattern affect mitochondrial structure and function. Finally, we present preliminary data on how extracellular matrix stiffness influences mitochondrial morphology and ATP generation. We conclude by discussing the more general role that mitochondria may play in mechanobiology and how the mechanosensitivity of mitochondria may contribute to the development of several diseases and aging.

Actomyosin meshwork mechanosensing enables tissue shape to orient cell force

Sculpting organism shape requires that cells produce forces with proper directionality. Thus, it is critical to understand how cells orient the cytoskeleton to produce forces that deform tissues. During Drosophila gastrulation, actomyosin contraction in ventral cells generates a long, narrow epithelial furrow, termed the ventral furrow, in which actomyosin fibres and tension are directed along the length of the furrow. Using a combination of genetic and mechanical perturbations that alter tissue shape, we demonstrate that geometrical and mechanical constraints act as cues to orient the cytoskeleton and tension during ventral furrow formation. We developed an in silico model of two-dimensional actomyosin meshwork contraction, demonstrating that actomyosin meshworks exhibit an inherent force orienting mechanism in response to mechanical constraints. Together, our in vivo and in silico data provide a framework for understanding how cells orient force generation, establishing a role for geometrical and mechanical patterning of force production in tissues.

Large-scale tissue reorganization requires the generation of directional tension, which requires orientation of the cytoskeleton. Here Chanet et al. alter tissue shape and tension in the Drosophila embryo to show that geometric and mechanical constraints act as cues to orient the cytoskeleton and tension.

Regulatory Roles of Fluctuation-Driven Mechanotransduction in Cell Function

Cells in the body are exposed to irregular mechanical stimuli. Here, we review the so-called fluctuation-driven mechanotransduction in which stresses stretching cells vary on a cycle-by-cycle basis. We argue that such mechanotransduction is an emergent network phenomenon and offer several potential mechanisms of how it regulates cell function. Several examples from the vasculature, the lung, and tissue engineering are discussed. We conclude with a list of important open questions.

Homeostatic maintenance via degradation and repair of elastic fibers under tension

Cellular maintenance of the extracellular matrix requires an effective regulation that balances enzymatic degradation with the repair of collagen fibrils and fibers. Here, we investigate the long-term maintenance of elastic fibers under tension combined with diffusion of general degradative and regenerative particles associated with digestion and repair processes. Computational results show that homeostatic fiber stiffness can be achieved by assuming that cells periodically probe fiber stiffness to adjust the production and release of degradative and regenerative particles. However, this mechanism is unable to maintain a homogeneous fiber. To account for axial homogeneity, we introduce a robust control mechanism that is locally governed by how the binding affinity of particles is modulated by mechanical forces applied to the ends of the fiber. This model predicts diameter variations along the fiber that are in agreement with the axial distribution of collagen fibril diameters obtained from scanning electron microscopic images of normal rat thoracic aorta. The model predictions match the experiments only when the applied force on the fiber is in the range where the variance of local stiffness along the fiber takes a minimum value. Our model thus predicts that the biophysical properties of the fibers play an important role in the long-term regulatory maintenance of these fibers.

Multiscale mechanobiology: computational models for integrating molecules to multicellular systems

Mechanical signals exist throughout the biological landscape. Across all scales, these signals, in the form of force, stiffness, and deformations, are generated and processed, resulting in an active mechanobiological circuit that controls many fundamental aspects of life, from protein unfolding and cytoskeletal remodeling to collective cell motions. The multiple scales and complex feedback involved present a challenge for fully understanding the nature of this circuit, particularly in development and disease in which it has been implicated. Computational models that accurately predict and are based on experimental data enable a means to integrate basic principles and explore fine details of mechanosensing and mechanotransduction in and across all levels of biological systems. Here we review recent advances in these models along with supporting and emerging experimental findings.

Can breathing-like pressure oscillations reverse or prevent narrowing of small intact airways?

Periodic length fluctuations of airway smooth muscle during breathing are thought to modulate airway responsiveness in vivo. Recent animal and human intact airway studies have shown that pressure fluctuations simulating breathing can only marginally reverse airway narrowing and are ineffective at protecting against future narrowing. However, these previous studies were performed on relatively large (>5 mm diameter) airways, which are inherently stiffer than smaller airways for which a preponderance of airway constriction in asthma likely occurs. The goal of this study was to determine the effectiveness of breathing-like transmural pressure oscillations to reverse induced narrowing and/or protect against future narrowing of smaller, more compliant intact airways. We constricted smaller (luminal diameter = 2.92 ± 0.29 mm) intact airway segments twice with ACh (10(-6) M), once while applying tidal-like pressure oscillations (5-15 cmH2O) before, during, and after inducing constriction (Pre + Post) and again while only imposing the tidal-like pressure oscillation after induced constriction (Post Only). Smaller airways were 128% more compliant than previously studied larger airways. This increased compliance translated into 196% more strain and 76% greater recovery (41 vs. 23%) because of tidal-like pressure oscillations. Larger pressure oscillations (5-25 cmH2O) caused more recovery (77.5 ± 16.5%). However, pressure oscillations applied before and during constriction resulted in the same steady-state diameter as when pressure oscillations were only applied after constriction. These data show that reduced straining of the airways before a challenge likely does not contribute to the emergence of airway hyperreactivity observed in asthma but may serve to sustain a given level of constriction.

Cells as liquid motors: mechanosensitivity emerges from collective dynamics of actomyosin cortex

Living cells adapt and respond actively to the mechanical properties of their environment. In addition to biochemical mechanotransduction, evidence exists for a myosin-dependent purely mechanical sensitivity to the stiffness of the surroundings at the scale of the whole cell. Using a minimal model of the dynamics of actomyosin cortex, we show that the interplay of myosin power strokes with the rapidly remodeling actin network results in a regulation of force and cell shape that adapts to the stiffness of the environment. Instantaneous changes of the environment stiffness are found to trigger an intrinsic mechanical response of the actomyosin cortex. Cortical retrograde flow resulting from actin polymerization at the edges is shown to be modulated by the stress resulting from myosin contractility, which in turn, regulates the cell length in a force-dependent manner. The model describes the maximum force that cells can exert and the maximum speed at which they can contract, which are measured experimentally. These limiting cases are found to be associated with energy dissipation phenomena, which are of the same nature as those taking place during the contraction of a whole muscle. This similarity explains the fact that single nonmuscle cell and whole-muscle contraction both follow a Hill-like force-velocity relationship.

Matrix stiffness-modulated proliferation and secretory function of the airway smooth muscle cells

Multiple pulmonary conditions are characterized by an abnormal misbalance between various tissue components, for example, an increase in the fibrous connective tissue and loss/increase in extracellular matrix proteins (ECM). Such tissue remodeling may adversely impact physiological function of airway smooth muscle cells (ASMCs) responsible for contraction of airways and release of a variety of bioactive molecules. However, few efforts have been made to understand the potentially significant impact of tissue remodeling on ASMCs. Therefore, this study reports how ASMCs respond to a change in mechanical stiffness of a matrix, to which ASMCs adhere because mechanical stiffness of the remodeled airways is often different from the physiological stiffness. Accordingly, using atomic force microscopy (AFM) measurements, we found that the elastic modulus of the mouse bronchus has an arithmetic mean of 23.1 ± 14 kPa (SD) (median 18.6 kPa). By culturing ASMCs on collagen-conjugated polyacrylamide hydrogels with controlled elastic moduli, we found that gels designed to be softer than average airway tissue significantly increased cellular secretion of vascular endothelial growth factor (VEGF). Conversely, gels stiffer than average airways stimulated cell proliferation, while reducing VEGF secretion and agonist-induced calcium responses of ASMCs. These dependencies of cellular activities on elastic modulus of the gel were correlated with changes in the expression of integrin-β1 and integrin-linked kinase (ILK). Overall, the results of this study demonstrate that changes in matrix mechanics alter cell proliferation, calcium signaling, and proangiogenic functions in ASMCs.

Airway smooth muscle in asthma: linking contraction and mechanotransduction to disease pathogenesis and remodelling

Asthma is an obstructive airway disease, with a heterogeneous and multifactorial pathogenesis. Although generally considered to be a disease principally driven by chronic inflammation, it is becoming increasingly recognised that the immune component of the pathology poorly correlates with the clinical symptoms of asthma, thus highlighting a potentially central role for non-immune cells. In this context airway smooth muscle (ASM) may be a key player, as it comprises a significant proportion of the airway wall and is the ultimate effector of acute airway narrowing. Historically, the contribution of ASM to asthma pathogenesis has been contentious, yet emerging evidence suggests that ASM contractile activation imparts chronic effects that extend well beyond the temporary effects of bronchoconstriction. In this review article we describe the effects that ASM contraction, in combination with cellular mechanotransduction and novel contraction-inflammation synergies, contribute to asthma pathogenesis. Specific emphasis will be placed on the effects that ASM contraction exerts on the mechanical properties of the airway wall, as well as novel mechanisms by which ASM contraction may contribute to more established features of asthma such as airway wall remodelling.