Multiscale mechanobiology: Coupling models of adhesion kinetics and nonlinear tissue mechanics

The mechanical behavior of tissues at the macroscale is tightly coupled to cellular activity at the microscale. Dermal wound healing is a prominent example of a complex system in which multiscale mechanics regulate restoration of tissue form and function. In cutaneous wound healing, a fibrin matrix is populated by fibroblasts migrating in from a surrounding tissue made mostly out of collagen. Fibroblasts both respond to mechanical cues, such as fiber alignment and stiffness, as well as exert active stresses needed for wound closure.Here, we develop a multiscale model with a two-way coupling between a microscale cell adhesion model and a macroscale tissue mechanics model. Starting from the well-known model of adhesion kinetics proposed by Bell, we extend the formulation to account for nonlinear mechanics of fibrin and collagen and show how this nonlinear response naturally captures stretch-driven mechanosensing. We then embed the new nonlinear adhesion model into a custom finite element implementation of tissue mechanical equilibrium. Strains and stresses at the tissue level are coupled with the solution of the microscale adhesion model at each integration point of the finite element mesh. In addition, solution of the adhesion model is coupled with the active contractile stress of the cell population. The multiscale model successfully captures the mechanical response of biopolymer fibers and gels, contractile stresses generated by fibroblasts, and stress-strain contours observed during wound healing. We anticipate that this framework will not only increase our understanding of how mechanical cues guide cellular behavior in cutaneous wound healing, but will also be helpful in the study of mechanobiology, growth, and remodeling in other tissues.     

Eigenstrain as a mechanical set-point of cells

Cell contraction regulates how cells sense their mechanical environment. We sought to identify the set-point of cell contraction, also referred to as tensional homeostasis. In this work, bovine aortic endothelial cells (BAECs), cultured on substrates with different stiffness, were characterized using traction force microscopy (TFM). Numerical models were developed to provide insights into the mechanics of cell–substrate interactions. Cell contraction was modeled as eigenstrain which could induce isometric cell contraction without external forces. The predicted traction stresses matched well with TFM measurements. Furthermore, our numerical model provided cell stress and displacement maps for inspecting the fundamental regulating mechanism of cell mechanosensing. We showed that cell spread area, traction force on a substrate, as well as the average stress of a cell were increased in response to a stiffer substrate. However, the cell average strain, which is cell type-specific, was kept at the same level regardless of the substrate stiffness. This indicated that the cell average strain is the tensional homeostasis that each type of cell tries to maintain. Furthermore, cell contraction in terms of eigenstrain was found to be the same for both BAECs and fibroblast cells in different mechanical environments. This implied a potential mechanical set-point across different cell types. Our results suggest that additional measurements of contractility might be useful for monitoring cell mechanosensing as well as dynamic remodeling of the extracellular matrix (ECM). This work could help to advance the understanding of the cell-ECM relationship, leading to better regenerative strategies.     

Filamin structure,function and mechanics: are altered filamin-mediated force responses associated with human disease?

The cytoskeleton framework is essential not only for cell structure and stability but also for dynamic processes such as cell migration, division and differentiation. The F-actin cytoskeleton is mechanically stabilised and regulated by various actin-binding proteins, one family of which are the filamins that cross-link F-actin into networks that greatly alter the elastic properties of the cytoskeleton. Filamins also interact with cell membrane-associated extracellular matrix receptors and intracellular signalling proteins providing a potential mechanism for cells to sense their external environment by linking these signalling systems. The stiffness of the external matrix to which cells are attached is an important environmental variable for cellular behaviour. In order for a cell to probe matrix stiffness, a mechanosensing mechanism functioning via alteration of protein structure and/or binding events in response to external tension is required. Current structural, mechanical, biochemical and human disease-associated evidence suggests filamins are good candidates for a role in mechanosensing.     

Stress and strain localization in stretched collagenous tissues via a multiscale modelling approach

Mechanobiology of cells in soft collagenous tissues is highly affected by both tissue response at the macroscale and stress/strain localization mechanisms due to features at lower scales. In this paper, the macroscale mechanical behaviour of soft collagenous tissues is modelled by a three-level multiscale approach, based on a multi-step homogenisation technique from nanoscale up to the macroscale. Nanoscale effects, related to both intermolecular cross-links and collagen mechanics, are accounted for, together with geometric nonlinearities at the microscale. Moreover, an effective submodelling procedure is conceived in order to evaluate the local stress and strain fields at the microscale, which is around and within cells. Numerical results, obtained by using an incremental finite element formulation and addressing stretched tendinous tissues, prove consistency and accuracy of the model at both macroscale and microscale, confirming also the effectiveness of the multiscale modelling concept for successfully analysing physiopathological processes in biological tissues.     

Transfer of macroscale tissue strain to microscale cell regions in the deformed meniscus

Cells within fibrocartilaginous tissues, including chondrocytes and fibroblasts of the meniscus, ligament, and tendon, regulate cell biosynthesis in response to local mechanical stimuli. The processes by which an applied mechanical load is transferred through the extracellular matrix to the environment of a cell are not fully understood. To better understand the role of mechanics in controlling cell phenotype and biosynthetic activity, this study was conducted to measure strain at different length scales in tissue of the fibrocartilaginous meniscus of the knee joint, and to define a quantitative parameter that describes the strain transferred from the far-field tissue to a microenvironment surrounding a cell. Experiments were performed to apply a controlled uniaxial tensile deformation to explants of porcine meniscus containing live cells. Using texture correlation analyses of confocal microscopy images, two-dimensional Lagrangian and principal strains were measured at length scales representative of the tissue (macroscale) and microenvironment in the region of a cell (microscale) to yield a strain transfer ratio as a measure of median microscale to macroscale strain. The data demonstrate that principal strains at the microscale are coupled to and amplified from macroscale principal strains for a majority of cell microenvironments located across diverse microstructural regions, with average strain transfer ratios of 1.6 and 2.9 for the maximum and minimum principal strains, respectively. Lagrangian strain components calculated along the experimental axes of applied deformations exhibited considerable spatial heterogeneity and intersample variability, and suggest the existence of both strain amplification and attenuation. This feature is consistent with an in-plane rotation of the principal strain axes relative to the experimental axes at the microscale that may result from fiber sliding, fiber twisting, and fiber-matrix interactions that are believed to be important for regulating deformation in other fibrocartilaginous tissues. The findings for consistent amplification of macroscale to microscale principal strains suggest a coordinated pattern of strain transfer from applied deformation to the microscale environment of a cell that is largely independent of these microstructural features in the fibrocartilaginous meniscus.     

Mechanical properties of a mature biofilm from a wastewater system: from microscale to macroscale level

A fundamental understanding of biofilm mechanical stability is critical in order to describe detachment and develop biofouling control strategies. It is thus important to characterise the elastic deformation and flow behaviour of the biofilm under different modes of applied force. In this study, the mechanical properties of a mature wastewater biofilm were investigated with methods including macroscale compression and microscale indentation using atomic force microscopy (AFM). The mature biofilm was found to be mechanically isotropic at the macroscale level as its mechanical properties did not depend on the scales and modes of loading. However, the biofilm showed a tendency for mechanical inhomogeneity at the microscale level as indentation progressed deeper into the matrix. Moreover, it was observed that the adhesion force had a significant influence on the elastic properties of the biofilm at the surface, subjected to microscale tensile loading. These results are expected to inform a damage-based model for biofilm detachment.     

Shear Force at the Cell-Matrix Interface: Enhanced Analysis for Microfabricated Post Array Detectors

The interplay of mechanical forces between the extracellular environment and the cytoskeleton drives development, repair, and senescence in many tissues. Quantitative definition of these forces is a vital step in understanding cellular mechanosensing. Microfabricated post array detectors (mPADs) provide direct measurements of cell-generated forces during cell adhesion to extracellular matrix. A new approach to mPAD post labeling, volumetric imaging, and an analysis of post bending mechanics determined that cells apply shear forces and not point moments at the matrix interface. In addition, these forces could be accurately resolved from post deflections by using images of post tops and bases. Image analysis tools were then developed to increase the precision and throughput of post centroid location. These studies resulted in an improved method of force measurement with broad applicability and concise execution using a fully automated force analysis system. The new method measures cell-generated forces with less than 5% error and less than 90 seconds of computational time. Using this approach, we demonstrated direct and distinct relationships between cellular traction force and spread cell surface area for fibroblasts, endothelial cells, epithelial cells and smooth muscle cells.     

Mix and (mis-)match – The mechanosensing machinery in the changing environment of the developing,healthy adult and diseased heart

The composition and the stiffness of cardiac microenvironment change during development and/or in heart disease. Cardiomyocytes (CMs) and their progenitors sense these changes, which decides over the cell fate and can trigger CM (progenitor) proliferation, differentiation, de-differentiation or death. The field of mechanobiology has seen a constant increase in output that also includes a wealth of new studies specific to cardiac or cardiomyocyte mechanosensing. As a result, mechanosensing and transduction in the heart is increasingly being recognised as a main driver of regulating the heart formation and function. Recent work has for instance focused on measuring the molecular, physical and mechanical changes of the cellular environment - as well as intracellular contributors to the passive stiffness of the heart. On the other hand, a variety of new studies shed light into the molecular machinery that allow the cardiomyocytes to sense these properties. Here we want to discuss the recent work on this topic, but also specifically focus on how the different components are regulated at various stages during development, in health or disease in order to highlight changes that might contribute to disease progression and heart failure.     

Versatile and inexpensive Hall-Effect force sensor for mechanical characterization of soft biological materials

Mismatch of hierarchical structure and mechanical properties between tissue-engineered implants and native tissue may result in signal cues that negatively impact repair and remodeling. With bottom-up tissue engineering approaches, designing tissue components with proper microscale mechanical properties is crucial to achieve necessary macroscale properties in the final implant. However, characterizing microscale mechanical properties is challenging, and current methods do not provide the versatility and sensitivity required to measure these fragile, soft biological materials. Here, we developed a novel, highly sensitive Hall-Effect based force sensor that is capable of measuring mechanical properties of biological materials over wide force ranges (μN to N), allowing its use at all steps in layer-by-layer fabrication of engineered tissues. The force sensor design can be easily customized to measure specific force ranges, while remaining easy to fabricate using inexpensive, commercial materials. Although we used the force sensor to characterize mechanics of single-layer cell sheets and silk fibers, the design can be easily adapted for different applications spanning larger force ranges (>N). This platform is thus a novel, versatile, and practical tool for mechanically characterizing biological and biomimetic materials.     

Micromechanical model of a surrogate for collagenous soft tissues: development, validation and analysis of mesoscale size effects

Aligned, collagenous tissues such as tendons and ligaments are composed primarily of water and type I collagen, organized hierarchically into nanoscale fibrils, microscale fibers and mesoscale fascicles. Force transfer across scales is complex and poorly understood. Since innervation, the vasculature, damage mechanisms and mechanotransduction occur at the microscale and mesoscale, understanding multiscale interactions is of high importance. This study used a physical model in combination with a computational model to isolate and examine the mechanisms of force transfer between scales. A collagen-based surrogate served as the physical model. The surrogate consisted of extruded collagen fibers embedded within a collagen gel matrix. A micromechanical finite element model of the surrogate was validated using tensile test data that were recorded using a custom tensile testing device mounted on a confocal microscope. Results demonstrated that the experimentally measured macroscale strain was not representative of the microscale strain, which was highly inhomogeneous. The micromechanical model, in combination with a macroscopic continuum model, revealed that the microscale inhomogeneity resulted from size effects in the presence of a constrained boundary. A sensitivity study indicated that significant scale effects would be present over a range of physiologically relevant inter-fiber spacing values and matrix material properties. The results indicate that the traditional continuum assumption is not valid for describing the macroscale behavior of the surrogate and that boundary-induced size effects are present.     

Imaging methods in mechanosensing: a historical perspective and visions for the future

Over the past three decades, as mechanobiology has become a distinct area of study, researchers have developed novel imaging tools to discover the pathways of biomechanical signaling. Early work with substrate engineering and particle tracking demonstrated the importance of cell–extracellular matrix interactions on the cell cycle as well as the mechanical flux of the intracellular environment. Most recently, tension sensor approaches allowed directly measuring tension in cell–cell and cell–substrate interactions. We retrospectively analyze how these various optical techniques progressed the field and suggest our vision forward for a unified theory of cell mechanics, mapping cellular mechanosensing, and novel biomedical applications for mechanobiology.     

Multiscale analysis of morphology and mechanics in tail tendon from the ZDSD rat model of type 2 diabetes

Type 2 diabetes (T2D) impacts multiple organ systems including the circulatory, renal, nervous and musculoskeletal systems. In collagen-based tissues, one mechanism that may be responsible for detrimental mechanical impacts of T2D is the formation of advanced glycation end products (AGEs) leading to increased collagen stiffness and decreased toughness, resulting in brittle tissue behavior. The purpose of this study was to investigate tendon mechanical properties from normal and diabetic rats at two distinct length scales, testing the hypothesis that increased stiffness and strength and decreased toughness at the fiber level would be associated with alterations in nanoscale morphology and mechanics. Individual fascicles from female Zucker diabetic Sprague-Dawley (ZDSD) rats had no differences in fascicle-level mechanical properties but had increased material-level strength and stiffness versus control rats (CD). At the nanoscale, collagen fibril D-spacing was shifted towards higher spacing values in diabetic ZDSD fibrils. The distribution of nanoscale modulus values was also shifted to higher values. Material-level strength and stiffness from whole fiber tests were increased in ZDSD tails. Correlations between nanoscale and microscale properties indicate a direct positive relationship between the two length scales, most notably in the relationship between nanoscale and microscale modulus. These findings indicate that diabetes-induced changes in material strength and modulus were driven by alterations at the nanoscale.     

Mechanosensitivity and compositional dynamics of cell–matrix adhesions

Cells perceive information about the biochemical and biophysical properties of their tissue microenvironment through integrin‐mediated cell–matrix adhesions, which connect the cytoskeleton with the extracellular matrix and thereby allow cohesion and long‐range mechanical connections within tissues. The formation of cell–matrix adhesions and integrin signalling involves the dynamic recruitment and assembly of an inventory of proteins, collectively termed the ‘adhesome’, at the adhesive site. The recruitment of some adhesome proteins, most notably the Lin11‐, Isl1‐ and Mec3‐domain‐containing proteins, depends on mechanical tension generated by myosin II‐mediated contractile forces exerted on cell–matrix adhesions. When exposed to force, mechanosensitive adhesome proteins can change their conformation or expose cryptic‐binding sites leading to the recruitment of proteins, rearrangement of the cytoskeleton, reinforcement of the adhesive site and signal transduction. Biophysical methods and proteomics revealed force ranges within the adhesome and cytoskeleton, and also force‐dependent changes in adhesome composition. In this review, we provide an overview of the compositional dynamics of cell–matrix adhesions, discuss the most prevalent functional domains in adhesome proteins and review literature and concepts about mechanosensing mechanisms that operate at the adhesion site.     

Substrate Resistance to Traction Forces Controls Fibroblast Polarization

The mechanics of fibronectin-rich extracellular matrix regulate cell physiology in a number of diseases, prompting efforts to elucidate cell mechanosensing mechanisms at the molecular and cellular scale. Here, the use of fibronectin-functionalized silicone elastomers that exhibit considerable frequency dependence in viscoelastic properties unveiled the presence of two cellular processes that respond discreetly to substrate mechanical properties. Weakly cross-linked elastomers supported efficient focal adhesion maturation and fibroblast spreading because of an apparent stiff surface layer. However, they did not enable cytoskeletal and fibroblast polarization; elastomers with high cross-linking and low deformability were required for polarization. Our results suggest as an underlying reason for this behavior the inability of soft elastomer substrates to resist traction forces rather than a lack of sufficient traction force generation. Accordingly, mild inhibition of actomyosin contractility rescued fibroblast polarization even on the softer elastomers. Our findings demonstrate differential dependence of substrate physical properties on distinct mechanosensitive processes and provide a premise to reconcile previously proposed local and global models of cell mechanosensing.     

Local force and geometry sensing regulate cell functions

The shapes of eukaryotic cells and ultimately the organisms that they form are defined by cycles of mechanosensing, mechanotransduction and mechanoresponse. Local sensing of force or geometry is transduced into biochemical signals that result in cell responses even for complex mechanical parameters such as substrate rigidity and cell-level form. These responses regulate cell growth, differentiation, shape changes and cell death. Recent tissue scaffolds that have been engineered at the micro- and nanoscale level now enable better dissection of the mechanosensing, transduction and response mechanisms.     

Mechanotransduction at cadherin-mediated adhesions

Cell-to-cell junctions are crucial mechanical and signaling hubs that connect cells within tissues and probe the mechanics of the surrounding environment. Although the capacity of cell-to-extracellular-matrix (ECM) adhesions to sense matrix mechanics and proportionally modify cell functions is well established, cell-cell adhesions only recently emerged as a new class of force sensors. This finding exposes new pathways through which force can instruct cell functions. This review highlights recent findings, which demonstrate that protein complexes associated with classical cadherins, the principal architectural proteins at cell-cell junctions in all soft tissues, are mechanosensors. We further discuss the current understanding of the rudiments of a cadherin-based mechanosensing and transduction pathway, which is distinct from the force sensing machinery of cell-ECM adhesions.     

A cell-based framework for modeling cardiac mechanics

Cardiomyocytes are the functional building blocks of the heart—yet most models developed to simulate cardiac mechanics do not represent the individual cells and their surrounding matrix. Instead, they work on a homogenized tissue level, assuming that cellular and subcellular structures and processes scale uniformly. Here we present a mathematical and numerical framework for exploring tissue-level cardiac mechanics on a microscale given an explicit three-dimensional geometrical representation of cells embedded in a matrix. We defined a mathematical model over such a geometry and parametrized our model using publicly available data from tissue stretching and shearing experiments. We then used the model to explore mechanical differences between the extracellular and the intracellular space. Through sensitivity analysis, we found the stiffness in the extracellular matrix to be most important for the intracellular stress values under contraction. Strain and stress values were observed to follow a normal-tangential pattern concentrated along the membrane, with substantial spatial variations both under contraction and stretching. We also examined how it scales to larger size simulations, considering multicellular domains. Our work extends existing continuum models, providing a new geometrical-based framework for exploring complex cell–cell and cell–matrix interactions.

     

A multiscale whole-cell theory for mechanosensitive migration on viscoelastic substrates

Increasing experimental evidence validates that both the elastic stiffness and viscosity of the extracellular matrix regulate mesenchymal cell behavior, such as the rational switch between durotaxis (cell migration to stiffer regions), anti-durotaxis (migration to softer regions), and adurotaxis (stiffness-insensitive migration). To reveal the mechanisms underlying the crossover between these motility regimes, we have developed a multiscale chemomechanical whole-cell theory for mesenchymal migration. Our framework couples the subcellular focal adhesion dynamics at the cell-substrate interface with the cellular cytoskeletal mechanics and the chemical signaling pathways involving Rho GTPase proteins. Upon polarization by the Rho GTPase gradients, our simulated cell migrates by concerted peripheral protrusions and contractions, a hallmark of the mesenchymal mode. The resulting cell dynamics quantitatively reproduces the experimental migration speed as a function of the uniform substrate stiffness and explains the influence of viscosity on the migration efficiency. In the presence of stiffness gradients and absence of chemical polarization, our simulated cell can exhibit durotaxis, anti-durotaxis, and adurotaxis respectively with increasing substrate stiffness or viscosity. The cell moves toward an optimally stiff region from softer regions during durotaxis and from stiffer regions during anti-durotaxis. We show that cell polarization through steep Rho GTPase gradients can reverse the migration direction dictated by the mechanical cues. Overall, our theory demonstrates that opposing durotactic behaviors emerge via the interplay between intracellular signaling and cell-medium mechanical interactions in agreement with experiments, thereby elucidating complex mechanosensing at the single-cell level.     

Multicellular Architecture of Malignant Breast Epithelia Influences Mechanics

Cell–matrix and cell–cell mechanosensing are important in many cellular processes, particularly for epithelial cells. A crucial question, which remains unexplored, is how the mechanical microenvironment is altered as a result of changes to multicellular tissue structure during cancer progression. In this study, we investigated the influence of the multicellular tissue architecture on mechanical properties of the epithelial component of the mammary acinus. Using creep compression tests on multicellular breast epithelial structures, we found that pre-malignant acini with no lumen (MCF10AT) were significantly stiffer than normal hollow acini (MCF10A) by 60%. This difference depended on structural changes in the pre-malignant acini, as neither single cells nor normal multicellular acini tested before lumen formation exhibited these differences. To understand these differences, we simulated the deformation of the acini with different multicellular architectures and calculated their mechanical properties; our results suggest that lumen filling alone can explain the experimentally observed stiffness increase. We also simulated a single contracting cell in different multicellular architectures and found that lumen filling led to a 20% increase in the “perceived stiffness” of a single contracting cell independent of any changes to matrix mechanics. Our results suggest that lumen filling in carcinogenesis alters the mechanical microenvironment in multicellular epithelial structures, a phenotype that may cause downstream disruptions to mechanosensing.