An Integrated Stochastic Model of Matrix-Stiffness-Dependent Filopodial Dynamics

A multiscale theory for spreading and migration of adhesion-reinforced mesenchymal cells

We present a chemomechanical whole-cell theory for the spreading and migration dynamics of mesenchymal cells that can actively reinforce their adhesion to an underlying viscoelastic substrate as a function of its stiffness. Our multiscale model couples the adhesion reinforcement effect at the subcellular scale with the nonlinear mechanics of the nucleus-cytoskeletal network complex at the cellular scale to explain the concurrent monotonic area-stiffness and non-monotonic speed-stiffness relationships observed in experiments: we consider that large cell spreading on stiff substrates flattens the nucleus, increasing the viscous drag force on it. The resulting force balance dictates a reduction in the migration speed on stiff substrates. We also reproduce the experimental influence of the substrate viscosity on the cell spreading area and migration speed by elucidating how the viscosity may either maintain adhesion reinforcement or prevent it depending on the substrate stiffness. Additionally, our model captures the experimental directed migration behaviour of the adhesion-reinforced cells along a stiffness gradient, known as durotaxis, as well as up or down a viscosity gradient (viscotaxis or anti-viscotaxis), the cell moving towards an optimal viscosity in either case. Overall, our theory explains the intertwined mechanics of the cell spreading, migration speed and direction in the presence of the molecular adhesion reinforcement mechanism.

Force-dependent focal adhesion assembly and disassembly: A computational study

Cells interact with the extracellular matrix (ECM) via cell-ECM adhesions. These physical interactions are transduced into biochemical signals inside the cell which influence cell behaviour. Although cell-ECM interactions have been studied extensively, it is not completely understood how immature (nascent) adhesions develop into mature (focal) adhesions and how mechanical forces influence this process. Given the small size, dynamic nature and short lifetimes of nascent adhesions, studying them using conventional microscopic and experimental techniques is challenging. Computational modelling provides a valuable resource for simulating and exploring various "what if?" scenarios in silico and identifying key molecular components and mechanisms for further investigation. Here, we present a simplified mechano-chemical model based on ordinary differential equations with three major proteins involved in adhesions: integrins, talin and vinculin. Additionally, we incorporate a hypothetical signal molecule that influences adhesion (dis)assembly rates. We find that assembly and disassembly rates need to vary dynamically to limit maturation of nascent adhesions. The model predicts biphasic variation of actin retrograde velocity and maturation fraction with substrate stiffness, with maturation fractions between 18-35%, optimal stiffness of ∼1 pN/nm, and a mechanosensitive range of 1-100 pN/nm, all corresponding to key experimental findings. Sensitivity analyses show robustness of outcomes to small changes in parameter values, allowing model tuning to reflect specific cell types and signaling cascades. The model proposes that signal-dependent disassembly rate variations play an underappreciated role in maturation fraction regulation, which should be investigated further. We also provide predictions on the changes in traction force generation under increased/decreased vinculin concentrations, complementing previous vinculin overexpression/knockout experiments in different cell types. In summary, this work proposes a model framework to robustly simulate the mechanochemical processes underlying adhesion maturation and maintenance, thereby enhancing our fundamental knowledge of cell-ECM interactions.

A multi-scale clutch model for adhesion complex mechanics

Cell-matrix adhesion is a central mechanical function to a large number of phenomena in physiology and disease, including morphogenesis, wound healing, and tumor cell invasion. Today, how single cells respond to different extracellular cues has been comprehensively studied. However, how the mechanical behavior of the main individual molecules that form an adhesion complex cooperatively responds to force within the adhesion complex is still poorly understood. This is a key aspect of cell adhesion because how these cell adhesion molecules respond to force determines not only cell adhesion behavior but, ultimately, cell function. To answer this question, we develop a multi-scale computational model for adhesion complexes mechanics. We extend the classical clutch hypothesis to model individual adhesion chains made of a contractile actin network, a talin rod, and an integrin molecule that binds at individual adhesion sites on the extracellular matrix. We explore several scenarios of integrins dynamics and analyze the effects of diverse extracellular matrices on the behavior of the adhesion molecules and on the whole adhesion complex. Our results describe how every single component of the adhesion chain mechanically responds to the contractile actomyosin force and show how they control the traction forces exerted by the cell on the extracellular space. Importantly, our computational results agree with previous experimental data at the molecular and cellular levels. Our multi-scale clutch model presents a step forward not only to further understand adhesion complexes mechanics but also to impact, e.g., the engineering of biomimetic materials, tissue repairment, or strategies to arrest tumor progression.

Cell response to mechanical microenvironment cues via Rho signaling: From mechanobiology to mechanomedicine

Mechanical cues in the cell microenvironment such as those from extracellular matrix properties, stretching, compression and shear stress, play a critical role in maintaining homeostasis. Upon sensing mechanical stimuli, cells can translate these external forces into intracellular biochemical signals to regulate their cellular behaviors, but the specific mechanisms of mechanotransduction at the molecular level remain elusive. As a subfamily of the Ras superfamily, Rho GTPases have been recognized as key intracellular mechanotransduction mediators that can regulate multiple cell activities such as proliferation, migration and differentiation as well as biological processes such as cytoskeletal dynamics, metabolism, and organ development. However, the upstream mechanosensors for Rho proteins and downstream effectors that respond to Rho signal activation have not been well illustrated. Moreover, Rho-mediated mechanical signals in previous studies are highly context-dependent. In this review, we systematically summarize the types of mechanical cues in the cell microenvironment and provide recent advances on the roles of the Rho-based mechanotransduction in various cell activities, physiological processes and diseases. Comprehensive insights into the mechanical roles of Rho GTPase partners would open a new paradigm of mechanomedicine for a variety of diseases. STATEMENT OF SIGNIFICANCE: In this review, we highlight the critical role of Rho GTPases as signal mediators to respond to physical cues in microenvironment. This article will add a distinct contribution to this set of knowledge by intensively addressing the relationship between Rho signaling and mechanobiology/mechanotransduction/mechanomedcine. This topic has not been discussed by the journal, nor has it yet been developed by the field. The comprehensive picture that will develop, from molecular mechanisms and engineering methods to disease treatment strategies, represents an important and distinct contribution to the field. We hope that this review would help researchers in various fields, especially clinicians, oncologists and bioengineers, who study Rho signal pathway and mechanobiology/mechanotransduction, understand the critical role of Rho GTPase in mechanotransduction.

Biomechanical, biophysical and biochemical modulators of cytoskeletal remodelling and emergent stem cell lineage commitment

Across complex, multi-time and -length scale biological systems, redundancy confers robustness and resilience, enabling adaptation and increasing survival under dynamic environmental conditions; this review addresses ubiquitous effects of cytoskeletal remodelling, triggered by biomechanical, biophysical and biochemical cues, on stem cell mechanoadaptation and emergent lineage commitment. The cytoskeleton provides an adaptive structural scaffold to the cell, regulating the emergence of stem cell structure-function relationships during tissue neogenesis, both in prenatal development as well as postnatal healing. Identification and mapping of the mechanical cues conducive to cytoskeletal remodelling and cell adaptation may help to establish environmental contexts that can be used prospectively as translational design specifications to target tissue neogenesis for regenerative medicine. In this review, we summarize findings on cytoskeletal remodelling in the context of tissue neogenesis during early development and postnatal healing, and its relevance in guiding lineage commitment for targeted tissue regeneration. We highlight how cytoskeleton-targeting chemical agents modulate stem cell differentiation and govern responses to mechanical cues in stem cells' emerging form and function. We further review methods for spatiotemporal visualization and measurement of cytoskeletal remodelling, as well as its effects on the mechanical properties of cells, as a function of adaptation. Research in these areas may facilitate translation of stem cells' own healing potential and improve the design of materials, therapies, and devices for regenerative medicine.

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.

Unified multiscale theory of cellular mechanical adaptations to substrate stiffness

Rigidity of the extracellular matrix markedly regulates many cellular processes. However, how cells detect and respond to matrix rigidity remains incompletely understood. Here, we propose a unified two-dimensional multiscale framework accounting for the chemomechanical feedback to explore the interrelated cellular mechanosensing, polarization, and migration, which constitute the dynamic cascade in cellular response to matrix stiffness but are often modeled separately in previous theories. By combining integrin dynamics and intracellular force transduction, we show that substrate stiffness can act as a switch to activate or deactivate cell polarization. Our theory quantitatively reproduces rich stiffness-dependent cellular dynamics, including spreading, polarity selection, migration pattern, durotaxis, and even negative durotaxis, reported in a wide spectrum of cell types, and reconciles some inconsistent experimental observations. We find that a specific bipolarized mode can determine the optimal substrate stiffness, which enables the fastest cell migration rather than the largest traction forces that cells apply on the substrate. We identify that such a mechanical adaptation stems from the force balance across the whole cell. These findings could yield universal insights into various stiffness-mediated cellular processes within the context of tissue morphogenesis, wound healing, and cancer invasion.

Directed cell migration towards softer environments

How cells sense tissue stiffness to guide cell migration is a fundamental question in development, fibrosis and cancer. Although durotaxis-cell migration towards increasing substrate stiffness-is well established, it remains unknown whether individual cells can migrate towards softer environments. Here, using microfabricated stiffness gradients, we describe the directed migration of U-251MG glioma cells towards less stiff regions. This 'negative durotaxis' does not coincide with changes in canonical mechanosensitive signalling or actomyosin contractility. Instead, as predicted by the motor-clutch-based model, migration occurs towards areas of 'optimal stiffness', where cells can generate maximal traction. In agreement with this model, negative durotaxis is selectively disrupted and even reversed by the partial inhibition of actomyosin contractility. Conversely, positive durotaxis can be switched to negative by lowering the optimal stiffness by the downregulation of talin-a key clutch component. Our results identify the molecular mechanism driving context-dependent positive or negative durotaxis, determined by a cell's contractile and adhesive machinery.

Substrate Viscoelasticity Amplifies Distinctions between Transient and Persistent LPS-Induced Signals

Macrophages settle in heterogeneous microenvironments rendered by other cells and extracellular matrices. It is well known that chemical stimuli direct macrophage behavior; however, the contributions of viscosity, which increases in inflammatory tissues but not in tumors, are ignored in immune responses including effective activation and timely attenuation. This paper demonstrates that transient lipopolysaccharide (LPS)-treated macrophages benefit from elastic substrates, whereas viscoelastic substrates with similar storage moduli support the inflammatory responses of macrophages under persistent stimulations and consequently amplify the distinctions between the transient and persistent LPS-induced transcriptional programs. Actin filaments (F-actin) fluctuate in line with transcriptional profiles and can be mathematically predicted by a clutch-like model. Moreover, viscosity modifies immune responses through transcription factors NF-κB and C/EBPδ, which act as switches discriminating transient and persistent infections. Interestingly, enhanced immune responses, consistent with the lower activated states, are attenuated promptly by the actin nucleation-related translocation of ATF3 to nuclei. These findings suggest that the substrate viscoelasticity induces more intense inflammation only in the case of persistent infection and promotes more sensitively perceiving the duration of infection through the F-actin correlated transcription factors. In addition, it may facilitate the cognition of immune response in inflammatory and cancerous microenvironments and have a wide range of applications in inflammatory regulations.

Modeling cell protrusion predicts how myosin II and actin turnover affect adhesion-based signaling

Orchestration of cell migration is essential for development, tissue regeneration, and the immune response. This dynamic process integrates adhesion, signaling, and cytoskeletal subprocesses across spatial and temporal scales. In mesenchymal cells, adhesion complexes bound to extracellular matrix mediate both biochemical signal transduction and physical interaction with the F-actin cytoskeleton. Here, we present a mathematical model that offers insight into both aspects, considering spatiotemporal dynamics of nascent adhesions, active signaling molecules, mechanical clutching, actin treadmilling, and nonmuscle myosin II contractility. At the core of the model is a positive feedback loop, whereby adhesion-based signaling promotes generation of barbed ends at, and protrusion of, the cell's leading edge, which in turn promotes formation and stabilization of nascent adhesions. The model predicts a switch-like transition and optimality of membrane protrusion, determined by the balance of actin polymerization and retrograde flow, with respect to extracellular matrix density. The model, together with new experimental measurements, explains how protrusion can be modulated by mechanical effects (nonmuscle myosin II contractility and adhesive bond stiffness) and F-actin turnover.

Nanoscale integrin cluster dynamics controls cellular mechanosensing via FAKY397 phosphorylation

Transduction of extracellular matrix mechanics affects cell migration, proliferation, and differentiation. While this mechanotransduction is known to depend on the regulation of focal adhesion kinase phosphorylation on Y397 (FAKpY397), the mechanism remains elusive. To address this, we developed a mathematical model to test the hypothesis that FAKpY397-based mechanosensing arises from the dynamics of nanoscale integrin clustering, stiffness-dependent disassembly of integrin clusters, and FAKY397 phosphorylation within integrin clusters. Modeling results predicted that integrin clustering dynamics governs how cells convert substrate stiffness to FAKpY397, and hence governs how different cell types transduce mechanical signals. Existing experiments on MDCK cells and HT1080 cells, as well as our new experiments on 3T3 fibroblasts, confirmed our predictions and supported our model. Our results suggest a new pathway by which integrin clusters enable cells to calibrate responses to their mechanical microenvironment.

Heterogeneity in The Mechanical Properties of Integrins Determines Mechanotransduction Dynamics in Bone Osteoblasts

Bone cells are exposed to dynamic mechanical stimulation that is transduced into cellular responses by mechanotransduction mechanisms. The extracellular matrix (ECM) provides a physical link between loading and bone cells, where mechanoreceptors, such as integrins, initiate mechanosensation. Though this relationship is well studied, the dynamic interplay between mechanosensation, mechanotransduction and cellular responses is unclear. A hybrid-multiscale model combining molecular, cellular and tissue interactions was developed to examine links between integrins’ mechanosensation and effects on mechanotransduction, ECM modulation and cell-ECM interaction. The model shows that altering integrin mechanosensitivity threshold (MT) increases mechanotransduction durations from hours to beyond 4 days, where bone formation starts. This is relevant to bone, where it is known that a brief stimulating period provides persistent influences for over 24 hours. Furthermore, the model forecasts that integrin heterogeneity, with respect to MT, would be able to induce sustained increase in pERK baseline > 15% beyond 4 days. This is analogous to the emergence of molecular mechanical memory signalling dynamics. Therefore, the model can provide a greater understanding of mechanical adaptation to differential mechanical responses at different times. Given reduction of bone sensitivity to mechanical stimulation with age, these findings may lead towards useful therapeutic targets for upregulation of bone mass.

Synergistic Effect of Matrix Stiffness and Inflammatory Factors on Osteogenic Differentiation of MSC

Mesenchymal stem cells (MSCs) in vivo reside in a complex microenvironment. Changes of both biochemical and biophysical cues in the microenvironment caused by inflammation affect the differentiation behaviors of MSCs. Most studies, however, only focus on either biochemical or biophysical cues, although the synergistic effect of matrix stiffness and inflammatory factors on osteogenic differentiation of MSCs has not been explored yet. Here, we showed that there was a matrix stiffness-dependent modulation in the osteogenic differentiation of human MSCs (hMSCs) with higher matrix stiffness favoring osteogenesis bias. However, when interleukin-1 β (IL-1β) was added, the osteogenic differentiation of hMSCs was suppressed, which was independent of increasing matrix stiffness. Both experimental observations and mathematical modeling confirmed that matrix stiffness and IL-1β could activate the ERK1/2 signaling and contribute to osteogenic differentiation. The p38 signaling activated by IL-1β has a strong role in inhibiting osteoblastic differentiation, thus diminishing the vital effect of ERK1/2 signaling. In addition, sensitivity analysis of the model parameters revealed that activation/deactivation dynamics of sensitive factors (e.g., FAK, ERK, and p38) also played a key role in the synergistic effect of matrix stiffness and IL-1β on the osteogenic differentiation of hMSCs. The outcomes of this study provide new insights into the synergistic effect of biochemical and biophysical microenvironments on regulating MSC differentiation.

Biofabrication of phenotypic pulmonary fibrosis assays

Biofabrication techniques have enabled the formation of complex models of many biological tissues. We present a framework to contextualize biofabrication techniques within a disease modeling application. Fibrosis is a progressive disease interfering with tissue structure and function, which stems from an aberrant wound healing response. Epithelial injury and clot formation lead to fibroblast invasion and activation, followed by contraction and remodeling of the extracellular matrix. These stages have healthy wound healing variants in addition to the pathogenic analogs that are seen in fibrosis. This review evaluates biofabrication of a variety of phenotypic cell-based fibrosis assays. By recapitulating different contributors to fibrosis, these assays are able to evaluate biochemical pathways and therapeutic candidates for specific stages of fibrosis pathogenesis. Biofabrication of these culture models may enable phenotypic screening for improved understanding of fibrosis biology as well as improved screening of anti-fibrotic therapeutics.

3D Spatiotemporal Mechanical Microenvironment: A Hydrogel-Based Platform for Guiding Stem Cell Fate

Stem cells hold great promise for widespread biomedical applications, for which stem cell fate needs to be well tailored. Besides biochemical cues, accumulating evidence has demonstrated that spatiotemporal biophysical cues (especially mechanical cues) imposed by cell microenvironments also critically impact on the stem cell fate. As such, various biomaterials, especially hydrogels due to their tunable physicochemical properties and advanced fabrication approaches, are developed to spatiotemporally manipulate biophysical cues in vitro so as to recapitulate the 3D mechanical microenvironment where stem cells reside in vivo. Here, the main mechanical cues that stem cells experience in their native microenvironment are summarized. Then, recent advances in the design of hydrogel materials with spatiotemporally tunable mechanical properties for engineering 3D the spatiotemporal mechanical microenvironment of stem cells are highlighted. These in vitro engineered spatiotemporal mechanical microenvironments are crucial for guiding stem cell fate and their potential biomedical applications are subsequently discussed. Finally, the challenges and future perspectives are presented.

Dependence of cell adhesion on extracellular matrix materials formed on pore bridge boundaries by nanopore opening and closing geometry

In this study, we report experimental results for characterization of the growth and formation of pore bridge materials that modified the adhesion structures of cells cultured on nanomembranes with opening and closing geometry. To perform the proof-of-concept experiments, we fabricated two types of anodized alumina oxide substrates with single-sided opening (i.e., one side open, but closed at the other side) and double-sided opening (i.e., both sides open). In our experiment, we compared the densities of pores formed and of bridge materials which differently act as connective proteins depending on the size of pores. The results show that the pore opening geometry can be used to promote the net contact force between pores, resulting in the growth and formation of pore bridge materials before and after cell culture. The results also imply that the bridge materials can be used to attract the structural protrusion of filopodia that can promote the adhesion of cell-to-cell and cell-to-pore bridge. It is observed that the shape and size of cellular structures of filopodia depend on the presence of pore bridge materials. Overall, this observation brought us a significant clue that cells cultured on nanopore substrates would change the adhesion property depending on not only the formation of nanopores formed on the surface of topological substrates, but also that of pore bridge materials by its morphological growth.

Cellular mechanosensing of the biophysical microenvironment: A review of mathematical models of biophysical regulation of cell responses

Cells in vivo reside within complex microenvironments composed of both biochemical and biophysical cues. The dynamic feedback between cells and their microenvironments hinges upon biophysical cues that regulate critical cellular behaviors. Understanding this regulation from sensing to reaction to feedback is therefore critical, and a large effort is afoot to identify and mathematically model the fundamental mechanobiological mechanisms underlying this regulation. This review provides a critical perspective on recent progress in mathematical models for the responses of cells to the biophysical cues in their microenvironments, including dynamic strain, osmotic shock, fluid shear stress, mechanical force, matrix rigidity, porosity, and matrix shape. The review highlights key successes and failings of existing models, and discusses future opportunities and challenges in the field.

Functional and Biomimetic Materials for Engineering of the Three-Dimensional Cell Microenvironment

The cell microenvironment has emerged as a key determinant of cell behavior and function in development, physiology, and pathophysiology. The extracellular matrix (ECM) within the cell microenvironment serves not only as a structural foundation for cells but also as a source of three-dimensional (3D) biochemical and biophysical cues that trigger and regulate cell behaviors. Increasing evidence suggests that the 3D character of the microenvironment is required for development of many critical cell responses observed in vivo, fueling a surge in the development of functional and biomimetic materials for engineering the 3D cell microenvironment. Progress in the design of such materials has improved control of cell behaviors in 3D and advanced the fields of tissue regeneration, in vitro tissue models, large-scale cell differentiation, immunotherapy, and gene therapy. However, the field is still in its infancy, and discoveries about the nature of cell-microenvironment interactions continue to overturn much early progress in the field. Key challenges continue to be dissecting the roles of chemistry, structure, mechanics, and electrophysiology in the cell microenvironment, and understanding and harnessing the roles of periodicity and drift in these factors. This review encapsulates where recent advances appear to leave the ever-shifting state of the art, and it highlights areas in which substantial potential and uncertainty remain.