A model of fibroblast motility on substrates with different rigidities

Positive and negative durotaxis - mechanisms and emerging concepts

Cell migration is controlled by the coordinated action of cell adhesion, cytoskeletal dynamics, contractility and cell extrinsic cues. Integrins are the main adhesion receptors to ligands of the extracellular matrix (ECM), linking the actin cytoskeleton to the ECM and enabling cells to sense matrix rigidity and mount a directional cell migration response to stiffness gradients. Most models studied show preferred migration of single cells or cell clusters towards increasing rigidity. This is referred to as durotaxis, and since its initial discovery in 2000, technical advances and elegant computational models have provided molecular level details of stiffness sensing in cell migration. However, modeling has long predicted that, depending on cell intrinsic factors, such as the balance of cell adhesion molecules (clutches) and the motor proteins pulling on them, cells might also prefer adhesion to intermediate rigidity. Recently, experimental evidence has supported this notion and demonstrated the ability of cells to migrate towards lower rigidity, in a process called negative durotaxis. In this Review, we discuss the significant conceptual advances that have been made in our appreciation of cell plasticity and context dependency in stiffness-guided directional cell migration.

In silico analysis shows that dynamic changes in curvature guide cell migration over long distances

In vitro experiments have shown that cell scale curvatures influence cell migration; cells avoid convex hills and settle in concave valleys. However, it is not known whether dynamic changes in curvature can guide cell migration. This study extends a previous in-silico model to explore the effects over time of changing the substrate curvature on cell migration guidance. By simulating a dynamic surface curvature using traveling wave patterns, we investigate the influence of wave height and speed, and find that long-distance cell migration guidance can be achieved on specific wave patterns. We propose a mechanistic explanation of what we call dynamic curvotaxis and highlight those cellular features that may be involved. Our results open a new area of study for understanding cell mobility in dynamic environments, from single-cell in vitro experiments to multi-cellular in vivo mechanisms.

A non local model for cell migration in response to mechanical stimuli

Cell migration is one of the most studied phenomena in biology since it plays a fundamental role in many physiological and pathological processes such as morphogenesis, wound healing and tumorigenesis. In recent years, researchers have performed experiments showing that cells can migrate in response to mechanical stimuli of the substrate they adhere to. Motion towards regions of the substrate with higher stiffness is called durotaxis, while motion guided by the stress or the deformation of the substrate itself is called tensotaxis. Unlike chemotaxis (i.e. the motion in response to a chemical stimulus), these migratory processes are not yet fully understood from a biological point of view. In this respect, we present a mathematical model of single-cell migration in response to mechanical stimuli, in order to simulate these two processes. Specifically, the cell moves by changing its direction of polarization and its motility according to material properties of the substrate (e.g., stiffness) or in response to proper scalar measures of the substrate strain or stress. The equations of motion of the cell are non-local integro-differential equations, with the addition of a stochastic term to account for random Brownian motion. The mechanical stimulus to be integrated in the equations of motion is defined according to experimental measurements found in literature, in the case of durotaxis. Conversely, in the case of tensotaxis, substrate strain and stress are given by the solution of the mechanical problem, assuming that the extracellular matrix behaves as a hyperelastic Yeoh's solid. In both cases, the proposed model is validated through numerical simulations that qualitatively reproduce different experimental scenarios.

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.

Environmental stiffness restores mechanical homeostasis in vimentin-depleted cells

Recent experimental evidence indicates a role for the intermediate filament vimentin in regulating cellular mechanical homeostasis, but its precise contribution remains to be discovered. Mechanical homeostasis requires a balanced bi-directional interplay between the cell's microenvironment and the cellular morphological and mechanical state-this balance being regulated via processes of mechanotransduction and mechanoresponse, commonly referred to as mechanoreciprocity. Here, we systematically analyze vimentin-expressing and vimentin-depleted cells in a swatch of in vitro cellular microenvironments varying in stiffness and/or ECM density. We find that vimentin-expressing cells maintain mechanical homeostasis by adapting cellular morphology and mechanics to micromechanical changes in the microenvironment. However, vimentin-depleted cells lose this mechanoresponse ability on short timescales, only to reacquire it on longer time scales. Indeed, we find that the morphology and mechanics of vimentin-depleted cell in stiffened microenvironmental conditions can get restored to the homeostatic levels of vimentin-expressing cells. Additionally, we observed vimentin-depleted cells increasing collagen matrix synthesis and its crosslinking, a phenomenon which is known to increase matrix stiffness, and which we now hypothesize to be a cellular compensation mechanism for the loss of vimentin. Taken together, our findings provide further insight in the regulating role of intermediate filament vimentin in mediating mechanoreciprocity and mechanical homeostasis.

Mathematical model of mechano-sensing and mechanically induced collective motility of cells on planar elastic substrates

Cells mechanically interact with their environment to sense, for example, topography, elasticity and mechanical cues from other cells. Mechano-sensing has profound effects on cellular behaviour, including motility. The current study aims to develop a mathematical model of cellular mechano-sensing on planar elastic substrates and demonstrate the model's predictive capabilities for the motility of individual cells in a colony. In the model, a cell is assumed to transmit an adhesion force, derived from a dynamic focal adhesion integrin density, that locally deforms a substrate, and to sense substrate deformation originating from neighbouring cells. The substrate deformation from multiple cells is expressed as total strain energy density with a spatially varying gradient. The magnitude and direction of the gradient at the cell location define the cell motion. Cell-substrate friction, partial motion randomness, and cell death and division are included. The substrate deformation by a single cell and the motility of two cells are presented for several substrate elasticities and thicknesses. The collective motility of 25 cells on a uniform substrate mimicking the closure of a circular wound of 200 µm is predicted for deterministic and random motion. Cell motility on substrates with varying elasticity and thickness is explored for four cells and 15 cells, the latter again mimicking wound closure. Wound closure by 45 cells is used to demonstrate the simulation of cell death and division during migration. The mathematical model can adequately simulate the mechanically induced collective cell motility on planar elastic substrates. The model is suitable for extension to other cell and substrates shapes and the inclusion of chemotactic cues, offering the potential to complement in vitro and in vivo studies.

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.

The interplay between physical cues and mechanosensitive ion channels in cancer metastasis

Physical cues have emerged as critical influencers of cell function during physiological processes, like development and organogenesis, and throughout pathological abnormalities, including cancer progression and fibrosis. While ion channels have been implicated in maintaining cellular homeostasis, their cell surface localization often places them among the first few molecules to sense external cues. Mechanosensitive ion channels (MICs) are especially important transducers of physical stimuli into biochemical signals. In this review, we describe how physical cues in the tumor microenvironment are sensed by MICs and contribute to cancer metastasis. First, we highlight mechanical perturbations, by both solid and fluid surroundings typically found in the tumor microenvironment and during critical stages of cancer cell dissemination from the primary tumor. Next, we describe how Piezo1/2 and transient receptor potential (TRP) channels respond to these physical cues to regulate cancer cell behavior during different stages of metastasis. We conclude by proposing alternative mechanisms of MIC activation that work in tandem with cytoskeletal components and other ion channels to bestow cells with the capacity to sense, respond and navigate through the surrounding microenvironment. Collectively, this review provides a perspective for devising treatment strategies against cancer by targeting MICs that sense aberrant physical characteristics during metastasis, the most lethal aspect of cancer.

Aquaponics-Derived Tilapia Skin Collagen for Biomaterials Development

Collagen is one of the most widely used biomaterials in health-related sectors. The industrial production of collagen mostly relies on its extraction from mammals, but several issues limited its use. In the last two decades, marine organisms attracted interest as safe, abundant, and alternative source for collagen extraction. In particular, the possibility to valorize the huge quantity of fish industry waste and byproducts as collagen source reinforced perception of fish collagen as eco-friendlier and particularly attractive in terms of profitability and cost-effectiveness. Especially fish byproducts from eco-sustainable aquaponics production allow for fish biomass with additional added value and controlled properties over time. Among fish species, Oreochromis niloticus is one of the most widely bred fish in large-scale aquaculture and aquaponics systems. In this work, type I collagen was extracted from aquaponics-raised Tilapia skin and characterized from a chemical, physical, mechanical, and biological point of view in comparison with a commercially available analog. Performed analysis confirmed that the proprietary process optimized for type I collagen extraction allowed to isolate pure native collagen and to preserve its native conformational structure. Preliminary cellular studies performed with mouse fibroblasts indicated its optimal biocompatibility. All data confirmed the eligibility of the extracted Tilapia-derived native type I collagen as a biomaterial for healthcare applications.

Cellular mechanics of wound formation in single cell layer under cyclic stretching

Wounds can be produced when cells and tissues are subjected to excessive forces, for instance, under pathological conditions or nonphysiological loading. However, the cellular behaviors in the wound formation process are not clear. Here we tested the behaviors of wound formation in the epithelial layer with an in-suit uniaxial stretching device. We found that the wound often nucleates at the position where the cells are dividing. The polarization direction of cells near the wound is preferentially along the wound edge, whereas the cells far from the wound are preferentially perpendicular to the stretching direction. The larger the wound area is, the higher is the aspect ratio of the cells around the wound. Increasing the cell density will strengthen the cell layer. The higher the cell density is, the smaller is the area of the wounds, and the weaker is the effect of stretching on the polarization of the cells. Furthermore, we built a coarse-grained cell model that can explicitly consider the elasticity and viscoelasticity of cells, cell-cell interaction, and cell active stress, by which we simulated the wound formation process and quantitatively analyzed the force and stress fields in the cell layer, particularly around the wound. These analyses reveal the cellular mechanisms of wound formation behaviors in the cell layer under stretching and shed useful light on tissue engineering and regenerative medicine for biomedical applications.

Durotaxis: the mechanical control of directed cell migration

Directed cell migration is essential for cells to efficiently migrate in physiological and pathological processes. While migrating in their native environment, cells interact with multiple types of cues, such as mechanical and chemical signals. The role of chemical guidance via chemotaxis has been studied in the past, the understanding of mechanical guidance of cell migration via durotaxis remained unclear until very recently. Nonetheless, durotaxis has become a topic of intensive research and several advances have been made in the study of mechanically guided cell migration across multiple fields. Thus, in this article we provide a state of the art about durotaxis by discussing in silico, in vitro and in vivo data. We also present insights on the general mechanisms by which cells sense, transduce and respond to environmental mechanics, to then contextualize these mechanisms in the process of durotaxis and explain how cells bias their migration in anisotropic substrates. Furthermore, we discuss what is known about durotaxis in vivo and we comment on how haptotaxis could arise from integrating durotaxis and chemotaxis in native environments.

Two-Photon Polymerized Poly(2-Ethyl-2-Oxazoline) Hydrogel 3D Microstructures with Tunable Mechanical Properties for Tissue Engineering

The main task of tissue engineering (TE) is to reproduce, replicate, and mimic all kinds of tissues in the human body. Nowadays, it has been proven useful in TE to mimic the natural extracellular matrix (ECM) by an artificial ECM (scaffold) based on synthetic or natural biomaterials to regenerate the physiological tissue/organ architecture and function. Hydrogels have gained interest in the TE community because of their ability to absorb water similar to physiological tissues, thus mechanically simulating the ECM. In this work, we present a novel hydrogel platform based on poly(2-ethyl-2-oxazoline)s, which can be processed to 3D microstructures via two-photon polymerization (2PP) with tunable mechanical properties using monomers and crosslinker with different degrees of polymerization (DP) for future applications in TE. The ideal parameters (laser power and writing speed) for optimal polymerization via 2PP were obtained using a specially developed evaluation method in which the obtained structures were binarized and compared to the computer-aided design (CAD) model. This evaluation was performed for each composition. We found that it was possible to tune the mechanical properties not only by application of different laser parameters but also by mixing poly(2-ethyl-2-oxazoline)s with different chain lengths and variation of the crosslink density. In addition, the swelling behavior of different fabricated hydrogels were investigated. To gain more insight into the viscoelastic behavior of different fabricated materials, stress relaxation tests via nanoindentation experiments were performed. These new hydrogels can be processed to 3D microstructures with high structural integrity using optimal laser parameter settings, opening a wide range of application properties in TE for this material platform.

Cell-substrate mechanics guide collective cell migration through intercellular adhesion: a dynamic finite element cellular model

During the process of tissue formation and regeneration, cells migrate collectively while remaining connected through intercellular adhesions. However, the roles of cell-substrate and cell-cell mechanical interactions in regulating collective cell migration are still unclear. In this study, we employ a newly developed finite element cellular model to study collective cell migration by exploring the effects of mechanical feedback between cell and substrate and mechanical signal transmission between adjacent cells. Our viscoelastic model of cells consists many triangular elements and is of high resolution. Cadherin adhesion between cells is modeled explicitly as linear springs at subcellular level. In addition, we incorporate a mechano-chemical feedback loop between cell-substrate mechanics and Rac-mediated cell protrusion. Our model can reproduce a number of experimentally observed patterns of collective cell migration during wound healing, including cell migration persistence, separation distance between cell pairs and migration direction. Moreover, we demonstrate that cell protrusion determined by the cell-substrate mechanics plays an important role in guiding persistent and oriented collective cell migration. Furthermore, this guidance cue can be maintained and transmitted to submarginal cells of long distance through intercellular adhesions. Our study illustrates that our finite element cellular model can be employed to study broad problems of complex tissue in dynamic changes at subcellular level.

Cell Shape and Durotaxis Explained from Cell-Extracellular Matrix Forces and Focal Adhesion Dynamics

Many cells are small and rounded on soft extracellular matrices (ECM), elongated on stiffer ECMs, and flattened on hard ECMs. Cells also migrate up stiffness gradients (durotaxis). Using a hybrid cellular Potts and finite-element model extended with ODE-based models of focal adhesion (FA) turnover, we show that the full range of cell shape and durotaxis can be explained in unison from dynamics of FAs, in contrast to previous mathematical models. In our 2D cell-shape model, FAs grow due to cell traction forces. Forces develop faster on stiff ECMs, causing FAs to stabilize and, consequently, cells to spread on stiff ECMs. If ECM stress further stabilizes FAs, cells elongate on substrates of intermediate stiffness. We show that durotaxis follows from the same set of assumptions. Our model contributes to the understanding of the basic responses of cells to ECM stiffness, paving the way for future modeling of more complex cell-ECM interactions.

Rheological Properties of Coordinated Physical Gelation and Chemical Crosslinking in Gelatin Methacryloyl (GelMA) Hydrogels

Synthetically modified proteins, such as gelatin methacryloyl (GelMA), are growing in popularity for bioprinting and biofabrication. GelMA is a photocurable macromer that can rapidly form hydrogels, while also presenting bioactive peptide sequences for cellular adhesion and proliferation. The mechanical properties of GelMA are highly tunable by modifying the degree of substitution via synthesis conditions, though the effects of source material and thermal gelation have not been comprehensively characterized for lower concentration gels. Herein, the effects of animal source and processing sequence are investigated on scaffold mechanical properties. Hydrogels of 4-6 wt% are characterized. Depending on the temperature at crosslinking, the storage moduli for GelMA derived from pigs, cows, and cold-water fish range from 723 to 7340 Pa, 516 to 3484 Pa, and 294 to 464 Pa, respectively. The maximum storage moduli are achieved only by coordinated physical gelation and chemical crosslinking. In this method, the classic thermo-reversible gelation of gelatin occurs when GelMA is cooled below a thermal transition temperature, which is subsequently "locked in" by chemical crosslinking via photocuring. The effects of coordinated physical gelation and chemical crosslinking are demonstrated by precise photopatterning of cell-laden microstructures, inducing different cellular behavior depending on the selected mechanical properties of GelMA.

A mechanobiological model to study upstream cell migration guided by tensotaxis

Cell migration is a process of crucial importance for the human body. It is responsible for important processes such as wound healing and tumor metastasis. Migration may occur in response to stimuli of chemical, physical and mechanical nature occurring in the cellular microenvironment. The interstitial flow (IF) can generate mechanical stimuli in cells that influence the cell behavior and interactions of the cells with the extracellular matrix (ECM). One of the phenomena is upstream migration, which is observed in some tumors. In this work, we present a new approach to study the adherent cell migration in a porous medium using a mechanobiological model, attempting to understand if upstream migration can be generated exclusively by mechanical factors. The influence of IF on the behavior of cells and the extracellular matrix was considered. The model is based on a system of coupled nonlinear differential equations solved by the finite element method. Several simulations were performed to study the upstream cell migration and evaluate the effects of pressure, permeability, ECM stiffness and cellular concentration variations on the cell velocity. The results indicated that upstream migration can occur in the presence of mechanical stimuli generated by IF and that the tested parameters have a direct influence on the cellular velocity, especially the pressure and the permeability.

A mechanical toy model linking cell-substrate adhesion to multiple cellular migratory responses

During cell migration, forces applied to a cell from its environment influence the motion. When the cell is placed on a substrate, such a force is provided by the cell-substrate adhesion. Modulation of adhesivity, often performed by the modulation of the substrate stiffness, tends to cause common responses for cell spreading, cell speed, persistence, and random motility coefficient. Although the reasons for the response of cell spreading and cell speed have been suggested, other responses are not well understood. In this study, we develop a simple toy model for cell migration driven by the relation of two forces: the adhesive force and the plasma membrane tension. The simplicity of the model allows us to perform the calculation not only numerically but also analytically, and the analysis provides formulas directly relating the adhesivity to cell spreading, persistence, and the random motility coefficient. Accordingly, the results offer a unified picture on the causal relations between those multiple cellular responses. In addition, cellular properties that would influence the migratory behavior are suggested.

An Agent-Based Discrete Collagen Fiber Network Model of Dynamic Traction Force-Induced Remodeling

Microstructural properties of extracellular matrix (ECM) promote cell and tissue homeostasis as well as contribute to the formation and progression of disease. In order to understand how microstructural properties influence the mechanical properties and traction force-induced remodeling of ECM, we developed an agent-based model that incorporates repetitively applied traction force within a discrete fiber network. An important difference between our model and similar finite element models is that by implementing more biologically realistic dynamic traction, we can explore a greater range of matrix remodeling. Here, we validated our model by reproducing qualitative trends observed in three sets of experimental data reported by others: tensile and shear testing of cell-free collagen gels, collagen remodeling around a single isolated cell, and collagen remodeling between pairs of cells. In response to tensile and shear strain, simulated acellular networks with straight fibrils exhibited biphasic stress-strain curves indicative of strain-stiffening. When fibril curvature was introduced, stress-strain curves shifted to the right, delaying the onset of strain-stiffening. Our data support the notion that strain-stiffening might occur as individual fibrils successively align along the axis of strain and become engaged in tension. In simulations with a single, contractile cell, peak collagen displacement occurred closest to the cell and decreased with increasing distance. In simulations with two cells, compaction of collagen between cells appeared inversely related to the initial distance between cells. These results for cell-populated collagen networks match in vitro findings. A demonstrable benefit of modeling is that it allows for further analysis not feasible with experimentation. Within two-cell simulations, strain energy within the collagen network measured from the final state was relatively uniform around the outer surface of cells separated by 250 μm, but became increasingly nonuniform as the distance between cells decreased. For cells separated by 75 and 100 μm, strain energy peaked in the direction toward the other cell in the region in which fibrils become highly aligned and reached a minimum adjacent to this region, not on the opposite side of the cell as might be expected. This pattern of strain energy was partly attributable to the pattern of collagen compaction, but was still present when mapping strain energy divided by collagen density. Findings like these are of interest because fibril alignment, density, and strain energy may each contribute to contact guidance during tissue morphogenesis.

Mechanical Model for Durotactic Cell Migration

Cell migration is a fundamental process in biological systems, playing an important role for diverse physiological processes. Cells often exhibit directed migration in a specific direction in response to various types of cues. In particular, cells are able to sense the rigidity of surrounding environments and then migrate toward stiffer regions. To understand this mechanosensitive behavior called durotaxis, several computational models have been developed. However, most of the models employed cell decision making to recapitulate durotactic behaviors, significantly limiting insights provided from these studies. In this study, we developed a computational biomechanical model without any cell decision making to illuminate intrinsic mechanisms of durotactic behaviors of cells migrating on a two-dimensional substrate. The model consists of a simplified cell generating contractile forces and a deformable substrate coarse-grained into an irregular triangulated mesh. Using the model, we demonstrated that durotactic behaviors emerge from purely mechanical interactions between the cell and the underlying substrate. We investigated how durotactic migration is regulated by biophysical properties of the substrate, including elasticity, viscosity, and stiffness profile.

Cellular architecture and migration behavior of fibroblast cells on polyhydroxyoctanoate (PHO): A natural polymer of bacterial origin

Biodegradable and biocompatible novel materials of natural origin are gaining more and more attention in recent years. These so called biopolymers, characterized by their biointegrity and biocompatibility, find completely new and promising applications in biomedical sciences. The presented work focuses on the medium chain length elastomeric polyhydroxyalkanoate biopolymer-polyhydroxyoctanoate (PHO). This biopolymer is fully biodegradable without formation of harmful byproducts.We investigated PHO's physical properties with nanoindentation technique and scratch testing to determine Young's modulus and friction coefficient. Further, the work focused on the impact of PHO, used as growth substrate, on the physiology and morphology of mouse embryonic fibroblast cells (MEF 3T3). Application of fluorescent staining protocols and advanced microscopic techniques allowed to study the morphological changes in the cytoskeletons of cells grown on PHO and also gave an insight into their migration strategies on the polymer surface. We found that PHO exhibits no cellular cytotoxicity, similarly to a glass substrate. MEF cells spread better on glass surface than on each tested PHO substrate though there was almost no difference between PHO substrates cast from different solvents. However, a detailed analysis of actin and microtubule cytoskeletal architecture reveals changes in the density of actin and microtubular networks. Migration of MEF cells on PHO substrates was slower than on the glass substrate. To elucidate the molecular mechanisms of observed changes in cytoskeletal architecture and migration parameters can be of special interest for future medical application of PHO polymer.

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.

Mechanochemical Coupling and Junctional Forces during Collective Cell Migration

Cell migration, a fundamental physiological process in which cells sense and move through their surrounding physical environment, plays a critical role in development and tissue formation, as well as pathological processes, such as cancer metastasis and wound healing. During cell migration, dynamics are governed by the bidirectional interplay between cell-generated mechanical forces and the activity of Rho GTPases, a family of small GTP-binding proteins that regulate actin cytoskeleton assembly and cellular contractility. These interactions are inherently more complex during the collective migration of mechanically coupled cells because of the additional regulation of cell-cell junctional forces. In this study, we adapted a recent minimal modeling framework to simulate the interactions between mechanochemical signaling in individual cells and interactions with cell-cell junctional forces during collective cell migration. We find that migration of individual cells depends on the feedback between mechanical tension and Rho GTPase activity in a biphasic manner. During collective cell migration, waves of Rho GTPase activity mediate mechanical contraction/extension and thus synchronization throughout the tissue. Further, cell-cell junctional forces exhibit distinct spatial patterns during collective cell migration, with larger forces near the leading edge. Larger junctional force magnitudes are associated with faster collective cell migration and larger tissue size. Simulations of heterogeneous tissue migration exhibit a complex dependence on the properties of both leading and trailing cells. Computational predictions demonstrate that collective cell migration depends on both the emergent dynamics and interactions between cellular-level Rho GTPase activity and contractility and multicellular-level junctional forces.

Binding of intercellular adhesion molecule 1 to β2-integrin regulates distinct cell adhesion processes on hepatic and cerebral endothelium

Flowing polymorphonuclear neutrophils (PMNs) are forced to recruit toward inflamed tissue and adhere to vascular endothelial cells, which is primarily mediated by the binding of β₂-integrins to ICAM-1. This process is distinct among different organs such as liver and brain; however, the underlying kinetic and mechanical mechanisms regulating tissue-specific recruitment of PMNs remain unclear. Here, binding kinetics measurement showed that ICAM-1 on murine hepatic sinusoidal endothelial cells (LSECs) bound to lymphocyte function-associated antigen-1 (LFA-1) with higher on- and off-rates but lower effective affinity compared with macrophage-1 antigen (Mac-1), whereas ICAM-1 on cerebral endothelial cells (BMECs or bEnd.3 cells) bound to LFA-1 with higher on-rates, similar off-rates, and higher effective affinity compared with Mac-1. Physiologically, free crawling tests of PMN onto LSEC, BMEC, or bEnd.3 monolayers were consistent with those kinetics differences between two β₂-integrins interacting with hepatic sinusoid or cerebral endothelium. Numerical calculations and Monte Carlo simulations validated tissue-specific contributions of β₂-integrin-ICAM-1 kinetics to PMN crawling on hepatic sinusoid or cerebral endothelium. Thus, this work first quantified the biophysical regulation of PMN adhesion in hepatic sinusoids compared with cerebral endothelium.

Mechanochemical modeling of neutrophil migration based on four signaling layers, integrin dynamics, and substrate stiffness

Directional neutrophil migration during human immune responses is a highly coordinated process regulated by both biochemical and biomechanical environments. In this paper, we developed an integrative mathematical model of neutrophil migration using a lattice Boltzmann-particle method built in-house to solve the moving boundary problem with spatiotemporal regulation of biochemical components. The mechanical features of the cell cortex are modeled by a series of spring-connected nodes representing discrete cell-substrate adhesive sites. The intracellular signaling cascades responsible for cytoskeletal remodeling [e.g., small GTPases, phosphoinositide-3-kinase (PI3K), and phosphatase and tensin homolog] are built based on our previous four-layered signaling model centered on the bidirectional molecular transport mechanism and implemented as reaction-diffusion equations. Focal adhesion dynamics are determined by force-dependent integrin-ligand binding kinetics and integrin recycling and are thus integrated with cell motion. Using numerical simulations, the model reproduces the major features of cell migration in response to uniform and gradient biochemical stimuli based on the quantitative spatiotemporal regulation of signaling molecules, which agree with experimental observations. The existence of multiple types of integrins with different binding kinetics could act as an adaptation mechanism for substrate stiffness. Moreover, cells can perform reversal, U-turn, or lock-on behaviors depending on the steepness of the reversal biochemical signals received. Finally, this model is also applied to predict the responses of mutants in which PTEN is overexpressed or disrupted.

A DISCRETE MATHEMATICAL MODEL FOR SINGLE AND COLLECTIVE MOVEMENT IN AMOEBOID CELLS

In this paper, we develop a new discrete mathematical model for individual and collective cell motility. We introduce a mechanical model for the movement of a cell on a two-dimensional rigid surface to describe and investigate the cell–cell and cell–substrate interactions. The cell cytoskeleton is modeled as a series of springs and dashpots connected in parallel. The cell–substrate attachments and the cell protrusions are also included. In particular, this model is used to describe the directed movement of endothelial cells on a Matrigel plate. We compare the results from our model with experimental data. We show that cell density and substrate rigidity play an important role in network formation.

Computational modeling of single-cell mechanics and cytoskeletal mechanobiology

Cellular cytoskeletal mechanics plays a major role in many aspects of human health from organ development to wound healing, tissue homeostasis and cancer metastasis. We summarize the state-of-the-art techniques for mathematically modeling cellular stiffness and mechanics and the cytoskeletal components and factors that regulate them. We highlight key experiments that have assisted model parameterization and compare the advantages of different models that have been used to recapitulate these experiments. An overview of feed-forward mechanisms from signaling to cytoskeleton remodeling is provided, followed by a discussion of the rapidly growing niche of encapsulating feedback mechanisms from cytoskeletal and cell mechanics to signaling. We discuss broad areas of advancement that could accelerate research and understanding of cellular mechanobiology. A precise understanding of the molecular mechanisms that affect cell and tissue mechanics and function will underpin innovations in medical device technologies of the future. WIREs Syst Biol Med 2018, 10:e1407. doi: 10.1002/wsbm.1407 This article is categorized under: Models of Systems Properties and Processes > Mechanistic Models Physiology > Mammalian Physiology in Health and Disease Models of Systems Properties and Processes > Cellular Models.

Stiffness-dependent motility and proliferation uncoupled by deletion of CD44

Information in the microenvironment guides complex cellular decisions such as whether or not to proliferate and migrate. The effects of soluble extracellular signals on these cellular functions are fairly well understood, but relatively little is known about how the extracellular matrix (ECM), and particularly the mechanical information in the ECM, guides these cellular decisions. Here, we show that CD44, a major receptor for the glycosaminoglycan ECM component hyaluronan, coordinates the motility and proliferative responses to ECM stiffening. We analyzed these cellular responses on fibronectin-coated polyacrylamide hydrogels prepared at a physiologic range of ECM stiffness and found that stiffening of the ECM leads to both cell cycling and cell motility in serum-stimulated primary mouse dermal fibroblasts. Remarkably, deletion of CD44 impaired stiffness-stimulated motility of the primary cells without affecting other hallmark cellular responses to ECM stiffening including cell spread area, stress fiber formation, focal adhesion maturation, and intracellular stiffening. Even stiffness-mediated cell proliferation was unaffected by deletion of CD44. Our results reveal a novel effect of CD44, which is imposed downstream of ECM-mechanosensing and determines if cells couple or uncouple their proliferative and motility responses to ECM stiffness.

Emerging roles for LPP in metastatic cancer progression

LIM domain containing proteins are important regulators of diverse cellular processes, and play pivotal roles in regulating the actin cytoskeleton. Lipoma Preferred Partner (LPP) is a member of the zyxin family of LIM proteins that has long been characterized as a promoter of mesenchymal/fibroblast cell migration. More recently, LPP has emerged as a critical inducer of tumor cell migration, invasion and metastasis. LPP is thought to contribute to these malignant phenotypes by virtue of its ability to shuttle into the nucleus, localize to adhesions and, most recently, to promote invadopodia formation. In this review, we will examine the mechanisms through which LPP regulates the functions of adhesions and invadopodia, and discuss potential roles of LPP in mediating cellular responses to mechanical cues within these mechanosensory structures.

Chiral Orientation of Skeletal Muscle Cells Requires Rigid Substrate

Reconstitution of tissue morphology with inherent left–right (LR) asymmetry is essential for tissue/organ functions. For skeletal muscle, the largest tissue in mammalian organisms, successful myogenesis requires the regulation of the LR asymmetry to form the appropriate muscle alignment. However, the key factor for reproducing the LR asymmetry of skeletal tissues in a controllable, engineering context remains largely unknown. Recent reports indicate that cell chirality may underlie the LR development in tissue morphogenesis. Here, we report that a rigid substrate is required for the chirality of skeletal muscle cells. By using alternating micropatterned cell-adherent and cell-repellent stripes on a rigid substrate, we found that C2C12 skeletal muscle myoblasts exhibited a unidirectional tilted orientation with respect to the stripe boundary. Importantly, such chiral orientation was reduced when soft substrates were used instead. In addition, we demonstrated the key role of actin stress fibers in the formation of the chiral orientation. This study reveals that a rigid substrate is required for the chiral pattern of myoblasts, paving the way for reconstructing damaged muscle tissue with inherent LR asymmetry in the future.

A phenomenological cohesive model for the macroscopic simulation of cell-matrix adhesions

Cell adhesion is crucial for cells to not only physically interact with each other but also sense their microenvironment and respond accordingly. In fact, adherent cells can generate physical forces that are transmitted to the surrounding matrix, regulating the formation of cell-matrix adhesions. The main purpose of this work is to develop a computational model to simulate the dynamics of cell-matrix adhesions through a cohesive formulation within the framework of the finite element method and based on the principles of continuum damage mechanics. This model enables the simulation of the mechanical adhesion between cell and extracellular matrix (ECM) as regulated by local multidirectional forces and thus predicts the onset and growth of the adhesion. In addition, this numerical approach allows the simulation of the cell as a whole, as it models the complete mechanical interaction between cell and ECM. As a result, we can investigate and quantify how different mechanical conditions in the cell (e.g., contractile forces, actin cytoskeletal properties) or in the ECM (e.g., stiffness, external forces) can regulate the dynamics of cell-matrix adhesions.

Substrate Stiffness Regulates the Development of Left-Right Asymmetry in Cell Orientation

Left-right (LR) asymmetry of tissue/organ structure is a morphological feature essential for many tissue functions. The ability to incorporate the LR formation in constructing tissue/organ replacement is important for recapturing the inherent tissue structure and functions. However, how LR asymmetry is formed remains largely underdetermined, which creates significant hurdles to reproduce and regulate the formation of LR asymmetry in an engineering context. Here, we report substrate rigidity functioning as an effective switch that turns on the development of LR asymmetry. Using micropatterned cell-adherent stripes on rigid substrates, we found that cells collectively oriented at a LR-biased angle relative to the stripe boundary. This LR asymmetry was initiated by a LR-biased migration of cells at stripe boundary, which later generated a velocity gradient propagating from stripe boundary to the center. After a series of cell translocations and rotations, ultimately, an LR-biased cell orientation within the micropatterned stripe was formed. Importantly, this initiation and propagation of LR asymmetry was observed only on rigid but not on soft substrates, suggesting that the LR asymmetry was regulated by rigid substrate probably through the organization of actin cytoskeleton. Together, we demonstrated substrate rigidity as a determinant factor that mediates the self-organizing LR asymmetry being unfolded from single cells to multicellular organization. More broadly, we anticipate that our findings would pave the way for rebuilding artificial tissue constructs with inherent LR asymmetry in the future.

Augmenting Surgery via Multi-scale Modeling and Translational Systems Biology in the Era of Precision Medicine: A Multidisciplinary Perspective

In this era of tremendous technological capabilities and increased focus on improving clinical outcomes, decreasing costs, and increasing precision, there is a need for a more quantitative approach to the field of surgery. Multiscale computational modeling has the potential to bridge the gap to the emerging paradigms of Precision Medicine and Translational Systems Biology, in which quantitative metrics and data guide patient care through improved stratification, diagnosis, and therapy. Achievements by multiple groups have demonstrated the potential for (1) multiscale computational modeling, at a biological level, of diseases treated with surgery and the surgical procedure process at the level of the individual and the population; along with (2) patient-specific, computationally-enabled surgical planning, delivery, and guidance and robotically-augmented manipulation. In this perspective article, we discuss these concepts, and cite emerging examples from the fields of trauma, wound healing, and cardiac surgery.

A Cellular Potts Model of single cell migration in presence of durotaxis

Cell migration is a fundamental biological phenomenon during which cells sense their surroundings and respond to different types of signals. In presence of durotaxis, cells preferentially crawl from soft to stiff substrates by reorganizing their cytoskeleton from an isotropic to an anisotropic distribution of actin filaments. In the present paper, we propose a Cellular Potts Model to simulate single cell migration over flat substrates with variable stiffness. We have tested five configurations: (i) a substrate including a soft and a stiff region, (ii) a soft substrate including two parallel stiff stripes, (iii) a substrate made of successive stripes with increasing stiffness to create a gradient and (iv) a stiff substrate with four embedded soft squares. For each simulation, we have evaluated the morphology of the cell, the distance covered, the spreading area and the migration speed. We have then compared the numerical results to specific experimental observations showing a consistent agreement.

Cell motility regulation on a stepped micro pillar array device (SMPAD) with a discrete stiffness gradient

Our tissues consist of individual cells that respond to the elasticity of their environment, which varies between and within tissues. To better understand mechanically driven cell migration, it is necessary to manipulate the stiffness gradient across a substrate. Here, we have demonstrated a new variant of the microfabricated polymeric pillar array platform that can decouple the stiffness gradient from the ECM protein area. This goal is achieved via a "stepped" micro pillar array device (SMPAD) in which the contact area with the cell was kept constant while the diameter of the pillar bodies was altered to attain the proper mechanical stiffness. Using double-step SU-8 mold fabrication, the diameter of the top of every pillar was kept uniform, whereas that of the bottom was changed, to achieve the desired substrate rigidity. Fibronectin was immobilized on the pillar tops, providing a focal adhesion site for cells. C2C12, HeLa and NIH3T3 cells were cultured on the SMPAD, and the motion of the cells was observed by time-lapse microscopy. Using this simple platform, which produces a purely physical stimulus, we observed that various types of cell behavior are affected by the mechanical stimulus of the environment. We also demonstrated directed cell migration guided by a discrete rigidity gradient by varying stiffness. Interestingly, cell velocity was highest at the highest stiffness. Our approach enables the regulation of the mechanical properties of the polymeric pillar array device and eliminates the effects of the size of the contact area. This technique is a unique tool for studying cellular motion and behavior relative to various stiffness gradients in the environment.

Computational Tension Mapping of Adherent Cells Based on Actin Imaging

Forces transiting through the cytoskeleton are known to play a role in adherent cell activity. Up to now few approaches haves been able to determine theses intracellular forces. We thus developed a computational mechanical model based on a reconstruction of the cytoskeleton of an adherent cell from fluorescence staining of the actin network and focal adhesions (FA). Our custom made algorithm converted the 2D image of an actin network into a map of contractile interactions inside a 2D node grid, each node representing a group of pixels. We assumed that actin filaments observed under fluorescence microscopy, appear brighter when thicker, we thus presumed that nodes corresponding to pixels with higher actin density were linked by stiffer interactions. This enabled us to create a system of heterogeneous interactions which represent the spatial organization of the contractile actin network. The contractility of this interaction system was then adapted to match the level of force the cell truly exerted on focal adhesions; forces on focal adhesions were estimated from their vinculin expressed size. This enabled the model to compute consistent mechanical forces transiting throughout the cell. After computation, we applied a graphical approach on the original actin image, which enabled us to calculate tension forces throughout the cell, or in a particular region or even in single stress fibers. It also enabled us to study different scenarios which may indicate the mechanical role of other cytoskeletal components such as microtubules. For instance, our results stated that the ratio between intra and extra cellular compression is inversely proportional to intracellular tension.

p53/PUMA expression in human pulmonary fibroblasts mediates cell activation and migration in silicosis

Phagocytosis of SiO₂ into the lung causes an inflammatory cascade that results in fibroblast proliferation and migration, followed by fibrosis. Clinical evidence has indicated that the activation of alveolar macrophages by SiO₂ produces rapid and sustained inflammation characterized by the generation of monocyte chemotactic protein 1, which, in turn, induces fibrosis. However, the details of events downstream of monocyte chemotactic protein 1 activity in pulmonary fibroblasts remain unclear. Here, to elucidate the role of p53 in fibrosis induced by silica, both the upstream molecular mechanisms and the functional effects on cell proliferation and migration were investigated. Experiments using primary cultured adult human pulmonary fibroblasts led to the following results: 1) SiO₂ treatment resulted in a rapid and sustained increase in p53 and PUMA protein levels; 2) the MAPK and PI3K pathways were involved in the SiO₂-induced alteration of p53 and PUMA expression; and 3) RNA interference targeting p53 and PUMA prevented the SiO₂-induced increases in fibroblast activation and migration. Our study elucidated a link between SiO₂-induced p53/PUMA expression in fibroblasts and cell migration, thereby providing novel insight into the potential use of p53/PUMA in the development of novel therapeutic strategies for silicosis treatment.

Combinative in vitro studies and computational model to predict 3D cell migration response to drug insult

The development of drugs to counter diseases related to cell migration has resulted in a multi-billion dollar endeavor. Unfortunately, few drugs have emerged from this effort highlighting the need for new methods to enhance assays to study, analyze and control cell migration. In response to this complex process, computational models have emerged as potent tools to describe migration providing a high throughput and low cost method. However, most models are unable to predict migration response to drug with direct application to in vitro experiments. In addition to this, no model to date has attempted to describe migration in response to drugs while incorporating simultaneously protein signaling, proteolytic activity, and 3D culture. In this paper, we describe an integrated computational approach, in conjunction with in vitro observations, to serve as a platform to accurately predict migration in 3D matrices incorporating the function of matrix metalloproteinases (MMPs) and their interaction with the Extracellular signal-related kinase (ERK) signaling pathway. Our results provide biological insight into how matrix density, MMP activity, integrin adhesions, and p-ERK expression all affect speed and persistence in 3D. Predictions from the model provide insight toward improving drug combinations to more effectively reduce both speed and persistence during migration and the role of integrin adhesions in motility. In this way our integrated platform provides future potential to streamline and improve throughput toward the testing and development of migration targeting drugs with tangible application to current in vitro assays.

Three-dimensional numerical model of cell morphology during migration in multi-signaling substrates

Cell Migration associated with cell shape changes are of central importance in many biological processes ranging from morphogenesis to metastatic cancer cells. Cell movement is a result of cyclic changes of cell morphology due to effective forces on cell body, leading to periodic fluctuations of the cell length and cell membrane area. It is well-known that the cell can be guided by different effective stimuli such as mechanotaxis, thermotaxis, chemotaxis and/or electrotaxis. Regulation of intracellular mechanics and cell's physical interaction with its substrate rely on control of cell shape during cell migration. In this notion, it is essential to understand how each natural or external stimulus may affect the cell behavior. Therefore, a three-dimensional (3D) computational model is here developed to analyze a free mode of cell shape changes during migration in a multi-signaling micro-environment. This model is based on previous models that are presented by the same authors to study cell migration with a constant spherical cell shape in a multi-signaling substrates and mechanotaxis effect on cell morphology. Using the finite element discrete methodology, the cell is represented by a group of finite elements. The cell motion is modeled by equilibrium of effective forces on cell body such as traction, protrusion, electrostatic and drag forces, where the cell traction force is a function of the cell internal deformations. To study cell behavior in the presence of different stimuli, the model has been employed in different numerical cases. Our findings, which are qualitatively consistent with well-known related experimental observations, indicate that adding a new stimulus to the cell substrate pushes the cell to migrate more directionally in more elongated form towards the more effective stimuli. For instance, the presence of thermotaxis, chemotaxis and electrotaxis can further move the cell centroid towards the corresponding stimulus, respectively, diminishing the mechanotaxis effect. Besides, the stronger stimulus imposes a greater cell elongation and more cell membrane area. The present model not only provides new insights into cell morphology in a multi-signaling micro-environment but also enables us to investigate in more precise way the cell migration in the presence of different stimuli.

Nasal ectomesenchymal stem cells: multi-lineage differentiation and transformation effects on fibrin gels

Ectomesenchymal stem cells (EMSCs) are novel adult stem cells derived from the cranial neural crest. However, their stemness and multi-lineage differentiation potential on three-dimensional fibrin gels has not yet been explored. The objective of this study was to investigate induced differentiation of EMSCs on fibrin gels and their remodeling effects on the scaffolds during the induced differentiation process. The results indicated that CD133(+)/nestin(+)/CD44(+) EMSCs were extensively distributed in the lamina propria of the nasal mucosa. The passaged cells could be induced to differentiate to a greater degree into neurons, Schwann cells and osteoblasts on three-dimensional fibrin gels than on two-dimensional glass slides. More importantly, the induced Schwann cells and osteoblasts exerted channelized and calcified remodeling effects, respectively, on the fibrin gels. Thus, these reshaped scaffolds have desirable biological properties, such as good cell adhesion, biocompatibility and guidance over the cell behavior, providing a tissue-committed niche for specific tissue generation.

Unidirectional cell crawling model guided by extracellular cues

Cell migration is a highly regulated and complex cellular process to maintain proper homeostasis for various biological processes. Extracellular environment was identified as the main affecting factors determining the direction of cell crawling. It was observed experimentally that the cell prefers migrating to the area with denser or stiffer array of microposts. In this article, an integrated unidirectional cell crawling model was developed to investigate the spatiotemporal dynamics of unidirectional cell migration, which incorporates the dominating intracellular biochemical processes, biomechanical processes and the properties of extracellular micropost arrays. The interpost spacing and the stiffness of microposts are taken into account, respectively, to study the mechanism of unidirectional cell locomotion and the guidance of extracellular influence cues on the direction of unidirectional cell crawling. The model can explain adequately the unidirectional crawling phenomena observed in experiments such as "spatiotaxis" and "durotaxis," which allows us to obtain further insights into cell migration.

Probabilistic Voxel-Fe model for single cell motility in 3D

BACKGROUND

Cells respond to a variety of external stimuli regulated by the environment conditions. Mechanical, chemical and biological factors are of great interest and have been deeply studied. Furthermore, mathematical and computational models have been rapidly growing over the past few years, permitting researches to run complex scenarios saving time and resources. Usually these models focus on specific features of cell migration, making them only suitable to study restricted phenomena.

METHODS

Here we present a versatile finite element (FE) cell-scale 3D migration model based on probabilities depending in turn on ECM mechanical properties, chemical, fluid and boundary conditions.

RESULTS

With this approach we are able to capture important outcomes of cell migration such as: velocities, trajectories, cell shape and aspect ratio, cell stress or ECM displacements.

CONCLUSIONS

The modular form of the model will allow us to constantly update and redefine it as advancements are made in clarifying how cellular events take place.

A novel mechanotactic 3D modeling of cell morphology

Cell morphology plays a critical role in many biological processes, such as cell migration, tissue development, wound healing and tumor growth. Recent investigations demonstrate that, among other stimuli, cells adapt their shapes according to their substrate stiffness. Until now, the development of this process has not been clear. Therefore, in this work, a new three-dimensional (3D) computational model for cell morphology has been developed. This model is based on a previous cell migration model presented by the same authors. The new model considers that during cell-substrate interaction, cell shape is governed by internal cell deformation, which leads to an accurate prediction of the cell shape according to the mechanical characteristic of its surrounding micro-environment. To study this phenomenon, the model has been applied to different numerical cases. The obtained results, which are qualitatively consistent with well-known related experimental works, indicate that cell morphology not only depends on substrate stiffness but also on the substrate boundary conditions. A cell located within an unconstrained soft substrate (several kPa) with uniform stiffness is unable to adhere to its substrate or to send out pseudopodia. When the substrate stiffness increases to tens of kPa (intermediate and rigid substrates), the cell can adequately adhere to its substrate. Subsequently, as the traction forces exerted by the cell increase, the cell elongates and its shape changes. Within very stiff (hard) substrates, the cell cannot penetrate into its substrate or send out pseudopodia. On the other hand, a cell is found to be more elongated within substrates with a constrained surface. However, this elongation decreases when the cell approaches it. It can be concluded that the higher the net traction force, the greater the cell elongation, the larger the cell membrane area, and the less random the cell alignment.

A peptide functionalized poly(ethylene glycol) (PEG) hydrogel for investigating the influence of biochemical and biophysical matrix properties on tumor cell migration

To address the challenges associated with defined control over matrix properties in 3D cell culture systems, we employed a peptide functionalized poly(ethylene glycol) (PEG) hydrogel matrix in which mechanical modulus and adhesive properties were tuned. An HT-1080 human fibrosarcoma cell line was chosen as a model for probing matrix influences on tumor cell migration using the PEG hydrogel platform. HT-1080 speed varied with a complex dependence on both matrix modulus and Cys-Arg-Gly-Asp-Ser (CRGDS) adhesion ligand concentration, with regimes in which motility increased, decreased, or was minimally altered being observed. We further investigated cell motility by forming matrix interfaces that mimic aspects of tissue boundaries that might be encountered during invasion by taking advantage of the spatial control of the thiol-ene photochemistry to form patterned regions of low and high cross-linking densities. HT-1080s in 100 Pa regions of patterned PEG hydrogels tended to reverse direction or aggregate at the interface when they encountered a 360 Pa boundary. In contrast, HT-1080s were apparently unimpeded when migrating from the stiff to the soft regions of PEG peptide hydrogels, which may indicate that cells are capable of "reverse durotaxis" within at least some matrix regimes. Taken together, our results identified matrix regimes in which HT-1080 motility was both positively and negatively influenced by cell adhesion or matrix modulus.

The emergence of extracellular matrix mechanics and cell traction forces as important regulators of cellular self-organization

Physical cues play a fundamental role in a wide range of biological processes, such as embryogenesis, wound healing, tumour invasion and connective tissue morphogenesis. Although it is well known that during these processes, cells continuously interact with the local extracellular matrix (ECM) through cell traction forces, the role of these mechanical interactions on large scale cellular and matrix organization remains largely unknown. In this study, we use a simple theoretical model to investigate cellular and matrix organization as a result of mechanical feedback signals between cells and the surrounding ECM. The model includes bi-directional coupling through cellular traction forces to deform the ECM and through matrix deformation to trigger cellular migration. In addition, we incorporate the mechanical contribution of matrix fibres and their reorganization by the cells. We show that a group of contractile cells will self-polarize at a large scale, even in homogeneous environments. In addition, our simulations mimic the experimentally observed alignment of cells in the direction of maximum stiffness and the building up of tension as a consequence of cell and fibre reorganization. Moreover, we demonstrate that cellular organization is tightly linked to the mechanical feedback loop between cells and matrix. Cells with a preference for stiff environments have a tendency to form chains, while cells with a tendency for soft environments tend to form clusters. The model presented here illustrates the potential of simple physical cues and their impact on cellular self-organization. It can be used in applications where cell-matrix interactions play a key role, such as in the design of tissue engineering scaffolds and to gain a basic understanding of pattern formation in organogenesis or tissue regeneration.

ONE-DIMENSIONAL MODELING AND SIMULATIONS OF MIGRATION OF CULTURED FIBROBLASTS

Cell migration is crucial for many physiological functions such as wound healing, immuno-response and carcinogenesis. In this study an one-dimensional model of migration of fibroblasts was developed by modeling and integrating five subcellular processes, namely, actin protrusion, focal adhesion formation, stress fiber formation, polarization and retraction. The direction of migration was determined by polarization, which was related to direction of the stiffness gradient of the substrate. By controlling intensity of ultraviolet exposure on type-I collagen, a substrate with a stiffness gradient could be fabricated. Kinematic analyses of positions of the cell front, the nucleus and the cell rear, were utilized as inputs to the model. Simulation results of five live NIH 3T3 fibroblasts showed that the model was capable of simulating fast moving, slow moving and back-and-forth moving of the cells on the substrate.

Complex matrix remodeling and durotaxis can emerge from simple rules for cell-matrix interaction in agent-based models

Using a top-down approach, an agent-based model was developed within NetLogo where cells and extracellular matrix (ECM) fibers were composed of multiple agents to create deformable structures capable of exerting, reacting to, and transmitting mechanical force. At the beginning of the simulation, long fibers were randomly distributed and cross linked. Throughout the simulation, imposed rules allowed cells to exert traction forces by extending pseudopodia, binding to fibers and pulling them towards the cell. Simulated cells remodeled the fibrous matrix to change both the density and alignment of fibers and migrated within the matrix in ways that are consistent with previous experimental work. For example, cells compacted the matrix in their pericellular regions much more than the average compaction experienced for the entire matrix (696% versus 21%). Between pairs of cells, the matrix density increased (by 92%) and the fibers became more aligned (anisotropy index increased from 0.45 to 0.68) in the direction parallel to a line connecting the two cells, consistent with the "lines of tension" observed in experiments by others. Cells migrated towards one another at an average rate of ∼0.5 cell diameters per 10,000 arbitrary units (AU); faster migration occurred in simulations where the fiber density in the intercellular area was greater. To explore the potential contribution of matrix stiffness gradients in the observed migration (i.e., durotaxis), the model was altered to contain a regular lattice of fibers possessing a stiffness gradient and just a single cell. In these simulations cells migrated preferentially in the direction of increasing stiffness at a rate of ∼2 cell diameter per 10,000 AU. This work demonstrates that matrix remodeling and durotaxis, both complex phenomena, might be emergent behaviors based on just a few rules that control how a cell can interact with a fibrous ECM.