Dynamic modeling of cell migration and spreading behaviors on fibronectin coated planar substrates and micropatterned geometries

Lidocaine inhibits migration of tenocytes by downregulating focal adhesion kinase and paxillin phosphorylation

Lidocaine is the most frequently applied local infiltration anesthetic agent for treating tendinopathies. However, studies have discovered lidocaine to negatively affect tendon healing. In the current study, the molecular mechanisms and effects of lidocaine on tenocyte migration were evaluated. We treated tenocytes intrinsic to the Achilles tendons of Sprague-Dawley rats with lidocaine. The migration ability of cells was analyzed using electric cell-substrate impedance sensing (ECIS) and scratch wound assay. We then used a microscope to evaluate the cell spread. We assessed filamentous actin (F-actin) cytoskeleton formation through immunofluorescence staining. In addition, we used Western blot analysis to analyze the expression of phospho-focal adhesion kinase (FAK), FAK, phospho-paxillin, paxillin, and F-actin. We discovered that lidocaine had an inhibitory effect on the migration of tenocytes in the scratch wound assay and on the ECIS chip. Lidocaine treatment suppressed cell spreading and changed the cell morphology and F-actin distribution. Lidocaine reduced F-actin formation in the tenocyte during cell spreading; furthermore, it inhibited phospho-FAK, F-actin, and phospho-paxillin expression in the tenocytes. Our study revealed that lidocaine inhibits the spread and migration of tenocytes. The molecular mechanism potentially underlying this effect is downregulation of F-actin, phospho-FAK, and phospho-paxillin expression when cells are treated with lidocaine.

Long-term adherent cell dynamics emerging from energetic and frictional interactions at the interface

Cell adhesion plays an important role in a wide range of biological situations, including embryonic development, cancer invasion, and wound healing. Although several computational models describing adhesion dynamics have been proposed, models applicable to long-term, large-length-scale cell dynamics are lacking. In this study we investigated possible states of long-term adherent cell dynamics in three-dimensional space by constructing a continuum model of interfacial interactions between adhesive surfaces. In this model a pseudointerface is supposed between each pair of triangular elements that discretize cell surfaces. By introducing a distance between each pair of elements, the physical properties of the interface are given by interfacial energy and friction. The proposed model was implemented into the model of a nonconservative fluid cell membrane where the cell membrane dynamically flows with turnover. Using the implemented model, numerical simulations of adherent cell dynamics on a substrate under flow were performed. The simulations not only reproduced the previously reported dynamics of adherent cells, such as detachment, rolling, and fixation on the substrate, but also discovered other dynamic states, including cell slipping and membrane flow patterns, corresponding to behaviors that occur on much longer timescales than the dissociation of adhesion molecules. These results illustrate the variety of long-term adherent cell dynamics, which are more diverse than the short-term ones. The proposed model can be extended to arbitrarily shaped membranes, thus being useful for the mechanical analysis of a wide range of long-term cell dynamics where adhesion is essential.

A novel integrated experimental and computational approach to unravel fibroblast motility in response to chemical gradients in 3D collagen matrices

Fibroblasts play an essential role in tissue repair and regeneration as they migrate to wounded areas to secrete and remodel the extracellular matrix. Fibroblasts recognize chemical substances such as growth factors, which enhance their motility towards the wounded tissues through chemotaxis. Although several studies have characterized single-cell fibroblast motility before, the migration patterns of fibroblasts in response to external factors have not been fully explored in 3D environments. We present a study that combines experimental and computational efforts to characterize the effect of chemical stimuli on the invasion of 3D collagen matrices by fibroblasts. Experimentally, we used microfluidic devices to create chemical gradients using collagen matrices of distinct densities. We evaluated how cell migration patterns were affected by the presence of growth factors and the mechanical properties of the matrix. Based on these results, we present a discrete-based computational model to simulate cell motility, which we calibrated through the quantitative comparison of experimental and computational data via Bayesian optimization. By combining these approaches, we predict that fibroblasts respond to both the presence of chemical factors and their spatial location. Furthermore, our results show that the presence of these chemical gradients could be reproduced by our computational model through increases in the magnitude of cell-generated forces and enhanced cell directionality. Although these model predictions require further experimental validation, we propose that our framework can be applied as a tool that takes advantage of experimental data to guide the calibration of models and predict which mechanisms at the cellular level may justify the experimental findings. Consequently, these new insights may also guide the design of new experiments, tailored to validate the variables of interest identified by the model.

On modeling the multiscale mechanobiology of soft tissues: Challenges and progress

Tissues grow and remodel in response to mechanical cues, extracellular and intracellular signals experienced through various biological events, from the developing embryo to disease and aging. The macroscale response of soft tissues is typically nonlinear, viscoelastic anisotropic, and often emerges from the hierarchical structure of tissues, primarily their biopolymer fiber networks at the microscale. The adaptation to mechanical cues is likewise a multiscale phenomenon. Cell mechanobiology, the ability of cells to transform mechanical inputs into chemical signaling inside the cell, and subsequent regulation of cellular behavior through intra- and inter-cellular signaling networks, is the key coupling at the microscale between the mechanical cues and the mechanical adaptation seen macroscopically. To fully understand mechanics of tissues in growth and remodeling as observed at the tissue level, multiscale models of tissue mechanobiology are essential. In this review, we summarize the state-of-the art modeling tools of soft tissues at both scales, the tissue level response, and the cell scale mechanobiology models. To help the interested reader become more familiar with these modeling frameworks, we also show representative examples. Our aim here is to bring together scientists from different disciplines and enable the future leap in multiscale modeling of tissue mechanobiology.

A computational modeling of invadopodia protrusion into an extracellular matrix fiber network

Invadopodia are dynamic actin-rich membrane protrusions that have been implicated in cancer cell invasion and metastasis. In addition, invasiveness of cancer cells is strongly correlated with invadopodia formation, which are observed during extravasation and colonization of metastatic cancer cells at secondary sites. However, quantitative understanding of the interaction of invadopodia with extracellular matrix (ECM) is lacking, and how invadopodia protrusion speed is associated with the frequency of protrusion-retraction cycles remains unknown. Here, we present a computational framework for the characterization of invadopodia protrusions which allows two way interactions between intracellular branched actin network and ECM fibers network. We have applied this approach to predicting the invasiveness of cancer cells by computationally knocking out actin-crosslinking molecules, such as α-actinin, filamin and fascin. The resulting simulations reveal distinct invadopodia dynamics with cycles of protrusion and retraction. Specifically, we found that (1) increasing accumulation of MT1-MMP at tips of invadopodia as the duration of protrusive phase is increased, and (2) the movement of nucleus toward the leading edge of the cell becomes unstable as duration of the retractile phase (or myosin turnover time) is longer than 1 min.

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

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

Cardiac Cell Patterning on Customized Microelectrode Arrays for Electrophysiological Recordings

Cardiomyocytes (CMs) and fibroblast cells are two essential elements for cardiac tissue structure and function. The interactions between them can alter cardiac electrophysiology and thus contribute to cardiac diseases, such as arrhythmogenesis. One possible explanation is that fibroblasts can directly affect cardiac electrophysiology through electrical coupling with CMs. Therefore, detecting the electrical activities in the CM-fibroblast network is vital for understanding the coupling dynamics among them. Current commercialized platforms for studying cardiac electrophysiology utilize planar microelectrode arrays (MEAs) to record the extracellular field potential (FP) in real-time, but the prearranged electrode configuration highly limits the measurement capabilities at specific locations. Here, we report a custom-designed MEA device with a novel micropatterning method to construct a controlled network of neonatal rat CMs (rCMs) and fibroblast connections for monitoring the electrical activity of rCM-fibroblast co-cultures in a spatially controlled fashion. For the micropatterning of the co-culture, surface topographical features and mobile blockers were used to control the initial attachment locations of a mixture of rCMs and fibroblasts, to form separate beating rCM-fibroblast clusters while leaving empty space for fibroblast growth to connect these clusters. Once the blockers are removed, the proliferating fibroblasts connect and couple the separate beating clusters. Using this method, electrical activity of both rCMs and human-induced-pluripotent-stem-cell-derived cardiomyocytes (iCMs) was examined. The coupling dynamics were studied through the extracellular FP and impedance profile recorded from the MEA device, indicating that the fibroblast bridge provided an RC-type coupling of physically separate rCM-containing clusters and enabled synchronization of these clusters.

Computational models of migration modes improve our understanding of metastasis

Tumor cells migrate through changing microenvironments of diseased and healthy tissue, making their migration particularly challenging to describe. To better understand this process, computational models have been developed for both the ameboid and mesenchymal modes of cell migration. Here, we review various approaches that have been used to account for the physical environment's effect on cell migration in computational models, with a focus on their application to understanding cancer metastasis and the related phenomenon of durotaxis. We then discuss how mesenchymal migration models typically simulate complex cell–extracellular matrix (ECM) interactions, while ameboid migration models use a cell-focused approach that largely ignores ECM when not acting as a physical barrier. This approach greatly simplifies or ignores the mechanosensing ability of ameboid migrating cells and should be reevaluated in future models. We conclude by describing future model elements that have not been included to date but would enhance model accuracy.

Modulation of Actin Filament Dynamics by Inward Rectifying of Potassium Channel Kir2.1

Apart from its ion channel properties, the Kir2.1 channel has been found in tumors and cancer cells to facilitate cancer cell motility. It is assumed that Kir2.1 might be associated with cell actin filament dynamics. With the help of structured illumination microscopy (SIM), we show that Kir2.1 overexpression promotes actin filament dynamics, cell invasion, and adhesion. Mutated Kir2.1 channels, with impaired membrane expression, present much weaker actin regulatory effects, which indicates that precise Kir2.1 membrane localization is key to its actin filament remolding effect. It is found that Kir2.1 membrane expression and anchoring are associated with PIP₂ affinity, and PIP₂ depletion inhibits actin filament dynamics. We also report that membrane-expressed Kir2.1 regulates redistribution and phosphorylation of FLNA (filamin A), which may be the mechanism underlying Kir2.1 and actin filament dynamics. In conclusion, Kir2.1 membrane localization regulates cell actin filaments, and not the ion channel properties. These data indicate that Kir2.1 may have additional cellular functions distinct from the regulation of excitability, which provides new insight into the study of channel proteins.

A Cellular Potts energy-based approach to analyse the influence of the surface topography on single cell motility

The surface shape is an important aspect to take into account to ensure the success of an implant. At the cellular scale level, the cell behaviour, especially its migration, is affected by the specificities of the surface of the substrate, such as the stiffness of the surface and its roughness topography. The latter has been shown to have a great impact on various cell mechanisms, such as the cell adhesion, migration, or proliferation. In fact, the mere presence of micro roughness leads to an improvement of those mechanisms, with a better integration of the implants. However, the phenomena behind those improvements are still not clear. In this paper, we propose a three-dimensional (3D) model of a single cell migration using a Cellular Potts (CP) model to study the influence of the surface topography on cell motility. To do so, various configurations were tested, such as: (i) a substrate with a random roughness, (ii) a substrate with a rectangular groove pattern (parallel and perpendicular to the direction of motion), (ii) a substrate with a sinusoidal groove pattern. To evaluate the influence of the surface topography on cell motility, for each configuration, the cell speed and shape as well as the contact surface between the cell and the substrate have been quantified. Our numerical results demonstrate that, in agreement with the experimental observations of the literature, the substrate topography has an influence on the cell efficiency (i.e. cell speed), orientation and shape. Besides, we also show that the increase of the contact surface alone in presence of roughness is not enough to explain the improvement of cell migration on the various rough surfaces. Finally, we highlight the importance of the roughness dimension on cell motility. This could be a critical aspect to consider for further analyses and applications, such as surface treatments for medical applications.

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

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

An Active Biomechanical Model of Cell Adhesion Actuated by Intracellular Tensioning-Taxis

Cell adhesion to the extracellular matrix (ECM) is highly active and plays a crucial role in various physiological functions. The active response of cells to physicochemical cues has been universally discovered in multiple microenvironments. However, the mechanisms to rule these active behaviors of cells are still poorly understood. Here, we establish an active model to probe the biomechanical mechanisms governing cell adhesion. The framework of cells is modeled as a tensional integrity that is maintained by cytoskeletons and extracellular matrices. Active movement of the cell model is self-driven by its intrinsic tendency to intracellular tensioning, defined as tensioning-taxis in this study. Tensioning-taxis is quantified as driving potential to actuate cell adhesion, and the traction forces are solved by our proposed numerical method of local free energy adaptation. The modeling results account for the active adhesion of cells with dynamic protruding of leading edge and power-law development of mechanical properties. Furthermore, the morphogenesis of cells evolves actively depending on actin filaments alignments by a predicted mechanism of scaling and directing traction forces. The proposed model provides a quantitative way to investigate the active mechanisms of cell adhesion and holds the potential to guide studies of more complex adhesion and motion of cells coupled with multiple external cues.

Membrane dynamics in cell migration

Migration of cells is required in multiple tissue-level processes, such as in inflammation or cancer metastasis. Endocytosis is an extremely regulated cellular process by which cells uptake extracellular molecules or internalise cell surface receptors. While the role of endocytosis of focal adhesions (FA) and plasma membrane (PM) turnover at the leading edge of migratory cells is wide known, the contribution of endocytic proteins per se in migration has been frequently disregarded. In this review, we describe the novel functions of the most well-known endocytic proteins in cancer cell migration, focusing on clathrin, caveolin, flotillins and GRAF1. In addition, we highlight the relevance of the macropinocytic pathway in amoeboid-like cell migration.

In vitro effects of vasoconstrictive retraction agents on primary human gingival fibroblasts

The biological activity of chemical retraction/displacement agents in surrounding periodontal tissues is of unquestionable importance, but the activity of these agents has not been completely elucidated. In the present study, we aimed to evaluate the in vitro effects of vasoconstrictive retraction agents on primary human gingival fibroblasts (HGFs). A total of six commercial adrenergic solutions (0.05 and 0.01% HCl-epinephrine, two based on 0.05% HCl-tetrahydrozoline, 0.05% HCl-oxymetazoline, and 10% HCl-phenylephrine) and three experimental gel formulations (EG-1, EG-2, and EG-3) were used to treat primary HGFs. The biological effect of the retraction treatment on the expression of collagen types I and III was detected by performing immunocytochemical analysis. The generation of reactive oxygen species triggered by the retraction agents were evaluated by using the dichlorofluorescein (DCF) fluorescent probe. The effect of retraction agents on the expression of fibronectin was visualized by confocal laser scanning microscopy. According to the results, experimental retraction gels did not limit the expression of collagen types I and III. EG-3 even induced the synthesis of both types of collagen. The DCF assay indicated oxidative stress similar to the control cells for most of the selected retraction agents. Experimental gels did not cause degradation of the cellular shape and morphology of the primary HGFs. The proposed experimental retraction gels in the present study demonstrated higher biocompatibility with primary HGFs, suggesting their use as clinical vasoconstrictive agents for the application of gingival retraction with minimal damage to periodontal tissues.

A quantitative high-resolution computational mechanics cell model for growing and regenerating tissues

Mathematical models are increasingly designed to guide experiments in biology, biotechnology, as well as to assist in medical decision making. They are in particular important to understand emergent collective cell behavior. For this purpose, the models, despite still abstractions of reality, need to be quantitative in all aspects relevant for the question of interest. This paper considers as showcase example the regeneration of liver after drug-induced depletion of hepatocytes, in which the surviving and dividing hepatocytes must squeeze in between the blood vessels of a network to refill the emerged lesions. Here, the cells' response to mechanical stress might significantly impact the regeneration process. We present a 3D high-resolution cell-based model integrating information from measurements in order to obtain a refined and quantitative understanding of the impact of cell-biomechanical effects on the closure of drug-induced lesions in liver. Our model represents each cell individually and is constructed by a discrete, physically scalable network of viscoelastic elements, capable of mimicking realistic cell deformation and supplying information at subcellular scales. The cells have the capability to migrate, grow, and divide, and the nature and parameters of their mechanical elements can be inferred from comparisons with optical stretcher experiments. Due to triangulation of the cell surface, interactions of cells with arbitrarily shaped (triangulated) structures such as blood vessels can be captured naturally. Comparing our simulations with those of so-called center-based models, in which cells have a largely rigid shape and forces are exerted between cell centers, we find that the migration forces a cell needs to exert on its environment to close a tissue lesion, is much smaller than predicted by center-based models. To stress generality of the approach, the liver simulations were complemented by monolayer and multicellular spheroid growth simulations. In summary, our model can give quantitative insight in many tissue organization processes, permits hypothesis testing in silico, and guide experiments in situations in which cell mechanics is considered important.

Ibuprofen inhibited migration of skeletal muscle cells in association with downregulation of p130cas and CrkII expressions

Background

Nonsteroidal anti-inflammatory drugs (NSAIDs) are commonly used to treat sports-related muscle injuries. However, NSAIDs were recently shown to impede the muscle healing process after acute injury. Migration of skeletal muscle cells is a crucial step during the muscle healing process. The present study was performed to investigate the effect and molecular mechanisms of action of ibuprofen, a commonly used NSAID, on the migration of skeletal muscle cells.

Methods

Skeletal muscle cells isolated from the gastrocnemius muscle of Sprague-Dawley rats were treated with ibuprofen. MTT assay (3-[4,5-dimethylthiazol-2-yl]-2,5-diphenyltetrazolium bromide) was used to evaluate cell viability, and cell apoptosis was evaluated by TUNEL assay, after ibuprofen treatment. Skeletal muscle cell migration and spreading were evaluated using the transwell filter migration assay and F-actin staining, respectively. The protein expression of p130cas and CrkII, which are cell migration facilitating genes, was determined by western blot analysis. The overexpression of p130cas of muscle cells was achieved by p130cas vector transfection.

Results

The results demonstrated that ibuprofen did not have a significant negative effect on cell viability and apoptosis. Ibuprofen inhibited the migration and spreading of skeletal muscle cells in a dose-dependent manner. Ibuprofen also dose-dependently decreased the protein expression of p130cas and CrkII. Furthermore, overexpression of p130cas resulted in the promotion of cell migration and spreading and counteracted ibuprofen-mediated inhibition.

Conclusion

This study suggested that ibuprofen exerts a potentially adverse effect on the migration of skeletal muscle cells by downregulating protein expression of p130cas and CrkII. These results indicate a possible mechanism underlying the possible negative effect of NSAIDs on muscle regeneration.

A checkpoint-oriented cell cycle simulation model

Modeling and in silico simulations are of major conceptual and applicative interest in studying the cell cycle and proliferation in eukaryotic cells. In this paper, we present a cell cycle checkpoint-oriented simulator that uses agent-based simulation modeling to reproduce the dynamics of a cancer cell population in exponential growth. Our in silico simulations were successfully validated by experimental in vitro supporting data obtained with HCT116 colon cancer cells. We demonstrated that this model can simulate cell confluence and the associated elongation of the G1 phase. Using nocodazole to synchronize cancer cells at mitosis, we confirmed the model predictivity and provided evidence of an additional and unexpected effect of nocodazole on the overall cell cycle progression. We anticipate that this cell cycle simulator will be a potential source of new insights and research perspectives.

Interplay Between the Persistent Random Walk and the Contact Inhibition of Locomotion Leads to Collective Cell Behaviors

Cell migration plays an important role in physiology and pathophysiology. It was observed in the experiments that cells, such as fibroblast, leukocytes, and cancer cells, exhibit a wide variety of migratory behaviors, such as persistent random walk, contact inhibition of locomotion, and ordered behaviors. To identify biophysical mechanisms for these cellular behaviors, we developed a rigorous computational model of cell migration on a two-dimensional non-deformable substrate. Cells in the model undergo motion driven by mechanical interactions between cellular protrusions and the substrate via the balance of tensile forces. Properties of dynamic formation of lamellipodia induced the persistent random walk behavior of a migrating cell. When multiple cells are included in the simulation, the model recapitulated the contact inhibition of locomotion between cells at low density without any phenomenological assumptions or momentum transfer. Instead, the model showed that contact inhibition of locomotion can emerge via indirect interactions between the cells through their interactions with the underlying substrate. At high density, contact inhibition of locomotion between numerous cells gave rise to confined motions or ordered behaviors, depending on cell density and how likely lamellipodia turn over due to contact with other cells. Results in our study suggest that various collective migratory behaviors may emerge without more restrictive assumptions or direct cell-to-cell biomechanical interactions.

Exosomes from Nischarin-Expressing Cells Reduce Breast Cancer Cell Motility and Tumor Growth

Exosomes are small extracellular microvesicles that are secreted by cells when intracellular multivesicular bodies fuse with the plasma membrane. We have previously demonstrated that Nischarin inhibits focal adhesion formation, cell migration, and invasion, leading to reduced activation of focal adhesion kinase. In this study, we propose that the tumor suppressor Nischarin regulates the release of exosomes. When cocultured on exosomes from Nischarin-positive cells, breast cancer cells exhibited reduced survival, migration, adhesion, and spreading. The same cocultures formed xenograft tumors of significantly reduced volume following injection into mice. Exosomes secreted by Nischarin-expressing tumors inhibited tumor growth. Expression of only one allele of Nischarin increased secretion of exosomes, and Rab14 activity modulated exosome secretions and cell growth. Taken together, this study reveals a novel role for Nischarin in preventing cancer cell motility, which contributes to our understanding of exosome biology. SIGNIFICANCE: Regulation of Nischarin-mediated exosome secretion by Rab14 seems to play an important role in controlling tumor growth and migration.See related commentary by McAndrews and Kalluri, p. 2099.

Influence of Micropatterned Grill Lines on Entamoeba histolytica Trophozoites Morphology and Migration

Entamoeba histolytica, the causal agent of human amoebiasis, has two morphologically different phases: a resistant cyst and a trophozoite responsible for the invasion of the host tissues such as the colonic mucosa and the intestinal epithelium. During in vitro migration, trophozoites usually produce protuberances such as pseudopods and rarely filopodia, structures that have been observed in the interaction of trophozoites with human colonic epithelial tissue. To study the different membrane projections produced by the trophozoites, including pseudopods, filopodia, uropods, blebs, and others, we designed an induction system using erythrocyte extract or fibronectin (FN) in micropatterned grill lines (each micro-line containing multiple micro-portions of FN or erythrocyte extract) on which the trophozoites were placed in culture for migration assays. Using light, confocal, and scanning electron microscopy, we established that E. histolytica trophozoites frequently produce short and long filopodia, large retractile uropods in the rear, pseudopods, blebs, and others structures, also showing continuous migration periods. The present study provides a simple migration method to induce trophozoites to generate abundant membrane protrusion structures that are rarely obtained in normal or induced cultures, such as long filopodia; this method will allow a–better understanding of the interactions of trophozoites with FN and cell debris. E. histolytica trophozoites motility plays an important role in invasive amoebiasis. It has been proposed that both physical forces and chemical signals are involved in the trophozoite motility and migration. However, the in vivo molecules that drive the chemotactic migration remain to be determined. We propose the present assay to study host molecules that guide chemotactic behavior because the method is highly reproducible, and a live image of cell movement and migration can be quantified.

Mechanical and Systems Biology of Cancer

Mechanics and biochemical signaling are both often deregulated in cancer, leading toincreased cell invasiveness, proliferation, and survival. The dynamics and interactions of cytoskeletal components control basic mechanical properties, such as cell tension, stiffness, and engagement with the extracellular environment, which can lead to extracellular matrix remodeling. Intracellular mechanics can alter signaling and transcription factors, impacting cell decision making. Additionally, signaling from soluble and mechanical factors in the extracellular environment, such as substrate stiffness and ligand density, can modulate cytoskeletal dynamics. Computational models closely integrated with experimental support, incorporating cancer-specific parameters, can provide quantitative assessments and serve as predictive tools toward dissecting the feedback between signaling and mechanics and across multiple scales and domains in tumor progression.

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.

Cell migration on material-driven fibronectin microenvironments

Cell migration is a fundamental process involved in a wide range of biological phenomena. However, how the underlying mechanisms that control migration are orchestrated is not fully understood. In this work, we explore the migratory characteristics of human fibroblasts using different organisations of fibronectin (FN) triggered by two chemically similar surfaces, poly(ethyl acrylate) (PEA) and poly(methyl acrylate) (PMA); cell migration is mediated via an intermediate layer of fibronectin (FN). FN is organised into nanonetworks upon simple adsorption on PEA whereas a globular conformation is observed on PMA. We studied cell speed over the course of 24 h and the morphology of focal adhesions in terms of area and length. Additionally, we analysed the amount of cell-secreted FN as well as FN remodelling. Velocity of human fibroblasts was found to exhibit a biphasic behaviour on PEA, whereas it remained fairly constant on PMA. FA analysis revealed more mature focal adhesions on PEA over time contrary to smaller FAs found on PMA. Finally, human fibroblasts seemed to remodel adsorbed FN more on PMA than on PEA. Overall, these results indicate that the cell-protein-material interface affects cell migratory behaviour. Analysis of FAs together with FN secretion and remodelling were associated with differences in cell velocity providing insights into the factors that can modulate cell motility.

A Chemomechanical Model for Nuclear Morphology and Stresses during Cell Transendothelial Migration

It is now evident that the cell nucleus undergoes dramatic shape changes during important cellular processes such as cell transmigration through extracellular matrix and endothelium. Recent experimental data suggest that during cell transmigration the deformability of the nucleus could be a limiting factor, and the morphological and structural alterations that the nucleus encounters can perturb genomic organization that in turn influences cellular behavior. Despite its importance, a biophysical model that connects the experimentally observed nuclear morphological changes to the underlying biophysical factors during transmigration through small constrictions is still lacking. Here, we developed a universal chemomechanical model that describes nuclear strains and shapes and predicts thresholds for the rupture of the nuclear envelope and for nuclear plastic deformation during transmigration through small constrictions. The model includes actin contraction and cytosolic back pressure that squeeze the nucleus through constrictions and overcome the mechanical resistance from deformation of the nucleus and the constrictions. The nucleus is treated as an elastic shell encompassing a poroelastic material representing the nuclear envelope and inner nucleoplasm, respectively. Tuning the chemomechanical parameters of different components such as cell contractility and nuclear and matrix stiffnesses, our model predicts the lower bounds of constriction size for successful transmigration. Furthermore, treating the chromatin as a plastic material, our model faithfully reproduced the experimentally observed irreversible nuclear deformations after transmigration in lamin-A/C-deficient cells, whereas the wild-type cells show much less plastic deformation. Along with making testable predictions, which are in accord with our experiments and existing literature, our work provides a realistic framework to assess the biophysical modulators of nuclear deformation during cell transmigration.

How Nucleus Mechanics and ECM Microstructure Influence the Invasion of Single Cells and Multicellular Aggregates

In order to move in a three-dimensional extracellular matrix, the nucleus of a cell must squeeze through the narrow spacing among the fibers and, by adhering to them, the cell needs to exert sufficiently strong traction forces. If the nucleus is too stiff, the spacing too narrow, or traction forces too weak, the cell is not able to penetrate the network. In this article, we formulate a mathematical model based on an energetic approach, for cells entering cylindrical channels composed of extracellular matrix fibers. Treating the nucleus as an elastic body covered by an elastic membrane, the energetic balance leads to the definition of a necessary criterion for cells to pass through the regular network of fibers, depending on the traction forces exerted by the cells (or possibly passive stresses), the stretchability of the nuclear membrane, the stiffness of the nucleus, and the ratio of the pore size within the extracellular matrix with respect to the nucleus diameter. The results obtained highlight the importance of the interplay between mechanical properties of the cell and microscopic geometric characteristics of the extracellular matrix and give an estimate for a critical value of the pore size that represents the physical limit of migration and can be used in tumor growth models to predict their invasive potential in thick regions of ECM.

Computational model of mesenchymal migration in 3D under chemotaxis

Cell chemotaxis is an important characteristic of cellular migration, which takes part in crucial aspects of life and development. In this work, we propose a novel in silico model of mesenchymal 3D migration with competing protrusions under a chemotactic gradient. Based on recent experimental observations, we identify three main stages that can regulate mesenchymal chemotaxis: chemosensing, dendritic protrusion dynamics and cell-matrix interactions. Therefore, each of these features is considered as a different module of the main regulatory computational algorithm. The numerical model was particularized for the case of fibroblast chemotaxis under a PDGF-bb gradient. Fibroblasts migration was simulated embedded in two different 3D matrices - collagen and fibrin - and under several PDGF-bb concentrations. Validation of the model results was provided through qualitative and quantitative comparison with in vitro studies. Our numerical predictions of cell trajectories and speeds were within the measured in vitro ranges in both collagen and fibrin matrices. Although in fibrin, the migration speed of fibroblasts is very low, because fibrin is a stiffer and more entangling matrix. Testing PDGF-bb concentrations, we noticed that an increment of this factor produces a speed increment. At 1 ng mL-1 a speed peak is reached after which the migration speed diminishes again. Moreover, we observed that fibrin exerts a dampening behavior on migration, significantly affecting the migration efficiency.

Laser Direct-Write Onto Live Tissues: A Novel Model for Studying Cancer Cell Migration

Investigation into the mechanisms driving cancer cell behavior and the subsequent development of novel targeted therapeutics requires comprehensive experimental models that mimic the complexity of the tumor microenvironment. Recently, our laboratories have combined a novel tissue culture model and laser direct-write, a form of bioprinting, to spatially position single or clustered cancer cells onto ex vivo microvascular networks containing blood vessels, lymphatic vessels, and interstitial cell populations. Herein, we highlight this new model as a tool for quantifying cancer cell motility and effects on angiogenesis and lymphangiogenesis in an intact network that matches the complexity of a real tissue. Application of our proposed methodology offers an innovative ex vivo tissue perspective for evaluating the effects of gene expression and targeted molecular therapies on cancer cell migration and invasion. J. Cell. Physiol. 231: 2333-2338, 2016. © 2016 Wiley Periodicals, Inc.

Modeling cell shape and dynamics on micropatterns

Adhesive micropatterns have become a standard tool to study cells under defined conditions. Applications range from controlling the differentiation and fate of single cells to guiding the collective migration of cell sheets. In long-term experiments, single cell normalization is challenged by cell division. For all of these setups, mathematical models predicting cell shape and dynamics can guide pattern design. Here we review recent advances in predicting and explaining cell shape, traction forces and dynamics on micropatterns. Starting with contour models as the simplest approach to explain concave cell shapes, we move on to network and continuum descriptions as examples for static models. To describe dynamic processes, cellular Potts, vertex and phase field models can be used. Different types of model are appropriate to address different biological questions and together, they provide a versatile tool box to predict cell behavior on micropatterns.

Fibronectin Deposition Participates in Extracellular Matrix Assembly and Vascular Morphogenesis

The extracellular matrix (ECM) has been demonstrated to facilitate angiogenesis. In particular, fibronectin has been documented to activate endothelial cells, resulting in their transition from a quiescent state to an active state in which the cells exhibit enhanced migration and proliferation. The goal of this study is to examine the role of polymerized fibronectin during vascular tubulogenesis using a 3 dimensional (3D) cell-derived de-cellularized matrix. A fibronectin-rich 3D de-cellularized ECM was used as a scaffold to study vascular morphogenesis of endothelial cells (ECs). Confocal analyses of several matrix proteins reveal high intra- and extra-cellular deposition of fibronectin in formed vascular structures. Using a small peptide inhibitor of fibronectin polymerization, we demonstrate that inhibition of fibronectin fibrillogenesis in ECs cultured atop de-cellularized ECM resulted in decreased vascular morphogenesis. Further, immunofluorescence and ultrastructural analyses reveal decreased expression of stromal matrix proteins in the absence of polymerized fibronectin with high co-localization of matrix proteins found in association with polymerized fibronectin. Evaluating vascular kinetics, live cell imaging showed that migration, migration velocity, and mean square displacement, are disrupted in structures grown in the absence of polymerized fibronectin. Additionally, vascular organization failed to occur in the absence of a polymerized fibronectin matrix. Consistent with these observations, we tested vascular morphogenesis following the disruption of EC adhesion to polymerized fibronectin, demonstrating that block of integrins α₅β₁ and α_vβ_3, abrogated vascular morphogenesis. Overall, fibronectin deposition in a 3D cell-derived de-cellularized ECM appears to be imperative for matrix assembly and vascular morphogenesis.

Cell Invasion Dynamics into a Three Dimensional Extracellular Matrix Fibre Network

The dynamics of filopodia interacting with the surrounding extracellular matrix (ECM) play a key role in various cell-ECM interactions, but their mechanisms of interaction with the ECM in 3D environment remain poorly understood. Based on first principles, here we construct an individual-based, force-based computational model integrating four modules of 1) filopodia penetration dynamics; 2) intracellular mechanics of cellular and nuclear membranes, contractile actin stress fibers, and focal adhesion dynamics; 3) structural mechanics of ECM fiber networks; and 4) reaction-diffusion mass transfers of seven biochemical concentrations in related with chemotaxis, proteolysis, haptotaxis, and degradation in ECM to predict dynamic behaviors of filopodia that penetrate into a 3D ECM fiber network. The tip of each filopodium crawls along ECM fibers, tugs the surrounding fibers, and contracts or retracts depending on the strength of the binding and the ECM stiffness and pore size. This filopodium-ECM interaction is modeled as a stochastic process based on binding kinetics between integrins along the filopodial shaft and the ligands on the surrounding ECM fibers. This filopodia stochastic model is integrated into migratory dynamics of a whole cell in order to predict the cell invasion into 3D ECM in response to chemotaxis, haptotaxis, and durotaxis cues. Predicted average filopodia speed and that of the cell membrane advance agreed with experiments of 3D HUVEC migration at r(2) > 0.95 for diverse ECMs with different pore sizes and stiffness.

Multiscale mechanobiology: computational models for integrating molecules to multicellular systems

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

Probing fibronectin-antibody interactions using AFM force spectroscopy and lateral force microscopy

The first experiment showing the effects of specific interaction forces using lateral force microscopy (LFM) was demonstrated for lectin-carbohydrate interactions some years ago. Such measurements are possible under the assumption that specific forces strongly dominate over the non-specific ones. However, obtaining quantitative results requires the complex and tedious calibration of a torsional force. Here, a new and relatively simple method for the calibration of the torsional force is presented. The proposed calibration method is validated through the measurement of the interaction forces between human fibronectin and its monoclonal antibody. The results obtained using LFM and AFM-based classical force spectroscopies showed similar unbinding forces recorded at similar loading rates. Our studies verify that the proposed lateral force calibration method can be applied to study single molecule interactions.

Investigating biomechanical noise in neuroblastoma cells using the quartz crystal microbalance

Quantifying cellular behaviour by motility and morphology changes is increasingly important in formulating an understanding of fundamental physiological phenomena and cellular mechanisms of disease. However, cells are complex biological units, which often respond to external environmental factors by manifesting subtle responses that may be difficult to interpret using conventional biophysical measurements. This paper describes the adaptation of the quartz crystal microbalance (QCM) to monitor neuroblastoma cells undergoing environmental stress wherein the frequency stability of the device can be correlated to changes in cellular state. By employing time domain analysis of the resulting frequency fluctuations, it is possible to study the variations in cellular motility and distinguish between different cell states induced by applied external heat stress. The changes in the frequency fluctuation data are correlated to phenotypical physical response recorded using optical microscopy under identical conditions of environmental stress. This technique, by probing the associated biomechanical noise, paves the way for its use in monitoring cell activity, and intrinsic motility and morphology changes, as well as the modulation resulting from the action of drugs, toxins and environmental stress.

Molecular force spectroscopy on cells

Molecular force spectroscopy has become a powerful tool to study how mechanics regulates biology, especially the mechanical regulation of molecular interactions and its impact on cellular functions. This force-driven methodology has uncovered a wealth of new information of the physical chemistry of molecular bonds for various biological systems. The new concepts, qualitative and quantitative measures describing bond behavior under force, and structural bases underlying these phenomena have substantially advanced our fundamental understanding of the inner workings of biological systems from the nanoscale (molecule) to the microscale (cell), elucidated basic molecular mechanisms of a wide range of important biological processes, and provided opportunities for engineering applications. Here, we review major force spectroscopic assays, conceptual developments of mechanically regulated kinetics of molecular interactions, and their biological relevance. We also present current challenges and highlight future directions.

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.

Environmental physical cues determine the lineage specification of mesenchymal stem cells

BACKGROUND

Physical cues of cellular environment affect cell fate and differentiation. For example, an environment with high stiffness drives mesenchymal stem cells (MSCs) to undergo osteogenic differentiation, while low stiffness leads to lipogenic differentiation. Such effects could be independent of chemical/biochemical inducers.

SCOPE OF REVIEW

Stiffness and/or topography of cellular environment can control MSC differentiation and fate determination. In addition, physical factors such as tension, which resulted from profound cytoskeleton reorganization during MSC differentiation, affect the gene expression essential for the differentiation. Although physical cues control MSC lineage specification probably by reorganizing and tuning cytoskeleton, the full mechanism is largely unclear. It also remains elusive how physical signals are sensed by cells and transformed into biochemical and biological signals. More importantly, it becomes pivotal to define explicitly the physical cue(s) essential for cell differentiation and fate decision. With a focus on MSC, we present herein current understanding of the interplay between i) physical cue and factors and ii) MSC differentiation and fate determination.

MAJOR CONCLUSIONS

Biophysical cues can initiate or strengthen the biochemical signaling for MSC fate determination and differentiation. Physical properties of cellular environment direct the structural adaptation and functional coupling of the cells to their environment.

GENERAL SIGNIFICANCE

These observations not only open a simple avenue to engineer cell fate in vitro, but also start to reveal the physical elements that regulate and determine cell fate.

Direct measurement of cell protrusion force utilizing a robot-aided cell manipulation system with optical tweezers for cell migration control

Cell migration refers to the directional cell movement in response to a chemoattractant gradient, a key process that occurs in a wide variety of biological phenomena. Cell protrusion force is generated by the actin polymerization of a cell, which drives the cell to move toward the stimulus as induced by the chemoattractant gradient. This paper presents a new methodology for the direct measurement of cell protrusion force utilizing a robot-aided optical tweezer system. The functionalized beads that are robotically trapped and placed near the cell serve as both cell migration stimulators and protrusion force probes. The force generated by the actin polymerization of the cell propels the bead to move away from the trapping center when the cell comes in contact with the bead. Such a deviation can be determined and used to calculate the trapping force, which is equal to the protrusion force at a balanced position. With the quantitative measurement of the protrusion, we find that the protrusion force of a live cell in response to a chemoattractant within the range of hundreds of piconewtons. We further probe the protrusion force distribution at the cell leading edge and find that the highest protrusion force appears at the cell migration direction. These measurements can help us characterize the mechanism of cell migration and lay a solid foundation for further proactive control of cell movement.

Influence of the microenvironment on cell fate determination and migration

Several critical cell functions are influenced not only by internal cellular machinery but also by external mechanical and biochemical cues from the surrounding microenvironment. Slight changes to the microenvironment can result in dramatic changes to the cell's phenotype; for example, a change in the nutrients or pH of a tumor microenvironment can result in increased tumor metastasis. While cellular fate and the regulators of cell fate have been studied in detail for several decades now, our understanding of the extracellular regulators remains qualitative and far from comprehensive. In this review, we discuss the microenvironment influence on cell fate in terms of adhesion, migration, and differentiation and focus on both developments in experimental and computation tools to analyze cellular fate.

Analysis of initial cell spreading using mechanistic contact formulations for a deformable cell model

Adhesion governs to a large extent the mechanical interaction between a cell and its microenvironment. As initial cell spreading is purely adhesion driven, understanding this phenomenon leads to profound insight in both cell adhesion and cell-substrate interaction. It has been found that across a wide variety of cell types, initial spreading behavior universally follows the same power laws. The simplest cell type providing this scaling of the radius of the spreading area with time are modified red blood cells (RBCs), whose elastic responses are well characterized. Using a mechanistic description of the contact interaction between a cell and its substrate in combination with a deformable RBC model, we are now able to investigate in detail the mechanisms behind this universal power law. The presented model suggests that the initial slope of the spreading curve with time results from a purely geometrical effect facilitated mainly by dissipation upon contact. Later on, the spreading rate decreases due to increasing tension and dissipation in the cell's cortex as the cell spreads more and more. To reproduce this observed initial spreading, no irreversible deformations are required. Since the model created in this effort is extensible to more complex cell types and can cope with arbitrarily shaped, smooth mechanical microenvironments of the cells, it can be useful for a wide range of investigations where forces at the cell boundary play a decisive role.

How cells spread on a newly encountered surface is an important issue, since it hints at how cells interact physically with the specific material in general. It has been shown before that many cell types have very similar early spreading behavior. This observation has been linked to the mechanical nature of the phenomenon, during which a cell cannot yet react by changing its structure and behavior. Understanding in detail how this passive spreading occurs, and what clues a cell may later respond to is the goal of this work. At the same time, the model we develop here should be very valuable for more complex situations of interacting cells, since it is able to reproduce the purely mechanical response in detail. We find that spreading is limited mainly by energy dissipation upon contact and later dissipation in the cell's cortex and that no irreversible deformation occurs during the spreading of red blood cells on an adhesive surface.

Differences in α-β transmembrane domain interactions among integrins enable diverging integrin signaling

Integrins are transmembrane adhesion molecules composed of α and β subunits. In humans, 24 integrins are expressed in a tissue-specific manner. Each integrin plays a specific role within a tissue type to control cell adhesion. We previously found that the degree of transmembrane domain (TMD) interaction between the integrin αIIb and β3 subunits is reversely correlated with the affinity of integrin αIIbβ3 to its ligand. Here, we examined the TMD interactions of various integrins, including α4β1, αLβ2, α5β1, αVβ1, αIIbβ3, and αVβ3. Our findings revealed that the degree of the TMD interactions in integrins α4β1 and αLβ2 expressed in immune cells was low and in integrins αIIbβ3 and αVβ3 expressed in platelets was high, while integrins α5β1 and αVβ1 that are expressed in most adherent cells displayed intermediate TMD interactions. We identified sequence variation within the N-terminal TMD region as a factor responsible for the observed differential degree of TMD interaction among integrins. When the N-terminal interaction that was missing in integrin α5β1 was restored with mutagenesis, the increase in TMD interaction inhibited the outside-in but not inside-out signaling of integrin α5β1 and also accelerated the speed of cell migration. We suggest, therefore, that the degree of TMD interaction is designed to accommodate the specific, desired function of each integrin.