Cell Invasion Dynamics into a Three Dimensional Extracellular Matrix Fibre Network

A biomechanical model for cell sensing and migration

We developed an original computational model for cell deformation and migration capable of accounting for the cell sensitivity to the environment and its appropriate adaptation. This cell model is ultimately intended to be used to address tissue morphogenesis. Hence it has been designed to comply with four requirements: (1) the cell should be able to probe and sense its environment and respond accordingly; (2) the model should be easy to parametrize to adapt to different cell types; (3) the model should be able to extend to 3D cases; (4) simulations should be fast enough to integrate many interacting cells. The simulations carried out focused on two aspects: first, the general behaviour of the cell on a homogeneous substrate, as observed experimentally, for model validation. This enabled us to decipher the mechanisms by which the cell can migrate, highlighting respective influences of the adhesions lifetimes and their sensitivity to traction; second, it predicts the sensitivity of the cell to an anisotropic patterned substrate, in agreement with recently published experiments. The results show that mechanosensors simulated by the model make it possible to reproduce such experiments in terms of migration bias generated by the substrate anisotropy. Here again, the model provides a biomechanical explanation of this phenomenon, depending on cell-matrix interactions and adhesion maturation rate.

Understanding the interplay between extracellular matrix topology and tumor-immune interactions: Challenges and opportunities

Modern cancer management comprises a variety of treatment strategies. Immunotherapy, while successful at treating many cancer subtypes, is often hindered by tumor immune evasion and T cell exhaustion as a result of an immunosuppressive tumor microenvironment (TME). In solid malignancies, the extracellular matrix (ECM) embedded within the TME plays a central role in T cell recognition and cancer growth by providing structural support and regulating cell behavior. Relative to healthy tissues, tumor associated ECM signatures include increased fiber density and alignment. These and other differentiating features contributed to variation in clinically observed tumor-specific ECM configurations, collectively referred to as Tumor-Associated Collagen Signatures (TACS) 1-3. TACS is associated with disease progression and immune evasion. This review explores our current understanding of how ECM geometry influences the behaviors of both immune cells and tumor cells, which in turn impacts treatment efficacy and cancer evolutionary progression. We discuss the effects of ECM remodeling on cancer cells and T cell behavior and review recent in silico models of cancer-immune interactions.

Disulfidptosis decoded: a journey through cell death mysteries, regulatory networks, disease paradigms and future directions

Cell death is an important part of the life cycle, serving as a foundation for both the orderly development and the maintenance of physiological equilibrium within organisms. This process is fundamental, as it eliminates senescent, impaired, or aberrant cells while also promoting tissue regeneration and immunological responses. A novel paradigm of programmed cell death, known as disulfidptosis, has recently emerged in the scientific circle. Disulfidptosis is defined as the accumulation of cystine by cancer cells with high expression of the solute carrier family 7 member 11 (SLC7A11) during glucose starvation. This accumulation causes extensive disulfide linkages between F-actins, resulting in their contraction and subsequent detachment from the cellular membrane, triggering cellular death. The RAC1-WRC axis is involved in this phenomenon. Disulfidptosis sparked growing interest due to its potential applications in a variety of pathologies, particularly oncology, neurodegenerative disorders, and metabolic anomalies. Nonetheless, the complexities of its regulatory pathways remain elusive, and its precise molecular targets have yet to be definitively identified. This manuscript aims to meticulously dissect the historical evolution, molecular underpinnings, regulatory frameworks, and potential implications of disulfidptosis in various disease contexts, illuminating its promise as a groundbreaking therapeutic pathway and target.

Actin-based protrusions at a glance

Actin-based protrusions are at the base of many fundamental cellular processes, such as cell adhesion, migration and intercellular communication. In recent decades, the discovery of new types of actin-based protrusions with unique functions has enriched our comprehension of cellular processes. However, as the repertoire of protrusions continues to expand, the rationale behind the classification of newly identified and previously known structures becomes unclear. Although current nomenclature allows good categorization of protrusions based on their functions, it struggles to distinguish them when it comes to structure, composition or formation mechanisms. In this Cell Science at a Glance article, we discuss the different types of actin-based protrusions, focusing on filopodia, cytonemes and tunneling nanotubes, to help better distinguish and categorize them based on their structural and functional differences and similarities.

Effect of Porous Substrate Topographies on Cell Dynamics: A Computational Study

Controlling cell-substrate interactions via the microstructural characteristics of biomaterials offers an advantageous path for modulating cell dynamics, mechanosensing, and migration, as well as for designing immune-modulating implants, all without the drawbacks of chemical-based triggers. Specifically, recent in vivo studies have suggested that a porous implant's microscale curvature landscape can significantly impact cell behavior and ultimately the immune response. To investigate such cell-substrate interactions, we utilized a 3D computational model incorporating the minimum necessary physics of cell migration and cell-substrate interactions needed to replicate known in vitro behaviors. This model specifically incorporates the effect of membrane tension, which was found to be necessary to replicate in vitro cell behavior on curved surfaces. Our simulated substrates represent two classes of porous materials recently used in implant studies, which have markedly different microscale curvature distributions and pore geometries. We found distinct differences between the overall migration behaviors, shapes, and actin polymerization dynamics of cells interacting with the two substrates. These differences were correlated to the shape energy of the cells as they interacted with the porous substrates, in effect interpreting substrate topography as an energetic landscape interrogated by cells. Our results demonstrate that microscale curvature directly influences cell shape and migration and, therefore, is likely to influence cell behavior. This supports further investigation of the relationship between the surface topography of implanted materials and the characteristic immune response, a complete understanding of which would broadly advance principles of biomaterial design.

Hybrid cellular Potts and bead-spring modeling of cells in fibrous extracellular matrix

The mechanical interaction between cells and the extracellular matrix (ECM) is fundamental to coordinate collective cell behavior in tissues. Relating individual cell-level mechanics to tissue-scale collective behavior is a challenge that cell-based models such as the cellular Potts model (CPM) are well-positioned to address. These models generally represent the ECM with mean-field approaches, which assume substrate homogeneity. This assumption breaks down with fibrous ECM, which has nontrivial structure and mechanics. Here, we extend the CPM with a bead-spring model of ECM fiber networks modeled using molecular dynamics. We model a contractile cell pulling with discrete focal adhesion-like sites on the fiber network and demonstrate agreement with experimental spatiotemporal fiber densification and displacement. We show that at high network cross-linking, contractile cell forces propagate over at least eight cell diameters, decaying with distance with power law exponent n= 0.35 - 0.65 typical of viscoelastic ECMs. Further, we use in silico atomic force microscopy to measure local cell-induced network stiffening consistent with experiments. Our model lays the foundation for investigating how local and long-ranged cell-ECM mechanobiology contributes to multicellular morphogenesis.

Deformability and collision-induced reorientation enhance cell topotaxis in dense microenvironments

In vivo, cells navigate through complex environments filled with obstacles such as other cells and the extracellular matrix. Recently, the term "topotaxis" has been introduced for navigation along topographic cues such as obstacle density gradients. Experimental and mathematical efforts have analyzed topotaxis of single cells in pillared grids with pillar density gradients. A previous model based on active Brownian particles (ABPs) has shown that ABPs perform topotaxis, i.e., drift toward lower pillar densities, due to decreased effective persistence lengths at high pillar densities. The ABP model predicted topotactic drifts of up to 1% of the instantaneous speed, whereas drifts of up to 5% have been observed experimentally. We hypothesized that the discrepancy between the ABP and the experimental observations could be in 1) cell deformability and 2) more complex cell-pillar interactions. Here, we introduce a more detailed model of topotaxis based on the cellular Potts model (CPM). To model persistent cells we use the Act model, which mimics actin-polymerization-driven motility, and a hybrid CPM-ABP model. Model parameters were fitted to simulate the experimentally found motion of Dictyostelium discoideum on a flat surface. For starved D. discoideum, the topotactic drifts predicted by both CPM variants are closer to the experimental results than the previous ABP model due to a larger decrease in persistence length. Furthermore, the Act model outperformed the hybrid model in terms of topotactic efficiency, as it shows a larger reduction in effective persistence time in dense pillar grids. Also pillar adhesion can slow down cells and decrease topotaxis. For slow and less-persistent vegetative D. discoideum cells, both CPMs predicted a similar small topotactic drift. We conclude that deformable cell volume results in higher topotactic drift compared with ABPs, and that feedback of cell-pillar collisions on cell persistence increases drift only in highly persistent cells.

Physical confinement and cell proximity increase cell migration rates and invasiveness: A mathematical model of cancer cell invasion through flexible channels

Cancer cell migration between different body parts is the driving force behind cancer metastasis, which is the main cause of mortality of patients. Migration of cancer cells often proceeds by penetration through narrow cavities in locally stiff, yet flexible tissues. In our previous work, we developed a model for cell geometry evolution during invasion, which we extend here to investigate whether leader and follower (cancer) cells that only interact mechanically can benefit from sequential transmigration through narrow micro-channels and cavities. We consider two cases of cells sequentially migrating through a flexible channel: leader and follower cells being closely adjacent or distant. Using Wilcoxon's signed-rank test on the data collected from Monte Carlo simulations, we conclude that the modelled transmigration speed for the follower cell is significantly larger than for the leader cell when cells are distant, i.e. follower cells transmigrate after the leader has completed the crossing. Furthermore, it appears that there exists an optimum with respect to the width of the channel such that cell moves fastest. On the other hand, in the case of closely adjacent cells, effectively performing collective migration, the leader cell moves 12% faster since the follower cell pushes it. This work shows that mechanical interactions between cells can increase the net transmigration speed of cancer cells, resulting in increased invasiveness. In other words, interaction between cancer cells can accelerate metastatic invasion.

Interplay of adherens junctions and matrix proteolysis determines the invasive pattern and growth of squamous cell carcinoma

Cancers, such as squamous cell carcinoma, frequently invade as multicellular units. However, these invading units can be organised in a variety of ways, ranging from thin discontinuous strands to thick 'pushing' collectives. Here we employ an integrated experimental and computational approach to identify the factors that determine the mode of collective cancer cell invasion. We find that matrix proteolysis is linked to the formation of wide strands but has little effect on the maximum extent of invasion. Cell-cell junctions also favour wide strands, but our analysis also reveals a requirement for cell-cell junctions for efficient invasion in response to uniform directional cues. Unexpectedly, the ability to generate wide invasive strands is coupled to the ability to grow effectively when surrounded by extracellular matrix in three-dimensional assays. Combinatorial perturbation of both matrix proteolysis and cell-cell adhesion demonstrates that the most aggressive cancer behaviour, both in terms of invasion and growth, is achieved at high levels of cell-cell adhesion and high levels of proteolysis. Contrary to expectation, cells with canonical mesenchymal traits - no cell-cell junctions and high proteolysis - exhibit reduced growth and lymph node metastasis. Thus, we conclude that the ability of squamous cell carcinoma cells to invade effectively is also linked to their ability to generate space for proliferation in confined contexts. These data provide an explanation for the apparent advantage of retaining cell-cell junctions in squamous cell carcinomas.

Transzonal projections: Essential structures mediating intercellular communication in the mammalian ovarian follicle

The development of germ cells relies on contact and communication with neighboring somatic cells that provide metabolic support and regulatory signals. In females, contact is achieved through thin cytoplasmic processes that project from follicle cells surrounding the oocyte, extend through an extracellular matrix (ECM) that lies between them, and reach its surface. In mammals, the ECM is termed the zona pellucida and the follicular cell processes are termed transzonal projections (TZPs). TZPs become detectable when the zona pellucida is laid down during early folliculogenesis and subsequently increase in number as oocyte growth progresses. They then rapidly disappear at the time of ovulation, permanently breaking germ-soma contact. Here we review the life cycle and functions of the TZPs. We begin with an overview of the morphology and cytoskeletal structure of TZPs, in the context of actin- and tubulin-based cytoplasmic processes in other cell types. Next, we review the roles played by TZPs in mediating progression through successive stages of oocyte development. We then discuss two mechanisms that may generate TZPs-stretching at pre-existing points of granulosa cell-oocyte contact and elaboration of new processes that push through the zona pellucida-as well as gene products implicated in their formation or function. Finally, we describe the signaling pathways that cause TZPs to be retracted in response to signals that also trigger meiotic maturation and ovulation of the oocyte. The principles and mechanisms that govern TZP behavior may be relevant to understanding communication between physically separated cells in other physiological contexts.

Smart biomaterial platforms: Controlling and being controlled by cells

Across diverse research and application areas, dynamic functionality-such as programmable changes in biochemical property, in mechanical property, or in microscopic or macroscopic architecture-is an increasingly common biomaterials design criterion, joining long-studied criteria such as cytocompatibility and biocompatibility, drug release kinetics, and controlled degradability or long-term stability in vivo. Despite tremendous effort, achieving dynamic functionality while simultaneously maintaining other desired design criteria remains a significant challenge. Reversible dynamic functionality, rather than one-time or one-way dynamic functionality, is of particular interest but has proven especially challenging. Such reversible functionality could enable studies that address the current gap between the dynamic nature of in vivo biological and biomechanical processes, such as cell traction, cell-extracellular matrix (ECM) interactions, and cell-mediated ECM remodeling, and the static nature of the substrates and ECM constructs used to study the processes. This review assesses dynamic materials that have traditionally been used to control cell activity and static biomaterial constructs, experimental and computational techniques, with features that may inform continued advances in reversible dynamic materials. Taken together, this review presents a perspective on combining the reversibility of smart materials and the in-depth dynamic cell behavior probed by static polymers to design smart bi-directional ECM platforms that can reversibly and repeatedly communicate with cells.

In silico framework to inform the design of repair constructs for peripheral nerve injury repair

Peripheral nerve injuries affect millions of people per year and cause loss of sensation and muscle control alongside chronic pain. The most severe injuries are treated through a nerve autograft; however, donor site morbidity and poor outcomes mean alternatives are required. One option is to engineer nerve replacement tissues to provide a supportive microenvironment to encourage nerve regeneration as an alternative to nerve grafts. Currently, progress is hampered due to a lack of consensus on how to arrange materials and cells in space to maximize rate of regeneration. This is compounded by a reliance on experimental testing, which precludes extensive investigations of multiple parameters due to time and cost limitations. Here, a computational framework is proposed to simulate the growth of repairing neurites, captured using a random walk approach and parameterized against literature data. The framework is applied to a specific scenario where the engineered tissue comprises a collagen hydrogel with embedded biomaterial fibres. The size and number of fibres are optimized to maximize neurite regrowth, and the robustness of model predictions is tested through sensitivity analyses. The approach provides an in silico tool to inform the design of engineered replacement tissues, with the opportunity for further development to multi-cue environments.

Modeling and simulation of cell migration on the basis of force equilibrium

To study cell behavior, we developed a cell model to simulate cell movements and the interacting forces among cells and between cells and obstacles. The developed model simulates several cells simultaneously and examines correlations among characteristic parameters between cells and substrates during migration. We modified Odde's model to develop fundamental model, applied Gillespie's stochastic algorithm to design time during in the migration simulation, and employed Keren's membrane theory to analyze the equilibrium at the leading edges. Thus, the proposed model can analyze stresses due to substrate, the intracellular body, and the external interaction between cells and obstacles. Simulation results indicate that cell-cell interaction depends on the equilibrium between the forces at the leading edge of the membrane, namely the cell-substrate interaction force, cell-cell interaction forces, and the cell membrane force. These results also indicate that the migration direction is dependent on the resultant forces. The membrane force and substrate force directions are "low correlation," and the polymerization rate exhibits "little correlative" with the migration direction. We propose a modified cell migration model for simulating allocation and interaction among multiple cells. This model helps indicate the weightings of characteristic parameters that affect the cell migration direction and velocity.

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.

Real-Time Ratiometric Imaging of Micelles Assembly State in a Microfluidic Cancer-on-a-Chip

The performance of supramolecular nanocarriers as drug delivery systems depends on their stability in the complex and dynamic biological media. After administration, nanocarriers are challenged by physiological barriers such as shear stress and proteins present in blood, endothelial wall, extracellular matrix, and eventually cancer cell membrane. While early disassembly will result in a premature drug release, extreme stability of the nanocarriers can lead to poor drug release and low efficiency. Therefore, comprehensive understanding of the stability and assembly state of supramolecular carriers in each stage of delivery is the key factor for the rational design of these systems. One of the main challenges is that current 2D in vitro models do not provide exhaustive information, as they fail to recapitulate the 3D tumor microenvironment. This deficiency in the 2D model complexity is the main reason for the differences observed in vivo when testing the performance of supramolecular nanocarriers. Herein, we present a real-time monitoring study of self-assembled micelles stability and extravasation, combining spectral confocal microscopy and a microfluidic cancer-on-a-chip. The combination of advanced imaging and a reliable 3D model allows tracking of micelle disassembly by following the spectral properties of the amphiphiles in space and time during the crucial steps of drug delivery. The spectrally active micelles were introduced under flow and their position and conformation continuously followed by spectral imaging during the crossing of barriers, revealing the interplay between carrier structure, micellar stability, and extravasation. Integrating the ability of the micelles to change their fluorescent properties when disassembled, spectral confocal imaging and 3D microfluidic tumor blood vessel-on-a-chip resulted in the establishment of a robust testing platform suitable for real-time imaging and evaluation of supramolecular drug delivery carrier's stability.

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.

Modeling multicellular dynamics regulated by extracellular-matrix-mediated mechanical communication via active particles with polarized effective attraction

Collective cell migration is crucial to many physiological and pathological processes such as embryo development, wound healing, and cancer invasion. Recent experimental studies have indicated that the active traction forces generated by migrating cells in a fibrous extracellular matrix (ECM) can mechanically remodel the ECM, giving rise to bundlelike mesostructures bridging individual cells. Such fiber bundles also enable long-range propagation of cellular forces, leading to correlated migration dynamics regulated by the mechanical communication among the cells. Motivated by these experimental discoveries, we develop an active-particle model with polarized effective attractions (APPA) to investigate emergent multicellular migration dynamics resulting from ECM-mediated mechanical communications. In particular, the APPA model generalizes the classic active-Brownian-particle (ABP) model by imposing a pairwise polarized attractive force between the particles, which depends on the instantaneous dynamic states of the particles and mimics the effective mutual pulling between the cells via the fiber bundle bridge. The APPA system exhibits enhanced aggregation behaviors compared to the classic ABP system, and the contrast is more apparent at lower particle densities and higher rotational diffusivities. Importantly, in contrast to the classic ABP system where the particle velocities are not correlated for all particle densities, the high-density phase of the APPA system exhibits strong dynamic correlations, which are characterized by the slowly decaying velocity correlation functions with a correlation length comparable to the linear size of the high-density phase domain (i.e., the cluster of particles). The strongly correlated multicellular dynamics predicted by the APPA model is subsequently verified in in vitro experiments using MCF-10A cells. Our studies indicate the importance of incorporating ECM-mediated mechanical coupling among the migrating cells for appropriately modeling emergent multicellular dynamics in complex microenvironments.

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.

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.

Adhesion modulates cell morphology and migration within dense fibrous networks

One of the most fundamental abilities required for the sustainability of complex life forms is active cell migration, since it is essential in diverse processes from morphogenesis to leukocyte chemotaxis in immune response. The movement of a cell is the result of intricate mechanisms, that involve the coordination between mechanical forces, biochemical regulatory pathways and environmental cues. In particular, epithelial cancer cells have to employ mechanical strategies in order to migrate through the tissue's basement membrane and infiltrate the bloodstream during the invasion stage of metastasis. In this work we explore how mechanical interactions such as spatial restriction and adhesion affect migration of a self-propelled droplet in dense fibrous media. We have performed a systematic analysis using a phase-field model and we propose a novel approach to simulate cell migration with dissipative particle dynamics modelling. With this purpose we have measured in our simulation the cell's velocity and quantified its morphology as a function of the fibre density and of its adhesiveness to the matrix fibres. Furthermore, we have compared our results to a previousin vitromigration assay of fibrosarcoma cells in fibrous matrices. The results show good agreement between the two methodologies and experiments in the literature, which indicates that these minimalist descriptions are able to capture the main features of the system. Our results indicate that adhesiveness is critical for cell migration, by modulating cell morphology in crowded environments and by enhancing cell velocity. In addition, our analysis suggests that matrix metalloproteinases (MMPs) play an important role as adhesiveness modulators. We propose that new assays should be carried out to address the role of adhesion and the effect of different MMPs in cell migration under confined conditions.

Modeling cell migration regulated by cell extracellular-matrix micromechanical coupling

Cell migration in fibrous extracellular matrix (ECM) is crucial to many physiological and pathological processes such as tissue regeneration, immune response, and cancer progression. During migration, individual cells can generate active pulling forces via actomyosin contraction, which are transmitted to the ECM fibers through focal adhesion complexes, remodel the ECM, and eventually propagate to and can be sensed by other cells in the system. The microstructure and physical properties of the ECM can also significantly influence cell migration, e.g., via durotaxis and contact guidance. Here, we develop a computational model for two-dimensional cell migration regulated by cell-ECM micromechanical coupling. Our model explicitly takes into account a variety of cellular-level processes, including focal adhesion formation and disassembly, active traction force generation and cell locomotion due to actin filament contraction, transmission and propagation of tensile forces in the ECM, as well as the resulting ECM remodeling. We validate our model by accurately reproducing single-cell dynamics of MCF-10A breast cancer cells migrating on collagen gels and show that the durotaxis and contact guidance effects naturally arise as a consequence of the cell-ECM micromechanical interactions considered in the model. Moreover, our model predicts strongly correlated multicellular migration dynamics, which are resulted from the ECM-mediated mechanical coupling among the migrating cell and are subsequently verified in in vitro experiments using MCF-10A cells. Our computational model provides a robust tool to investigate emergent collective dynamics of multicellular systems in complex in vivo microenvironment and can be utilized to design in vitro microenvironments to guide collective behaviors and self-organization of cells.

Entamoeba histolytica and Entamoeba dispar: Morphological and Behavioral Differences Induced by Fibronectin through GTPases Activation and Actin-Binding Proteins

Early steps of tissue invasion by Entamoeba histolytica are mediated by adhesion and migration through matrix components such as fibronectin with the participation of the actin cytoskeleton. Striking differences in their produced structures, movement, and migration were found. These observations suggest differential changes in their ability to organize the actin cytoskeleton and, therefore, to modify its morphology after adhesion to fibronectin. To understand these observations, we explore deeper the cytoskeleton pathway of E. histolytica compared to Entamoeba dispar, analyzing the activation and involvement of actin cytoskeleton regulatory proteins such as small GTPases (Rho, Rac1 and Cdc42), myosin IB, paxillin, alpha-actinin, and ARP2/3 during interaction with fibronectin. Results showed a higher activation of Rac1 in E. histolytica compared to E. dispar, while Cdc42 and RhoA were equally activated in both amebae; besides, variations in the amount of myosin IB, paxillin, and ARP2/3 were detected among these species, coinciding and reflected in formation of lamellipodia in E. histolytica and filopodia in E. dispar. These could partially explain the higher invasive capacity of E. histolytica compared to E. dispar, due to its pleomorphic ability, high motility, migration, activation, and abundance of proteins involved in the cytoskeleton arrangement.

The Impact of Elastic Deformations of the Extracellular Matrix on Cell Migration

The mechanical properties of the extracellular matrix, in particular its stiffness, are known to impact cell migration. In this paper, we develop a mathematical model of a single cell migrating on an elastic matrix, which accounts for the deformation of the matrix induced by forces exerted by the cell, and investigate how the stiffness impacts the direction and speed of migration. We model a cell in 1D as a nucleus connected to a number of adhesion sites through elastic springs. The cell migrates by randomly updating the position of its adhesion sites. We start by investigating the case where the cell springs are constant, and then go on to assuming that they depend on the matrix stiffness, on matrices of both uniform stiffness as well as those with a stiffness gradient. We find that the assumption that cell springs depend on the substrate stiffness is necessary and sufficient for an efficient durotactic response. We compare simulations to recent experimental observations of human cancer cells exhibiting durotaxis, which show good qualitative agreement.

The stressful tumour environment drives plasticity of cell migration programmes, contributing to metastasis

Tumours evolve to cope with environmental stresses or challenges such as nutrient starvation, depletion of survival factors, and unbalanced mechanical forces. The uncontrolled growth and aberrant deregulation of core cell homeostatic pathways induced by genetic mutations create an environment of stress. Here, we explore how the adaptations of tumours to the changing environment can drive changes in the motility machinery of cells, affecting migration, invasion, and metastasis. Tumour cells can invade individually or collectively, or they can be extruded out of the surrounding epithelium. These mechanisms are thought to be modifications of normal processes occurring during development or tissue repair. Therefore, tumours may activate these pathways in response to environmental stresses, enabling them to survive in hostile environments and spread to distant sites. © 2020 The Authors. The Journal of Pathology published by John Wiley & Sons Ltd on behalf of Pathological Society of Great Britain and Ireland.

To lead or to herd: optimal strategies for 3D collective migration of cell clusters

Cells migrating in clusters play a significant role in a number of biological processes such as embryogenesis, wound healing, and tumor metastasis during cancer progression. A variety of environmental and biochemical factors can influence the collective migration of cells with differing degrees of cell autonomy and inter-cellular coupling strength. For example, weakly coupled cells can move collectively under the influence of contact guidance from neighboring cells or the environment. Alternatively strongly coupled cells might follow one or more leader cells to move as a single cohesive unit. Additionally, chemical and mechanical signaling between these cells may alter the degree of coupling and determine effective cluster sizes. Being able to understand this collective cell migration process is critical in the prediction and manipulation of outcomes of key biological processes. Here we focus on understanding how various environmental and cellular factors influence small clusters of cells migrating collectively within a 3D fibrous matrix. We combine existing knowledge of single-cell migration in 2D and 3D environments, prior experimental observations of cell-cell interactions and collective migration, and a newly developed stochastic model of cell migration in 3D matrices, to simulate the migration of cell clusters in different physiologically relevant environments. Our results show that based on the extracellular environment and the strength of cell-cell mechanical coupling, two distinct optimal approaches to driving collective cell migration emerge. The ability to effectively employ these two distinct migration strategies might be critical for cells to collectively migrate through the heterogeneous tissue environments within the body.

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.

Multi-cell ECM compaction is predictable via superposition of nonlinear cell dynamics linearized in augmented state space

Cells interacting through an extracellular matrix (ECM) exhibit emergent behaviors resulting from collective intercellular interaction. In wound healing and tissue development, characteristic compaction of ECM gel is induced by multiple cells that generate tensions in the ECM fibers and coordinate their actions with other cells. Computational prediction of collective cell-ECM interaction based on first principles is highly complex especially as the number of cells increase. Here, we introduce a computationally-efficient method for predicting nonlinear behaviors of multiple cells interacting mechanically through a 3-D ECM fiber network. The key enabling technique is superposition of single cell computational models to predict multicellular behaviors. While cell-ECM interactions are highly nonlinear, they can be linearized accurately with a unique method, termed Dual-Faceted Linearization. This method recasts the original nonlinear dynamics in an augmented space where the system behaves more linearly. The independent state variables are augmented by combining auxiliary variables that inform nonlinear elements involved in the system. This computational method involves a) expressing the original nonlinear state equations with two sets of linear dynamic equations b) reducing the order of the augmented linear system via principal component analysis and c) superposing individual single cell-ECM dynamics to predict collective behaviors of multiple cells. The method is computationally efficient compared to original nonlinear dynamic simulation and accurate compared to traditional Taylor expansion linearization. Furthermore, we reproduce reported experimental results of multi-cell induced ECM compaction.

Collective behaviors of multiple cells interacting through an ECM are prohibitively complex to predict with a mechanistic computational model due to its highly nonlinear dynamics and high dimensional space. We introduce a methodology where nonlinear dynamics of single cells are superposed to predict collective multi-cellular behaviors through a developed linearization method. We represent nonlinear single cell dynamics with linear state equations by augmenting the independent state variables with a set of auxiliary variables. We then transform the linear augmented state equations to a low-dimensional latent model and superpose the linear latent models of individual cells to predict collective behaviors that emerge from multi-cellular interactions. The method successfully reproduced experimental results of cell-induced ECM compaction.

Contribution of nascent cohesive fiber-fiber interactions to the non-linear elasticity of fibrin networks under tensile load

Fibrin is a viscoelastic proteinaceous polymer that determines the deformability and integrity of blood clots and fibrin-based biomaterials in response to biomechanical forces. Here, a previously unnoticed structural mechanism of fibrin clots' mechanical response to external tensile loads is tested using high-resolution confocal microscopy and recently developed three-dimensional computational model. This mechanism, underlying local strain-stiffening of individual fibers as well as global stiffening of the entire network, is based on previously neglected nascent cohesive pairwise interactions between individual fibers (crisscrossing) in fibrin networks formed under tensile load. Existence of fiber-fiber crisscrossings of reoriented fibers was confirmed using 3D imaging of experimentally obtained stretched fibrin clots. The computational model enabled us to study structural details and quantify mechanical effects of the fiber-fiber cohesive crisscrossing during stretching of fibrin gels at various spatial scales. The contribution of the fiber-fiber cohesive contacts to the elasticity of stretched fibrin networks was characterized by changes in individual fiber stiffness, the length, width, and alignment of fibers, as well as connectivity and density of the entire network. The results show that the nascent cohesive crisscrossing of fibers in stretched fibrin networks comprise an underappreciated important structural mechanism underlying the mechanical response of fibrin to (patho)physiological stresses that determine the course and outcomes of thrombotic and hemostatic disorders, such as heart attack and ischemic stroke. STATEMENT OF SIGNIFICANCE: Fibrin is a viscoelastic proteinaceous polymer that determines the deformability and integrity of blood clots and fibrin-based biomaterials in response to biomechanical forces. In this paper, a novel structural mechanism of fibrin clots' mechanical response to external tensile loads is tested using high-resolution confocal microscopy and newly developed computational model. This mechanism, underlying local strain-stiffening of individual fibers as well as global stiffening of the entire network, is based on previously neglected nascent cohesive pairwise interactions between individual fibers (crisscrossing) in fibrin networks formed under tensile load. Cohesive crisscrossing is an important structural mechanism that influences the mechanical response of blood clots and which can determine the outcomes of blood coagulation disorders, such as heart attacks and strokes.

Five-dimensional two-photon volumetric microscopy of in-vivo dynamic activities using liquid lens remote focusing

Multi-photon scanning microscopy provides a robust tool for optical sectioning, which can be used to capture fast biological events such as blood flow, mitochondrial activity, and neuronal action potentials. For many studies, it is important to visualize several different focal planes at a rate akin to the biological event frequency. Typically, a microscope is equipped with mechanical elements to move either the sample or the objective lens to capture volumetric information, but these strategies are limited due to their slow speeds or inertial artifacts. To overcome this problem, remote focusing methods have been developed to shift the focal plane axially without physical movement of the sample or the microscope. Among these methods is liquid lens technology, which adjusts the focus of the lens by changing the wettability of the liquid and hence its curvature. Liquid lenses are inexpensive active optical elements that have the potential for fast multi-photon volumetric imaging, hence a promising and accessible approach for the study of biological systems with complex dynamics. Although remote focusing using liquid lens technology can be used for volumetric point scanning multi-photon microscopy, optical aberrations and the effects of high energy laser pulses have been concerns in its implementation. In this paper, we characterize a liquid lens and validate its use in relevant biological applications. We measured optical aberrations that are caused by the liquid lens, and calculated its response time, defocus hysteresis, and thermal response to a pulsed laser. We applied this method of remote focusing for imaging and measurement of multiple in-vivo specimens, including mesenchymal stem cell dynamics, mouse tibialis anterior muscle mitochondrial electrical potential fluctuations, and mouse brain neural activity. Our system produces 5 dimensional (x,y,z,λ,t) data sets at the speed of 4.2 volumes per second over volumes as large as 160 x 160 x 35 µm³.

Mathematical modelling of cell migration: stiffness dependent jump rates result in durotaxis

Durotaxis, the phenomena where cells migrate up a gradient in substrate stiffness, remains poorly understood. It has been proposed that durotaxis results from the reinforcement of focal adhesions on stiff substrates. In this paper we formulate a mathematical model of single cell migration on elastic substrates with spatially varying stiffness. We develop a stochastic model where the cell moves by updating the position of its adhesion sites at random times, and the rate of updates is determined by the local stiffness of the substrate. We investigate two physiologically motivated mechanisms of stiffness sensing. From the stochastic model of single cell migration we derive a population level description in the form of a partial differential equation for the time evolution of the density of cells. The equation is an advection–diffusion equation, where the advective velocity is proportional to the stiffness gradient. The model shows quantitative agreement with experimental results in which cells tend to cluster when seeded on a matrix with periodically varying stiffness.

Modelling actin polymerization: the effect on confined cell migration

The aim of this work is to model cell motility under conditions of mechanical confinement. This cell migration mode may occur in extravasation of tumour and neutrophil-like cells. Cell migration is the result of the complex action of different forces exerted by the interplay between myosin contractility forces and actin processes. Here, we propose and implement a finite element model of the confined migration of a single cell. In this model, we consider the effects of actin and myosin in cell motility. Both filament and globular actin are modelled. We model the cell considering cytoplasm and nucleus with different mechanical properties. The migration speed in the simulation is around 0.1 μm/min, which is in agreement with existing literature. From our simulation, we observe that the nucleus size has an important role in cell migration inside the channel. In the simulation the cell moves further when the nucleus is smaller. However, this speed is less sensitive to nucleus stiffness. The results show that the cell displacement is lower when the nucleus is stiffer. The degree of adhesion between the channel walls and the cell is also very important in confined migration. We observe an increment of cell velocity when the friction coefficient is higher.

Extracellular matrix remodelling induced by alternating electrical and mechanical stimulations increases the contraction of engineered skeletal muscle tissues

Engineered skeletal muscles are inferior to natural muscles in terms of contractile force, hampering their potential use in practical applications. One major limitation is that the extracellular matrix (ECM) not only impedes the contraction but also ineffectively transmits the forces generated by myotubes to the load. In the present study, ECM remodelling improves contractile force in a short time, and a coordinated, combined electrical and mechanical stimulation induces the desired ECM remodelling. Notably, the application of single and combined stimulations to the engineered muscles remodels the structure of their ECM networks, which determines the mechanical properties of the ECM. Myotubes in the tissues are connected in parallel and in series to the ECM. The stiffness of the parallel ECM must be low not to impede contraction, while the stiffness of the serial ECM must be high to transmit the forces to the load. Both the experimental results and the mechanistic model suggest that the combined stimulation through coordination reorients the ECM fibres in such a way that the parallel ECM stiffness is reduced, while the serial ECM stiffness is increased. In particular, 3 and 20 minutes of alternating electrical and mechanical stimulations increase the force by 18% and 31%, respectively.

A stochastic algorithm for accurately predicting path persistence of cells migrating in 3D matrix environments

Cell mobility plays a critical role in immune response, wound healing, and the rate of cancer metastasis and tumor progression. Mobility within a three-dimensional (3D) matrix environment can be characterized by the average velocity of cell migration and the persistence length of the path it follows. Computational models that aim to predict cell migration within such 3D environments need to be able predict both of these properties as a function of the various cellular and extra-cellular factors that influence the migration process. A large number of models have been developed to predict the velocity of cell migration driven by cellular protrusions in 3D environments. However, prediction of the persistence of a cell's path is a more tedious matter, as it requires simulating cells for a long time while they migrate through the model extra-cellular matrix (ECM). This can be a computationally expensive process, and only recently have there been attempts to quantify cell persistence as a function of key cellular or matrix properties. Here, we propose a new stochastic algorithm that can simulate and analyze 3D cell migration occurring over days with a computation time of minutes, opening new possibilities of testing and predicting long-term cell migration behavior as a function of a large variety of cell and matrix properties. In this model, the matrix elements are generated as needed and stochastically based on the biophysical and biochemical properties of the ECM the cell migrates through. This approach significantly reduces the computational resources required to track and calculate cell matrix interactions. Using this algorithm, we predict the effect of various cellular and matrix properties such as cell polarity, cell mechanoactivity, matrix fiber density, matrix stiffness, fiber alignment, and fiber binding site density on path persistence of cellular migration and the mean squared displacement of cells over long periods of time.

A coupled approach for fluid saturated poroelastic media and immersed solids for modeling cell-tissue interactions

In this paper, we propose a finite element-based immersed method to treat the mechanical coupling between a deformable porous medium model (PM) and an immersed solid model (ISM). The PM is formulated as a homogenized, volume-coupled two-field model, comprising a nearly incompressible solid phase that interacts with an incompressible Darcy-Brinkman flow. The fluid phase is formulated with respect to the Lagrangian finite element mesh, following the solid phase deformation. The ISM is discretized with an independent Lagrangian mesh and may behave arbitrarily complex (it may, eg, be compressible, grow, and perform active deformations). We model two distinct types of interactions, namely, (1) the immersed fluid-structure interaction (FSI) between the ISM and the fluid phase in the PM and (2) the immersed structure-structure interaction (SSI) between the ISM and the solid phase in the PM. Within each time step, we solve both FSI and SSI, employing strongly coupled partitioned schemes. This novel finite element method establishes a main building block of an evolving computational framework for modeling and simulating complex biomechanical problems, with focus on key phenomena during cell migration. Cell movement is strongly influenced by mechanical interactions between the cell body and the surrounding tissue, ie, the extracellular matrix (ECM). In this context, the PM represents the ECM, ie, a fibrous scaffold of structural proteins interacting with interstitial flow, and the ISM represents the cell body. The FSI models the influence of fluid drag, and the SSI models the force transmission between cell and ECM at adhesions sites.

Integration of in vitro and in silico Models Using Bayesian Optimization With an Application to Stochastic Modeling of Mesenchymal 3D Cell Migration

Cellular migration plays a crucial role in many aspects of life and development. In this paper, we propose a computational model of 3D migration that is solved by means of the tau-leaping algorithm and whose parameters have been calibrated using Bayesian optimization. Our main focus is two-fold: to optimize the numerical performance of the mechano-chemical model as well as to automate the calibration process of in silico models using Bayesian optimization. The presented mechano-chemical model allows us to simulate the stochastic behavior of our chemically reacting system in combination with mechanical constraints due to the surrounding collagen-based matrix. This numerical model has been used to simulate fibroblast migration. Moreover, we have performed in vitro analysis of migrating fibroblasts embedded in 3D collagen-based fibrous matrices (2 mg/ml). These in vitro experiments have been performed with the main objective of calibrating our model. Nine model parameters have been calibrated testing 300 different parametrizations using a completely automatic approach. Two competing evaluation metrics based on the Bhattacharyya coefficient have been defined in order to fit the model parameters. These metrics evaluate how accurately the in silico model is replicating in vitro measurements regarding the two main variables quantified in the experimental data (number of protrusions and the length of the longest protrusion). The selection of an optimal parametrization is based on the balance between the defined evaluation metrics. Results show how the calibrated model is able to predict the main features observed in the in vitro experiments.

Novel proteins that regulate cell extension formation in fibroblasts

Cell extensions are critical structures that enable matrix remodeling in wound healing and cancer invasion but the regulation of their formation is not well-defined. We searched for new proteins that mediated cell extension formation over collagen by tandem mass tagged mass spectrometry analysis of purified extensions in 3T3 fibroblasts. Unexpectedly, importin-5, ENH isoform 1b (PDLIM5) and 26 S protease regulatory subunit 6B (PSMC4) were more abundant (> 10-fold) in membrane-penetrating cell extensions than cell bodies, which was confirmed by immunostaining and immunoblotting and also observed in human gingival fibroblasts. After siRNA knockdown of these proteins and plating cells on grid-supported floating collagen gels for 6 h, formation of cell extensions and collagen remodeling were examined. Knockdown of importin-5 reduced collagen compaction (1.9-fold), pericellular collagen degradation (~ 1.8-fold) and number of cell extensions (~ 69%). Knockdown of PSMC4 reduced collagen compaction (~ 1.5-fold), pericellular collagen degradation (~ 1.7-fold) and number of cell extensions (~ 42%). Knockdown of PDLIM5 reduced collagen compaction (~ 1.6-fold) and number of cell extensions (~ 21%). Inhibition of the TGF-β RI kinase, Smad3 or ROCK-II signaling pathways reduced the abundance of PDLIM5 in cell extensions but PSMC4 and importin-5 were reduced only by Smad3 or ROCK-II inhibitors. We conclude that these novel proteins are required for cell extension formation and their recruitment into extensions involves the Smad3 and ROCK signaling pathways.

Computational modeling of three-dimensional ECM-rigidity sensing to guide directed cell migration

Filopodia have a key role in sensing both chemical and mechanical cues in surrounding extracellular matrix (ECM). However, quantitative understanding is still missing in the filopodial mechanosensing of local ECM stiffness, resulting from dynamic interactions between filopodia and the surrounding 3D ECM fibers. Here we present a method for characterizing the stiffness of ECM that is sensed by filopodia based on the theory of elasticity and discrete ECM fiber. We have applied this method to a filopodial mechanosensing model for predicting directed cell migration toward stiffer ECM. This model provides us with a distribution of force and displacement as well as their time rate of changes near the tip of a filopodium when it is bound to the surrounding ECM fibers. Aggregating these effects in each local region of 3D ECM, we express the local ECM stiffness sensed by the cell and explain polarity in the cellular durotaxis mechanism.

Mechanoreciprocity in cell migration

Cell migration is an adaptive process that depends on and responds to physical and molecular triggers. Moving cells sense and respond to tissue mechanics and induce transient or permanent tissue modifications, including extracellular matrix stiffening, compression and deformation, protein unfolding, proteolytic remodelling and jamming transitions. Here we discuss how the bi-directional relationship of cell-tissue interactions (mechanoreciprocity) allows cells to change position and contributes to single-cell and collective movement, structural and molecular tissue organization, and cell fate decisions.

A model for cell migration in non-isotropic fibrin networks with an application to pancreatic tumor islets

Cell migration, known as an orchestrated movement of cells, is crucially important for wound healing, tumor growth, immune response as well as other biomedical processes. This paper presents a cell-based model to describe cell migration in non-isotropic fibrin networks around pancreatic tumor islets. This migration is determined by the mechanical strain energy density as well as cytokines-driven chemotaxis. Cell displacement is modeled by solving a large system of ordinary stochastic differential equations where the stochastic parts result from random walk. The stochastic differential equations are solved by the use of the classical Euler–Maruyama method. In this paper, the influence of anisotropic stromal extracellular matrix in pancreatic tumor islets on T-lymphocytes migration in different immune systems is investigated. As a result, tumor peripheral stromal extracellular matrix impedes the immune response of T-lymphocytes through changing direction of their migration.

A cytoskeletal clutch mediates cellular force transmission in a soft, three-dimensional extracellular matrix

The ability of cells to impart forces and deformations on their surroundings underlies cell migration and extracellular matrix (ECM) remodeling and is thus an essential aspect of complex, metazoan life. Previous work has resulted in a refined understanding, commonly termed the molecular clutch model, of how cells adhering to flat surfaces such as a microscope coverslip transmit cytoskeletally generated forces to their surroundings. Comparatively less is known about how cells adhere to and exert forces in soft, three-dimensional (3D), and structurally heterogeneous ECM environments such as occur in vivo. We used time-lapse 3D imaging and quantitative image analysis to determine how the actin cytoskeleton is mechanically coupled to the surrounding matrix for primary dermal fibroblasts embedded in a 3D fibrin matrix. Under these circumstances, the cytoskeletal architecture is dominated by contractile actin bundles attached at their ends to large, stable, integrin-based adhesions. Time-lapse imaging reveals that α-actinin-1 puncta within actomyosin bundles move more quickly than the paxillin-rich adhesion plaques, which in turn move more quickly than the local matrix, an observation reminiscent of the molecular clutch model. However, closer examination did not reveal a continuous rearward flow of the actin cytoskeleton over slower moving adhesions. Instead, we found that a subset of stress fibers continuously elongated at their attachment points to integrin adhesions, providing stable, yet structurally dynamic coupling to the ECM. Analytical modeling and numerical simulation provide a plausible physical explanation for this result and support a picture in which cells respond to the effective stiffness of local matrix attachment points. The resulting dynamic equilibrium can explain how cells maintain stable, contractile connections to discrete points within ECM during cell migration, and provides a plausible means by which fibroblasts contract provisional matrices during wound healing.

A biochemo-mechano coupled, computational model combining membrane transport and pericellular proteolysis in tissue mechanics

We present a computational model for the interaction of surface- and volume-bound scalar transport and reaction processes with a deformable porous medium. The application in mind is pericellular proteolysis, i.e. the dissolution of the solid phase of the extracellular matrix (ECM) as a response to the activation of certain chemical species at the cell membrane and in the vicinity of the cell. A poroelastic medium model represents the extra cellular scaffold and the interstitial fluid flow, while a surface-bound transport model accounts for the diffusion and reaction of membrane-bound chemical species. By further modelling the volume-bound transport, we consider the advection, diffusion and reaction of sequestered chemical species within the extracellular scaffold. The chemo-mechanical coupling is established by introducing a continuum formulation for the interplay of reaction rates and the mechanical state of the ECM. It is based on known experimental insights and theoretical work on the thermodynamics of porous media and degradation kinetics of collagen fibres on the one hand and a damage-like effect of the fibre dissolution on the mechanical integrity of the ECM on the other hand. The resulting system of partial differential equations is solved via the finite-element method. To the best of our knowledge, it is the first computational model including contemporaneously the coupling between (i) advection-diffusion-reaction processes, (ii) interstitial flow and deformation of a porous medium, and (iii) the chemo-mechanical interaction impelled by the dissolution of the ECM. Our numerical examples show good agreement with experimental data. Furthermore, we outline the capability of the methodology to extend existing numerical approaches towards a more comprehensive model for cellular biochemo-mechanics.

Modeling the two-way feedback between contractility and matrix realignment reveals a nonlinear mode of cancer cell invasion

Cancer cell invasion from primary tumors is mediated by a complex interplay between cellular adhesions, actomyosin-driven contractility, and the physical characteristics of the extracellular matrix (ECM). Here, we incorporate a mechanochemical free-energy-based approach to elucidate how the two-way feedback loop between cell contractility (induced by the activity of chemomechanical interactions such as Ca2+ and Rho signaling pathways) and matrix fiber realignment and strain stiffening enables the cells to polarize and develop contractile forces to break free from the tumor spheroids and invade into the ECM. Interestingly, through this computational model, we are able to identify a critical stiffness that is required by the matrix to break intercellular adhesions and initiate cell invasion. Also, by considering the kinetics of the cell movement, our model predicts a biphasic invasiveness with respect to the stiffness of the matrix. These predictions are validated by analyzing the invasion of melanoma cells in collagen matrices of varying concentration. Our model also predicts a positive correlation between the elongated morphology of the invading cells and the alignment of fibers in the matrix, suggesting that cell polarization is directly proportional to the stiffness and alignment of the matrix. In contrast, cells in nonfibrous matrices are found to be rounded and not polarized, underscoring the key role played by the nonlinear mechanics of fibrous matrices. Importantly, our model shows that mechanical principles mediated by the contractility of the cells and the nonlinearity of the ECM behavior play a crucial role in determining the phenotype of the cell invasion.

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.

Quantitative evaluation of single cell spread on collagen matrices

Cells change their morphology as a response to environmental cues. The quantitative evaluation of single cell spread on extracellular matrices, such as type I collagen, is a key tool in cancer research. Inherent to the manual scoring of cellular spread is inter-observer but also intra-observer variation. To overcome these problems, we have developed the Morphology Analysis Software (MAS). MAS scores phase-contrast images of cells on native type I collagen gels and identifies whether a cell has a spread or round morphology using a combination of four unique parameters: the presence of a cellular extension, the cell area, the cell eccentricity and cell circularity. The MAS software scores are equivalent to the average score of five independent observers but MAS is faster, more objective and standardized. A functional screening assay using six cytokines identified TGFα as a stimulator of HCT8/E11 and SK-BR-3 single cell spreading on top of type I collagen gels. This change in morphology correlates with increased migration potential as evidenced by xCELLigence migration assays and are counteracted by EGFR signaling pathway inhibitors. This underscores the use of morphology classification on a population of unlabeled cells as read-out of an important cancer cell property and the potential for the MAS software in drug screening strategies.

Cell-ECM Interactions in Tumor Invasion

The cancer cells obtain their invasion potential not only by genetic mutations, but also by changing their cellular biophysical and biomechanical features and adapting to the surrounding microenvironments. The extracellular matrix, as a crucial component of the tumor microenvironment, provides the mechanical support for the tissue, mediates the cell-microenvironment interactions, and plays a key role in cancer cell invasion. The biomechanics of the extracellular matrix, particularly collagen, have been extensively studied in the biomechanics community. Cell migration has also enjoyed much attention from both the experimental and modeling efforts. However, the detailed mechanistic understanding of tumor cell-ECM interactions, especially during cancer invasion, has been unclear. This chapter reviews the recent advances in the studies of ECM biomechanics, cell migration, and cell-ECM interactions in the context of cancer invasion.

Modeling cell adhesion and proliferation: a cellular-automata based approach

BACKGROUND

Cell adhesion is a process that involves the interaction between the cell membrane and another surface, either a cell or a substrate. Unlike experimental tests, computer models can simulate processes and study the result of experiments in a shorter time and lower costs. One of the tools used to simulate biological processes is the cellular automata, which is a dynamic system that is discrete both in space and time.

METHOD

This work describes a computer model based on cellular automata for the adhesion process and cell proliferation to predict the behavior of a cell population in suspension and adhered to a substrate. The values of the simulated system were obtained through experimental tests on fibroblast monolayer cultures.

RESULTS

The results allow us to estimate the cells settling time in culture as well as the adhesion and proliferation time. The change in the cells morphology as the adhesion over the contact surface progress was also observed. The formation of the initial link between cell and the substrate of the adhesion was observed after 100 min where the cell on the substrate retains its spherical morphology during the simulation. The cellular automata model developed is, however, a simplified representation of the steps in the adhesion process and the subsequent proliferation.

CONCLUSION

A combined framework of experimental and computational simulation based on cellular automata was proposed to represent the fibroblast adhesion on substrates and changes in a macro-scale observed in the cell during the adhesion process. The approach showed to be simple and efficient.