Computational model for cell migration in three-dimensional matrices

Mechanical deformation and death of circulating tumor cells in the bloodstream

The circulation of tumor cells through the bloodstream is a significant step in tumor metastasis. To better understand the metastatic process, circulating tumor cell (CTC) survival in the circulation must be explored. While immune interactions with CTCs in recent decades have been examined, research has yet to sufficiently explain some CTC behaviors in blood flow. Studies related to CTC mechanical responses in the bloodstream have recently been conducted to further study conditions under which CTCs might die. While experimental methods can assess the mechanical properties and death of CTCs, increasingly sophisticated computational models are being built to simulate the blood flow and CTC mechanical deformation under fluid shear stresses (FSS) in the bloodstream.Several factors contribute to the mechanical deformation and death of CTCs as they circulate. While FSS can damage CTC structure, diverse interactions between CTCs and blood components may either promote or hinder the next metastatic step-extravasation at a remote site. Overall understanding of how these factors influence the deformation and death of CTCs could serve as a basis for future experiments and simulations, enabling researchers to predict CTC death more accurately. Ultimately, these efforts can lead to improved metastasis-specific therapeutics and diagnostics specific in the future.

Comparative analysis of traction forces in normal and glaucomatous trabecular meshwork cells within a 3D, active fluid-structure interaction culture environment

This study presents a 3D in vitro cell culture model, meticulously 3D printed to replicate the conventional aqueous outflow pathway anatomical structure, facilitating the study of trabecular meshwork (TM) cellular responses under glaucomatous conditions. Glaucoma affects TM cell functionality, leading to extracellular matrix (ECM) stiffening, enhanced cell-ECM adhesion, and obstructed aqueous humor outflow. Our model, reconstructed from polyacrylamide gel with elastic moduli of 1.5 and 21.7 kPa, is based on serial block-face scanning electron microscopy images of the outflow pathway. It allows for quantifying 3D, depth-dependent, dynamic traction forces exerted by both normal and glaucomatous TM cells within an active fluid-structure interaction (FSI) environment. In our experimental design, we designed two scenarios: a control group with TM cells observed over 20 hours without flow (static setting), focusing on intrinsic cellular contractile forces, and a second scenario incorporating active FSI to evaluate its impact on traction forces (dynamic setting). Our observations revealed that active FSI results in higher traction forces (normal: 1.83-fold and glaucoma: 2.24-fold) and shear strains (normal: 1.81-fold and glaucoma: 2.41-fold), with stiffer substrates amplifying this effect. Glaucomatous cells consistently exhibited larger forces than normal cells. Increasing gel stiffness led to enhanced stress fiber formation in TM cells, particularly in glaucomatous cells. Exposure to active FSI dramatically altered actin organization in both normal and glaucomatous TM cells, particularly affecting cortical actin stress fiber arrangement. This model while preliminary offers a new method in understanding TM cell biomechanics and ECM stiffening in glaucoma, highlighting the importance of FSI in these processes. STATEMENT OF SIGNIFICANCE: This pioneering project presents an advanced 3D in vitro model, meticulously replicating the human trabecular meshwork's anatomy for glaucoma research. It enables precise quantification of cellular forces in a dynamic fluid-structure interaction, a leap forward from existing 2D models. This advancement promises significant insights into trabecular meshwork cell biomechanics and the stiffening of the extracellular matrix in glaucoma, offering potential pathways for innovative treatments. This research is positioned at the forefront of ocular disease study, with implications that extend to broader biomedical applications.

Dynamic traction force in trabecular meshwork cells: A 2D culture model for normal and glaucomatous states

Glaucoma, which is associated with intraocular pressure (IOP) elevation, results in trabecular meshwork (TM) cellular dysfunction, leading to increased rigidity of the extracellular matrix (ECM), larger adhesion forces between the TM cells and ECM, and higher resistance to aqueous humor drainage. TM cells sense the mechanical forces due to IOP dynamic and apply multidimensional forces on the ECM. Recognizing the importance of cellular forces in modulating various cellular activities and development, this study is aimed to develop a 2D in vitro cell culture model to calculate the 3D, depth-dependent, dynamic traction forces, tensile/compressive/shear strain of the normal and glaucomatous human TM cells within a deformable polyacrylamide (PAM) gel substrate. Normal and glaucomatous human TM cells were isolated, cultured, and seeded on top of the PAM gel substrate with embedded FluoSpheres, spanning elastic moduli of 1.5 to 80 kPa. Sixteen-hour post-seeding live confocal microscopy in an incubator was conducted to Z-stack image the 3D displacement map of the FluoSpheres within the PAM gels. Combined with the known PAM gel stiffness, we ascertained the 3D traction forces in the gel. Our results revealed meaningfully larger traction forces in the glaucomatous TM cells compared to the normal TM cells, reaching depths greater than 10-µm in the PAM gel substrate. Stress fibers in TM cells increased with gel rigidity, but diminished when stiffness rose from 20 to 80 kPa. The developed 2D cell culture model aids in understanding how altered mechanical properties in glaucoma impact TM cell behavior and aqueous humor outflow resistance. STATEMENT OF SIGNIFICANCE: Glaucoma, a leading cause of irreversible blindness, is intricately linked to elevated intraocular pressures and their subsequent cellular effects. The trabecular meshwork plays a pivotal role in this mechanism, particularly its interaction with the extracellular matrix. This research unveils an advanced 2D in vitro cell culture model that intricately maps the complex 3D forces exerted by trabecular meshwork cells on the extracellular matrix, offering unparalleled insights into the cellular biomechanics at play in both healthy and glaucomatous eyes. By discerning the changes in these forces across varying substrate stiffness levels, we bridge the gap in understanding between cellular mechanobiology and the onset of glaucoma. The findings stand as a beacon for potential therapeutic avenues, emphasizing the gravity of cellular/extracellular matrix interactions in glaucoma's pathogenesis and setting the stage for targeted interventions in its early stages.

Mechanical properties, and in vitro biocompatibility assessment of biomimetic dual layered keratin/ hydroxyapatite scaffolds

A novel biomimetic dual layered keratin/hydroxyapatite (keratin/HA) scaffold was designed using iterative freeze-drying technique. The prepared scaffolds were studied using several analytical techniques to better understand the biological, structural, and mechanical properties. The developed multilayered, interconnected, porous keratin scaffold with different hydroxyapatite (HA) content in the outer and inner layer, mimics the inherent gradient structure of alveolar bone. SEM studies showed an interconnected porous architecture of the prepared scaffolds with seamless integration between the upper and lower layers. The incorporation of HA improved the mechanical properties keratin/HA scaffolds. The keratin/HA scaffolds exhibited superior mechanical properties in terms of Young's modulus and compressive strength in comparison to pure keratin scaffolds. The biocompatibility studies suggested that both keratin and keratin/HA scaffolds were cyto-compatible, in terms of cell proliferation. Furthermore, it showed that both the tested materials can served as an ideal substrate for the differentiation of Saos-2 cells, leading to mineralization of the extracellular matrix. In summary, ionic liquid based green technique was employed for keratin extraction to fabricate keratin/HA scaffolds and our detailed in vitro investigations suggest the great potential for these composite scaffolds for bone tissue engineering in future.

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

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

Mechanically primed cells transfer memory to fibrous matrices for invasion across environments of distinct stiffness and dimensionality

Cells sense and migrate across mechanically dissimilar environments throughout development and disease progression. However, it remains unclear whether mechanical memory of past environments empowers cells to navigate new, three-dimensional extracellular matrices. Here, we show that cells previously primed on stiff, compared with soft, matrices generate a higher level of forces to remodel collagen fibers and promote invasion. This priming advantage persists in dense or stiffened collagen. We explain this memory-dependent, cross-environment cell invasion through a lattice-based model wherein stiff-primed cellular forces remodel collagen and minimize energy required for future cell invasion. According to our model, cells transfer their mechanical memory to the matrix via collagen alignment and tension, and this remodeled matrix informs future cell invasion. Thus, memory-laden cells overcome mechanosensing of softer or challenging future environments via a cell-matrix transfer of memory. Consistent with model predictions, depletion of yes-associated protein destabilizes the cellular memory required for collagen remodeling before invasion. We release tension in collagen fibers via laser ablation and disable fiber remodeling by lysyl-oxidase inhibition, both of which disrupt cell-to-matrix transfer of memory and hamper cross-environment invasion. These results have implications for cancer, fibrosis, and aging, where a potential cell-to-matrix transfer of mechanical memory of cells may generate a prolonged cellular response.

Reciprocal intra- and extra-cellular polarity enables deep mechanosensing through layered matrices

Adherent cells migrate on layered tissue interfaces to drive morphogenesis, wound healing, and tumor invasion. Although stiffer surfaces are known to enhance cell migration, it remains unclear whether cells sense basal stiff environments buried under softer, fibrous matrix. Using layered collagen-polyacrylamide gel systems, we unveil a migration phenotype driven by cell-matrix polarity. Here, cancer (but not normal) cells with stiff base matrix generate stable protrusions, faster migration, and greater collagen deformation because of "depth mechanosensing" through the top collagen layer. Cancer cell protrusions with front-rear polarity produce polarized collagen stiffening and deformations. Disruption of either extracellular or intracellular polarity via collagen crosslinking, laser ablation, or Arp2/3 inhibition independently abrogates depth-mechanosensitive migration of cancer cells. Our experimental findings, validated by lattice-based energy minimization modeling, present a cell migration mechanism whereby polarized cellular protrusions and contractility are reciprocated by mechanical extracellular polarity, culminating in a cell-type-dependent ability to mechanosense through matrix layers.

Computational modeling of multiple myeloma interactions with resident bone marrow cells

The interaction of multiple myeloma with bone marrow resident cells plays a key role in tumor progression and the development of drug resistance. The tumor cell response involves contact-mediated and paracrine interactions. The heterogeneity of myeloma cells and bone marrow cells makes it difficult to reproduce this environment in in-vitro experiments. The use of in-silico established tools can help to understand these complex problems. In this article, we present a computational model based on the finite element method to define the interactions of multiple myeloma cells with resident bone marrow cells. This model includes cell migration, which is controlled by stress-strain equilibrium, and cell processes such as proliferation, differentiation, and apoptosis. A series of computational experiments were performed to validate the proposed model. Cell proliferation by the growth factor IGF-1 is studied for different concentrations ranging from 0-10 ng/mL. Cell motility is studied for different concentrations of VEGF and fibronectin in the range of 0-100 ng/mL. Finally, cells were simulated under a combination of IGF-1 and VEGF stimuli whose concentrations are considered to be dependent on the cancer-associated fibroblasts in the extracellular matrix. Results show a good agreement with previous in-vitro results. Multiple myeloma growth and migration are shown to correlate linearly to the IGF-1 stimuli. These stimuli are coupled with the mechanical environment, which also improves cell growth. Moreover, cell migration depends on the fiber and VEGF concentration in the extracellular matrix. Finally, our computational model shows myeloma cells trigger mesenchymal stem cells to differentiate into cancer-associated fibroblasts, in a dose-dependent manner.

Predicting and elucidating the post-printing behavior of 3D printed cancer cells in hydrogel structures by integrating in-vitro and in-silico experiments

A key feature distinguishing 3D bioprinting from other 3D cell culture techniques is its precise control over created structures. This property allows for the high-resolution fabrication of biomimetic structures with controlled structural and mechanical properties such as porosity, permeability, and stiffness. However, analyzing post-printing cellular dynamics and optimizing their functions within the 3D fabricated environment is only possible through trial and error and replicating several experiments. This issue motivated the development of a cellular automata model for the first time to simulate post-printing cell behaviour within the 3D bioprinted construct. To improve our model, we bioprinted a 3D construct using MDA-MB-231 cell-laden hydrogel and evaluated cellular functions, including viability and proliferation in 11 days. The results showed that our model successfully simulated the 3D bioprinted structure and captured in-vitro observations. We demonstrated that in-silico model could predict and elucidate post-printing biological functions for different initial cell numbers in bioink and different bioink formulations with gelatine and alginate, without replicating several costly and time-consuming in-vitro measurements. We believe such a computational framework will substantially impact 3D bioprinting's future application. We hope this study inspires researchers to further realize how an in-silico model might be utilized to advance in-vitro 3D bioprinting research.

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.

Tissue-Wide Effects Override Cell-Intrinsic Gene Function in Radial Neuron Migration

The mammalian neocortex is composed of diverse neuronal and glial cell classes that broadly arrange in six distinct laminae. Cortical layers emerge during development and defects in the developmental programs that orchestrate cortical lamination are associated with neurodevelopmental diseases. The developmental principle of cortical layer formation depends on concerted radial projection neuron migration, from their birthplace to their final target position. Radial migration occurs in defined sequential steps, regulated by a large array of signaling pathways. However, based on genetic loss-of-function experiments, most studies have thus far focused on the role of cell-autonomous gene function. Yet, cortical neuron migration in situ is a complex process and migrating neurons traverse along diverse cellular compartments and environments. The role of tissue-wide properties and genetic state in radial neuron migration is however not clear. Here we utilized mosaic analysis with double markers (MADM) technology to either sparsely or globally delete gene function, followed by quantitative single-cell phenotyping. The MADM-based gene ablation paradigms in combination with computational modeling demonstrated that global tissue-wide effects predominate cell-autonomous gene function albeit in a gene-specific manner. Our results thus suggest that the genetic landscape in a tissue critically affects the overall migration phenotype of individual cortical projection neurons. In a broader context, our findings imply that global tissue-wide effects represent an essential component of the underlying etiology associated with focal malformations of cortical development in particular, and neurological diseases in general.

Deconstructing the role of myosin contractility in force fluctuations within focal adhesions

Force fluctuations exhibited in focal adhesions that connect a cell to its extracellular environment point to the complex role of the underlying machinery that controls cell migration. To elucidate the explicit role of myosin motors in the temporal traction force oscillations, we vary the contractility of these motors in a dynamical model based on the molecular clutch hypothesis. As the contractility is lowered, effected both by changing the motor velocity and the rate of attachment/detachment, we show analytically in an experimentally relevant parameter space, that the system goes from decaying oscillations to stable limit cycle oscillations through a supercritical Hopf bifurcation. As a function of the motor activity and the number of clutches, the system exhibits a rich array of dynamical states. We corroborate our analytical results with stochastic simulations of the motor-clutch system. We obtain limit cycle oscillations in the parameter regime as predicted by our model. The frequency range of oscillations in the average clutch and motor deformation compares well with experimental results.

A 3D Mathematical Model of Coupled Stem Cell-Nutrient Dynamics in Myocardial Regeneration Therapy

Stem cell therapy is a promising treatment for the regeneration of myocardial tissue injured by an ischemic event. Mathematical modeling of myocardial regeneration via stem cell therapy is a challenging task, since the mechanisms underlying the processes involved in the treatment are not yet fully understood. Many aspects must be accounted for, such as the spread of stem cells and nutrients, chemoattraction, cell proliferation, stages of cell maturation, differentiation, angiogenesis, stochastic effects, just to name a few. In this paper we propose a 3D mathematical model with a free boundary that aims to provide a qualitative description of some main aspects of the stem cell regenerative therapy in a simplified scenario. The paper mainly focuses on the description of the shrinking of the necrotic core during treatment. The stem cell and nutrients dynamics are described through coupled reaction-diffusion problems. Proliferation, chemoattraction, tissue regeneration and nutrient consumption are included in the model.

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

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

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.

Mechanics of 3D Cell-Hydrogel Interactions: Experiments, Models, and Mechanisms

Hydrogels are highly water-swollen molecular networks that are ideal platforms to create tissue mimetics owing to their vast and tunable properties. As such, hydrogels are promising cell-delivery vehicles for applications in tissue engineering and have also emerged as an important base for ex vivo models to study healthy and pathophysiological events in a carefully controlled three-dimensional environment. Cells are readily encapsulated in hydrogels resulting in a plethora of biochemical and mechanical communication mechanisms, which recapitulates the natural cell and extracellular matrix interaction in tissues. These interactions are complex, with multiple events that are invariably coupled and spanning multiple length and time scales. To study and identify the underlying mechanisms involved, an integrated experimental and computational approach is ideally needed. This review discusses the state of our knowledge on cell-hydrogel interactions, with a focus on mechanics and transport, and in this context, highlights recent advancements in experiments, mathematical and computational modeling. The review begins with a background on the thermodynamics and physics fundamentals that govern hydrogel mechanics and transport. The review focuses on two main classes of hydrogels, described as semiflexible polymer networks that represent physically cross-linked fibrous hydrogels and flexible polymer networks representing the chemically cross-linked synthetic and natural hydrogels. In this review, we highlight five main cell-hydrogel interactions that involve key cellular functions related to communication, mechanosensing, migration, growth, and tissue deposition and elaboration. For each of these cellular functions, recent experiments and the most up to date modeling strategies are discussed and then followed by a summary of how to tune hydrogel properties to achieve a desired functional cellular outcome. We conclude with a summary linking these advancements and make the case for the need to integrate experiments and modeling to advance our fundamental understanding of cell-matrix interactions that will ultimately help identify new therapeutic approaches and enable successful tissue engineering.

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.

Photocrosslinkable liver extracellular matrix hydrogels for the generation of 3D liver microenvironment models

Liver extracellular matrix (ECM)-based hydrogels have gained considerable interest as biomimetic 3D cell culture environments to investigate the mechanisms of liver pathology, metabolism, and toxicity. The preparation of current liver ECM hydrogels, however, is based on time-consuming thermal gelation and limits the control of mechanical properties. In this study, we used detergent-based protocols to produce decellularized porcine liver ECM, which in turn were solubilized and functionalized with methacrylic anhydride to generate photocrosslinkable methacrylated liver ECM (LivMA) hydrogels. Firstly, we explored the efficacy of two protocols to decellularize porcine liver tissue using varying combinations of commonly used chemical agents such as Triton X-100, Sodium Dodecyl Sulphate (SDS) and Ammonium hydroxide. Then, we demonstrated successful formation of stable, reproducible LivMA hydrogels from both the protocols by photocrosslinking. The LivMA hydrogels obtained from the two decellularization protocols showed distinct mechanical properties. The compressive modulus of the hydrogels was directly dependent on the hydrogel concentration, thereby demonstrating the tuneability of mechanical properties of these hydrogels. Immortalized Human Hepatocytes cells were encapsulated in the LivMA hydrogels and cytocompatibility of the hydrogels was demonstrated after one week of culture. In summary, the LivMA hydrogel system provides a simple, photocrosslinkable platform, which can potentially be used to simulate healthy versus damaged liver for liver disease research, drug studies and cancer metastasis modelling.

A mathematical framework for modelling 3D cell motility: applications to glioblastoma cell migration

The collection of 3D cell tracking data from live images of micro-tissues is a recent innovation made possible due to advances in imaging techniques. As such there is increased interest in studying cell motility in 3D in vitro model systems but a lack of rigorous methodology for analysing the resulting data sets. One such instance of the use of these in vitro models is in the study of cancerous tumours. Growing multicellular tumour spheroids in vitro allows for modelling of the tumour microenvironment and the study of tumour cell behaviours, such as migration, which improves understanding of these cells and in turn could potentially improve cancer treatments. In this paper, we present a workflow for the rigorous analysis of 3D cell tracking data, based on the persistent random walk model, but adaptable to other biologically informed mathematical models. We use statistical measures to assess the fit of the model to the motility data and to estimate model parameters and provide confidence intervals for those parameters, to allow for parametrization of the model taking correlation in the data into account. We use in silico simulations to validate the workflow in 3D before testing our method on cell tracking data taken from in vitro experiments on glioblastoma tumour cells, a brain cancer with a very poor prognosis. The presented approach is intended to be accessible to both modellers and experimentalists alike in that it provides tools for uncovering features of the data set that may suggest amendments to future experiments or modelling attempts.

Enhanced Piezoelectric Fibered Extracellular Matrix to Promote Cardiomyocyte Maturation and Tissue Formation: A 3D Computational Model

Mechanical and electrical stimuli play a key role in tissue formation, guiding cell processes such as cell migration, differentiation, maturation, and apoptosis. Monitoring and controlling these stimuli on in vitro experiments is not straightforward due to the coupling of these different stimuli. In addition, active and reciprocal cell-cell and cell-extracellular matrix interactions are essential to be considered during formation of complex tissue such as myocardial tissue. In this sense, computational models can offer new perspectives and key information on the cell microenvironment. Thus, we present a new computational 3D model, based on the Finite Element Method, where a complex extracellular matrix with piezoelectric properties interacts with cardiac muscle cells during the first steps of tissue formation. This model includes collective behavior and cell processes such as cell migration, maturation, differentiation, proliferation, and apoptosis. The model has employed to study the initial stages of in vitro cardiac aggregate formation, considering cell-cell junctions, under different extracellular matrix configurations. Three different cases have been purposed to evaluate cell behavior in fibered, mechanically stimulated fibered, and mechanically stimulated piezoelectric fibered extra-cellular matrix. In this last case, the cells are guided by the coupling of mechanical and electrical stimuli. Accordingly, the obtained results show the formation of more elongated groups and enhancement in cell proliferation.

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.

A Computational Model for Cardiomyocytes Mechano-Electric Stimulation to Enhance Cardiac Tissue Regeneration

Electrical and mechanical stimulations play a key role in cell biological processes, being essential in processes such as cardiac cell maturation, proliferation, migration, alignment, attachment, and organization of the contractile machinery. However, the mechanisms that trigger these processes are still elusive. The coupling of mechanical and electrical stimuli makes it difficult to abstract conclusions. In this sense, computational models can establish parametric assays with a low economic and time cost to determine the optimal conditions of in-vitro experiments. Here, a computational model has been developed, using the finite element method, to study cardiac cell maturation, proliferation, migration, alignment, and organization in 3D matrices, under mechano-electric stimulation. Different types of electric fields (continuous, pulsating, and alternating) in an intensity range of 50–350 Vm−1, and extracellular matrix with stiffnesses in the range of 10–40 kPa, are studied. In these experiments, the group’s morphology and cell orientation are compared to define the best conditions for cell culture. The obtained results are qualitatively consistent with the bibliography. The electric field orientates the cells and stimulates the formation of elongated groups. Group lengthening is observed when applying higher electric fields in lower stiffness extracellular matrix. Groups with higher aspect ratios can be obtained by electrical stimulation, with better results for alternating electric fields.

Computational estimates of mechanical constraints on cell migration through the extracellular matrix

Cell migration through a three-dimensional (3D) extracellular matrix (ECM) underlies important physiological phenomena and is based on a variety of mechanical strategies depending on the cell type and the properties of the ECM. By using computer simulations of the cell’s mid-plane, we investigate two such migration mechanisms—‘push-pull’ (forming a finger-like protrusion, adhering to an ECM node, and pulling the cell body forward) and ‘rear-squeezing’ (pushing the cell body through the ECM by contracting the cell cortex and ECM at the cell rear). We present a computational model that accounts for both elastic deformation and forces of the ECM, an active cell cortex and nucleus, and for hydrodynamic forces and flow of the extracellular fluid, cytoplasm, and nucleoplasm. We find that relations between three mechanical parameters—the cortex’s contractile force, nuclear elasticity, and ECM rigidity—determine the effectiveness of cell migration through the dense ECM. The cell can migrate persistently even if its cortical contraction cannot deform a near-rigid ECM, but then the contraction of the cortex has to be able to sufficiently deform the nucleus. The cell can also migrate even if it fails to deform a stiff nucleus, but then it has to be able to sufficiently deform the ECM. Simulation results show that nuclear stiffness limits the cell migration more than the ECM rigidity. Simulations show the rear-squeezing mechanism of motility results in more robust migration with larger cell displacements than those with the push-pull mechanism over a range of parameter values. Additionally, results show that the rear-squeezing mechanism is aided by hydrodynamics through a pressure gradient.

Computational simulations of two different mechanisms of 3D cell migration in an extracellular matrix are presented. One mechanism represents a mesenchymal mode, characterized by finger-like actin protrusions, while the second mode is more amoeboid in that rear contraction of the cortex propels the cell forward. In both mechanisms, the cell generates a thin actin protrusion on the cortex that attaches to an ECM node. The cell is then either pulled (mesenchymal) or pushed (amoeboid) forward. Results show both mechanisms result in successful migration over a range of simulated parameter values as long as the contractile tension of the cortex exceeds either the nuclear stiffness or ECM stiffness, but not necessarily both. However, the distance traveled by the amoeboid migration mode is more robust to changes in parameter values, and is larger than in simulations of the mesenchymal mode. Additionally, cells experience a favorable fluid pressure gradient when migrating in the amoeboid mode, and an adverse fluid pressure gradient in the mesenchymal mode.

A computational study of amoeboid motility in 3D: the role of extracellular matrix geometry, cell deformability, and cell-matrix adhesion

Amoeboid cells often migrate using pseudopods, which are membrane protrusions that grow, bifurcate, and retract dynamically, resulting in a net cell displacement. Many cells within the human body, such as immune cells, epithelial cells, and even metastatic cancer cells, can migrate using the amoeboid phenotype. Amoeboid motility is a complex and multiscale process, where cell deformation, biochemistry, and cytosolic and extracellular fluid motions are coupled. Furthermore, the extracellular matrix (ECM) provides a confined, complex, and heterogeneous environment for the cells to navigate through. Amoeboid cells can migrate without significantly remodeling the ECM using weak or no adhesion, instead utilizing their deformability and the microstructure of the ECM to gain enough traction. While a large volume of work exists on cell motility on 2D substrates, amoeboid motility is 3D in nature. Despite recent progress in modeling cellular motility in 3D, there is a lack of systematic evaluations of the role of ECM microstructure, cell deformability, and adhesion on 3D motility. To fill this knowledge gap, here we present a multiscale, multiphysics modeling study of amoeboid motility through 3D-idealized ECM. The model is a coupled fluid‒structure and coarse-grain biochemistry interaction model that accounts for large deformation of cells, pseudopod dynamics, cytoplasmic and extracellular fluid motion, stochastic dynamics of cell-ECM adhesion, and microstructural (pore-scale) geometric details of the ECM. The key finding of the study is that cell deformation and matrix porosity strongly influence amoeboid motility, while weak adhesion and microscale structural details of the ECM have secondary but subtle effects.

Recovery of Tractions Exerted by Single Cells in Three-Dimensional Nonlinear Matrices

Cell-generated tractions play an important role in various physiological and pathological processes such as stem-cell differentiation, cell migration, wound healing, and cancer metastasis. Traction force microscopy (TFM) is a technique for quantifying cellular tractions during cell-matrix interactions. Most applications of this technique have heretofore assumed that the matrix surrounding the cells is linear elastic and undergoes infinitesimal strains, but recent experiments have shown that the traction-induced strains can be large (e.g., more than 50%). In this paper, we propose a novel three-dimensional (3D) TFM approach that consistently accounts for both the geometric nonlinearity introduced by large strains in the matrix, and the material nonlinearity due to strain-stiffening of the matrix. In particular, we pose the TFM problem as a nonlinear inverse hyperelasticity problem in the stressed configuration of the matrix, with the objective of determining the cellular tractions that are consistent with the measured displacement field in the matrix. We formulate the inverse problem as a constrained minimization problem and develop an efficient adjoint-based minimization procedure to solve it. We first validate our approach using simulated data, and quantify its sensitivity to noise. We then employ the new approach to recover tractions exerted by NIH 3T3 cells fully encapsulated in hydrogel matrices of varying stiffness. We find that neglecting nonlinear effects can induce significant errors in traction reconstructions. We also find that cellular tractions roughly increase with gel stiffness, while the strain energy appears to saturate.

CompuCell3D Simulations Reproduce Mesenchymal Cell Migration on Flat Substrates

Mesenchymal cell crawling is a critical process in normal development, in tissue function, and in many diseases. Quantitatively predictive numerical simulations of cell crawling thus have multiple scientific, medical, and technological applications. However, we still lack a low-computational-cost approach to simulate mesenchymal three-dimensional (3D) cell crawling. Here, we develop a computationally tractable 3D model (implemented as a simulation in the CompuCell3D simulation environment) of mesenchymal cells crawling on a two-dimensional substrate. The Fürth equation, the usual characterization of mean-squared displacement (MSD) curves for migrating cells, describes a motion in which, for increasing time intervals, cell movement transitions from a ballistic to a diffusive regime. Recent experiments have shown that for very short time intervals, cells exhibit an additional fast diffusive regime. Our simulations' MSD curves reproduce the three experimentally observed temporal regimes, with fast diffusion for short time intervals, slow diffusion for long time intervals, and intermediate time -interval-ballistic motion. The resulting parameterization of the trajectories for both experiments and simulations allows the definition of time- and length scales that translate between computational and laboratory units. Rescaling by these scales allows direct quantitative comparisons among MSD curves and between velocity autocorrelation functions from experiments and simulations. Although our simulations replicate experimentally observed spontaneous symmetry breaking, short-timescale diffusive motion, and spontaneous cell-motion reorientation, their computational cost is low, allowing their use in multiscale virtual-tissue simulations. Comparisons between experimental and simulated cell motion support the hypothesis that short-time actomyosin dynamics affects longer-time cell motility. The success of the base cell-migration simulation model suggests its future application in more complex situations, including chemotaxis, migration through complex 3D matrices, and collective cell motion.

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.

Development of a tunable method to generate various three-dimensional microstructures by replenishing macromolecules such as extracellular matrix components and polysaccharides

Multicellular spheroids (spheroids) are expected to be a promising approach to mimic in vivo organ functions and cell microenvironments. However, conventional spheroids do not fully consider the existence of extracellular matrices (ECMs). In this study, we developed a tunable method for replenishing macromolecules, including ECM components and polysaccharides, into spheroids without compromising cell viability by injecting a microvolume cell suspension into a high density of methylcellulose dissolved in the culture medium. Adjusting the ECM concentration in the cell suspension enabled the generation of different three-dimensional microstructures, such as "ECM gel capsules", which contained individually separated cells, and "ECM-loaded spheroids", which had thin ECM layers between cells. ECM-loaded spheroids with a 30-fold dilution of Matrigel (0.3 mg/ml) showed significantly higher albumin secretion than control spheroids composed of Hep G2 or HuH-7 cells. Additionally, the expression levels of major CYP genes were decreased in ECM gel capsules with undiluted Matrigel (9 mg/ml) compared to those in control spheroids. However, 0.3 mg/ml Matrigel did not disrupt gene expression. Furthermore, cell polarity associated with tight junction proteins (ZO-1 and Claudin-1) and the transporter protein MRP2 was markedly induced by using 0.3 mg/ml Matrigel. Thus, high-performance three-dimensional tissues fabricated by this method are applicable to increasing the efficiency of drug screening and to regenerative medicine.

Tumor cell-organized fibronectin maintenance of a dormant breast cancer population

Tumors can undergo long periods of dormancy, with cancer cells entering a largely quiescent, nonproliferative state before reactivation and outgrowth. To understand the role of the extracellular matrix (ECM) in regulating tumor dormancy, we created an in vitro cell culture system with carefully controlled ECM substrates to observe entrance into and exit from dormancy with live imaging. We saw that cell populations capable of surviving entrance into long-term dormancy were heterogeneous, containing quiescent, cell cycle-arrested, and actively proliferating cells. Cell populations capable of entering dormancy formed an organized, fibrillar fibronectin matrix via αvβ3 and α5β1 integrin adhesion, ROCK-generated tension, and TGFβ2 stimulation, and cancer cell outgrowth after dormancy required MMP-2-mediated fibronectin degradation. We propose this approach as a useful, in vitro method to study factors important in regulating dormancy, and we used it here to elucidate a role for fibronectin deposition and MMP activation.

ROLE OF OXYGEN CONCENTRATION IN THE OSTEOBLASTS BEHAVIOR: A FINITE ELEMENT MODEL

Oxygen concentration plays a key role in cell survival and viability. Besides, it has important effects on essential cellular biological processes such as cell migration, differentiation, proliferation and apoptosis. Therefore, the prediction of the cellular response to the alterations of the oxygen concentration can help significantly in the advances of cell culture research. Here, we present a 3D computational mechanotactic model to simulate all the previously mentioned cell processes under different oxygen concentrations. With this model, three cases have been studied. Starting with mesenchymal stem cells within an extracellular matrix with mechanical properties suitable for its differentiation into osteoblasts, and under different oxygen conditions to evaluate their behavior under normoxia, hypoxia and anoxia. The obtained results, which are consistent with the experimental observations, indicate that cells tend to migrate toward zones with higher oxygen concentration where they accelerate their differentiation and proliferation. This technique can be employed to control cell migration toward fracture zones to accelerate the healing process. Besides, as expected, to avoid cell apoptosis under conditions of anoxia and to avoid the inhibition of the differentiation and proliferation processes under conditions of hypoxia, the state of normoxia should be maintained throughout the entire cell-culture process.

A mechanobiological model to study upstream cell migration guided by tensotaxis

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

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.

Matrix stiffness-regulated cellular functions under different dimensionalities

The microenvironments that cells encounter with in vitro.

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

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

Are the Effects of Independent Biophysical Factors Linearly Additive? A 3D Tumor Migration Model

Interstitial fluid flow plays a critical role in tumor cell invasion, yet this role has not been explored extensively in combination with other microenvironmental factors. Here, we establish a novel computational model of three-dimensional breast cancer cell migration to unveil the effect of interstitial fluid flow in the dependence of various extracellular matrix (ECM) physical properties. Our model integrates several principal factors: fluid dynamics, autologous chemotaxis, collagen fiber network structure, ECM stiffness, and cell-fiber and cell-flow interaction. First, independently with an aligned collagen fiber network and interstitial fluid flow, this model is validated by successfully reproducing the cell migration patterns. In the model, the interstitial fluid flow leads to directional symmetry breaking of chemotactic migration and synergizes with the ECM orientation to regulate cell migration. This synergy is universal in both the mesenchymal and the amoeboid migration modes, despite the fact that the cell-ECM interaction are different. Consequently, we construct a cell displacement function depending on these factors. Our cell migration model enables three-dimensional cancer migration prediction, mechanism exploration, and inhibition treatment design in a complex tumor microenvironment.

Modeling Cell Migration Mechanics

Cell migration is the physical movement of cells and is responsible for the extensive cellular invasion and metastasis that occur in high-grade tumors. Motivated by decades of direct observation of cell migration via light microscopy, theoretical models have emerged to capture various aspects of the fundamental physical phenomena underlying cell migration. Yet, the motility mechanisms actually used by tumor cells during invasion are still poorly understood, as is the role of cellular interactions with the extracellular environment. In this chapter, we review key physical principles of cytoskeletal self-assembly and force generation, membrane tension, biological adhesion, hydrostatic and osmotic pressures, and their integration in mathematical models of cell migration. With the goal of modeling-driven cancer therapy, we provide examples to guide oncologists and physical scientists in developing next-generation models to predict disease progression and treatment.

Brownian-like deviation of neighboring cells in the early embryogenesis of the zebrafish

We investigate cell trajectories during zebrafish early embryogenesis based on 3D+time photonic microscopy imaging data. To remove the collective flow motion and focus on fluctuations, we analyze the deviations of pairs of neighboring cells. These deviations resemble Brownian motion and reveal different behaviors between pairs containing daughter cells generated by cell division and other pairs of neighboring cells. This observation justifies a common practice of using white noise fluctuations in modeling cell movement.

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.

Recent advances in understanding the complexities of metastasis

Tumour metastasis is a dynamic and systemic process. It is no longer seen as a tumour cell-autonomous program but as a multifaceted and complex series of events, which is influenced by the intrinsic cellular mutational burden of cancer cells and the numerous bidirectional interactions between malignant and non-malignant cells and fine-tuned by the various extrinsic cues of the extracellular matrix. In cancer biology, metastasis as a process is one of the most technically challenging aspects of cancer biology to study. As a result, new platforms and technologies are continually being developed to better understand this process. In this review, we discuss some of the recent advances in metastasis and how the information gleaned is re-shaping our understanding of metastatic dissemination.

Recent advances in understanding the complexities of metastasis

Tumour metastasis is a dynamic and systemic process. It is no longer seen as a tumour cell-autonomous program but as a multifaceted and complex series of events, which is influenced by the intrinsic cellular mutational burden of cancer cells and the numerous bidirectional interactions between malignant and non-malignant cells and fine-tuned by the various extrinsic cues of the extracellular matrix. In cancer biology, metastasis as a process is one of the most technically challenging aspects of cancer biology to study. As a result, new platforms and technologies are continually being developed to better understand this process. In this review, we discuss some of the recent advances in metastasis and how the information gleaned is re-shaping our understanding of metastatic dissemination.

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

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

The Biophysics of 3D Cell Migration

Three-dimensional (3D) cell culture systems have gained increasing interest not only for 3D migration studies but also for their use in drug screening, tissue engineering, and ex vivo modeling of metastatic behavior in the field of cancer biology and morphogenesis in the field of developmental biology. The goal of studying cells in a 3D context is to attempt to more faithfully recapitulate the physiological microenvironment of tissues, including mechanical and structural parameters that we envision will reveal more predictive data for development programs and disease states. In this review, we discuss the pros and cons of several well-characterized 3D cell culture systems for performing 3D migration studies. We discuss the intracellular and extracellular signaling mechanisms that govern cell migration. We also describe the mathematical models and relevant assumptions that can be used to describe 3D cell movement.

Relevant biological processes for tissue development with stem cells and their mechanistic modeling: A review

A potential alternative for tissue transplants is tissue engineering, in which the interaction of cells and biomaterials can be optimized. Tissue development in vitro depends on the complex interaction of several biological processes such as extracellular matrix synthesis, vascularization and cell proliferation, adhesion, migration, death, and differentiation. The complexity of an individual phenomenon or of the combination of these processes can be studied with phenomenological modeling techniques. This work reviews the main biological phenomena in tissue development and their mathematical modeling, focusing on mesenchymal stem cell growth in three-dimensional scaffolds.

Microfluidics in Malignant Glioma Research and Precision Medicine

Glioblastoma multiforme (GBM) is an aggressive form of brain cancer that has no effective treatments and a prognosis of only 12-15 months. Microfluidic technologies deliver microscale control of fluids and cells, and have aided cancer therapy as point-of-care devices for the diagnosis of breast and prostate cancers. However, a few microfluidic devices are developed to study malignant glioma. The ability of these platforms to accurately replicate the complex microenvironmental and extracellular conditions prevailing in the brain and facilitate the measurement of biological phenomena with high resolution and in a high-throughput manner could prove useful for studying glioma progression. These attributes, coupled with their relatively simple fabrication process, make them attractive for use as point-of-care diagnostic devices for detection and treatment of GBM. Here, the current issues that plague GBM research and treatment, as well as the current state of the art in glioma detection and therapy, are reviewed. Finally, opportunities are identified for implementing microfluidic technologies into research and diagnostics to facilitate the rapid detection and better therapeutic targeting of GBM.

Whole Cardiac Tissue Bioscaffolds

Bioscaffolds serve as structures for cells in building complex tissues and full organs including heart. Decellularizing cardiac tissue results in cell-free extracellular matrix (ECM) that can be used as a cardiac tissue bioscaffold. The field of whole-heart tissue engineering has been revolutionized since the 2008 publication of the first perfusion-decellularized whole heart, and since then, studies have shown how decellularized cardiac tissue retains its native architecture and biochemistry following recellularization. Chemical, enzymatic, and physical decellularization methods preserve the ECM to varying degrees with the widely accepted standard of less than 50 ng/mg of double-stranded DNA present in decellularized ECM. Following decellularization, replacement of cells occurs via recellularization: seeding cells into the decellularized ECM structure either via perfusion of cells into the vascular conduits, injection into parenchyma, or a combination of perfusion and injection. Endothelial cells are often perfused through existing vessel conduits to provide an endothelial lining of the vasculature, with cardiomyocytes and other parenchymal cells injected into the myocardium of decellularized ECM bioscaffolds. Uniform cell density and cell retention throughout the bioscaffold still needs to be addressed in larger animal models of the whole heart. Generating the necessary cell numbers and types remains a challenge. Still, recellularized cardiac tissue bioscaffolds offer therapeutic solutions to heart failure, heart valve replacement, and acute myocardial infarction. New technologies allow for decellularized ECM to be bioprinted into cardiac bioscaffolds or formed into a cardiac hydrogel patch. This chapter reviews the advances made in decellularization and recellularization of cardiac ECM bioscaffolds with a discussion of the potential clinical applications of ECM bioscaffolds.

Microenvironmental Stiffness of 3D Polymeric Structures to Study Invasive Rates of Cancer Cells

Cells are highly dynamic elements, continuously interacting with the extracellular environment. Mechanical forces sensed and applied by cells are responsible for cellular adhesion, motility, and deformation, and are heavily involved in determining cancer spreading and metastasis formation. Cell/extracellular matrix interactions are commonly analyzed with the use of hydrogels and 3D microfabricated scaffolds. However, currently available techniques have a limited control over the stiffness of microscaffolds and do not allow for separating environmental properties from biological processes in driving cell mechanical behavior, including nuclear deformability and cell invasiveness. Herein, a new approach is presented to study tumor cell invasiveness by exploiting an innovative class of polymeric scaffolds based on two-photon lithography to control the stiffness of deterministic microenvironments in 3D. This is obtained by fine-tuning of the laser power during the lithography, thus locally modifying both structural and mechanical properties in the same fabrication process. Cage-like structures and cylindric stent-like microscaffolds are fabricated with different Young's modulus and stiffness gradients, allowing obtaining new insights on the mechanical interplay between tumor cells and the surrounding environments. In particular, cell invasion is mostly driven by softer architectures, and the introduction of 3D stiffness "weak spots" is shown to boost the rate at which cancer cells invade the scaffolds. The possibility to modulate structural compliance also allowed estimating the force distribution exerted by a single cell on the scaffold, revealing that both pushing and pulling forces are involved in the cell-structure interaction. Overall, exploiting this method to obtain a wide range of 3D architectures with locally engineered stiffness can pave the way for unique applications to study tumor cell dynamics.

A Novel Computational Model Predicts Key Regulators of Chemokine Gradient Formation in Lymph Nodes and Site-Specific Roles for CCL19 and ACKR4

The chemokine receptor CCR7 drives leukocyte migration into and within lymph nodes (LNs). It is activated by chemokines CCL19 and CCL21, which are scavenged by the atypical chemokine receptor ACKR4. CCR7-dependent navigation is determined by the distribution of extracellular CCL19 and CCL21, which form concentration gradients at specific microanatomical locations. The mechanisms underpinning the establishment and regulation of these gradients are poorly understood. In this article, we have incorporated multiple biochemical processes describing the CCL19–CCL21–CCR7–ACKR4 network into our model of LN fluid flow to establish a computational model to investigate intranodal chemokine gradients. Importantly, the model recapitulates CCL21 gradients observed experimentally in B cell follicles and interfollicular regions, building confidence in its ability to accurately predict intranodal chemokine distribution. Parameter variation analysis indicates that the directionality of these gradients is robust, but their magnitude is sensitive to these key parameters: chemokine production, diffusivity, matrix binding site availability, and CCR7 abundance. The model indicates that lymph flow shapes intranodal CCL21 gradients, and that CCL19 is functionally important at the boundary between B cell follicles and the T cell area. It also predicts that ACKR4 in LNs prevents CCL19/CCL21 accumulation in efferent lymph, but does not control intranodal gradients. Instead, it attributes the disrupted interfollicular CCL21 gradients observed in Ackr4-deficient LNs to ACKR4 loss upstream. Our novel approach has therefore generated new testable hypotheses and alternative interpretations of experimental data. Moreover, it acts as a framework to investigate gradients at other locations, including those that cannot be visualized experimentally or involve other chemokines.