Cell elongation is key to in silico replication of in vitro vasculogenesis and subsequent remodeling

Simulation of Soluble and Bound VEGF-stimulated in vitro Capillary-like Network Formation on Deformed Substrate

Capillary plexus cultivation is crucial in tissue engineering and regenerative medicine. Theoretical simulations have been conducted to supplement the expensive experimental works. However, the mechanisms connecting mechanical and chemical stimuli remained undefined, and the functions of the different VEGF forms in the culture environment were still unclear. In this paper, we developed a hybrid model for simulating short-term in vitro capillary incubations. We used the Cellular Potts model to predict individual cell migration, morphology change, and continuum mechanics to quantify biogel deformation and VEGF transport dynamics. By bridging the mechanical regulation and chemical stimulation in the model, the results showed good agreement between the predicted network topology and experiments, in which elongated cells connected, forming the network cords and round cells gathered, creating cobblestone-like aggregates. The results revealed that the capillary-like networks could develop in high integrity only when the mechanical and chemical couplings worked adequately, with the cell morphology and haptotaxis driven by the soluble and bound forms of VEGF, respectively, functioning simultaneously.

Neuraminidase inhibition promotes the collective migration of neurons and recovery of brain function

In the injured brain, new neurons produced from endogenous neural stem cells form chains and migrate to injured areas and contribute to the regeneration of lost neurons. However, this endogenous regenerative capacity of the brain has not yet been leveraged for the treatment of brain injury. Here, we show that in healthy brain chains of migrating new neurons maintain unexpectedly large non-adherent areas between neighboring cells, allowing for efficient migration. In instances of brain injury, neuraminidase reduces polysialic acid levels, which negatively regulates adhesion, leading to increased cell-cell adhesion and reduced migration efficiency. The administration of zanamivir, a neuraminidase inhibitor used for influenza treatment, promotes neuronal migration toward damaged regions, fosters neuronal regeneration, and facilitates functional recovery. Together, these findings shed light on a new mechanism governing efficient neuronal migration in the adult brain under physiological conditions, pinpoint the disruption of this mechanism during brain injury, and propose a promising therapeutic avenue for brain injury through drug repositioning.

Endothelial Response to the Combined Biomechanics of Vessel Stiffness and Shear Stress Is Regulated via Piezo1

How endothelial cells sense and respond to dynamic changes in their biophysical surroundings as we age is not fully understood. Vascular stiffness is clearly a contributing factor not only in several cardiovascular diseases but also in physiological processes such as aging and vascular dementia. To address this gap, we utilized a microfluidic model to explore how substrate stiffness in the presence of shear stress affects endothelial morphology, senescence, proliferation, and inflammation. We also studied the role of mechanosensitive ion channel Piezo1 in endothelial responses under the combined effect of shear stress and substrate stiffness. To do so, we cultured endothelial cells inside microfluidic channels covered with fibronectin-coated elastomer with elastic moduli of 40 and 200 kPa, respectively, mimicking the stiffness of the vessel walls in young and aged arteries. The endothelial cells were exposed to atheroprotective and atherogenic shear stress levels of 10 and 2 dyn/cm2, respectively. Our findings show that substrate stiffness affects senescence under atheroprotective flow conditions and cytoskeleton remodeling, senescence, and inflammation under atherogenic flow conditions. Additionally, we found that the expression of Piezo1 plays a crucial role in endothelial adaptation to flow and regulation of inflammation under both atheroprotective and atherogenic shear stress levels. However, Piezo1 contribution to endothelial senescence was limited to the soft substrate and atheroprotective shear stress level. Overall, our study characterizes the response of endothelial cells to the combined effect of shear stress and substrate stiffness and reveals a previously unidentified role of Piezo1 in endothelial response to vessel stiffening, which potentially can be therapeutically targeted to alleviate endothelial dysfunction in aging adults.

A three-dimensional model with two-body interactions for endothelial cells in angiogenesis

We introduce a three-dimensional mathematical model for the dynamics of vascular endothelial cells during sprouting angiogenesis. Angiogenesis is the biological process by which new blood vessels form from existing ones. It has been the subject of numerous theoretical models. These models have successfully replicated various aspects of angiogenesis. Recent studies using particle-based models have highlighted the significant influence of cell shape on network formation, with elongated cells contributing to the formation of branching structures. While most mathematical models are two-dimensional, we aim to investigate whether ellipsoids also form branch-like structures and how their shape affects the pattern. In our model, the shape of a vascular endothelial cell is represented as a spheroid, and a discrete dynamical system is constructed based on the simple assumption of two-body interactions. Numerical simulations demonstrate that our model reproduces the patterns of elongation and branching observed in the early stages of angiogenesis. We show that the pattern formation of the cell population is strongly dependent on the cell shape. Finally, we demonstrate that our current mathematical model reproduces the cell behaviours, specifically cell-mixing, observed in sprouts.

Self-organized and directed branching results in optimal coverage in developing dermal lymphatic networks

Branching morphogenesis is a ubiquitous process that gives rise to high exchange surfaces in the vasculature and epithelial organs. Lymphatic capillaries form branched networks, which play a key role in the circulation of tissue fluid and immune cells. Although mouse models and correlative patient data indicate that the lymphatic capillary density directly correlates with functional output, i.e., tissue fluid drainage and trafficking efficiency of dendritic cells, the mechanisms ensuring efficient tissue coverage remain poorly understood. Here, we use the mouse ear pinna lymphatic vessel network as a model system and combine lineage-tracing, genetic perturbations, whole-organ reconstructions and theoretical modeling to show that the dermal lymphatic capillaries tile space in an optimal, space-filling manner. This coverage is achieved by two complementary mechanisms: initial tissue invasion provides a non-optimal global scaffold via self-organized branching morphogenesis, while VEGF-C dependent side-branching from existing capillaries rapidly optimizes local coverage by directionally targeting low-density regions. With these two ingredients, we show that a minimal biophysical model can reproduce quantitatively whole-network reconstructions, across development and perturbations. Our results show that lymphatic capillary networks can exploit local self-organizing mechanisms to achieve tissue-scale optimization.

Tumor-mediated immunosuppression and cytokine spreading affects the relation between EMT and PD-L1 status

Epithelial-mesenchymal transition (EMT) and immune resistance mediated by Programmed Death-Ligand 1 (PD-L1) upregulation are established drivers of tumor progression. Their bi-directional crosstalk has been proposed to facilitate tumor immunoevasion, yet the impact of immunosuppression and spatial heterogeneity on the interplay between these processes remains to be characterized. Here we study the role of these factors using mathematical and spatial models. We first designed models incorporating immunosuppressive effects on T cells mediated via PD-L1 and the EMT-inducing cytokine Transforming Growth Factor beta (TGFβ). Our models predict that PD-L1-mediated immunosuppression merely reduces the difference in PD-L1 levels between EMT states, while TGFβ-mediated suppression also causes PD-L1 expression to correlate negatively with TGFβ within each EMT phenotype. We subsequently embedded the models in multi-scale spatial simulations to explicitly describe heterogeneity in cytokine levels and intratumoral heterogeneity. Our multi-scale models show that Interferon gamma (IFNγ)-induced partial EMT of a tumor cell subpopulation can provide some, albeit limited protection to bystander tumor cells. Moreover, our simulations show that the true relationship between EMT status and PD-L1 expression may be hidden at the population level, highlighting the importance of studying EMT and PD-L1 status at the single-cell level. Our findings deepen the understanding of the interactions between EMT and the immune response, which is crucial for developing novel diagnostics and therapeutics for cancer patients.

Pattern formation of elliptic particles by two-body interactions: A model for dynamics of endothelial cells in angiogenesis

A two-dimensional mathematical model for dynamics of endothelial cells in angiogenesis is investigated. Angiogenesis is a morphogenic process in which new blood vessels emerge from an existing vascular network. Recently a one-dimensional discrete dynamical model has been proposed to reproduce elongation, bifurcation, and cell motility such as cell-mixing during angiogenesis on the assumption of a simple two-body interaction between endothelial cells. The present model is its two-dimensional extension, where endothelial cells are represented as the ellipses with the two-body interactions: repulsive interaction due to excluded volume effect, attractive interaction through pseudopodia and rotation by contact. We show that the oblateness of ellipses and the magnitude of contact rotation significantly affect the shape of created vascular patterns and elongation of branches.

Density-Dependent Migration Characteristics of Cancer Cells Driven by Pseudopod Interaction

The ability of cancer cells to invade neighboring tissue from primary tumors is an important determinant of metastatic behavior. Quantification of cell migration characteristics such as migration speed and persistence helps to understand the requirements for such invasiveness. One factor that may influence invasion is how local tumor cell density shapes cell migration characteristics, which we here investigate with a combined experimental and computational modeling approach. First, we generated and analyzed time-lapse imaging data on two aggressive Triple-Negative Breast Cancer (TNBC) cell lines, HCC38 and Hs578T, during 2D migration assays at various cell densities. HCC38 cells exhibited a counter-intuitive increase in speed and persistence with increasing density, whereas Hs578T did not exhibit such an increase. Moreover, HCC38 cells exhibited strong cluster formation with active pseudopod-driven migration, especially at low densities, whereas Hs578T cells maintained a dispersed positioning. In order to obtain a mechanistic understanding of the density-dependent cell migration characteristics and cluster formation, we developed realistic spatial simulations using a Cellular Potts Model (CPM) with an explicit description of pseudopod dynamics. Model analysis demonstrated that pseudopods exerting a pulling force on the cell and interacting via increased adhesion at pseudopod tips could explain the experimentally observed increase in speed and persistence with increasing density in HCC38 cells. Thus, the density-dependent migratory behavior could be an emergent property of single-cell characteristics without the need for additional mechanisms. This implies that pseudopod dynamics and interaction may play a role in the aggressive nature of cancers through mediating dispersal.

Thermodynamic Signatures of Structural Transitions and Dissociation of Charged Colloidal Clusters: A Parallel Tempering Monte Carlo Study

Computational simulation of colloidal systems make use of empirical interaction potentials that are founded in well-established theory. In this work, we have performed parallel tempering Monte Carlo (PTMC) simulations to calculate heat capacity and to assess structural transitions, which may occur in charged colloidal clusters whose effective interactions are described by a sum of pair potentials with attractive short-range and repulsive long-range components. Previous studies on these systems have shown that the global minimum structure varies from spherical-type shapes for small-size clusters to Bernal spiral and “beaded-necklace” shapes at intermediate and larger sizes, respectively. In order to study both structural transitions and dissociation, we have organized the structures appearing in the PTMC calculations by three sets according to their energy: (i) low-energy structures, including the global minimum; (ii) intermediate-energy “beaded-necklace” motifs; (iii) high-energy linear and branched structures that characterize the dissociative clusters. We observe that, depending on the cluster, either peaks or shoulders on the heat–capacity curve constitute thermodynamics signatures of dissociation and structural transitions. The dissociation occurs at T=0.20 for all studied clusters and it is characterized by the appearance of a significant number of linear structures, while the structural transitions corresponding to unrolling the Bernal spiral are quite dependent on the size of the colloidal system.

Extracellular matrix in cancer progression and therapy

The tumor ecosystem with heterogeneous cellular compositions and the tumor microenvironment has increasingly become the focus of cancer research in recent years. The extracellular matrix (ECM), the major component of the tumor microenvironment, and its interactions with the tumor cells and stromal cells have also enjoyed tremendously increased attention. Like the other components of the tumor microenvironment, the ECM in solid tumors differs significantly from that in normal organs and tissues. We review recent studies of the complex roles the tumor ECM plays in cancer progression, from tumor initiation, growth to angiogenesis and invasion. We highlight that the biomolecular, biophysical, and mechanochemical interactions between the ECM and cells not only regulate the steps of cancer progression, but also affect the efficacy of systemic cancer treatment. We further discuss the strategies to target and modify the tumor ECM to improve cancer therapy.

A novel nonlocal partial differential equation model of endothelial progenitor cell cluster formation during the early stages of vasculogenesis

The formation of new vascular networks is essential for tissue development and regeneration, in addition to playing a key role in pathological settings such as ischemia and tumour development. Experimental findings in the past two decades have led to the identification of a new mechanism of neovascularisation, known as cluster-based vasculogenesis, during which endothelial progenitor cells (EPCs) mobilised from the bone marrow are capable of bridging distant vascular beds in a variety of hypoxic settings in vivo. This process is characterised by the formation of EPC clusters during its early stages and, while much progress has been made in identifying various mechanisms underlying cluster formation, we are still far from a comprehensive description of such spatio-temporal dynamics. In order to achieve this, we propose a novel mathematical model of the early stages of cluster-based vasculogenesis, comprising of a system of nonlocal partial differential equations including key mechanisms such as endogenous chemotaxis, matrix degradation, cell proliferation and cell-to-cell adhesion. We conduct a linear stability analysis on the system and solve the equations numerically. We then conduct a parametric analysis of the numerical solutions of the one-dimensional problem to investigate the role of underlying dynamics on the speed of cluster formation and the size of clusters, measured via appropriate metrics for the cluster width and compactness. We verify the key results of the parametric analysis with simulations of the two-dimensional problem. Our results, which qualitatively compare with data from in vitro experiments, elucidate the complementary role played by endogenous chemotaxis and matrix degradation in the formation of clusters, suggesting chemotaxis is responsible for the cluster topology while matrix degradation is responsible for the speed of cluster formation. Our results also indicate that the nonlocal cell-to-cell adhesion term in our model, even though it initially causes cells to aggregate, is not sufficient to ensure clusters are stable over long time periods. Consequently, new modelling strategies for cell-to-cell adhesion are required to stabilise in silico clusters. We end the paper with a thorough discussion of promising, fruitful future modelling and experimental research perspectives.

New Heterocyclic Combretastatin A-4 Analogs: Synthesis and Biological Activity of Styryl-2(3H)-benzothiazolones

Here, we describe the synthesis, characterization, and biological activities of a series of 26 new styryl-2(3H)-benzothiazolone analogs of combretastatin-A4 (CA-4). The cytotoxic activities of these compounds were tested in several cell lines (EA.hy926, A549, BEAS-2B, MDA-MB-231, HT-29, MCF-7, and MCF-10A), and the relations between structure and cytotoxicity are discussed. From the series, compound (Z)-3-methyl-6-(3,4,5-trimethoxystyryl)-2(3H)-benzothiazolone (26Z) exhibits the most potent cytotoxic activity (IC50 0.13 ± 0.01 µM) against EA.hy926 cells. 26Z not only inhibits vasculogenesis but also disrupts pre-existing vasculature. 26Z is a microtubule-modulating agent and inhibits a spectrum of angiogenic events in EA.hy926 cells by interfering with endothelial cell invasion, migration, and proliferation. 26Z also shows anti-proliferative activity in CA-4 resistant cells with the following IC50 values: HT-29 (0.008 ± 0.001 µM), MDA-MB-231 (1.35 ± 0.42 µM), and MCF-7 (2.42 ± 0.48 µM). Cell-cycle phase-specific experiments show that 26Z treatment results in G2/M arrest and mitotic spindle multipolarity, suggesting that drug-induced centrosome amplification could promote cell death. Some 26Z-treated adherent cells undergo aberrant cytokinesis, resulting in aneuploidy that perhaps contributes to drug-induced cell death. These data indicate that spindle multipolarity induction by 26Z has an exciting chemotherapeutic potential that merits further investigation.

The environment topography alters the way to multicellularity in Myxococcus xanthus

The social soil-dwelling bacterium Myxococcus xanthus can form multicellular structures, known as fruiting bodies. Experiments in homogeneous environments have shown that this process is affected by the physicochemical properties of the substrate, but they have largely neglected the role of complex topographies. We experimentally demonstrate that the topography alters single-cell motility and multicellular organization in M. xanthus In topographies realized by randomly placing silica particles over agar plates, we observe that the cells' interaction with particles drastically modifies the dynamics of cellular aggregation, leading to changes in the number, size, and shape of the fruiting bodies and even to arresting their formation in certain conditions. We further explore this type of cell-particle interaction in a computational model. These results provide fundamental insights into how the environment topography influences the emergence of complex multicellular structures from single cells, which is a fundamental problem of biological, ecological, and medical relevance.

The canonical smooth muscle cell marker TAGLN is present in endothelial cells and is involved in angiogenesis

Elongation of vascular endothelial cells (ECs) is an important process in angiogenesis; however, the molecular mechanisms remain unknown. The actin-crosslinking protein TAGLN (transgelin, also known as SM22 or SM22α) is abundantly expressed in smooth muscle cells (SMCs) and is widely used as a canonical marker for this cell type. In the course of studies using mouse embryonic stem cells (ESCs) carrying an Tagln promoter-driven fluorescence marker, we noticed activation of the Tagln promoter during EC elongation. Tagln promoter activation co-occurred with EC elongation in response to vascular endothelial growth factor A (VEGF-A). Inhibition of phosphoinositide 3-kinase (PI3K)-Akt signaling and mTORC1 also induced EC elongation and Tagln promoter activation. Human umbilical vein endothelial cells (HUVECs) elongated, activated the TAGLN promoter and increased TAGLN transcripts in an angiogenesis model. Genetic disruption of TAGLN augmented angiogenic behaviors of HUVECs, as did the disruption of TAGLN2 and TAGLN3 genes. Tagln expression was found in ECs in mouse embryos. Our results identify TAGLN as a putative regulator of angiogenesis whose expression is activated in elongating ECs. This finding provides insight into the cytoskeletal regulation of EC elongation and an improved understanding of the molecular mechanisms underlying the regulation of angiogenesis.

Enhanced persistence and collective migration in cooperatively aligning cell clusters

Most cells possess the capacity to locomote. Alone or collectively, this allows them to adapt, to rearrange, and to explore their surroundings. The biophysical characterization of such motile processes, in health and in disease, has so far focused mostly on two limiting cases: single-cell motility on the one hand and the dynamics of confluent tissues such as the epithelium on the other. The in-between regime of clusters, composed of relatively few cells moving as a coherent unit, has received less attention. Such small clusters are, however, deeply relevant in development but also in cancer metastasis. In this work, we use cellular Potts models and analytical active matter theory to understand how the motility of small cell clusters changes with N, the number of cells in the cluster. Modeling and theory reveal our two main findings: cluster persistence time increases with N, whereas the intrinsic diffusivity decreases with N. We discuss a number of settings in which the motile properties of more complex clusters can be analytically understood, revealing that the focusing effects of small-scale cooperation and cell-cell alignment can overcome the increased bulkiness and internal disorder of multicellular clusters to enhance overall migrational efficacy. We demonstrate this enhancement for small-cluster collective durotaxis, which is shown to proceed more effectively than for single cells. Our results may provide some novel, to our knowledge, insights into the connection between single-cell and large-scale collective motion and may point the way to the biophysical origins of the enhanced metastatic potential of small tumor cell clusters.

Heterogeneity in 2,6-Linked Sialic Acids Potentiates Invasion of Breast Cancer Epithelia

Heterogeneity in phenotypes of malignantly transformed cells and aberrant glycan expression on their surface are two prominent hallmarks of cancers that have hitherto not been linked to each other. In this paper, we identify differential levels of a specific glycan linkage: α2,6-linked sialic acids within breast cancer cells in vivo and in culture. Upon sorting out two populations with moderate, and relatively higher, cell surface α2,6-linked sialic acid levels from the triple-negative breast cancer cell line MDA-MB-231, both populations (denoted as medium and high 2,6-Sial cells, respectively) stably retained their levels in early passages. Upon continuous culturing, medium 2,6-Sial cells recapitulated the heterogeneity of the unsorted line whereas high 2,6-Sial cells showed no such tendency. Compared with high 2,6-Sial cells, the medium 2,6-Sial counterparts showed greater adhesion to reconstituted extracellular matrices (ECMs) and invaded faster as single cells. The level of α2,6-linked sialic acids in the two sublines was found to be consistent with the expression of a specific glycosyl transferase, ST6GAL1. Stably knocking down ST6GAL1 in the high 2,6-Sial cells enhanced their invasiveness. When cultured together, medium 2,6-Sial cells differentially migrated to the edge of growing tumoroid-like cocultures, whereas high 2,6-Sial cells formed the central bulk. Multiscale simulations in a Cellular Potts model-based computational environment calibrated to our experimental findings suggest that differential levels of cell-ECM adhesion, likely regulated by α2,6-linked sialic acids, facilitate niches of highly invasive cells to efficiently migrate centrifugally as the invasive front of a malignant breast tumor.

Integrating Quantitative Assays with Biologically Based Mathematical Modeling for Predictive Oncology

We provide an overview on the use of biological assays to calibrate and initialize mechanism-based models of cancer phenomena. Although artificial intelligence methods currently dominate the landscape in computational oncology, mathematical models that seek to explicitly incorporate biological mechanisms into their formalism are of increasing interest. These models can guide experimental design and provide insights into the underlying mechanisms of cancer progression. Historically, these models have included a myriad of parameters that have been difficult to quantify in biologically relevant systems, limiting their practical insights. Recently, however, there has been much interest calibrating biologically based models with the quantitative measurements available from (for example) RNA sequencing, time-resolved microscopy, and in vivo imaging. In this contribution, we summarize how a variety of experimental methods quantify tumor characteristics from the molecular to tissue scales and describe how such data can be directly integrated with mechanism-based models to improve predictions of tumor growth and treatment response.

Roles of Remote and Contact Forces in Epithelial Cell Structure Formation

Cancer cells collectively form a large-scale structure for their growth. In this article, we report that HeLa cells, epithelial-like human cervical cancer cells, aggressively migrate on Matrigel and form a large-scale structure in a cell-density-dependent manner. To explain the experimental results, we develop a simple model in which cells interact and migrate using the two fundamentally different types of force, remote and contact forces, and show how cells form a large-scale structure. We demonstrate that the simple model reproduces experimental observations, suggesting that the remote and contact forces considered in this work play a major role in large-scale structure formation of HeLa cells. This article provides important evidence that cancer cells form a large-scale structure and develops an understanding into the poorly understood mechanisms of their structure formation.

Mechanisms of endothelial cell coverage by pericytes: computational modelling of cell wrapping and in vitro experiments

Pericytes (PCs) wrap around endothelial cells (ECs) and perform diverse functions in physiological and pathological processes. Although molecular interactions between ECs and PCs have been extensively studied, the morphological processes at the cellular level and their underlying mechanisms have remained elusive. In this study, using a simple cellular Potts model, we explored the mechanisms for EC wrapping by PCs. Based on the observed in vitro cell wrapping in three-dimensional PC-EC coculture, the model identified four putative contributing factors: preferential adhesion of PCs to the extracellular matrix (ECM), strong cell-cell adhesion, PC surface softness and larger PC size. While cell-cell adhesion can contribute to the prevention of cell segregation and the degree of cell wrapping, it cannot determine the orientation of cell wrapping alone. While atomic force microscopy revealed that PCs have a larger Young's modulus than ECs, the experimental analyses supported preferential ECM adhesion and size asymmetry. We also formulated the corresponding energy minimization problem and numerically solved this problem for specific cases. These results give biological insights into the role of PC-ECM adhesion in PC coverage. The modelling framework presented here should also be applicable to other cell wrapping phenomena observed in vivo.

Notch signaling and taxis mechanisms regulate early stage angiogenesis: A mathematical and computational model

During angiogenesis, new blood vessels sprout and grow from existing ones. This process plays a crucial role in organ development and repair, in wound healing and in numerous pathological processes such as cancer progression or diabetes. Here, we present a mathematical model of early stage angiogenesis that permits exploration of the relative importance of mechanical, chemical and cellular cues. Endothelial cells proliferate and move over an extracellular matrix by following external gradients of Vessel Endothelial Growth Factor, adhesion and stiffness, which are incorporated to a Cellular Potts model with a finite element description of elasticity. The dynamics of Notch signaling involving Delta-4 and Jagged-1 ligands determines tip cell selection and vessel branching. Through their production rates, competing Jagged-Notch and Delta-Notch dynamics determine the influence of lateral inhibition and lateral induction on the selection of cellular phenotypes, branching of blood vessels, anastomosis (fusion of blood vessels) and angiogenesis velocity. Anastomosis may be favored or impeded depending on the mechanical configuration of strain vectors in the ECM near tip cells. Numerical simulations demonstrate that increasing Jagged production results in pathological vasculatures with thinner and more abundant vessels, which can be compensated by augmenting the production of Delta ligands.

Angiogenesis is the process by which new blood vessels grow from existing ones. This process plays a crucial role in organ development, in wound healing and in numerous pathological processes such as cancer growth or in diabetes. Angiogenesis is a complex, multi-step and well regulated process where biochemistry and physics are intertwined. The process entails signaling in vessel cells being driven by both chemical and mechanical mechanisms that result in vascular cell movement, deformation and proliferation. Mathematical models have the ability to bring together these mechanisms in order to explore their relative relevance in vessel growth. Here, we present a mathematical model of early stage angiogenesis that is able to explore the role of biochemical signaling and tissue mechanics. We use this model to unravel the regulating role of Jagged, Notch and Delta dynamics in vascular cells. These membrane proteins have an important part in determining the leading cell in each neo-vascular sprout. Numerical simulations demonstrate that increasing Jagged production results in pathological vasculatures with thinner and more abundant vessels, which can be compensated by augmenting the production of Delta ligands.

Colloidal Gels for Guiding Endothelial Cell Organization via Microstructural Morphology

One of the fundamental challenges in vascular morphogenesis is to understand how the microstructural morphology of a 3D matrix can provide the spatial cues to organize the endothelial cells (ECs) into specific vascular structures. Colloidal gels can provide well-controlled distinct morphological matrices because these gels are formed by the aggregation of particles. By altering the aggregation mode, the spatial organization of the particles can be controlled to yield different microstructural morphology. To demonstrate this, colloidal aggregates and gels were developed by electrostatic interaction-mediated aggregation of cationic polyurethane (PU) colloidal particles by using low molecular weight electrolyte and polyelectrolyte to develop microstructurally different colloidal gels without altering their bulk elasticity. Compact dense colloidal aggregates with constricted voids were developed via electrolyte-mediated aggregation, whereas stranded branched networks with interconnected voids were formed via polyelectrolyte-mediated bridging interactions. Results show that the microstructure of aggregated colloids and gels can regulate EC organizations. Within endothelial matrices, ECs track the microstructure of particulate phase to interconnect with stranded colloidal network but cluster around compact colloidal aggregate. Similarly, in colloidal gels, ECs formed capillary-like structures by interconnecting along the stranded networks with enhanced cell-matrix interactions and increased cell extension but aggregated within the constricted voids of compact dense gel with enhanced cell-cell interaction. Both morphometric analysis and expression of EC markers corroborated the cell organizations in these gels. Using these colloidal gels, we demonstrated the role of 3D microstructural morphology as an important regulator for spatial guidance of ECs and simultaneously established the significance of colloidal gels as 3D matrix to regulate cellular morphogenesis.

Adapting a Plant Tissue Model to Animal Development: Introducing Cell Sliding into VirtualLeaf

Cell-based, mathematical modeling of collective cell behavior has become a prominent tool in developmental biology. Cell-based models represent individual cells as single particles or as sets of interconnected particles and predict the collective cell behavior that follows from a set of interaction rules. In particular, vertex-based models are a popular tool for studying the mechanics of confluent, epithelial cell layers. They represent the junctions between three (or sometimes more) cells in confluent tissues as point particles, connected using structural elements that represent the cell boundaries. A disadvantage of these models is that cell-cell interfaces are represented as straight lines. This is a suitable simplification for epithelial tissues, where the interfaces are typically under tension, but this simplification may not be appropriate for mesenchymal tissues or tissues that are under compression, such that the cell-cell boundaries can buckle. In this paper, we introduce a variant of VMs in which this and two other limitations of VMs have been resolved. The new model can also be seen as on off-the-lattice generalization of the Cellular Potts Model. It is an extension of the open-source package VirtualLeaf, which was initially developed to simulate plant tissue morphogenesis where cells do not move relative to one another. The present extension of VirtualLeaf introduces a new rule for cell-cell shear or sliding, from which cell rearrangement (T1) and cell extrusion (T2) transitions emerge naturally, allowing the application of VirtualLeaf to problems of animal development. We show that the updated VirtualLeaf yields different results than the traditional vertex-based models for differential adhesion-driven cell sorting and for the neighborhood topology of soft cellular networks.

Experimental and computational analyses reveal that environmental restrictions shape HIV-1 spread in 3D cultures

Pathogens face varying microenvironments in vivo, but suitable experimental systems and analysis tools to dissect how three-dimensional (3D) tissue environments impact pathogen spread are lacking. Here we develop an Integrative method to Study Pathogen spread by Experiment and Computation within Tissue-like 3D cultures (INSPECT-3D), combining quantification of pathogen replication with imaging to study single-cell and cell population dynamics. We apply INSPECT-3D to analyze HIV-1 spread between primary human CD4 T-lymphocytes using collagen as tissue-like 3D-scaffold. Measurements of virus replication, infectivity, diffusion, cellular motility and interactions are combined by mathematical analyses into an integrated spatial infection model to estimate parameters governing HIV-1 spread. This reveals that environmental restrictions limit infection by cell-free virions but promote cell-associated HIV-1 transmission. Experimental validation identifies cell motility and density as essential determinants of efficacy and mode of HIV-1 spread in 3D. INSPECT-3D represents an adaptable method for quantitative time-resolved analyses of 3D pathogen spread.

Here, using an integrative experimental and computational approach, Imle et al. show how cell motility and density affect HIV cell-associated transmission in a three-dimensional tissue-like culture system of CD4⁺ T cells and collagen, and how different collagen matrices restrict infection by cell-free virions.

Agent-based modeling of morphogenetic systems: Advantages and challenges

The complexity of morphogenesis poses a fundamental challenge to understanding the mechanisms governing the formation of biological patterns and structures. Over the past century, numerous processes have been identified as critically contributing to morphogenetic events, but the interplay between the various components and aspects of pattern formation have been much harder to grasp. The combination of traditional biology with mathematical and computational methods has had a profound effect on our current understanding of morphogenesis and led to significant insights and advancements in the field. In particular, the theoretical concepts of reaction–diffusion systems and positional information, proposed by Alan Turing and Lewis Wolpert, respectively, dramatically influenced our general view of morphogenesis, although typically in isolation from one another. In recent years, agent-based modeling has been emerging as a consolidation and implementation of the two theories within a single framework. Agent-based models (ABMs) are unique in their ability to integrate combinations of heterogeneous processes and investigate their respective dynamics, especially in the context of spatial phenomena. In this review, we highlight the benefits and technical challenges associated with ABMs as tools for examining morphogenetic events. These models display unparalleled flexibility for studying various morphogenetic phenomena at multiple levels and have the important advantage of informing future experimental work, including the targeted engineering of tissues and organs.

Putting VE-cadherin into JAIL for junction remodeling

Junction dynamics of endothelial cells are based on the integration of signal transduction, cytoskeletal remodeling and contraction, which are necessary for the formation and maintenance of monolayer integrity, but also enable repair and regeneration. The VE-cadherin–catenin complex forms the molecular basis of the adherence junctions and cooperates closely with actin filaments. Several groups have recently described small actin-driven protrusions at the cell junctions that are controlled by the Arp2/3 complex, contributing to cell junction regulation. We identified these protrusions as the driving force for VE-cadherin dynamics, as they directly induce new VE-cadherin-mediated adhesion sites, and have accordingly referred to these structures as junction-associated intermittent lamellipodia (JAIL). JAIL extend over only a few microns and thus provide the basis for a subcellular regulation of adhesion. The local (subcellular) VE-cadherin concentration and JAIL formation are directly interdependent, which enables autoregulation. Therefore, this mechanism can contribute a subcellularly regulated adaptation of cell contact dynamics, and is therefore of great importance for monolayer integrity and relative cell migration during wound healing and angiogenesis, as well as for inflammatory responses. In this Review, we discuss the mechanisms and functions underlying these actin-driven protrusions and consider their contribution to the dynamic regulation of endothelial cell junctions.

Soluble VEGFR1 signaling guides vascular patterns into dense branching morphologies

Vascular patterning is a key process during development and disease. The diffusive decoy receptor sVEGFR1 (sFlt1) is a known regulator of endothelial cell behavior, yet the mechanism by which it controls vascular structure is little understood. We propose computational models to shed light on how vascular patterning is guided by self-organized gradients of the VEGF/sVEGFR1 factors. We demonstrate that a diffusive inhibitor can generate structures with a dense branching morphology in models where the activator elicits directed growth. Inadequate presence of the inhibitor leads to compact growth, while excessive production of the inhibitor blocks expansion and stabilizes existing structures. Model predictions were compared with time-resolved experimental data obtained from endothelial sprout kinetics in fibrin gels. In the presence of inhibitory antibodies against VEGFR1 vascular sprout density increases while the speed of sprout expansion remains unchanged. Thus, the rate of secretion and stability of extracellular sVEGFR1 can modulate vascular sprout density.

AutoTube: a novel software for the automated morphometric analysis of vascular networks in tissues

Due to their involvement in many physiologic and pathologic processes, there is a great interest in identifying new molecular pathways that mediate the formation and function of blood and lymphatic vessels. Vascular research increasingly involves the image-based analysis and quantification of vessel networks in tissue whole-mounts or of tube-like structures formed by cultured endothelial cells in vitro. While both types of experiments deliver important mechanistic insights into (lymph)angiogenic processes, the manual analysis and quantification of such experiments are typically labour-intensive and affected by inter-experimenter variability. To bypass these problems, we developed AutoTube, a new software that quantifies parameters like the area covered by vessels, vessel width, skeleton length and branching or crossing points of vascular networks in tissues and in in vitro assays. AutoTube is freely downloadable, comprises an intuitive graphical user interface and helps to perform otherwise highly time-consuming image analyses in a rapid, automated and reproducible manner. By analysing lymphatic and blood vascular networks in whole-mounts prepared from different tissues or from gene-targeted mice with known vascular abnormalities, we demonstrate the ability of AutoTube to determine vascular parameters in close agreement to the manual analyses and to identify statistically significant differences in vascular morphology in tissues and in vascular networks formed in in vitro assays.

Capillary network formation from dispersed endothelial cells: Influence of cell traction, cell adhesion, and extracellular matrix rigidity

The formation of a functional vascular network depends on biological, chemical, and physical processes being extremely well coordinated. Among them, the mechanical properties of the extracellular matrix and cell adhesion are fundamental to achieve a functional network of endothelial cells, able to fully cover a required domain. By the use of a Cellular Potts Model and Finite Element Method it is shown that there exists a range of values of endothelial traction forces, cell-cell adhesion, and matrix rigidities where the network can spontaneously be formed, and its properties are characterized. We obtain the analytical relation that the minimum traction force required for cell network formation must obey. This minimum value for the traction force is approximately independent on the considered cell number and cell-cell adhesion. We quantify how these two parameters influence the morphology of the resulting networks (size and number of meshes).

Transcriptional and epigenomic landscapes of CNS and non-CNS vascular endothelial cells

Vascular endothelial cell (EC) function depends on appropriate organ-specific molecular and cellular specializations. To explore genomic mechanisms that control this specialization, we have analyzed and compared the transcriptome, accessible chromatin, and DNA methylome landscapes from mouse brain, liver, lung, and kidney ECs. Analysis of transcription factor (TF) gene expression and TF motifs at candidate cis-regulatory elements reveals both shared and organ-specific EC regulatory networks. In the embryo, only those ECs that are adjacent to or within the central nervous system (CNS) exhibit canonical Wnt signaling, which correlates precisely with blood-brain barrier (BBB) differentiation and Zic3 expression. In the early postnatal brain, single-cell RNA-seq of purified ECs reveals (1) close relationships between veins and mitotic cells and between arteries and tip cells, (2) a division of capillary ECs into vein-like and artery-like classes, and (3) new endothelial subtype markers, including new validated tip cell markers.

A local uPAR-plasmin-TGFβ1 positive feedback loop in a qualitative computational model of angiogenic sprouting explains the in vitro effect of fibrinogen variants

In experimental assays of angiogenesis in three-dimensional fibrin matrices, a temporary scaffold formed during wound healing, the type and composition of fibrin impacts the level of sprouting. More sprouts form on high molecular weight (HMW) than on low molecular weight (LMW) fibrin. It is unclear what mechanisms regulate the number and the positions of the vascular-like structures in cell cultures. To address this question, we propose a mechanistic simulation model of endothelial cell migration and fibrin proteolysis by the plasmin system. The model is a hybrid, cell-based and continuum, computational model based on the cellular Potts model and sets of partial-differential equations. Based on the model results, we propose that a positive feedback mechanism between uPAR, plasmin and transforming growth factor β1 (TGFβ1) selects cells in the monolayer for matrix invasion. Invading cells releases TGFβ1 from the extracellular matrix through plasmin-mediated fibrin degradation. The activated TGFβ1 further stimulates fibrin degradation and keeps proteolysis active as the sprout invades the fibrin matrix. The binding capacity for TGFβ1 of LMW is reduced relative to that of HMW. This leads to reduced activation of proteolysis and, consequently, reduced cell ingrowth in LMW fibrin compared to HMW fibrin. Thus our model predicts that endothelial cells in LMW fibrin matrices compared to HMW matrices show reduced sprouting due to a lower bio-availability of TGFβ1.

Therapies for a range of medical conditions, including cancer, wound healing and diabetic retinopathy can benefit from a better control over the growth of blood vessels. The chemical properties of fibrin, the material that forms scabs in wounds and can also occur in large concentrations in tumors, can regulate the degree of blood vessel growth (angiogenesis). Angiogenesis can be mimicked in cell cultures. These allow us to modulate the chemical properties of fibrin and study the effect on angiogenesis. Fibrin occurs in high molecular weight (HMW) and in low molecular weight (LMW) forms. Interestingly, there is more ingrowth of angiogenic-like structures into HMW than in LMW fibrin, but the mechanisms are poorly understood. To get more insight into these, we constructed a computational model. Using the model, we propose and analyse a hypothetical mechanism for sprouting that could explain the differences in endothelial cell sprouting in LMW and HMW fibrin matrices. Our model suggests that cells digest fibrin, thus creating space for ingrowth. At the same time, digestion frees growth factors bound to fibrin, that activates further secretion of digestive enzymes by the cells. We propose that the resulting positive feedback loop spontaneously selects cells in the endothelial monolayer for ingrowth and helps the blood vessel sprout move deeper into the fibrin. This could be a complementary mechanism to lateral-inhibition by Delta-Notch for the selection of leader cells, also called ‘tip cells’. Our model predicts that endothelial cells in LMW fibrin compared to HMW fibrin show reduced sprouting due to a lower bio-availability of TGFβ1.

Mathematical modeling for meshwork formation of endothelial cells in fibrin gels

Vasculogenesis is the earliest process in development for spontaneous formation of a primitive capillary network from endothelial progenitor cells. When human umbilical vein endothelial cells (HUVECs) are cultured on Matrigel, they spontaneously form a network structure which is widely used as an in vitro model of vasculogenesis. Previous studies indicated that chemotaxis or gel deformation was involved in spontaneous pattern formation. In our study, we analyzed the mechanism of vascular pattern formation using a different system, meshwork formation by HUVECs embedded in fibrin gels. Unlike the others, this experimental system resulted in a perfusable endothelial network in vitro. We quantitatively observed the dynamics of endothelial cell protrusion and developed a mathematical model for one-dimensional dynamics. We then extended the one-dimensional model to two-dimensions. The model showed that random searching by endothelial cells was sufficient to generate the observed network structure in fibrin gels.

Cell-alignment patterns in the collective migration of cells with polarized adhesion

Dictyostelium discoideum (Dd) utilizes inhomogeneities in the distribution of cell-cell adhesion molecules on cell membranes for collective cell migration. A simple example of an inhomogeneity is a front-side (leading-edge) polarization in the distribution at the early streaming stage. Experiments have shown that the polarized cell-cell adhesion induces side-by-side contact between cells [Beug et al., Nature (London) 274, 445 (1978)NATUAS0028-083610.1038/274445a0]. This result is counterintuitive, as one would expect cells to align front to front in contact with each other on the basis of front-side polarization. In this work, we theoretically examine whether front-side polarization induces side-by-side contact in collective cell migration. We construct a model for expressing cells with this polarization based on the two-dimensional cellular Potts model. By a numerical simulation with this model, we find cell-cell alignment wherein cells form lateral arrays with side-by-side contacts as observed in the experiments.

Quantification of Multicellular Organization, Junction Integrity, and Substrate Features in Collective Cell Migration

Quantitative analysis of multicellular organization, cell-cell junction integrity, and substrate properties is essential to understand the mechanisms underlying collective cell migration. However, spatially and temporally defining these properties is difficult within collectively migrating cell groups due to challenges in accurate cell segmentation within the monolayer. In this paper, we present Matlab®-based algorithms to spatially quantify multicellular organization (migration distance, interface roughness, and cell alignment, area, and morphology), cell-cell junction integrity, and substrate features in confocal microscopy images of two-dimensional collectively migrating endothelial monolayers. We used novel techniques, including measuring the migrating front roughness using a parametric curve formulation, automatically binning cells to obtain data as a function of distance from the migrating front, using iterative morphological closings to fully define cell boundaries, quantifying β-catenin localization as a measure of cell-cell junction integrity, and skeletonizing fibronectin to determine fiber length and orientation. These algorithms are widely accessible, as they use common fluorescent markers and Matlab® functions, and provide high-throughput critical feature quantification within collectively migrating cell groups. These image analysis algorithms can help standardize feature quantification among different experimental techniques, cell types, and research groups studying collective cell migration.

Preferred cell alignment along concave microgrooves

The radius of curvature affects cell body characteristics on microfabricated concave microgrooves.

Spatiotemporal Dynamics of Insulitis in Human Type 1 Diabetes

Type 1 diabetes (T1D) is an auto-immune disease characterized by the selective destruction of the insulin secreting beta cells in the pancreas during an inflammatory phase known as insulitis. Patients with T1D are typically dependent on the administration of externally provided insulin in order to manage blood glucose levels. Whilst technological developments have significantly improved both the life expectancy and quality of life of these patients, an understanding of the mechanisms of the disease remains elusive. Animal models, such as the NOD mouse model, have been widely used to probe the process of insulitis, but there exist very few data from humans studied at disease onset. In this manuscript, we employ data from human pancreases collected close to the onset of T1D and propose a spatio-temporal computational model for the progression of insulitis in human T1D, with particular focus on the mechanisms underlying the development of insulitis in pancreatic islets. This framework allows us to investigate how the time-course of insulitis progression is affected by altering key parameters, such as the number of the CD20+ B cells present in the inflammatory infiltrate, which has recently been proposed to influence the aggressiveness of the disease. Through the analysis of repeated simulations of our stochastic model, which track the number of beta cells within an islet, we find that increased numbers of B cells in the peri-islet space lead to faster destruction of the beta cells. We also find that the balance between the degradation and repair of the basement membrane surrounding the islet is a critical component in governing the overall destruction rate of the beta cells and their remaining number. Our model provides a framework for continued and improved spatio-temporal modeling of human T1D.

Computational Screening of Tip and Stalk Cell Behavior Proposes a Role for Apelin Signaling in Sprout Progression

Angiogenesis involves the formation of new blood vessels by sprouting or splitting of existing blood vessels. During sprouting, a highly motile type of endothelial cell, called the tip cell, migrates from the blood vessels followed by stalk cells, an endothelial cell type that forms the body of the sprout. To get more insight into how tip cells contribute to angiogenesis, we extended an existing computational model of vascular network formation based on the cellular Potts model with tip and stalk differentiation, without making a priori assumptions about the differences between tip cells and stalk cells. To predict potential differences, we looked for parameter values that make tip cells (a) move to the sprout tip, and (b) change the morphology of the angiogenic networks. The screening predicted that if tip cells respond less effectively to an endothelial chemoattractant than stalk cells, they move to the tips of the sprouts, which impacts the morphology of the networks. A comparison of this model prediction with genes expressed differentially in tip and stalk cells revealed that the endothelial chemoattractant Apelin and its receptor APJ may match the model prediction. To test the model prediction we inhibited Apelin signaling in our model and in an in vitro model of angiogenic sprouting, and found that in both cases inhibition of Apelin or of its receptor APJ reduces sprouting. Based on the prediction of the computational model, we propose that the differential expression of Apelin and APJ yields a "self-generated" gradient mechanisms that accelerates the extension of the sprout.

A nanobiosensor for dynamic single cell analysis during microvascular self-organization

The formation of microvascular networks plays essential roles in regenerative medicine and tissue engineering. Nevertheless, the self-organization mechanisms underlying the dynamic morphogenic process are poorly understood due to a paucity of effective tools for mapping the spatiotemporal dynamics of single cell behaviors. By establishing a single cell nanobiosensor along with live cell imaging, we perform dynamic single cell analysis of the morphology, displacement, and gene expression during microvascular self-organization. Dynamic single cell analysis reveals that endothelial cells self-organize into subpopulations with specialized phenotypes to form microvascular networks and identifies the involvement of Notch1-Dll4 signaling in regulating the cell subpopulations. The cell phenotype correlates with the initial Dll4 mRNA expression level and each subpopulation displays a unique dynamic Dll4 mRNA expression profile. Pharmacological perturbations and RNA interference of Notch1-Dll4 signaling modulate the cell subpopulations and modify the morphology of the microvascular network. Taken together, a nanobiosensor enables a dynamic single cell analysis approach underscoring the importance of Notch1-Dll4 signaling in microvascular self-organization.

A node-based version of the cellular Potts model

The cellular Potts model (CPM) is a lattice-based Monte Carlo method that uses an energetic formalism to describe the phenomenological mechanisms underlying the biophysical problem of interest. We here propose a CPM-derived framework that relies on a node-based representation of cell-scale elements. This feature has relevant consequences on the overall simulation environment. First, our model can be implemented on any given domain, provided a proper discretization (which can be regular or irregular, fixed or time evolving). Then, it allowed an explicit representation of cell membranes, whose displacements realistically result in cell movement. Finally, our node-based approach can be easily interfaced with continuous mechanics or fluid dynamics models. The proposed computational environment is here applied to some simple biological phenomena, such as cell sorting and chemotactic migration, also in order to achieve an analysis of the performance of the underlying algorithm. This work is finally equipped with a critical comparison between the advantages and disadvantages of our model with respect to the traditional CPM and to some similar vertex-based approaches.

Computational immuno-biology for organ transplantation and regenerative medicine

Organ transplantation and regenerative medicine are adopted platforms that provide replacement tissues and organs from natural or engineered sources. Acceptance, tolerance and rejection depend greatly on the proper control of the immune response against graft antigens, motivating the development of immunological and genetical therapies that prevent organ failure. They rely on a complete, or partial, understanding of the immune system. Ultimately, they are innovative technologies that ensure permanent graft tolerance and indefinite graft survival through the modulation of the immune system. Computational immunology has arisen as a tool towards a mechanistic understanding of the biological and physicochemical processes surrounding an immune response. It comprehends theoretical and computational frameworks that simulate immuno-biological systems. The challenge is centered on the multi-scale character of the immune system that spans from atomistic scales, during peptide-epitope and protein interactions, to macroscopic scales, for lymph transport and organ-organ reactions. In this paper, we discuss, from an engineering perspective, the biological processes that are involved during the immune response of organ transplantation. Previous computational efforts, including their characteristics and visible limitations, are described. Finally, future perspectives and challenges are listed to motivate further developments.

Extracellular matrix motion and early morphogenesis

For over a century, embryologists who studied cellular motion in early amniotes generally assumed that morphogenetic movement reflected migration relative to a static extracellular matrix (ECM) scaffold. However, as we discuss in this Review, recent investigations reveal that the ECM is also moving during morphogenesis. Time-lapse studies show how convective tissue displacement patterns, as visualized by ECM markers, contribute to morphogenesis and organogenesis. Computational image analysis distinguishes between cell-autonomous (active) displacements and convection caused by large-scale (composite) tissue movements. Modern quantification of large-scale 'total' cellular motion and the accompanying ECM motion in the embryo demonstrates that a dynamic ECM is required for generation of the emergent motion patterns that drive amniote morphogenesis.

In vivo confinement promotes collective migration of neural crest cells

Collective cell migration is fundamental throughout development and in many diseases. Spatial confinement using micropatterns has been shown to promote collective cell migration in vitro, but its effect in vivo remains unclear. Combining computational and experimental approaches, we show that the in vivo collective migration of neural crest cells (NCCs) depends on such confinement. We demonstrate that confinement may be imposed by the spatiotemporal distribution of a nonpermissive substrate provided by versican, an extracellular matrix molecule previously proposed to have contrasting roles: barrier or promoter of NCC migration. We resolve the controversy by demonstrating that versican works as an inhibitor of NCC migration and also acts as a guiding cue by forming exclusionary boundaries. Our model predicts an optimal number of cells in a given confinement width to allow for directional migration. This optimum coincides with the width of neural crest migratory streams analyzed across different species, proposing an explanation for the highly conserved nature of NCC streams during development.

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

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