A mechanical model for the formation of vascular networks in vitro

Formation of vascular-like structures using a chemotaxis-driven multiphase model

We propose a continuum model for pattern formation, based on the multiphase model framework, to explore in vitro cell patterning within an extracellular matrix (ECM). We demonstrate that, within this framework, chemotaxis-driven cell migration can lead to the formation of cell clusters and vascular-like structures in 1D and 2D respectively. The influence on pattern formation of additional mechanisms commonly included in multiphase tissue models, including cell-matrix traction, contact inhibition, and cell-cell aggregation, are also investigated. Using sensitivity analysis, the relative impact of each model parameter on the simulation outcomes is assessed to identify the key parameters involved. Chemoattractant-matrix binding is further included, motivated by previous experimental studies, and found to reduce the spatial scale of patterning to within a biologically plausible range for capillary structures. Key findings from the in-depth parameter analysis of the 1D models, both with and without chemoattractant-matrix binding, are demonstrated to translate well to the 2D model, obtaining vascular-like cell patterning for multiple parameter regimes. Overall, we demonstrate a biologically-motivated multiphase model capable of generating long-term pattern formation on a biologically plausible spatial scale both in 1D and 2D, with applications for modelling in vitro vascular network formation.

Pro-vasculogenic Fibers by PDA-Mediated Surface Functionalization Using Cell-Free Fat Extract (CEFFE)

Formation of adequate vascular network within engineered three-dimensional (3D) tissue substitutes postimplantation remains a major challenge for the success of biomaterials-based tissue regeneration. To better mimic the in vivo angiogenic and vasculogenic processes, nowadays increasing attention is given to the strategy of functionalizing biomaterial scaffolds with multiple bioactive agents. Aimed at engineering electrospun biomimicking fibers with pro-vasculogenic capability, this study was proposed to functionalize electrospun fibers of polycaprolactone/gelatin (PCL/GT) by cell-free fat extract (CEFFE or FE), a newly emerging natural "cocktail" of cytokines and growth factors extracted from human adipose tissue. This was achieved by having the electrospun PCL/GT fiber surface coated with polydopamine (PDA) followed by PDA-mediated immobilization of FE to generate the pro-vasculogenic fibers of FE-PDA@PCL/GT. It was found that the PDA-coated fibrous mat of PCL/GT exhibited a high FE-loading efficiency (∼90%) and enabled the FE to be released in a highly sustained manner. The engineered FE-PDA@PCL/GT fibers possess improved cytocompatibility, as evidenced by the enhanced cellular proliferation, migration, and RNA and protein expressions (e.g., CD31, vWF, VE-cadherin) in the human umbilical vein endothelial cells (huvECs) used. Most importantly, the FE-PDA@PCL/GT fibrous scaffolds were found to enormously stimulate tube formation in vitro, microvascular development in the in ovo chick chorioallantoic membrane (CAM) assay, and vascularization of 3D construct in a rat subcutaneous embedding model. This study highlights the potential of currently engineered pro-vasculogenic fibers as a versatile platform for engineering vascularized biomaterial constructs for functional tissue regeneration.

Computational modeling of angiogenesis: The importance of cell rearrangements during vascular growth

Angiogenesis is the process wherein endothelial cells (ECs) form sprouts that elongate from the pre-existing vasculature to create new vascular networks. In addition to its essential role in normal development, angiogenesis plays a vital role in pathologies such as cancer, diabetes and atherosclerosis. Mathematical and computational modeling has contributed to unraveling its complexity. Many existing theoretical models of angiogenic sprouting are based on the "snail-trail" hypothesis. This framework assumes that leading ECs positioned at sprout tips migrate toward low-oxygen regions while other ECs in the sprout passively follow the leaders' trails and proliferate to maintain sprout integrity. However, experimental results indicate that, contrary to the snail-trail assumption, ECs exchange positions within developing vessels, and the elongation of sprouts is primarily driven by directed migration of ECs. The functional role of cell rearrangements remains unclear. This review of the theoretical modeling of angiogenesis is the first to focus on the phenomenon of cell mixing during early sprouting. We start by describing the biological processes that occur during early angiogenesis, such as phenotype specification, cell rearrangements and cell interactions with the microenvironment. Next, we provide an overview of various theoretical approaches that have been employed to model angiogenesis, with particular emphasis on recent in silico models that account for the phenomenon of cell mixing. Finally, we discuss when cell mixing should be incorporated into theoretical models and what essential modeling components such models should include in order to investigate its functional role. This article is categorized under: Cardiovascular Diseases > Computational Models Cancer > Computational Models.

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.

Optimal mechanical interactions direct multicellular network formation on elastic substrates

Cells self-organize into functional, ordered structures during tissue morphogenesis, a process that is evocative of colloidal self-assembly into engineered soft materials. Understanding how intercellular mechanical interactions may drive the formation of ordered and functional multicellular structures is important in developmental biology and tissue engineering. Here, by combining an agent-based model for contractile cells on elastic substrates with endothelial cell culture experiments, we show that substrate deformation-mediated mechanical interactions between cells can cluster and align them into branched networks. Motivated by the structure and function of vasculogenic networks, we predict how measures of network connectivity like percolation probability and fractal dimension as well as local morphological features including junctions, branches, and rings depend on cell contractility and density and on substrate elastic properties including stiffness and compressibility. We predict and confirm with experiments that cell network formation is substrate stiffness dependent, being optimal at intermediate stiffness. We also show the agreement between experimental data and predicted cell cluster types by mapping a combined phase diagram in cell density substrate stiffness. Overall, we show that long-range, mechanical interactions provide an optimal and general strategy for multicellular self-organization, leading to more robust and efficient realizations of space-spanning networks than through just local intercellular interactions.

A Novel High Content Angiogenesis Assay Reveals That Lacidipine, L-Type Calcium Channel Blocker, Induces In Vitro Vascular Lumen Expansion

Angiogenesis is a critical cellular process toward establishing a functional circulatory system capable of delivering oxygen and nutrients to the tissue in demand. In vitro angiogenesis assays represent an important tool for elucidating the biology of blood vessel formation and for drug discovery applications. Herein, we developed a novel, high content 2D angiogenesis assay that captures endothelial morphogenesis’s cellular processes, including lumen formation. In this assay, endothelial cells form luminized vascular-like structures in 48 h. The assay was validated for its specificity and performance. Using the optimized assay, we conducted a phenotypic screen of a library containing 150 FDA-approved cardiovascular drugs to identify modulators of lumen formation. The screening resulted in several L-type calcium channel blockers being able to expand the lumen space compared to controls. Among these blockers, Lacidipine was selected for follow-up studies. We found that the endothelial cells treated with Lacidipine showed enhanced activity of caspase-3 in the luminal space. Pharmacological inhibition of caspase activity abolished the Lacidipine-enhancing effect on lumen formation, suggesting the involvement of apoptosis. Using a Ca²⁺ biosensor, we found that Lacipidine reduces the intracellular Ca²⁺ oscillations amplitude in the endothelial cells at the early stage, whereas Lacidipine blocks these Ca²⁺ oscillations completely at the late stage. The inhibition of MLCK exhibits a phenotype of lumen expansion similar to that of Lacidipine. In conclusion, this study describes a novel high-throughput phenotypic assay to study angiogenesis. Our findings suggest that calcium signalling plays an essential role during lumen morphogenesis. L-type Ca²⁺ channel blockers could be used for more efficient angiogenesis-mediated therapies.

Tropoelastin Promotes the Formation of Dense, Interconnected Endothelial Networks

Tropoelastin, the soluble precursor of elastin, has been used for regenerative and wound healing purposes and noted for its ability to accelerate wound repair by enhancing vascularization at the site of implantation. However, it is not clear whether these effects are directly due to the interaction of tropoelastin with endothelial cells or communicated to endothelial cells following interactions between tropoelastin and neighboring cells, such as mesenchymal stem cells (MSCs). We adapted an endothelial tube formation assay to model in vivo vascularization with the goal of exploring the stimulatory mechanism of tropoelastin. In the presence of tropoelastin, endothelial cells formed less tubes, with reduced spreading into capillary-like networks. In contrast, conditioned media from MSCs that had been cultured on tropoelastin enhanced the formation of more dense, complex, and interconnected endothelial tube networks. This pro-angiogenic effect of tropoelastin is mediated indirectly through the action of tropoelastin on co-cultured cells. We conclude that tropoelastin inhibits endothelial tube formation, and that this effect is reversed by pro-angiogenic crosstalk from tropoelastin-treated MSCs. Furthermore, we find that the known in vivo pro-angiogenic effects of tropoelastin can be modeled in vitro, highlighting the value of tropoelastin as an indirect mediator of angiogenesis.

A minimalist model for coevolving supply and drainage networks

Numerous complex systems, both natural and artificial, are characterized by the presence of intertwined supply and/or drainage networks. Here, we present a minimalist model of such coevolving networks in a spatially continuous domain, where the obtained networks can be interpreted as a part of either the counter-flowing drainage or co-flowing supply and drainage mechanisms. The model consists of three coupled, nonlinear partial differential equations that describe spatial density patterns of input and output materials by modifying a mediating scalar field, on which supply and drainage networks are carved. In the two-dimensional case, the scalar field can be viewed as the elevation of a hypothetical landscape, of which supply and drainage networks are ridges and valleys, respectively. In the three-dimensional case, the scalar field serves the role of a chemical signal, according to which vascularization of the supply and drainage networks occurs above a critical 'erosion' strength. The steady-state solutions are presented as a function of non-dimensional channelization indices for both materials. The spatial patterns of the emerging networks are classified within the branched and congested extreme regimes, within which the resulting networks are characterized based on the absolute as well as the relative values of two non-dimensional indices.

Spatial Statistics-Based Image Analysis Methods for the Study of Vascular Morphogenesis

Several studies are available addressing the mechanisms of vascular morphogenesis in order to unravel how cooperative cell behavior can follow from the underlying, genetically regulated behavior of endothelial cells and from cell-to-cell and cell-to-extracellular matrix interactions. From the morphological standpoint several aspects of the process are of interest. They include the way the pattern of vessels fills the available tissue space and how the network grows during the angiogenic process, namely how a main trunk divides into smaller branches, and how branching occurs at different distances from the root point of a vascular tree. A third morphological aspect of interest concerns the spatial relationship between vessels and tissue cells able to secrete factors modulating endothelial cells self-organization, thus influencing vascular rearrangement.In the present chapter image analysis methods allowing for a quantitative characterization of these morphological aspects will be detailed and discussed. They are almost based on concepts derived from the theoretical framework represented by spatial statistics.

Multicellular contractility contributes to the emergence of mesothelioma nodules

Malignant pleural mesothelioma (MPM) has an overall poor prognosis and unsatisfactory treatment options. MPM nodules, protruding into the pleural cavity may have growth and spreading dynamics distinct that of other solid tumors. We demonstrate that multicellular aggregates can develop spontaneously in the majority of tested MPM cell lines when cultured at high cell density. Surprisingly, the nodule-like aggregates do not arise by excessive local cell proliferation, but by myosin II-driven cell contractility. Prominent actin cables, spanning several cells, are abundant both in cultured aggregates and in MPM surgical specimens. We propose a computational model for in vitro MPM nodule development. Such a self-tensioned Maxwell fluid exhibits a pattern-forming instability that was studied by analytical tools and computer simulations. Altogether, our findings may underline a rational for targeting the actomyosin system in MPM.

Caveolin-1 Knockdown Decreases SMMC7721 Human Hepatocellular Carcinoma Cell Invasiveness by Inhibiting Vascular Endothelial Growth Factor-Induced Angiogenesis

BACKGROUND

Recently, several studies have demonstrated that caveolin-1 overexpression is involved in apoptosis resistance, angiogenesis, and invasiveness in hepatocellular carcinoma (HCC). However, the mechanisms underlying caveolin-1-mediated tumor progression remain unclear. Methodogy. Lentiviral vectors were used to construct caveolin-1 small interfering RNA- (siRNA-) expressing cells. Secreted VEGF levels in SMMC7721 cells were evaluated by enzyme-linked immunosorbent assay (ELISA). SMMC7721 cell proliferation, cycle, apoptosis, and invasiveness were detected by MTT, flow cytometry, Annexin V-FITC/PI, and invasion assay, respectively. Phospho-eNOS levels in human umbilical vein endothelial cells (HUVECs) cocultured with SMMC7721 cell supernatants were analyzed by Western blot. Capillary-like tubule formation assay was performed to analyze endothelial tubular structure formation in HUVECs treated with supernatants from caveolin-1 siRNA-expressing SMMC7721 cells. SMMC7721 implantation and growth in nude mice were observed. Angiogenesis in vivo was analyzed by immunohistochemical angiogenesis assay.

RESULTS

Caveolin-1 siRNA-expressing SMMC7721 cells secreted reduced levels of VEGF. Caveolin-1 RNAi also caused an inhibition of SMMC7721 cell proliferation and cell cycle progression that was accompanied by increased apoptosis. Supernatants from caveolin-1 siRNA-expressing SMMC7721 cells inhibited cell cycle progression and decreased phospho-eNOS levels in HUVECs. Endothelial tubular structure formation in HUVECs treated with supernatants from caveolin-1 siRNA-expressing SMMC7721 cells was considerably reduced. Caveolin-1 siRNA-expressing SMMC7721 cells also showed reduced tumorigenicity and angiogenesis induction in vivo.

CONCLUSION

Our results reveal a novel mechanism, whereby caveolin-1 positively regulates human HCC cell invasiveness by coordinating VEGF-induced angiogenesis.

From tumour perfusion to drug delivery and clinical translation of in silico cancer models

In silico cancer models have demonstrated great potential as a tool to improve drug design, optimise the delivery of drugs to target sites in the host tissue and, hence, improve therapeutic efficacy and patient outcome. However, there are significant barriers to the successful translation of in silico technology from bench to bedside. More precisely, the specification of unknown model parameters, the necessity for models to adequately reflect in vivo conditions, and the limited amount of pertinent validation data to evaluate models' accuracy and assess their reliability, pose major obstacles in the path towards their clinical translation. This review aims to capture the state-of-the-art in in silico cancer modelling of vascularised solid tumour growth, and identify the important advances and barriers to success of these models in clinical oncology. Particular emphasis has been put on continuum-based models of cancer since they - amongst the class of mechanistic spatio-temporal modelling approaches - are well-established in simulating transport phenomena and the biomechanics of tissues, and have demonstrated potential for clinical translation. Three important avenues in in silico modelling are considered in this contribution: first, since systemic therapy is a major cancer treatment approach, we start with an overview of the tumour perfusion and angiogenesis in silico models. Next, we present the state-of-the-art in silico work encompassing the delivery of chemotherapeutic agents to cancer nanomedicines through the bloodstream, and then review continuum-based modelling approaches that demonstrate great promise for successful clinical translation. We conclude with a discussion of what we view to be the key challenges and opportunities for in silico modelling in personalised and precision medicine.

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.

Self-assembly, buckling and density-invariant growth of three-dimensional vascular networks

The experimental actualization of organoids modelling organs from brains to pancreases has revealed that much of the diverse morphologies of organs are emergent properties of simple intercellular 'rules' and not the result of top-down orchestration. In contrast to other organs, the initial plexus of the vascular system is formed by aggregation of cells in the process known as vasculogenesis. Here we study this self-assembling process of blood vessels in three dimensions through a set of simple rules that align intercellular apical-basal and planar cell polarity. We demonstrate that a fully connected network of tubes emerges above a critical initial density of cells. Through planar cell polarity, our model demonstrates convergent extension, and this polarity furthermore allows for both morphology-maintaining growth and growth-induced buckling. We compare this buckling with the special vasculature of the islets of Langerhans in the pancreas and suggest that the mechanism behind the vascular density-maintaining growth of these islets could be the result of growth-induced buckling.

Matrigel patterning reflects multicellular contractility

Non-muscle myosin II (NMII)-induced multicellular contractility is essential for development, maintenance and remodeling of tissue morphologies. Dysregulation of the cytoskeleton can lead to birth defects or enable cancer progression. We demonstrate that the Matrigel patterning assay, widely used to characterize endothelial cells, is a highly sensitive tool to evaluate cell contractility within a soft extracellular matrix (ECM) environment. We propose a computational model to explore how cell-exerted contractile forces can tear up the cell-Matrigel composite material and gradually remodel it into a network structure. We identify measures that are characteristic for cellular contractility and can be obtained from image analysis of the recorded patterning process. The assay was calibrated by inhibition of NMII activity in A431 epithelial carcinoma cells either directly with blebbistatin or indirectly with Y27632 Rho kinase inhibitor. Using Matrigel patterning as a bioassay, we provide the first functional demonstration that overexpression of S100A4, a calcium-binding protein that is frequently overexpressed in metastatic tumors and inhibits NMIIA activity by inducing filament disassembly, effectively reduces cell contractility.

Sensing and exerting forces is a fundamental aspect of tissue organization. We demonstrate that contractile cells form an intricate network structure when placed in a pliable culture environment, a phenomenon often associated with vascular networks and is being actively used to characterize endothelial cells in culture. We propose a computational model that operates with mechanical stresses, plastic deformation and material failure within the cell-extracellular matrix composite to explain the patterning process. In addition to re-interpret a decades-old tool of experimental cell biology, our work suggests a potentially high throughput computational assay to characterize cellular contractility within a soft ECM environment.

microRNA-21-5p dysregulation in exosomes derived from heart failure patients impairs regenerative potential

Exosomes, as functional paracrine units of therapeutic cells, can partially reproduce the reparative properties of their parental cells. The constitution of exosomes, as well as their biological activity, largely depends on the cells that secrete them. We isolated exosomes from explant-derived cardiac stromal cells from patients with heart failure (FEXO) or from normal donor hearts (NEXO) and compared their regenerative activities in vitro and in vivo. Patients in the FEXO group exhibited an impaired ability to promote endothelial tube formation and cardiomyocyte proliferation in vitro. Intramyocardial injection of NEXO resulted in structural and functional improvements in a murine model of acute myocardial infarction. In contrast, FEXO therapy exacerbated cardiac function and left ventricular remodeling. microRNA array and PCR analysis revealed dysregulation of miR-21-5p in FEXO. Restoring miR-21-5p expression rescued FEXO's reparative function, whereas blunting miR-21-5p expression in NEXO diminished its therapeutic benefits. Further mechanistic studies revealed that miR-21-5p augmented Akt kinase activity through the inhibition of phosphatase and tensin homolog. Taken together, the heart failure pathological condition altered the miR cargos of cardiac-derived exosomes and impaired their regenerative activities. miR-21-5p contributes to exosome-mediated heart repair by enhancing angiogenesis and cardiomyocyte survival through the phosphatase and tensin homolog/Akt pathway.

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.

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).

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.

Tissue growth pressure drives early blood flow in the chicken yolk sac

BACKGROUND

Understanding how molecular and physical cues orchestrate vascular morphogenesis is a challenge for developmental biology. Only little attention has been paid to the impact of mechanical stress caused by tissue growth on early blood distribution. Here we study the peripheral accumulation of blood in the chicken embryonic yolk sac, which precedes sinus vein formation.

RESULTS

We report that blood accumulation starts before heart-induced blood circulation. We hypothesized that the driving force for the primitive blood flow is a growth-induced gradient of tissue pressure in the yolk sac mesoderm. Therefore, we studied embryos in which heart development was arrested after 2 days of incubation, and found that yolk sac growth and blood peripheral accumulation still occurred. This suggests that tissue growth is sufficient to initiate the flow and the formation of the sinus vein, whereas heart contractions are not required. We designed a simple mathematical model which makes explicit the growth-induced pressure gradient and the subsequent blood accumulation, and show that growth can indeed account for the observed blood accumulation.

CONCLUSIONS

This study shows that tissue growth pressure can drive early blood flow, and suggests that the mechanical environment, beyond hemodynamics, can contribute to vascular morphogenesis. Developmental Dynamics 246:573-584, 2017. © 2017 Wiley Periodicals, Inc.

3D hybrid modelling of vascular network formation

We develop an off-lattice, agent-based model to describe vasculogenesis, the de novo formation of blood vessels from endothelial progenitor cells during development. The endothelial cells that comprise our vessel network are viewed as linearly elastic spheres that move in response to the forces they experience. We distinguish two types of endothelial cells: vessel elements are contained within the network and tip cells are located at the ends of vessels. Tip cells move in response to mechanical forces caused by interactions with neighbouring vessel elements and the local tissue environment, chemotactic forces and a persistence force which accounts for their tendency to continue moving in the same direction. Vessel elements are subject to similar mechanical forces but are insensitive to chemotaxis. An angular persistence force representing interactions with the local tissue is introduced to stabilise buckling instabilities caused by cell proliferation. Only vessel elements proliferate, at rates which depend on their degree of stretch: elongated elements have increased rates of proliferation, and compressed elements have reduced rates. Following division, the fate of the new cell depends on the local mechanical environment: the probability of forming a new sprout is increased if the parent vessel is highly compressed and the probability of being incorporated into the parent vessel increased if the parent is stretched. Simulation results reveal that our hybrid model can reproduce the key qualitative features of vasculogenesis. Extensive parameter sensitivity analyses show that significant changes in network size and morphology are induced by varying the chemotactic sensitivity of tip cells, and the sensitivities of the proliferation rate and the sprouting probability to mechanical stretch. Varying the chemotactic sensitivity directly influences the directionality of the networks. The degree of branching, and thereby the density of the networks, is influenced by the sprouting probability. Glyphs that simultaneously depict several network properties are introduced to show how these and other network quantities change over time and also as model parameters vary. We also show how equivalent glyphs constructed from in vivo data could be used to discriminate between normal and tumour vasculature and, in the longer term, for model validation. We conclude that our biomechanical hybrid model can generate vascular networks that are qualitatively similar to those generated from in vitro and in vivo experiments.

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.

Asymmetries arising from the space-filling nature of vascular networks

Cardiovascular networks span the body by branching across many generations of vessels. The resulting structure delivers blood over long distances to supply all cells with oxygen via the relatively short-range process of diffusion at the capillary level. The structural features of the network that accomplish this density and ubiquity of capillaries are often called space-filling. There are multiple strategies to fill a space, but some strategies do not lead to biologically adaptive structures by requiring too much construction material or space, delivering resources too slowly, or using too much power to move blood through the system. We empirically measure the structure of real networks (18 humans and 1 mouse) and compare these observations with predictions of model networks that are space-filling and constrained by a few guiding biological principles. We devise a numerical method that enables the investigation of space-filling strategies and determination of which biological principles influence network structure. Optimization for only a single principle creates unrealistic networks that represent an extreme limit of the possible structures that could be observed in nature. We first study these extreme limits for two competing principles, minimal total material and minimal path lengths. We combine these two principles and enforce various thresholds for balance in the network hierarchy, which provides a novel approach that highlights the tradeoffs faced by biological networks and yields predictions that better match our empirical data.

Primary Phenomenon in the Network Formation of Endothelial Cells: Effect of Charge

Blood vessels are essential organs that are involved in the supply of nutrients and oxygen and play an important role in regulating the body's internal environment, including pH, body temperature, and water homeostasis. Many studies have examined the formation of networks of endothelial cells. The results of these studies have revealed that vascular endothelial growth factor (VEGF) affects the interactions of these cells and modulates the network structure. Though almost all previous simulation studies have assumed that the chemoattractant VEGF is present before network formation, vascular endothelial cells secrete VEGF only after the cells bind to the substrate. This suggests VEGF is not essential for vasculogenesis especially at the early stage. Using a simple experiment, we find chain-like structures which last quite longer than it is expected, unless the energetically stable cluster should be compact. Using a purely physical model and simulation, we find that the hydrodynamic interaction retard the compaction of clusters and that the chains are stabilized through the effects of charge. The charge at the surface of the cells affect the interparticle potential, and the resulting repulsive forces prevent the chains from folding. The ions surrounding the cells may also be involved in this process.

Tip cell overtaking occurs as a side effect of sprouting in computational models of angiogenesis

BACKGROUND

During angiogenesis, the formation of new blood vessels from existing ones, endothelial cells differentiate into tip and stalk cells, after which one tip cell leads the sprout. More recently, this picture has changed. It has become clear that endothelial cells compete for the tip position during angiogenesis: a phenomenon named tip cell overtaking. The biological function of tip cell overtaking is not yet known. From experimental observations, it is unclear to what extent tip cell overtaking is a side effect of sprouting or to what extent it is regulated through a VEGF-Dll4-Notch signaling network and thus might have a biological function. To address this question, we studied tip cell overtaking in computational models of angiogenic sprouting in absence and in presence of VEGF-Dll4-Notch signaling.

RESULTS

We looked for tip cell overtaking in two existing Cellular Potts models of angiogenesis. In these simulation models angiogenic sprouting-like behavior emerges from a small set of plausible cell behaviors. In the first model, cells aggregate through contact-inhibited chemotaxis. In the second model the endothelial cells assume an elongated shape and aggregate through (non-inhibited) chemotaxis. In both these sprouting models the endothelial cells spontaneously migrate forwards and backwards within sprouts, suggesting that tip cell overtaking might occur as a side effect of sprouting. In accordance with other experimental observations, in our simulations the cells' tendency to occupy the tip position can be regulated when two cell lines with different levels of Vegfr2 expression are contributing to sprouting (mosaic sprouting assay), where cell behavior is regulated by a simple VEGF-Dll4-Notch signaling network.

CONCLUSIONS

Our modeling results suggest that tip cell overtaking can occur spontaneously due to the stochastic motion of cells during sprouting. Thus, tip cell overtaking and sprouting dynamics may be interdependent and should be studied and interpreted in combination. VEGF-Dll4-Notch can regulate the ability of cells to occupy the tip cell position in our simulations. We propose that the function of VEGF-Dll4-Notch signaling might not be to regulate which cell ends up at the tip, but to assure that the cell that randomly ends up at the tip position acquires the tip cell phenotype.

Structural biology response of a collagen hydrogel synthetic extracellular matrix with embedded human fibroblast: computational and experimental analysis

Adherent cells exert contractile forces which play an important role in the spatial organization of the extracellular matrix (ECM). Due to these forces, the substrate experiments a volume reduction leading to a characteristic shape. ECM contraction is a key process in many biological processes such as embryogenesis, morphogenesis and wound healing. However, little is known about the specific parameters that control this process. With this aim, we present a 3D computational model able to predict the contraction process of a hydrogel matrix due to cell-substrate mechanical interaction. It considers cell-generated forces, substrate deformation, ECM density, cellular migration and proliferation. The model also predicts the cellular spatial distribution and concentration needed to reproduce the contraction process and confirms the minimum value of cellular concentration necessary to initiate the process observed experimentally. The obtained continuum formulation has been implemented in a finite element framework. In parallel, in vitro experiments have been performed to obtain the main model parameters and to validate it. The results demonstrate that cellular forces, migration and proliferation are acting simultaneously to display the ECM contraction.

Cell-based computational modeling of vascular morphogenesis using Tissue Simulation Toolkit

Computational modeling has become a widely used tool for unraveling the mechanisms of higher level cooperative cell behavior during vascular morphogenesis. However, experimenting with published simulation models or adding new assumptions to those models can be daunting for novice and even for experienced computational scientists. Here, we present a step-by-step, practical tutorial for building cell-based simulations of vascular morphogenesis using the Tissue Simulation Toolkit (TST). The TST is a freely available, open-source C++ library for developing simulations with the two-dimensional cellular Potts model, a stochastic, agent-based framework to simulate collective cell behavior. We will show the basic use of the TST to simulate and experiment with published simulations of vascular network formation. Then, we will present step-by-step instructions and explanations for building a recent simulation model of tumor angiogenesis. Demonstrated mechanisms include cell-cell adhesion, chemotaxis, cell elongation, haptotaxis, and haptokinesis.

Mechanical cell-matrix feedback explains pairwise and collective endothelial cell behavior in vitro

In vitro cultures of endothelial cells are a widely used model system of the collective behavior of endothelial cells during vasculogenesis and angiogenesis. When seeded in an extracellular matrix, endothelial cells can form blood vessel-like structures, including vascular networks and sprouts. Endothelial morphogenesis depends on a large number of chemical and mechanical factors, including the compliancy of the extracellular matrix, the available growth factors, the adhesion of cells to the extracellular matrix, cell-cell signaling, etc. Although various computational models have been proposed to explain the role of each of these biochemical and biomechanical effects, the understanding of the mechanisms underlying in vitro angiogenesis is still incomplete. Most explanations focus on predicting the whole vascular network or sprout from the underlying cell behavior, and do not check if the same model also correctly captures the intermediate scale: the pairwise cell-cell interactions or single cell responses to ECM mechanics. Here we show, using a hybrid cellular Potts and finite element computational model, that a single set of biologically plausible rules describing (a) the contractile forces that endothelial cells exert on the ECM, (b) the resulting strains in the extracellular matrix, and (c) the cellular response to the strains, suffices for reproducing the behavior of individual endothelial cells and the interactions of endothelial cell pairs in compliant matrices. With the same set of rules, the model also reproduces network formation from scattered cells, and sprouting from endothelial spheroids. Combining the present mechanical model with aspects of previously proposed mechanical and chemical models may lead to a more complete understanding of in vitro angiogenesis.

Exosomes as critical agents of cardiac regeneration triggered by cell therapy

The CADUCEUS trial of cardiosphere-derived cells (CDCs) has shown that it may be possible to regenerate injured heart muscle previously thought to be permanently scarred. The mechanisms of benefit are known to be indirect, but the mediators have yet to be identified. Here we pinpoint exosomes secreted by human CDCs as critical agents of regeneration and cardioprotection. CDC exosomes inhibit apoptosis and promote proliferation of cardiomyocytes, while enhancing angiogenesis. Injection of exosomes into injured mouse hearts recapitulates the regenerative and functional effects produced by CDC transplantation, whereas inhibition of exosome production by CDCs blocks those benefits. CDC exosomes contain a distinctive complement of microRNAs, with particular enrichment of miR-146a. Selective administration of a miR-146a mimic reproduces some (but not all) of the benefits of CDC exosomes. The findings identify exosomes as key mediators of CDC-induced regeneration, while highlighting the potential utility of exosomes as cell-free therapeutic candidates.

•

Cardiosphere-derived cells (CDCs) regenerate the heart by unclear indirect mechanisms

•

Exosomes from CDCs promote angiogenesis, cardiomyocyte survival and proliferation

•

CDC exosomes are necessary and sufficient to explain the therapeutic effects of CDCs

•

MicroRNAs transferred by CDC exosomes at least partially mediate the benefits of CDCs

Geometric control of capillary architecture via cell-matrix mechanical interactions

Capillary morphogenesis is a multistage, multicellular activity that plays a pivotal role in various developmental and pathological situations. In-depth understanding of the regulatory mechanism along with the capability of controlling the morphogenic process will have direct implications on tissue engineering and therapeutic angiogenesis. Extensive research has been devoted to elucidate the biochemical factors that regulate capillary morphogenesis. The roles of geometric confinement and cell-matrix mechanical interactions on the capillary architecture, nevertheless, remain largely unknown. Here, we show geometric control of endothelial network topology by creating physical confinements with microfabricated fences and wells. Decreasing the thickness of the matrix also results in comparable modulation of the network architecture, supporting the boundary effect is mediated mechanically. The regulatory role of cell-matrix mechanical interaction on the network topology is further supported by alternating the matrix stiffness by a cell-inert PEG-dextran hydrogel. Furthermore, reducing the cell traction force with a Rho-associated protein kinase inhibitor diminishes the boundary effect. Computational biomechanical analysis delineates the relationship between geometric confinement and cell-matrix mechanical interaction. Collectively, these results reveal a mechanoregulation scheme of endothelial cells to regulate the capillary network architecture via cell-matrix mechanical interactions.

In Vitro Microvessel Growth and Remodeling within a Three-dimensional Microfluidic Environment

This paper presents in vitro microvascular network formation within 3D gel scaffolds made from different concentrations of type-I collagen, fibrin, or a mixture of collagen and fibrin, using a simple microfluidic platform. Initially, microvascular network formation of human umbilical vein endothelial cells was examined using live time-lapse confocal microscopy every 90 min from 3 h to 12 h after seeding within three different concentrations of collagen gel scaffolds. Among the three conditions of collagen gel scaffolds (2.0 mg/ml, 2.5 mg/ml, and 3.0 mg/ml), the number of skeleton within collagen gel scaffolds was consistently the highest (3.0 mg/ml), followed by those of collagen gel scaffolds (2.5 mg/ml and 2.0 mg/ml). Results demonstrated that concentration of collagen gel scaffolds, which influences matrix stiffness and ligand density, may affect microvascular network formation during the early stages of vasculogenesis. In addition, the maturation of microvascular networks in monoculture under different gel compositions within gel scaffolds (2.5 mg/ml) was examined for 7 d using live confocal microscopy. It was confirmed that pure fibrin gel scaffolds are preferable to collagen gel or collagen/fibrin combinations, significantly reducing matrix retractions during maturation of microvascular networks for 7 d. Finally, early steps in the maturation process of microvascular networks for 14 d were characterized by demonstrating sequential steps of branching, expanding, remodeling, pruning, and clear delineation of lumens within fibrin gel scaffolds. Our findings demonstrate an in vitro model for generating mature microvascular networks within 3D microfluidic fibrin gel scaffolds (2.5 mg/ml), and furthermore suggest the importance of gel concentration and composition in promoting the maturation of microvascular networks.

Endothelial cell motility, coordination and pattern formation during vasculogenesis

How vascular networks assemble is a fundamental problem of developmental biology that also has medical importance. To explain the organizational principles behind vascular patterning, we must understand how can tissue level structures be controlled through cell behavior patterns like motility and adhesion that, in turn, are determined by biochemical signal transduction processes? We discuss the various ideas that have been proposed as mechanisms for vascular network assembly: cell motility guided by extracellular matrix alignment (contact guidance), chemotaxis guided by paracrine and autocrine morphogens, and multicellular sprouting guided by cell-cell contacts. All of these processes yield emergent patterns, thus endothelial cells can form an interconnected structure autonomously, without guidance from an external pre-pattern.

Cellular potts modeling of tumor growth, tumor invasion, and tumor evolution

Despite a growing wealth of available molecular data, the growth of tumors, invasion of tumors into healthy tissue, and response of tumors to therapies are still poorly understood. Although genetic mutations are in general the first step in the development of a cancer, for the mutated cell to persist in a tissue, it must compete against the other, healthy or diseased cells, for example by becoming more motile, adhesive, or multiplying faster. Thus, the cellular phenotype determines the success of a cancer cell in competition with its neighbors, irrespective of the genetic mutations or physiological alterations that gave rise to the altered phenotype. What phenotypes can make a cell "successful" in an environment of healthy and cancerous cells, and how? A widely used tool for getting more insight into that question is cell-based modeling. Cell-based models constitute a class of computational, agent-based models that mimic biophysical and molecular interactions between cells. One of the most widely used cell-based modeling formalisms is the cellular Potts model (CPM), a lattice-based, multi particle cell-based modeling approach. The CPM has become a popular and accessible method for modeling mechanisms of multicellular processes including cell sorting, gastrulation, or angiogenesis. The CPM accounts for biophysical cellular properties, including cell proliferation, cell motility, and cell adhesion, which play a key role in cancer. Multiscale models are constructed by extending the agents with intracellular processes including metabolism, growth, and signaling. Here we review the use of the CPM for modeling tumor growth, tumor invasion, and tumor progression. We argue that the accessibility and flexibility of the CPM, and its accurate, yet coarse-grained and computationally efficient representation of cell and tissue biophysics, make the CPM the method of choice for modeling cellular processes in tumor development.

A cell-based model of extracellular-matrix-guided endothelial cell migration during angiogenesis

Angiogenesis, the formation of new blood vessels sprouting from existing ones, occurs in several situations like wound healing, tissue remodeling, and near growing tumors. Under hypoxic conditions, tumor cells secrete growth factors, including VEGF. VEGF activates endothelial cells (ECs) in nearby vessels, leading to the migration of ECs out of the vessel and the formation of growing sprouts. A key process in angiogenesis is cellular self-organization, and previous modeling studies have identified mechanisms for producing networks and sprouts. Most theoretical studies of cellular self-organization during angiogenesis have ignored the interactions of ECs with the extra-cellular matrix (ECM), the jelly or hard materials that cells live in. Apart from providing structural support to cells, the ECM may play a key role in the coordination of cellular motility during angiogenesis. For example, by modifying the ECM, ECs can affect the motility of other ECs, long after they have left. Here, we present an explorative study of the cellular self-organization resulting from such ECM-coordinated cell migration. We show that a set of biologically-motivated, cell behavioral rules, including chemotaxis, haptotaxis, haptokinesis, and ECM-guided proliferation suffice for forming sprouts and branching vascular trees.

Vascular networks due to dynamically arrested crystalline ordering of elongated cells

Recent experimental and theoretical studies suggest that crystallization and glass-like solidification are useful analogies for understanding cell ordering in confluent biological tissues. It remains unexplored how cellular ordering contributes to pattern formation during morphogenesis. With a computational model we show that a system of elongated, cohering biological cells can get dynamically arrested in a network pattern. Our model provides an explanation for the formation of cellular networks in culture systems that exclude intercellular interaction via chemotaxis or mechanical traction.

Computational models for mechanics of morphogenesis

In the developing embryo, tissues differentiate, deform, and move in an orchestrated manner to generate various biological shapes driven by the complex interplay between genetic, epigenetic, and environmental factors. Mechanics plays a key role in regulating and controlling morphogenesis, and quantitative models help us understand how various mechanical forces combine to shape the embryo. Models allow for the quantitative, unbiased testing of physical mechanisms, and when used appropriately, can motivate new experimentaldirections. This knowledge benefits biomedical researchers who aim to prevent and treat congenital malformations, as well as engineers working to create replacement tissues in the laboratory. In this review, we first give an overview of fundamental mechanical theories for morphogenesis, and then focus on models for specific processes, including pattern formation, gastrulation, neurulation, organogenesis, and wound healing. The role of mechanical feedback in development is also discussed. Finally, some perspectives aregiven on the emerging challenges in morphomechanics and mechanobiology.

Directed endothelial cell morphogenesis in micropatterned gelatin methacrylate hydrogels

Engineering of organized vasculature is a crucial step in the development of functional and clinically relevant tissue constructs. A number of previous techniques have been proposed to spatially regulate the distribution of angiogenic biomolecules and vascular cells within biomaterial matrices to promote vascularization. Most of these approaches have been limited to two-dimensional (2D) micropatterned features or have resulted in formation of random vasculature within three-dimensional (3D) microenvironments. In this study, we investigate 3D endothelial cord formation within micropatterned gelatin methacrylate (GelMA) hydrogels with varying geometrical features (50-150 μm height). We demonstrated the significant dependence of endothelial cells proliferation, alignment and cord formation on geometrical dimensions of the patterned features. The cells were able to align and organize within the micropatterned constructs and assemble to form cord structures with organized actin fibers and circular/elliptical cross-sections. The inner layer of the cord structure was filled with gel showing that the micropatterned hydrogel constructs guided the assembly of endothelial cells into cord structures. Notably, the endothelial cords were retained within the hydrogel microconstructs for all geometries after two weeks of culture; however, only the 100 μm-high constructs provided the optimal microenvironment for the formation of circular and stable cord structures. Our findings suggest that endothelial cord formation is a preceding step to tubulogenesis and the proposed system can be used to develop organized vasculature for engineered tissue constructs.

Multilevel complexity of calcium signaling: Modeling angiogenesis

Intracellular calcium signaling is a universal, evolutionary conserved and versatile regulator of cell biochemistry. The complexity of calcium signaling and related cell machinery can be investigated by the use of experimental strategies, as well as by computational approaches. Vascular endothelium is a fascinating model to study the specific properties and roles of calcium signals at multiple biological levels. During the past 20 years, live cell imaging, patch clamp and other techniques have allowed us to detect and interfere with calcium signaling in endothelial cells (ECs), providing a huge amount of information on the regulation of vascularization (angiogenesis) in normal and tumoral tissues. These data range from the spatiotemporal dynamics of calcium within different cell microcompartments to those in entire multicellular and organized EC networks. Beside experimental strategies, in silico endothelial models, specifically designed for simulating calcium signaling, are contributing to our knowledge of vascular physiology and pathology. They help to investigate and predict the quantitative features of proangiogenic events moving through subcellular, cellular and supracellular levels. This review focuses on some recent developments of computational approaches for proangiogenic endothelial calcium signaling. In particular, we discuss the creation of hybrid simulation environments, which combine and integrate discrete Cellular Potts Models. They are able to capture the phenomenological mechanisms of cell morphological reorganization, migration, and intercellular adhesion, with single-cell spatiotemporal models, based on reaction-diffusion equations that describe the agonist-induced intracellular calcium events.

Pattern formation during vasculogenesis

Vasculogenesis, the assembly of the first vascular network, is an intriguing developmental process that yields the first functional organ system of the embryo. In addition to being a fundamental part of embryonic development, vasculogenic processes also have medical importance. To explain the organizational principles behind vascular patterning, we must understand how morphogenesis of tissue level structures can be controlled through cell behavior patterns that, in turn, are determined by biochemical signal transduction processes. Mathematical analyses and computer simulations can help conceptualize how to bridge organizational levels and thus help in evaluating hypotheses regarding the formation of vascular networks. Here, we discuss the ideas that have been proposed to explain the formation of the first vascular pattern: cell motility guided by extracellular matrix alignment (contact guidance), chemotaxis guided by paracrine and autocrine morphogens, and sprouting guided by cell-cell contacts.

On integrating experimental and theoretical models to determine physical mechanisms of morphogenesis

Researchers in developmental biology are increasingly recognizing the value of theoretical models in studies of morphogenesis. However, creating and testing realistic quantitative models for morphogenetic processes can be an extremely challenging task. The focus of this paper is on models for the mechanics of morphogenesis. Models for these problems often must include large changes in geometry, leading to highly nonlinear problems with the possibility of multiple solutions that must be sorted out using experimental data. Here, we illustrate our approach to these problems using the specific example of head fold formation in the early chick embryo. The interplay between experimental and theoretical results is emphasized throughout, as the model is gradually refined. Some of the limitations inherent in theoretical/computational modeling of biological systems are also discussed.

A computational model of in vitro angiogenesis based on extracellular matrix fibre orientation

Recent interest in the process of vascularisation within the biomedical community has motivated numerous new research efforts focusing on the process of angiogenesis. Although the role of chemical factors during angiogenesis has been well documented, the role of mechanical factors, such as the interaction between angiogenic vessels and the extracellular matrix, remains poorly understood. In vitro methods for studying angiogenesis exist; however, measurements available using such techniques often suffer from limited spatial and temporal resolutions. For this reason, computational models have been extensively employed to investigate various aspects of angiogenesis. This paper outlines the formulation and validation of a simple and robust computational model developed to accurately simulate angiogenesis based on length, branching and orientation morphometrics collected from vascularised tissue constructs. Microvessels were represented as a series of connected line segments. The morphology of the vessels was determined by a linear combination of the collagen fibre orientation, the vessel density gradient and a random walk component. Excellent agreement was observed between computational and experimental morphometric data over time. Computational predictions of microvessel orientation within an anisotropic matrix correlated well with experimental data. The accuracy of this modelling approach makes it a valuable platform for investigating the role of mechanical interactions during angiogenesis.

Invasion from a cell aggregate--the roles of active cell motion and mechanical equilibrium

Cell invasion from an aggregate into a surrounding extracellular matrix (ECM) is an important process during development disease, e.g., vascular network assembly or tumor progression. To describe the behavior emerging from autonomous cell motility, cell-cell adhesion and contact guidance by ECM filaments, we propose a suitably modified cellular Potts model. We consider an active cell motility process in which internal polarity is governed by a positive feedback from cell displacements, a mechanism that can result in highly persistent motion when constrained by an oriented ECM structure. The model allows us to explore the interplay between haptotaxis, matrix degradation and active cell movement. We show that for certain conditions the cells are able to both invade the ECM and follow the ECM tracks. Furthermore, we argue that enforcing mechanical equilibrium within a bulk cell mass is of key importance in multicellular simulations.