Mechanical signalling and angiogenesis. The integration of cell-extracellular matrix couplings

Falsifying computational models of endothelial cell network formation through quantitative comparison with in vitro models

During angiogenesis, endothelial cells expand the vasculature by migrating from existing blood vessels, proliferating and collectively organizing into new capillaries. In vitro and in vivo experimentation is instrumental for identifying the molecular players and cell behaviour that regulate angiogenesis. Alongside experimental work, computational and mathematical models of endothelial cell network formation have helped to analyse if the current molecular and cellular understanding of endothelial cell behaviour is sufficient to explain the formation of endothelial cell networks. As input, the models take (a subset of) the current knowledge or hypotheses of single cell behaviour and capture it into a dynamical, mathematical description. As output, they predict the multicellular behaviour following from the actions of many individual cells, i.e., formation of a vascular-like network. Paradoxically, computational modelling based on different assumptions, i.e., completely different, sometimes non-intersecting sets of observed single cell behaviour, can reproduce the same angiogenesis-like multicellular behaviour, making it practically impossible to decide which, if any, of these models is correct. Here we present dynamical analyses of time-lapses of in vitro endothelial cell network formation experiments and compare these with dynamic analyses of three mathematical models: (1) the cell elongation model; (2) the contact-inhibited chemotaxis model; and (3) the mechanical cell-cell communication model. We extract a variety of dynamical characteristics of endothelial cell network formation using a custom time-lapse video analysis pipeline in ImageJ. We compare the dynamical network characteristics of the in vitro experiments to those of the cellular networks produced by the computational models. We test the response of the in silico dynamical cell network characteristics to changes in cell density and make related changes in the in vitro experiments. Of the three computational models that we have considered, the cell elongation model best captures the remodelling phase of in vitro endothelial cell network formation. Furthermore, in the in vitro model, the final size and number of lacunae in the network are independent of the initial cell density. This observation is also reproduced in the cell elongation model, but not in the other two models that we have considered. Altogether, we present an approach to model validation based on comparisons of time-resolved data and variations of model conditions.

Modeling the extracellular matrix in cell migration and morphogenesis: a guide for the curious biologist

The extracellular matrix (ECM) is a highly complex structure through which biochemical and mechanical signals are transmitted. In processes of cell migration, the ECM also acts as a scaffold, providing structural support to cells as well as points of potential attachment. Although the ECM is a well-studied structure, its role in many biological processes remains difficult to investigate comprehensively due to its complexity and structural variation within an organism. In tandem with experiments, mathematical models are helpful in refining and testing hypotheses, generating predictions, and exploring conditions outside the scope of experiments. Such models can be combined and calibrated with in vivo and in vitro data to identify critical cell-ECM interactions that drive developmental and homeostatic processes, or the progression of diseases. In this review, we focus on mathematical and computational models of the ECM in processes such as cell migration including cancer metastasis, and in tissue structure and morphogenesis. By highlighting the predictive power of these models, we aim to help bridge the gap between experimental and computational approaches to studying the ECM and to provide guidance on selecting an appropriate model framework to complement corresponding experimental studies.

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.

Mechanical Models of Pattern and Form in Biological Tissues: The Role of Stress-Strain Constitutive Equations

Mechanical and mechanochemical models of pattern formation in biological tissues have been used to study a variety of biomedical systems, particularly in developmental biology, and describe the physical interactions between cells and their local surroundings. These models in their original form consist of a balance equation for the cell density, a balance equation for the density of the extracellular matrix (ECM), and a force-balance equation describing the mechanical equilibrium of the cell-ECM system. Under the assumption that the cell-ECM system can be regarded as an isotropic linear viscoelastic material, the force-balance equation is often defined using the Kelvin-Voigt model of linear viscoelasticity to represent the stress-strain relation of the ECM. However, due to the multifaceted bio-physical nature of the ECM constituents, there are rheological aspects that cannot be effectively captured by this model and, therefore, depending on the pattern formation process and the type of biological tissue considered, other constitutive models of linear viscoelasticity may be better suited. In this paper, we systematically assess the pattern formation potential of different stress-strain constitutive equations for the ECM within a mechanical model of pattern formation in biological tissues. The results obtained through linear stability analysis and the dispersion relations derived therefrom support the idea that fluid-like constitutive models, such as the Maxwell model and the Jeffrey model, have a pattern formation potential much higher than solid-like models, such as the Kelvin-Voigt model and the standard linear solid model. This is confirmed by the results of numerical simulations, which demonstrate that, all else being equal, spatial patterns emerge in the case where the Maxwell model is used to represent the stress-strain relation of the ECM, while no patterns are observed when the Kelvin-Voigt model is employed. Our findings suggest that further empirical work is required to acquire detailed quantitative information on the mechanical properties of components of the ECM in different biological tissues in order to furnish mechanical and mechanochemical models of pattern formation with stress-strain constitutive equations for the ECM that provide a more faithful representation of the underlying tissue rheology.

Modelling optimal delivery of bFGF to chronic wounds using ODEs

In this paper, we present an ordinary differential equation model depicting the interactions of basic fibroblast growth factor (bFGF) and its binding agents in a chronic wound. The delivery of bFGF was treated as a control variable and is coupled to an objective functional. By optimising the objective functional with respect to the control, predictions for optimal delivery rates of bFGF are proposed. The optimal control is then validated by comparing the cost of the objective functional for the optimal delivery rate and several alternative delivery rates. This paper addresses two objectives of effective drug delivery to chronic wounds. The first is to provide insight for the priority of delivering bFGF: to minimise the quantity of bFGF, or to optimise the distribution of bound bFGF. For effective concentrations of bound bFGF, the optimisation of bound bFGF must be prioritised over the minimisation of bFGF delivered. The second objective is to comment on the effect of the proteolytic environment within the wound, with the concentration of bound bFGF starting to decrease late in the treatment period for highly proteolytic environments. This will lead to long term complications with wound closure after the treatment has been completed. Also, it was found that for highly proteolytic environments, the cost of delivering bFGF increased. The need for optimal drug delivery is made apparent by the burden of chronic wounds on the medical industry across the developed world.

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

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

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.

Hydrogel-based microfluidics for vascular tissue engineering

In this work, we have explored 3-D co-culture of vasculogenic cells within a synthetically modified fibrin hydrogel. Fibrinogen was covalently linked with PEG-NHS in order to improve its degradability resistance and physico-optical properties. We have studied influences of the degree of protein PEGylation and the concentration of enzyme thrombin used for the gel preparation on cellular responses. Scanning electron microscopy analysis of prepared gels revealed that the degree of PEGylation and the concentration of thrombin strongly influenced microstructural characteristics of the protein hydrogel. Human umbilical vein endothelial cells (HUVECs) and human adipose-derived stem cells (hASCs), used as vasculogenic co-culture, could grow in 5:1 PEGylated fibrin gels prepared using 1:0.2 protein to thrombin ratio. This gel formulation supported hASCs and HUVECs spreading and the formation of cell extensions and cell-to-cell contacts. Expression of specific ECM proteins and vasculogenic process inherent cellular enzymatic activity were investigated by immunofluorescent staining, gelatin zymography, western blot and RT-PCR analysis. After evaluation of the optimal gel composition and PEGylation ratio, the hydrogel was utilized for investigation of vascular tube formation within a perfusable microfluidic system. The morphological development of this co-culture within a perfused hydrogel over 12 days led to the formation of interconnected HUVEC-hASC network. The demonstrated PEGylated fibrin microfluidic approach can be used for incorporating other cell types, thus representing a unique experimental platform for basic vascular tissue engineering and drug screening applications.

PDMS substrate stiffness affects the morphology and growth profiles of cancerous prostate and melanoma cells

A deep understanding of the interaction between cancerous cells and surfaces is particularly important for the design of lab-on-chip devices involving the use of polydimethylsiloxane (PDMS). In our studies, the effect of PDMS substrate stiffness on mechanical properties of cancerous cells was investigated in conditions where the PDMS substrate is not covered with any of extracellular matrix proteins. Two human prostate cancer (Du145 and PC-3) and two melanoma (WM115 and WM266-4) cell lines were cultured on two groups of PDMS substrates that were characterized by distinct stiffness, i.e. 0.75 ± 0.06 MPa and 2.92 ± 0.12 MPa. The results showed the strong effect on cellular behavior and morphology. The detailed analysis of chemical and physical properties of substrates revealed that cellular behavior occurs only due to substrate elasticity.

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.

Extracellular matrix density regulates the rate of neovessel growth and branching in sprouting angiogenesis

Angiogenesis is regulated by the local microenvironment, including the mechanical interactions between neovessel sprouts and the extracellular matrix (ECM). However, the mechanisms controlling the relationship of mechanical and biophysical properties of the ECM to neovessel growth during sprouting angiogenesis are just beginning to be understood. In this research, we characterized the relationship between matrix density and microvascular topology in an in vitro 3D organ culture model of sprouting angiogenesis. We used these results to design and calibrate a computational growth model to demonstrate how changes in individual neovessel behavior produce the changes in vascular topology that were observed experimentally. Vascularized gels with higher collagen densities produced neovasculatures with shorter vessel lengths, less branch points, and reduced network interconnectivity. The computational model was able to predict these experimental results by scaling the rates of neovessel growth and branching according to local matrix density. As a final demonstration of utility of the modeling framework, we used our growth model to predict several scenarios of practical interest that could not be investigated experimentally using the organ culture model. Increasing the density of the ECM significantly reduced angiogenesis and network formation within a 3D organ culture model of angiogenesis. Increasing the density of the matrix increases the stiffness of the ECM, changing how neovessels are able to deform and remodel their surroundings. The computational framework outlined in this study was capable of predicting this observed experimental behavior by adjusting neovessel growth rate and branching probability according to local ECM density, demonstrating that altering the stiffness of the ECM via increasing matrix density affects neovessel behavior, thereby regulated vascular topology during angiogenesis.

Direct observation of CD4 T cell morphologies and their cross-sectional traction force derivation on quartz nanopillar substrates using focused ion beam technique

Direct observations of the primary mouse CD4 T cell morphologies, e.g., cell adhesion and cell spreading by culturing CD4 T cells in a short period of incubation (e.g., 20 min) on streptavidin-functionalized quartz nanopillar arrays (QNPA) using a high-content scanning electron microscopy method were reported. Furthermore, we first demonstrated cross-sectional cell traction force distribution of surface-bound CD4 T cells on QNPA substrates by culturing the cells on top of the QNPA and further analysis in deflection of underlying QNPA via focused ion beam-assisted technique.

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.

Modelling the interaction of keratinocytes and fibroblasts during normal and abnormal wound healing processes

The crosstalk between fibroblasts and keratinocytes is a vital component of the wound healing process, and involves the activity of a number of growth factors and cytokines. In this work, we develop a mathematical model of this crosstalk in order to elucidate the effects of these interactions on the regeneration of collagen in a wound that heals by second intention. We consider the role of four components that strongly affect this process: transforming growth factor-β, platelet-derived growth factor, interleukin-1 and keratinocyte growth factor. The impact of this network of interactions on the degradation of an initial fibrin clot, as well as its subsequent replacement by a matrix that is mainly composed of collagen, is described through an eight-component system of nonlinear partial differential equations. Numerical results, obtained in a two-dimensional domain, highlight key aspects of this multifarious process, such as re-epithelialization. The model is shown to reproduce many of the important features of normal wound healing. In addition, we use the model to simulate the treatment of two pathological cases: chronic hypoxia, which can lead to chronic wounds; and prolonged inflammation, which has been shown to lead to hypertrophic scarring. We find that our model predictions are qualitatively in agreement with previously reported observations and provide an alternative pathway for gaining insight into this complex biological process.

Investigating metalloproteinases MMP-2 and MMP-9 mechanosensitivity to feedback loops involved in the regulation of in vitro angiogenesis by endogenous mechanical stresses

Angiogenesis is a complex morphogenetic process regulated by growth factors, but also by the force balance between endothelial cells (EC) traction stresses and extracellular matrix (ECM) viscoelastic resistance. Studies conducted with in vitro angiogenesis assays demonstrated that decreasing ECM stiffness triggers an angiogenic switch that promotes organization of EC into tubular cords or pseudo-capillaries. Thus, mechano-sensitivity of EC with regard to proteases secretion, and notably matrix metalloproteinases (MMPs), should likely play a pivotal role in this switching mechanism. While most studies analysing strain regulation of MMPs used cell cultured on stretched membranes, this work focuses on MMP expression during self-assembly of EC into capillary-like structures within fibrin gels, i.e. on conditions that mimics more closely the in vivo cellular mechanical microenvironment. The activity of MMP-2 and MMP-9, two MMPs that have a pivotal role in capillaries formation, has been monitored in pace with the progressive elongation of EAhy926 cells that takes place during the emergence of cellular cords. We found an increase of the zymogen proMMP-2 that correlates with the initial stages of EC cords formation. However, MMP-2 was not detected. ProMMP-9 secretion decreased, with levels of MMP-9 kept at a rather low value. In order to analyse more precisely the observed differences of EAhy926 response on fibrin and plastic substrates, we proposed a theoretical model of the mechano-regulation of proMMP-2 activation in the presence of type 2 tissue inhibitor of MMPs (TIMP-2). Using association/dissociation rates experimentally reported for this enzymatic network, the model adequately describes the synergism of proMMP-2 and TIMP-2 strain activation during pseudo-capillary morphogenesis. All together, these results provide a first step toward a systems biology approach of angiogenesis mechano-regulation by cell-generated extracellular stresses and strains.

Wave front migration of endothelial cells in a bone-implant interface

The neo-vascularization of the host site is crucial for the primary fixation and the long-term stability of the bone-implant interface. Our aim was to investigate the progression of endothelial cell population in the first weeks of healing. We proposed a theoretical reactive model to study the role of initial conditions, random motility, haptotaxis and chemotaxis in interactions with fibronectin factors and transforming angiogenic factors. The application of governing equations concerned a canine experimental implant and numerical experiments based upon statistical designs of experiments supported the discussion. We found that chemotaxis due to transforming angiogenic factors was attracting endothelial cells present into the host bone. Haptotaxis conditioned by fibronectin factors favored cells adhesion to the host bone. The combination of diffusive and reactive effects nourished the wave front migration of endothelial cells from the host bone towards the implant. Angiogenesis goes together with new-formed bone formation in clinics, so the similarity of distribution patterns of mineralized tissue observed in-vivo and the spatio-temporal concentration of endothelial cells predicted by the model, tended to support the reliability of our theoretical approach.

A finite element method approach for the mechanobiological modeling of the osseointegration of a dental implant

The aim of this paper is to introduce a new mathematical model using a mechanobiological approach describing the process of osseointegration at the bone-dental implant interface in terms of biological and mechanical factors and the implant surface. The model has been computationally implemented by using the finite element method. The results show the spatial-temporal patterns distribution at the bone-dental implant interface and demonstrate the ability of the model to reproduce features of the wound healing process such as blood clotting, osteogenic cell migration, granulation tissue formation, collagen-like matrix displacements and new osteoid formation. The model might be used as a methodological basis for designing a dental tool useful to predict the degree of osseointegration of dental implants and subsequent formulation of mathematical models associated with different types of bone injuries and different types of implantable devices.

Formation of human capillaries in vitro: the engineering of prevascularized matrices

Initial take, development, and function of transplanted engineered tissue substitutes are crucially dependent on rapid and adequate blood perfusion. Therefore, the development of rapidly and efficiently vascularized tissue grafts is vital for tissue engineering and regenerative medicine. Here we report on the construction of a network of highly organotypic capillaries in engineered tissue substitutes. We employed a three-dimensional culture system consisting of human microvascular endothelial cells. These were reproducibly expanded at high purity and subsequently seeded into biodegradable, fibrin-based hydrogels. The process of capillary formation in vitro followed the principles of both angiogenesis and postnatal vasculogenesis and a distinct sequence of other developmental steps that closely resemble embryonic neovascularization. Capillary lumen formation in vitro was initiated by the deposition of a basement membrane and intensive pinocytosis, followed by the generation of intracellular vacuoles, successive fusion of these vacuoles, and finally the formation of a long, continuous lumen. After transplantation the vascular structures were stabilized by mural cells of the recipient animal. Our findings suggest that the in vitro engineering of prevascularized matrices is within reach.

Interaction of angiogenic microvessels with the extracellular matrix

The extracellular matrix (ECM) plays a critical role in angiogenesis by providing biochemical and positional cues, as well as by mechanically influencing microvessel cell behavior. Considerable information is known concerning the biochemical cues relevant to angiogenesis, but less is known about the mechanical dynamics during active angiogenesis. The objective of this study was to characterize changes in the material properties of a simple angiogenic tissue before and during angiogenesis. During sprouting, there was an overall decrease in tissue stiffness followed by an increase during neovessel elongation. The fall in matrix stiffness coincided with peak matrix metalloproteinase mRNA expression and elevated proteolytic activity. An elevated expression of genes for ECM components and cell-ECM interaction molecules and a subsequent drop in proteolytic activity (although enzyme levels remained elevated) coincided with the subsequent stiffening. The results of this study show that the mechanical properties of a scaffold tissue may be actively modified during angiogenesis by the growing microvasculature.

The rigidity in fibrin gels as a contributing factor to the dynamics of in vitro vascular cord formation

While the formation of vascular cords in in vitro angiogenesis assay is commonly used to test the angiogenic properties of many molecular or cellular components, an extensive characterisation of the dynamics of this process is still lacking. Up to now, quantitative studies only focused on the resulting capillary structures characterised through static morphometric approaches. We therefore propose in this paper a rather extensive characterisation aiming to identify different stages in the dynamics of this process, through the investigation of the influence of the rigidity of the fibrin extracellular matrix on the growth of the vascular cords. Using time lapse videomicroscopy, the time evolution of relevant morphodynamical parameters has been considered both at the cell level and at the cell population level. At the cell level, a trajectography analysis of individual cells observed in different locations of the growing network has been conducted and analysed using a random walk model. From image sequence analysis and segmentation i.e. extraction of the boundaries of the lacunae formed through matrix degradation and cell tractions, the evolution of the lacunae surface has been precisely quantified, revealing different phases and transitions in the growth patterns. Our results indicate that the rigidity of the extracellular fibrin matrix strongly influences the different stages, i.e. the dynamics of the angiogenic process. Consequently, optimal rigidity conditions for the formation of stable vascular cord networks could be identified in the context of our experiments.

Mechanics and chemotaxis in the morphogenesis of vascular networks

The formation of vascular networks in vitro develops along two rather distinct stages: during the early migration-dominated stage the main features of the pattern emerge, later the mechanical interaction of the cells with the substratum stretches the network. Mathematical models in the relevant literature have been focusing just on either of the aspects of this complex system. In this paper, a unified view of the morphogenetic process is provided in terms of physical mechanisms and mathematical modeling.

QxDB: a generic database to support mathematical modelling in biology

QxDB (quantitative x-modelling database) is a web-based generic database package designed especially to house quantitative and structural information. Its development was motivated by the need for centralized access to such results for development of mathematical models, but its usefulness extends to the general research community of both modellers and experimentalists. Written in PHP (Hyper Preprocessor) and MYSQL, the database is easily adapted to new fields of research and ported to Apache-based web servers. Unlike most existing databases, experimental and observational results curated in QxDB are supplemented by comments from the experts who contribute input to the database, giving their evaluations of experimental techniques, breadth of validity of results, experimental conditions, and the like, thus providing the visitor with a basis for gauging the quality (or appropriateness) of each item for his/her needs. QxDB can be easily customized by adapting the contents of the database table containing the descriptors that characterize each data record according to an informal ontology of the research domain. We will illustrate this adaptability of QxDB by presenting two examples, the first dealing with modelling in oncology and the second with mechanical properties of cells and tissues.

Mechanical modelling of cell/ECM and cell/cell interactions during the contraction of a fibroblast-populated collagen microsphere: theory and model simulation

The cell-derived forces generated during wound healing may be beneficial in reducing the wound size by contraction, but are also detrimental because of the high mechanical stresses in and around the scar that can cause pain, disfigurement and loss of tissue function. The fibroblasts seeded collagen matrix is regarded as an in vitro model for this process and as a suitable way to study these mechanical aspects which are poorly understood. It is proposed here, to improve the continuum theory of Murray-Oster by assuming that more than one control system may be operative in wound contraction regulation. In particular, it is suggested that the wound contraction mechanism is not exclusively due to cell/ECM interaction forces but rather that both ECM/cell and the cell/cell interactions operate together in such process.

A Review of Vasculogenesis Models

Mechanical and chemical models of vasculogenesis are critically reviewed with an emphasis on their ability to predict experimentally measured quantities. Final remarks suggest a possibility to merge the capabilities of different models into a unified approach.

Critical conditions for pattern formation and in vitro tubulogenesis driven by cellular traction fields

In vitro angiogenesis assays have shown that tubulogenesis of endothelial cells within biogels, like collagen or fibrin gels, only appears for a critical range of experimental parameter values. These experiments have enabled us to develop and validate a theoretical model in which mechanical interactions of endothelial cells with extracellular matrix influence both active cell migration--haptotaxis--and cellular traction forces. Depending on the number of cells, cell motility and biogel rheological properties, various 2D endothelial patterns can be generated, from non-connected stripe patterns to fully connected networks, which mimic the spatial organization of capillary structures. The model quantitatively and qualitatively reproduces the range of critical values of cell densities and fibrin concentrations for which these cell networks are experimentally observed. We illustrate how cell motility is associated to the self-enhancement of the local traction fields exerted within the biogel in order to produce a pre-patterning of this matrix and subsequent formation of tubular structures, above critical thresholds corresponding to bifurcation points of the mathematical model. The dynamics of this morphogenetic process is discussed in the light of videomicroscopy time lapse sequences of endothelial cells (EAhy926 line) in fibrin gels. Our modeling approach also explains how the progressive appearance and morphology of the cellular networks are modified by gradients of extracellular matrix thickness.

Remodeled-matrix contraction by fibroblasts: numerical investigations

It is well known that the fibroblast-collagen-matrix contraction model is a unique way to study mechanical interactions that regulate wound contraction of connective tissue cells. This contraction, due to cell traction, plays important roles in wound healing and pathological contractures. A continuum model initially used for the study of mesenchymal morphogenesis is revisited and numerically investigated by assuming that the extracellular matrix has adaptive-elastic properties. The set of non-linear partial differential equations is solved numerically by a finite difference method and the obtained results are discussed.

Pattern formation in integrative biology--a marriage of theory and experiment

The interdisciplinary challenge to discover the underlying mechanisms in the generation of biological pattern and form are central issues in development. In this review we briefly discuss the philosophy of such an integrative biology approach. We then describe one pattern formation approach which has intimate ties to experiment, namely the mechano-chemical theory. We discuss, by way of example, the successful use of such a framework in the formation of cell-matrix networks, intimately associated with angiogenesis. All of the model parameters are estimated from experiment and the results of the model analysis compare well with experiment. We conclude with some general views on the use of models in biology.