Multiphase modelling of tumour growth and extracellular matrix interaction: mathematical tools and applications

Resorting to a multiphase modelling framework, tumours are described here as a mixture of tumour and host cells within a porous structure constituted by a remodelling extracellular matrix (ECM), which is wet by a physiological extracellular fluid. The model presented in this article focuses mainly on the description of mechanical interactions of the growing tumour with the host tissue, their influence on tumour growth, and the attachment/detachment mechanisms between cells and ECM. Starting from some recent experimental evidences, we propose to describe the interaction forces involving the extracellular matrix via some concepts coming from viscoplasticity. We then apply the model to the description of the growth of tumour cords and the formation of fibrosis

Controlled rotary motion of light-driven molecular motors assembled on a gold film

Using circular dichroism (CD) spectroscopy, we show that light-driven rotary molecular motors based on overcrowded alkenes can function in a self-assembled monolayer on semi-transparent gold films.

Computational Modeling of Single-Cell Migration::The Leading Role of Extracellular Matrix Fibers

Cell migration is vitally important in a wide variety of biological contexts ranging from embryonic development and wound healing to malignant diseases such as cancer. It is a very complex process that is controlled by intracellular signaling pathways as well as the cell's microenvironment. Due to its importance and complexity, it has been studied for many years in the biomedical sciences, and in the last 30 years it also received an increasing amount of interest from theoretical scientists and mathematical modelers. Here we propose a force-based, individual-based modeling framework that links single-cell migration with matrix fibers and cell-matrix interactions through contact guidance and matrix remodelling. With this approach, we can highlight the effect of the cell's environment on its migration. We investigate the influence of matrix stiffness, matrix architecture, and cell speed on migration using quantitative measures that allow us to compare the results to experiments

Cell_motility: a cross-platform, open source application for the study of cell motion paths

BACKGROUND: Migration is an important aspect of cellular behaviour and is therefore widely studied in cell biology. Numerous components are known to participate in this process in a highly dynamic manner. In order to obtain a better insight in cell migration, mutants or drugs are used and their motive phenotype is then linked with the disturbing factors. One of the typical approaches to study motion paths of individual cells relies on fitting mean square displacements to a persistent random walk function. Since the numerous calculations involved often rely on diverse commercial software packages, the analysis can be expensive, labour-intensive and error-prone work. Additionally, due to the nature of algorithms employed the calculations involved are not readily reproducible without access to the exact software package(s) used. RESULTS: We here present the cell_motility software, an open source Java application under the GNU-GPL license that provides a clear and concise analysis workbench for large amounts of cell motion data. Apart from performing the necessary calculations, the software also visualizes the original motion paths as well as the results of the calculations to help the user interpret the data. The application features an intuitive graphical user interface as well as full user and developer documentation and both source and binary files can be freely downloaded from the project website at . CONCLUSION: In providing a free, open source software solution for the automated processing of cell motion data, we aim to achieve two important goals: labs can greatly simplify their data analysis pipeline as switching between different computational software packages becomes obsolete (thus reducing the chances for human error during data manipulation and transfer) and secondly, to provide scientists in the field with a freely available common platform to perform their analyses, enabling more efficient data quality control through peer reviewing

Exploring hypotheses of the actions of TGF-beta 1 in epidermal wound healing using a 3D computational multiscale model of the human epidermis

In vivo and in vitro studies give a paradoxical picture of the actions of the key regulatory factor TGF-beta 1 in epidermal wound healing with it stimulating migration of keratinocytes but also inhibiting their proliferation. To try to reconcile these into an easily visualized 3D model of wound healing amenable for experimentation by cell biologists, a multiscale model of the formation of a 3D skin epithelium was established with TGF-beta 1 literature-derived rule sets and equations embedded within it. At the cellular level, an agent-based bottom-up model that focuses on individual interacting units ( keratinocytes) was used. This was based on literature-derived rules governing keratinocyte behavior and keratinocyte/ECM interactions. The selection of these rule sets is described in detail in this paper. The agent-based model was then linked with a subcellular model of TGF-beta 1 production and its action on keratinocytes simulated with a complex pathway simulator. This multiscale model can be run at a cellular level only or at a combined cellular/subcellular level. It was then initially challenged ( by wounding) to investigate the behavior of keratinocytes in wound healing at the cellular level. To investigate the possible actions of TGF-beta 1, several hypotheses were then explored by deliberately manipulating some of these rule sets at subcellular levels. This exercise readily eliminated some hypotheses and identified a sequence of spatial-temporal actions of TGF-beta 1 for normal successful wound healing in an easy-to-follow 3D model. We suggest this multiscale model offers a valuable, easy-to-visualize aid to our understanding of the actions of this key regulator in wound healing, and provides a model that can now be used to explore pathologies of wound healing

Differential regulation of β1 integrins by chemoattractants regulates neutrophil migration through fibrin

Chemoattractants differ in their capacity to stimulate neutrophils to adhere to and to migrate through matrices containing fibrin. Formyl methionyl leucyl phenylalanine (fMLP) stimulates neutrophils to adhere closely to, but not to migrate into, fibrin gels. Leukotriene B4 (LTB4) stimulates neutrophils to adhere loosely to and to migrate through fibrin gels. We report that α5β1 integrins regulate the different migratory behaviors on fibrin gels of neutrophils in response to these chemoattractants. fMLP, but not LTB4, activated neutrophil β1 integrins, as measured by binding of mAb 15/7 to an activation epitope on the β1 integrins. Antibodies or peptides that block α5β1 integrins prevented fMLP-stimulated neutrophils from forming zones of close apposition on fibrin and reversed fMLP's inhibitory effect on neutrophil chemotaxis through fibrin. In contrast, neither peptides nor antibodies that block β1 integrins affected the capacity of LTB4-stimulated neutrophils to form zones of loose apposition or to migrate through fibrin gels. These results suggest that chemoattractants generate at least two different messages that direct neutrophils, and perhaps other leukocytes, to accumulate at specific anatomic sites: a general message that induces neutrophils to crawl and a specific message that prepares neutrophils to stop when they contact appropriate matrix proteins for activated β1 integrins

In-Silico Patterning of Vascular Mesenchymal Cells in Three Dimensions

Cells organize in complex three-dimensional patterns by interacting with proteins along with the surrounding extracellular matrix. This organization provides the mechanical and chemical cues that ultimately influence a cell's differentiation and function. Here, we computationally investigate the pattern formation process of vascular mesenchymal cells arising from their interaction with Bone Morphogenic Protein-2 (BMP-2) and its inhibitor, Matrix Gla Protein (MGP). Using a first-principles approach, we derive a reaction-diffusion model based on the biochemical interactions of BMP-2, MGP and cells. Simulations of the model exhibit a wide variety of three-dimensional patterns not observed in a two-dimensional analysis. We demonstrate the emergence of three types of patterns: spheres, tubes, and sheets, and show that the patterns can be tuned by modifying parameters in the model such as the degradation rates of proteins and chemotactic coefficient of cells. Our model may be useful for improved engineering of three-dimensional tissue structures as well as for understanding three dimensional microenvironments in developmental processes.National Institutes of Health (U.S.) (GM69811)United States. Dept. of Energy (DOE CSGF fellowship

From Molecular Signal Activation to Locomotion: An Integrated, Multiscale Analysis of Cell Motility on Defined Matrices

The adhesion, mechanics, and motility of eukaryotic cells are highly sensitive to the ligand density and stiffness of the extracellular matrix (ECM). This relationship bears profound implications for stem cell engineering, tumor invasion and metastasis. Yet, our quantitative understanding of how ECM biophysical properties, mechanotransductive signals, and assembly of contractile and adhesive structures collude to control these cell behaviors remains extremely limited. Here we present a novel multiscale model of cell migration on ECMs of defined biophysical properties that integrates local activation of biochemical signals with adhesion and force generation at the cell-ECM interface. We capture the mechanosensitivity of individual cellular components by dynamically coupling ECM properties to the activation of Rho and Rac GTPases in specific portions of the cell with actomyosin contractility, cell-ECM adhesion bond formation and rupture, and process extension and retraction. We show that our framework is capable of recreating key experimentally-observed features of the relationship between cell migration and ECM biophysical properties. In particular, our model predicts for the first time recently reported transitions from filopodial to “stick-slip” to gliding motility on ECMs of increasing stiffness, previously observed dependences of migration speed on ECM stiffness and ligand density, and high-resolution measurements of mechanosensitive protrusion dynamics during cell motility we newly obtained for this study. It also relates the biphasic dependence of cell migration speed on ECM stiffness to the tendency of the cell to polarize. By enabling the investigation of experimentally-inaccessible microscale relationships between mechanotransductive signaling, adhesion, and motility, our model offers new insight into how these factors interact with one another to produce complex migration patterns across a variety of ECM conditions

An Adhesion-Dependent Switch between Mechanisms That Determine Motile Cell Shape

Keratocytes are fast-moving cells in which adhesion dynamics are tightly coupled to the actin polymerization motor that drives migration, resulting in highly coordinated cell movement. We have found that modifying the adhesive properties of the underlying substrate has a dramatic effect on keratocyte morphology. Cells crawling at intermediate adhesion strengths resembled stereotypical keratocytes, characterized by a broad, fan-shaped lamellipodium, clearly defined leading and trailing edges, and persistent rates of protrusion and retraction. Cells at low adhesion strength were small and round with highly variable protrusion and retraction rates, and cells at high adhesion strength were large and asymmetrical and, strikingly, exhibited traveling waves of protrusion. To elucidate the mechanisms by which adhesion strength determines cell behavior, we examined the organization of adhesions, myosin II, and the actin network in keratocytes migrating on substrates with different adhesion strengths. On the whole, our results are consistent with a quantitative physical model in which keratocyte shape and migratory behavior emerge from the self-organization of actin, adhesions, and myosin, and quantitative changes in either adhesion strength or myosin contraction can switch keratocytes among qualitatively distinct migration regimes