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

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

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

A Model for the Interplay of Receptor Recycling and Receptor-Mediated Contact in T Cells

Orientation of organelles inside T cells (TC) toward antigen-presenting cells (APC) ensures that the immune response is properly directed, but the orientation mechanisms remain largely unknown. Structural dynamics of TC are coupled to dynamics of T-cell receptor (TCR), which recognizes antigen on the APC surface. Engagement of the TCR triggers its internalization followed by delayed polarized recycling to the plasma membrane through the submembrane recycling compartment (RC), which organelle shares intracellular location with the TC effector apparatus. TCR engagement also triggers TC-APC interface expansion enabling further receptor engagement. To analyze the interplay of the cell-cell contact and receptor dynamics, we constructed a new numerical model. The new model displays the experimentally observed selective stabilization of the contact initiated next to the RC, and only transient formation of contact diametrically opposed to the RC. In the general case wherein the TC-APC contact is initiated in an arbitrary orientation to the RC, the modeling predicts that the contact dynamics and receptor recycling can interact, resulting effectively in migration of the contact to the TC surface domain adjacent to the submembrane RC. Using three-dimensional live-cell confocal microscopy, we obtain data consistent with this unexpected behavior. We conclude that a TC can stabilize its contact with an APC by aligning it with the polarized intracellular traffic of TCR. The results also suggest that the orientation of TC organelles, such as the RC and the effector apparatus, toward the APC can be achieved without any intracellular translocation of the organelles

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

A Quorum-Sensing Factor in Vegetative Dictyostelium Discoideum Cells Revealed by Quantitative Migration Analysis

Background: Many cells communicate through the production of diffusible signaling molecules that accumulate and once a critical concentration has been reached, can activate or repress a number of target genes in a process termed quorum sensing (QS). In the social amoeba Dictyostelium discoideum, QS plays an important role during development. However little is known about its effect on cell migration especially in the growth phase. Methods and Findings: To investigate the role of cell density on cell migration in the growth phase, we use multisite timelapse microscopy and automated cell tracking. This analysis reveals a high heterogeneity within a given cell population, and the necessity to use large data sets to draw reliable conclusions on cell motion. In average, motion is persistent for short periods of time (tƒ5min), but normal diffusive behavior is recovered over longer time periods. The persistence times are positively correlated with the migrated distances. Interestingly, the migrated distance decreases as well with cell density. The adaptation of cell migration to cell density highlights the role of a secreted quorum sensing factor (QSF) on cell migration. Using a simple model describing the balance between the rate of QSF generation and the rate of QSF dilution, we were able to gather all experimental results into a single master curve, showing a sharp cell transition between high and low motile behaviors with increasing QSF. Conclusion: This study unambiguously demonstrates the central role played by QSF on amoeboid motion in the growt

Surface plasmon resonance imaging of cells and surface-associated fibronectin

<p>Abstract</p> <p>Background</p> <p>A critical challenge in cell biology is quantifying the interactions of cells with their extracellular matrix (ECM) environment and the active remodeling by cells of their ECM. Fluorescence microscopy is a commonly employed technique for examining cell-matrix interactions. A label-free imaging method would provide an alternative that would eliminate the requirement of transfected cells and modified biological molecules, and if collected nondestructively, would allow long term observation and analysis of live cells.</p> <p>Results</p> <p>Using surface plasmon resonance imaging (SPRI), the deposition of protein by vascular smooth muscle cells (vSMC) cultured on fibronectin was quantified as a function of cell density and distance from the cell periphery. We observed that as much as 120 ng/cm²of protein was deposited by cells in 24 h.</p> <p>Conclusion</p> <p>SPRI is a real-time, low-light-level, label-free imaging technique that allows the simultaneous observation and quantification of protein layers and cellular features. This technique is compatible with live cells such that it is possible to monitor cellular modifications to the extracellular matrix in real-time.</p

An agent-based model of the response to angioplasty and bare-metal stent deployment in an atherosclerotic blood vessel

Purpose: While animal models are widely used to investigate the development of restenosis in blood vessels following an intervention, computational models offer another means for investigating this phenomenon. A computational model of the response of a treated vessel would allow investigators to assess the effects of altering certain vessel- and stent-related variables. The authors aimed to develop a novel computational model of restenosis development following an angioplasty and bare-metal stent implantation in an atherosclerotic vessel using agent-based modeling techniques. The presented model is intended to demonstrate the body's response to the intervention and to explore how different vessel geometries or stent arrangements may affect restenosis development. Methods: The model was created on a two-dimensional grid space. It utilizes the post-procedural vessel lumen diameter and stent information as its input parameters. The simulation starting point of the model is an atherosclerotic vessel after an angioplasty and stent implantation procedure. The model subsequently generates the final lumen diameter, percent change in lumen cross-sectional area, time to lumen diameter stabilization, and local concentrations of inflammatory cytokines upon simulation completion. Simulation results were directly compared with the results from serial imaging studies and cytokine levels studies in atherosclerotic patients from the relevant literature. Results: The final lumen diameter results were all within one standard deviation of the mean lumen diameters reported in the comparison studies. The overlapping-stent simulations yielded results that matched published trends. The cytokine levels remained within the range of physiological levels throughout the simulations. Conclusion: We developed a novel computational model that successfully simulated the development of restenosis in a blood vessel following an angioplasty and bare-metal stent deployment based on the characteristics of the vessel crosssection and stent. A further development of this model could ultimately be used as a predictive tool to depict patient outcomes and inform treatment options. © 2014 Curtin, Zhou

Acidic Extracellular pH Promotes Activation of Integrin αvβ3

Acidic extracellular pH is characteristic of the cell microenvironment in several important physiological and pathological contexts. Although it is well established that acidic extracellular pH can have profound effects on processes such as cell adhesion and migration, the underlying molecular mechanisms are largely unknown. Integrin receptors physically connect cells to the extracellular matrix, and are thus likely to modulate cell responses to extracellular conditions. Here, we examine the role of acidic extracellular pH in regulating activation of integrin [alpha]v[beta]3. Through computational molecular dynamics simulations, we find that acidic extracellular pH promotes opening of the [alpha]v[beta]3 headpiece, indicating that acidic pH can thereby facilitate integrin activation. This prediction is consistent with our flow cytometry and atomic force microscope-mediated force spectroscopy assays of integrin [alpha]v[beta]3 on live cells, which both demonstrate that acidic pH promotes activation at the intact cell surface. Finally, quantification of cell morphology and migration measurements shows that acidic extracellular pH affects cell behavior in a manner that is consistent with increased integrin activation. Taken together, these computational and experimental results suggest a new and complementary mechanism of integrin activation regulation, with associated implications for cell adhesion and migration in regions of altered pH that are relevant to wound healing and cancer.National Institute of Biomedical Imaging and Bioengineering (U.S.) (Award Number T32EB006348)Massachusetts Institute of Technology (Collamore-Rogers Fellowship)National Institutes of Health (U.S.) (NIH Cell Migration Consortium Grant U54-GM069668)National Science Foundation (U.S.) (CAREER Award)Singapore-MIT Alliance for Research and Technology (BioSystem and Micromechanics (BioSyM) Interdisciplinary Research Group