Multiscale modelling of palisade formation in gliobastoma multiforme.

Palisades are characteristic tissue aberrations that arise in glioblastomas. Observation of palisades is considered as a clinical indicator of the transition from a noninvasive to an invasive tumour. In this paper we propose a computational model to study the influence of the hypoxic switch in palisade formation. For this we produced three-dimensional realistic simulations, based on a multiscale hybrid model, coupling the evolution of tumour cells and the oxygen diffusion in tissue, that depict the shape of palisades during its formation. Our results can be summarized as follows: (1) the presented simulations can provide clinicians and biologists with a better understanding of three-dimensional structure of palisades as well as of glioblastomas growth dynamics; (2) we show that heterogeneity in cell response to hypoxia is a relevant factor in palisade and pseudopalisade formation; (3) we show how selective processes based on the hypoxia switch influence the tumour proliferation.

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.

From genotypes to phenotypes: classification of the tumour profiles for different variants of the cadherin adhesion pathway.

The E-cadherin adhesive profile expressed by a tumour is a characterization of the intracellular and intercellular protein interactions that control cell-cell adhesion. Within the intracellular proteins that determine the tumour adhesive profile, Src and PI3 are two essentials to initiate the formation of the E-cadherin adhesion complex. On the other hand, Src has also the capability of disrupting the ß-catenin-E-cadherin complex and down-regulating cell-cell adhesion. In this paper, using a multi-scale mathematical model, we study the role of each of these proteins in the adhesive profile and invasive properties of the tumour. To do this, we create three versions of an intracellular model that explains the interplay between the proteins E-cadherin, ß-catenin, Src and PI3; and we couple them to the strength of the cell-cell adhesion forces within an individual-cell-based model. The simulation results show how the tumour profile and its aggressive potential may change depending on the intrinsic characteristics of the protein pathways, and how these pathways may influence the early stages of cancer invasion. Our major findings may be summarized as follows. (1) Intermediate levels of Src synthesis rates generate the least invasive tumour phenotype. (2) Conclusions drawn from findings obtained from the intracellular molecular dynamics (here cadherin-catenin binding complexes) to the multi-cellular invasive potential of a tumour may be misleading or erroneous. The conclusions should be validated in a multi-cellular context on timescales relevant for population growth. (3) Monoclonal populations of more cohesive cells with otherwise equal properties tend to grow slower. (4) Less cohesive cells tend to outcompete more cohesive cells. (5) Less cohesive cells have a larger probability of invasion as migration forces can more easily outbalance cohesive forces.

Multi-scale modelling of cancer cell intravasation: the role of cadherins in metastasis.

Transendothelial migration is a crucial process of the metastatic cascade in which a malignant cell attaches itself to the endothelial layer forming the inner wall of a blood or lymph vessel and creates a gap through which it enters into the bloodstream (or lymphatic system) and then is transported to distant parts of the body. In this process both biological pathways involving cell adhesion molecules such as VE-cadherin and N-cadherin, and the biophysical properties of the cells play an important role. In this paper, we present one of the first mathematical models considering the problem of cancer cell intravasation. We use an individual force-based multi-scale approach which accounts for intra- and inter-cellular protein pathways and for the physical properties of the cells, and a modelling framework which accounts for the biological shape of the vessel. Using our model, we study the influence of different protein pathways in the achievement of transendothelial migration and give quantitative simulation results comparable with real experiments.

Modeling the influence of the E-cadherin-beta-catenin pathway in cancer cell invasion: a multiscale approach.

In this article, we show, using a mathematical multiscale model, how cell adhesion may be regulated by interactions between E-cadherin and beta-catenin and how the control of cell adhesion may be related to cell migration, to the epithelial-mesenchymal transition and to invasion in populations of eukaryotic cells. E-cadherin mediates cell-cell adhesion and plays a critical role in the formation and maintenance of junctional contacts between cells. Loss of E-cadherin-mediated adhesion is a key feature of the epithelial-mesenchymal transition. beta-catenin is an intracellular protein associated with the actin cytoskeleton of a cell. E-cadherins bind to beta-catenin to form a complex which can interact both with neighboring cells to form bonds, and with the cytoskeleton of the cell. When cells detach from one another, beta-catenin is released into the cytoplasm, targeted for degradation, and downregulated. In this process there are multiple protein-complexes involved which interact with beta-catenin and E-cadherin. Within a mathematical individual-based multiscale model, we are able to explain experimentally observed patterns solely by a variation of cell-cell adhesive interactions. Implications for cell migration and cancer invasion are also discussed.

Multi-scale modelling of the dynamics of cell colonies: insights into cell-adhesion forces and cancer invasion from in silico simulations.

Studying the biophysical interactions between cells is crucial to understanding how normal tissue develops, how it is structured and also when malfunctions occur. Traditional experiments try to infer events at the tissue level after observing the behaviour of and interactions between individual cells. This approach assumes that cells behave in the same biophysical manner in isolated experiments as they do within colonies and tissues. In this paper, we develop a multi-scale multi-compartment mathematical model that accounts for the principal biophysical interactions and adhesion pathways not only at a cell-cell level but also at the level of cell colonies (in contrast to the traditional approach). Our results suggest that adhesion/separation forces between cells may be lower in cell colonies than traditional isolated single-cell experiments infer. As a consequence, isolated single-cell experiments may be insufficient to deduce important biological processes such as single-cell invasion after detachment from a solid tumour. The simulations further show that kinetic rates and cell biophysical characteristics such as pressure-related cell-cycle arrest have a major influence on cell colony patterns and can allow for the development of protrusive cellular structures as seen in invasive cancer cell lines independent of expression levels of pro-invasion molecules.