Dynamic modeling of cancer cell migration in an extracellular matrix fiber network (original) (raw)

A model of cell migration within the extracellular matrix based on a phenotypic switching mechanism

Mathematical Medicine and Biology, 2010

Cell migration involves different mechanisms in different cell types and tissue environments. Changes in migratory behaviour have been observed experimentally and associated with phenotypic switching in various situations, such as the migration-proliferation dichotomy of glioma cells, the epithelialmesenchymal transition or the mesenchymal-amoeboid transition of fibrosarcoma cells in the extracellular matrix (ECM). In the present study, we develop a modelling framework to account for changes in migratory behaviour associated with phenotypic switching. We take into account the influence of the ECM on cell motion and more particularly the alignment process along the fibers. We use a mesoscopic description to model two cell populations with different migratory properties. We derive the corresponding continuum (macroscopic) model by appropriate rescaling, which leads to a generic reaction-diffusion system for the two cell phenotypes. We investigate phenotypic adaptation to dense and sparse environments and propose two complementary transition mechanisms. We study these mechanisms by using a combination of linear stability analysis and numerical simulations. Our investigations reveal that when the cell migratory ability is reduced by a crowded environment, a diffusive instability may appear and lead to the formation of aggregates of cells of the same phenotype. Finally, we discuss the importance of the results from a biological perspective.

Cell Invasion Dynamics into a Three Dimensional Extracellular Matrix Fibre Network

PLoS computational biology, 2015

The dynamics of filopodia interacting with the surrounding extracellular matrix (ECM) play a key role in various cell-ECM interactions, but their mechanisms of interaction with the ECM in 3D environment remain poorly understood. Based on first principles, here we construct an individual-based, force-based computational model integrating four modules of 1) filopodia penetration dynamics; 2) intracellular mechanics of cellular and nuclear membranes, contractile actin stress fibers, and focal adhesion dynamics; 3) structural mechanics of ECM fiber networks; and 4) reaction-diffusion mass transfers of seven biochemical concentrations in related with chemotaxis, proteolysis, haptotaxis, and degradation in ECM to predict dynamic behaviors of filopodia that penetrate into a 3D ECM fiber network. The tip of each filopodium crawls along ECM fibers, tugs the surrounding fibers, and contracts or retracts depending on the strength of the binding and the ECM stiffness and pore size. This filopod...

Modeling the motion of a cell population in the extracellular matrix

DYNAMICAL SYSTEMS, 2007

The paper aims at describing the motion of cells in fibrous tissues taking into account the interaction with the network fibers and among cells, chemotaxis, and contact guidance from network fibers. Both a kinetic model and its continuum limit are described.

Effects of Migrating Cell-Induced Matrix Reorganization on 3D Cancer Cell Migration

Cellular and Molecular Bioengineering, 2014

The migration of cells is fundamental to a number of physiological/pathological processes, ranging from embryonic development, tissue regeneration to cancer metastasis. Current research on cell migration is largely based on simplified in vitro models that assume a homogeneous microenvironment and overlook the modification of extracellular matrix (ECM) by the cells. To address this shortcoming, we developed a nested threedimensional (3D) collagen hydrogel model mimicking the connective tissue confronted by highly malignant breast cancer cells, MDA-MB-231. Strikingly, our findings revealed two distinct cell migration patterns: a rapid and directionally persistent collective migration of the leader cells and a more randomized migration in the regions that have previously been significantly modified by cells. The cell-induced modifications, which typically include clustering and alignment of fibers, effectively segmented the matrix into smaller sub-regions. Our results suggest that in an elastic 3D matrix, the presence of adjacent cells that have modified the matrix may in fact become physical hurdle to a migrating cell. Furthermore, our study emphasizes the need for a micromechanical understanding in the context of cancer invasion that allows for cell-induced modification of ECM and a heterogeneous cell migration.

Modeling the influence of nucleus elasticity on cell invasion in fiber networks and microchannels

Journal of Theoretical Biology, 2013

Cell migration in highly constrained extracellular matrices is exploited in scaffold-based tissue engineering and is fundamental in a wide variety of physiological and pathological phenomena, among others in cancer invasion and development. Research into the critical processes involved in cell migration has mainly focused on cell adhesion and proteolytic degradation of the external environment. However, rising evidence has recently shown that a number of cell-derived biophysical and mechanical parameters, among others nucleus stiffness and cell deformability, plays a major role in cell motility, especially in the ameboid-like migration mode in 3D confined tissue structures. We here present an extended cellular Potts model (CPM) first used to simulate a micro-fabricated migration chip, which tests the active invasive behavior of cancer cells into narrow channels. As distinct features of our approach, cells are modeled as compartmentalized discrete objects, differentiated in the nucleus and in the cytosolic region, while the migration chamber is composed of channels of different widths. We find that cell motile phenotype and velocity in open spaces (i.e., 2D flat surfaces or large channels) are not significantly influenced by cell elastic properties. On the contrary, the migratory behavior of cells within subcellular and subnuclear structures strongly relies on the deformability of the cytosol and of the nuclear cluster, respectively. Further, we characterize two migration dynamics: a stepwise way, characterized by fluctuations in cell length, within channels smaller than nucleus dimensions and a smooth sliding (i.e., maintaining constant cell length) behavior within channels larger than the nuclear cluster. These resulting observations are then extended looking at cell migration in an artificial fiber network, which mimics cell invasion in a 3D extracellular matrix. In particular, in this case, we analyze the effect of variations in elasticity of the nucleus on cell movement. In order to summarize, with our simulated migration assays, we demonstrate that the dimensionality of the environment strongly affects the migration phenotype and we suggest that the cytoskeletal and nuclear elastic characteristics correlate with the tumor cell's invasive potential.

Modeling cell movement in anisotropic and heterogeneous network tissues

Networks and heterogeneous …, 2007

Cell motion and interaction with the extracellular matrix is studied deriving a kinetic model and considering its diffusive limit. The model takes into account the chemotactic and haptotactic effects, and obtains friction as a result of the interactions between cells and between cells and the fibrous environment. The evolution depends on the fibre distribution, as cells preferentially move along the fibre direction and tend to cleave and remodel the extracellular matrix when their direction of motion is not aligned with the fibre direction. Simulations are performed to describe the behavior of an ensemble of cells under the action of a chemotactic field and in the presence of heterogeneous and anisotropic fibre networks.

Computational Model for Migration of a Cell Cluster in Three-Dimensional Matrices

Annals of Biomedical Engineering, 2011

This paper presents a first forced-based dynamics computer model of a cell cluster moving collectively in a 3D environment mimicking the extracellular matrix. In general, collective cell migration is a relevant part of the mechanisms for tissue repair, morphogenesis, and cancer invasion. Particularly in cancer, invasion occurs through multicellular 3D strands as well as collective cell clusters. Because cancer is a slow process, these clusters have not been carefully observed. However, the prevalence of this mechanism of cell locomotion makes it a target for study. Due to the different molecular mechanisms involved in this movement and the complex relations among them, a computer model would be of great use. The model presented here takes into account ligand concentration, matrix metalloproteinase activity, and cluster geometry based on experimental findings and experimentally validated single cell computer models; thus incorporating implicitly different underlying molecular properties. The velocity profiles of the cell clusters were recorded and analyzed. In particular seven different profiles are observed based on different participation of ligands, proteinases, and mechanical forces involved. The model is successful in showing potential effects of altering single variables in a system of cells in motion. Special emphasis is made on future directions for improvement and the variables to be potentially modulated to simulate particular physiological conditions.

Computational models of migration modes improve our understanding of metastasis

APL Bioengineering, 2020

Tumor cells migrate through changing microenvironments of diseased and healthy tissue, making their migration particularly challenging to describe. To better understand this process, computational models have been developed for both the ameboid and mesenchymal modes of cell migration. Here, we review various approaches that have been used to account for the physical environment's effect on cell migration in computational models, with a focus on their application to understanding cancer metastasis and the related phenomenon of durotaxis. We then discuss how mesenchymal migration models typically simulate complex cell-extracellular matrix (ECM) interactions, while ameboid migration models use a cell-focused approach that largely ignores ECM when not acting as a physical barrier. This approach greatly simplifies or ignores the mechanosensing ability of ameboid migrating cells and should be reevaluated in future models. We conclude by describing future model elements that have not been included to date but would enhance model accuracy.

Computational Model for Cell Migration in Three-Dimensional Matrices

Biophysical Journal, 2005

Although computational models for cell migration on two-dimensional (2D) substrata have described how various molecular and cellular properties and physiochemical processes are integrated to accomplish cell locomotion, the same issues, along with certain new ones, might contribute differently to a model for migration within three-dimensional (3D) matrices. To address this more complicated situation, we have developed a computational model for cell migration in 3D matrices using a forcebased dynamics approach. This model determines an overall locomotion velocity vector, comprising speed and direction, for individual cells based on internally generated forces transmitted into external traction forces and considering a timescale during which multiple attachment and detachment events are integrated. Key parameters characterize cell and matrix properties, including cell/matrix adhesion and mechanical and steric properties of the matrix; critical underlying molecular properties are incorporated explicitly or implicitly. Model predictions agree well with experimental results for the limiting case of migration on 2D substrata as well as with recent experiments in 3D natural tissues and synthetic gels. Certain predicted features such as biphasic behavior of speed with density of matrix ligands for 3D migration are qualitatively similar to their 2D counterparts, but new effects generally absent in 2D systems, such as effects due to matrix sterics and mechanics, are now predicted to arise in many 3D situations. As one particular sample manifestation of these effects, the optimal levels of cell receptor expression and matrix ligand density yielding maximal migration are dependent on matrix mechanical compliance.