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.
PLOS ONE, 2018
Cell mobility plays a critical role in immune response, wound healing, and the rate of cancer metastasis and tumor progression. Mobility within a three-dimensional (3D) matrix environment can be characterized by the average velocity of cell migration and the persistence length of the path it follows. Computational models that aim to predict cell migration within such 3D environments need to be able predict both of these properties as a function of the various cellular and extra-cellular factors that influence the migration process. A large number of models have been developed to predict the velocity of cell migration driven by cellular protrusions in 3D environments. However, prediction of the persistence of a cell's path is a more tedious matter, as it requires simulating cells for a long time while they migrate through the model extra-cellular matrix (ECM). This can be a computationally expensive process, and only recently have there been attempts to quantify cell persistence as a function of key cellular or matrix properties. Here, we propose a new stochastic algorithm that can simulate and analyze 3D cell migration occurring over days with a computation time of minutes, opening new possibilities of testing and predicting long-term cell migration behavior as a function of a large variety of cell and matrix properties. In this model, the matrix elements are generated as needed and stochastically based on the biophysical and biochemical properties of the ECM the cell migrates through. This approach significantly reduces the computational resources required to track and calculate cell matrix interactions. Using this algorithm, we predict the effect of various cellular and matrix properties such as cell polarity, cell mechanoactivity, matrix fiber density, matrix stiffness, fiber alignment, and fiber binding site density on path persistence of cellular migration and the mean squared displacement of cells over long periods of time.
Scientific Reports
Metastasis is the pathogenic spread of cancer cells from a primary tumor to a secondary site which happens at the late stages of cancer. It is caused by a variety of biological, chemical, and physical processes, such as molecular interactions, intercellular communications, and tissue-level activities. Complex interactions of cancer cells with their microenvironment components such as cancer associated fibroblasts (CAFs) and extracellular matrix (ECM) cause them to adopt an invasive phenotype that promotes tumor growth and migration. This paper presents a multiscale model for integrating a wide range of time and space interactions at the molecular, cellular, and tissue levels in a three-dimensional domain. The modeling procedure starts with presenting nonlinear dynamics of cancer cells and CAFs using ordinary differential equations based on TGFβ, CXCL12, and LIF signaling pathways. Unknown kinetic parameters in these models are estimated using hybrid unscented Kalman filter and the m...
Viscoelastic Gel-Strip Model for the Simulation of Migrating Cells
Annals of Biomedical Engineering, 2011
Migrating tumor cells can exhibit both mesenchymal-type and amoeboid-type behaviors. Recent studies have shown that both cellular and extracellular structural and mechanical variables control the transition of tumor cells from one mode to the other and provide them with morphological plasticity. The mesenchymal-mode migration is characterized by strong adhesion and proteolytic machinery to navigate through complex extracellular matrices. The amoeboid-mode migration is characterized by little or no adhesion and strong actomyosin contraction to squeeze through the matrices. While adhesion dependent migration has been computationally and experimentally studied in both 2D and 3D environments, quantitative models of amoeboid motion in native environments are lacking. In order to address this major gap in our understanding and to probe the mesenchymal to amoeboid transitions quantitatively and comprehensively, we have developed an axisymmetric viscoelastic gel-strip model of a single cell to investigate a cell migrating in native-like environments. In this model, cell migration and morphology are governed by internal stresses as well as external forces. The internal stresses are controlled by F-actin density distribution, protrusion strength, and contraction strength. The external forces are controlled by adhesion strength and steric resistance from the extracellular matrix. Our model predicts that the transition of the cell migration mode from mesenchymal-to amoeboid-type, and vice versa, is closely related to the loss of adhesion as well as increased contraction strength of the cells. Our results indicate that amoeboid migration is more suited for low-resistance environment while mesenchymal migration is preferred in high-resistance environment, which would explain the versatile behaviors of tumor cells in complex environments.
3D cancer cell migration in collagen matrices
Computer Methods in Biomechanics and Biomedical Engineering, 2015
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Nature Cell Biology, 2013
The molecular requirements and morphology of migrating cells can vary depending on matrix geometry; therefore, predicting the optimal migration strategy or the effect of experimental perturbation is difficult. We present a model of cell motility that encompasses actin-polymerization-based protrusions, actomyosin contractility, variable actin-plasma membrane linkage leading to membrane blebbing, cell-extracellular-matrix adhesion and varying extracellular matrix geometries. This is used to explore the theoretical requirements for rapid migration in different matrix geometries.
Biomechanics and Modeling in Mechanobiology
Cell migration, known as an orchestrated movement of cells, is crucially important for wound healing, tumor growth, immune response as well as other biomedical processes. This paper presents a cell-based model to describe cell migration in non-isotropic fibrin networks around pancreatic tumor islets. This migration is determined by the mechanical strain energy density as well as cytokines-driven chemotaxis. Cell displacement is modeled by solving a large system of ordinary stochastic differential equations where the stochastic parts result from random walk. The stochastic differential equations are solved by the use of the classical Euler-Maruyama method. In this paper, the influence of anisotropic stromal extracellular matrix in pancreatic tumor islets on T-lymphocytes migration in different immune systems is investigated. As a result, tumor peripheral stromal extracellular matrix impedes the immune response of Tlymphocytes through changing direction of their migration.
Computational Mechanics, 2014
Cell migration is fundamental in a wide variety of physiological and pathological phenomena, among other in cancer invasion and development. In particular, the migratory/invasive capability of single metastatic cells is fundamental in determining the malignancy of a solid tumor. Specific cell migration phenotypes result for instance from the reciprocal interplay between the biophysical and biochemical properties of both the malignant cells themselves and of the surrounding environment. In particular, the extracellular matrices (ECMs) forming connective tissues can provide both loosely organized zones and densely packed barriers, which may impact cell invasion mode and efficiency. The critical processes involved in cell movement within confined spaces are (i) the proteolytic activity of matrix metalloproteinases (MMPs) and (ii) the deformation of the entire cell body, and in particular of the nucleus. We here present an extended cellular Potts model (CPM) to simulate a bio-engineered matrix system, which tests the active motile behavior of a single cancer cell into narrow channels of different widths. As distinct features of our approach, the cell is modeled as a compartmentalized discrete element, differentiated in the nucleus and in the cytosolic region, while a directional shape-dependent movement is explicitly driven by the evolution of its polarity vector. As outcomes, we find that, in a large track, the tumor cell is not able to maintain a directional movement. On the contrary, a structure of subcellular width behaves as a contact guidance sustaining cell persistent locomotion. In particular, a MMP-deprived cell is able to repolarize and follow the micropattern geometry, while
A Cellular Potts model simulating cell migration on and in matrix environments
Mathematical Biosciences and Engineering, 2012
Cell migration on and through extracellular matrix is fundamental in a wide variety of physiological and pathological phenomena, and is exploited in scaffold-based tissue engineering. Migration is regulated by a number of extracellular matrix-or cell-derived biophysical parameters, such as matrix fiber orientation, pore size, and elasticity, or cell deformation, proteolysis, and adhesion. We here present an extended Cellular Potts Model (CPM) able to qualitatively and quantitatively describe cell migration efficiencies and phenotypes both on two-dimensional substrates and within three-dimensional matrices, close to experimental evidence. As distinct features of our approach, cells are modeled as compartmentalized discrete objects, differentiated into nucleus and cytosolic region, while the extracellular matrix is composed of a fibrous mesh and a homogeneous fluid. Our model provides a strong correlation of the directionality of migration with the topological extracellular matrix distribution and a biphasic dependence of migration on the matrix structure, density, adhesion, and stiffness, and, moreover, simulates that cell locomotion in highly constrained fibrillar obstacles requires the deformation of the cell's nucleus and/or the activity of cell-derived proteolysis. In conclusion, we here propose a mathematical modeling approach that serves to characterize cell migration as a biological phenomenon in healthy and diseased tissues and in engineering applications.
Mathematical analysis of a kinetic model for cell movement in network tissues
2008
Mesenchymal motion describes the movement of cells in biological tissues formed by fibre networks. An important example is the migration of tumour cells through collagen networks during the process of metastasis formation. We investigate the mesenchymal motion model proposed by T. Hillen in in higher dimensions. We formulate the problem as an evolution equation in a Banach space of measure-valued functions and use methods from semigroup theory to show the global existence of classical solutions. We investigate steady states of the model and show that patterns of network type exist as steady states. For the case of constant fibre distribution, we find an explicit solution and we prove the convergence to the parabolic limit.