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

Abstract

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.

Modeling the two-way feedback between contractility and matrix realignment reveals a nonlinear mode of cancer cell invasion

“…The cell-matrix interactions depend on the mechanical and microstructural properties of the matrix such as matrix rigidity (13, 14), fiber alignment (5, 6, 15, 16), interfibrillar pore size (17), and density of cell-adhesive ligands (18). Previous computational models of cell invasion have examined cellular interactions (19,20) and the interplay between protrusion forces (generated due to the polymerization of actin), traction forces (at the cell-matrix adhesions), and resisting forces (mostly the drag force caused by the viscosity of the matrix) (19,(21)(22)(23)(24). However, these models do not account for (i) cell-induced realignment of the fibers in the matrix and how stiffening due to realignment, in turn, can lead to increased contractility of the cells, and (ii) how the microstructural properties of the matrix (pore size and stiffness) and fiber alignment impact cell motility and morphology.…”

Simulating tissue mechanics with agent-based models: concepts, perspectives and some novel results

“…Vermolen and Gefen [167] proposed a model with cell movement assuming a mechanical stimulus arises from the cells sensing a change in strain energy density in the ECM. An explicit interaction model of CBM with ECM fibers has been introduced by Schlueter et al [66] in where the cells are able to interact and remodel the fiber orientation, showing the tendency of a cell to move to stiffer substrates. Harjanto et al [168] used an approach where the cells can degrade, deposit, or pull on local fibers, depending on the fiber density around each cell.…”

“…The latter indicates that a cell has a preferential direction, polar adhesion or biased motion [33,66,137]. Non-adherent neighboring cells can sense each others presence and move towards each other through mechanochemical signals, originating for instance by the formation of filopodia or cell-cell communication through a medium.…”

“…"Space-free" agent-based models have been considered for example in hematology and are reported elsewhere [40]. Spatial agent-based models can roughly been distinguished by those operating on space fixed lattices [41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58][59][60] and those operating without a lattice ("lattice-free", "off-lattice"; [52,[61][62][63][64][65][66]). Among lattice models, either (i) a lattice site may be occupied by many cells (e.g., [67]) permitting modeling of large cell population sizes, (ii) cells may occupy at most a single lattice site (e.g., [68]), or (iii) many lattice sites may be occupied by one biological cell (e.g., [53]).…”

Computational Modeling of Stem Cell Migration: A Mini Review

“…Researchers have considered the effect of contact guidance and matrix remodeling, taking into account matrix stiffness and architecture. 24, 51,52 Through experimental studies of cell migration, it has become apparent that dimensionality of the cellular environment affects cellular behavior and migration mode. Cells will display different behavior when on a one, two or three dimensional space 14 ; for example, while most cells have lower speeds in a 3D environment than on a 2D culture surface, neutrophils display almost no migration in 2D substrates and do migrate when embedded in 3D collagen gels.…”