Abstract

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.

Highlights

  • Cell migration through three-dimensional (3D) fibrous matrix environments is essential to a number of biological processes including immune response and cancer metastasis [1,2,3,4]

  • The cell moves by crawling along supporting matrix fibers that act as tracks to guide the cell

  • We have described above how the speed and persistence of cell migration varies as a function of binding site density, fiber alignment, gel concentration, cell mechanoactivity, cell polarity, and the combined effects of fiber alignment, fiber diameter, and fiber density

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Summary

Introduction

Cell migration through three-dimensional (3D) fibrous matrix environments is essential to a number of biological processes including immune response and cancer metastasis [1,2,3,4]. Numerous experimental and theoretical studies describe the individual or combined influence these cellular and extracellular factors have on the mechanisms, energetics, and the rate of cell migration within unique tissue environments [16,17,18]. The story describing cell migration is not complete, and assimilation of how all these concomitant factors influence cell migration within a given environment is necessary for a more comprehensive understanding. The directional persistence of the cell’s path is crucial in determining how far a cell can migrate within a certain matrix environment in a given amount of time and is as critical as the cell speed in predicting the time scales of key biological processes dependent on cell migration

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