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Register a new userSpontaneous contractility--mediated cortical flow generates cell migration in 3-dimensional environments
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We present a generic model of cell motility generated by acto-myosin contraction of the cell cortex. We identify analytically dynamical instabilities of the cortex and show that they trigger spontaneous cortical flows which in turn can induce cell migration in 3-dimensional (3D) environments as well as bleb formation. This contractility--based mechanism, widely independent of actin treadmilling, appears as an alternative to the classical picture of lamellipodial motility on flat substrates. Theoretical predictions are compared to experimental data of tumor cells migrating in 3D matrigel and suggest that this mechanism could be a general mode of cell migration in 3D environments.
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Cell proliferation is typically incorporated into stochastic mathematical models of cell migration by assuming that cell divisions occur after an exponentially distributed waiting time. Experimental observations, however, show that this assumption is often far from the real cell cycle time distribution (CCTD). Recent studies have suggested an alternative approach to modelling cell proliferation based on a multi-stage representation of the CCTD. In order to validate and parametrise these models, it is important to connect them to experimentally measurable quantities. In this paper we investigate the connection between the CCTD and the speed of the collective invasion. We first state a result for a general CCTD, which allows the computation of the invasion speed using the Laplace transform of the CCTD. We use this to deduce the range of speeds for the general case. We then focus on the more realistic case of multi-stage models, using both a stochastic agent-based model and a set of reaction-diffusion equations for the cells average density. By studying the corresponding travelling wave solutions, we obtain an analytical expression for the speed of invasion for a general N-stage model with identical transition rates, in which case the resulting cell cycle times are Erlang distributed. We show that, for a general N-stage model, the Erlang distribution and the exponential distribution lead to the minimum and maximum invasion speed, respectively. This result allows us to determine the range of possible invasion speeds in terms of the average proliferation time for any multi-stage model.
The dynamic interplay between collective cell movement and the various molecules involved in the accompanying cell signalling mechanisms plays a crucial role in many biological processes including normal tissue development and pathological scenarios such as wound healing and cancer. Information about the various structures embedded within these processes allows a detailed exploration of the binding of molecular species to cell-surface receptors within the evolving cell population. In this paper we establish a general spatio-temporal-structural framework that enables the description of molecular binding to cell membranes coupled with the cell population dynamics. We first provide a general theoretical description for this approach and then illustrate it with two examples arising from cancer invasion.
Cells crawling through tissues migrate inside a complex fibrous environment called the extracellular matrix (ECM), which provides signals regulating motility. Here we investigate one such well-known pathway, involving mutually antagonistic signalling molecules (small GTPases Rac and Rho) that control the protrusion and contraction of the cell edges (lamellipodia). Invasive melanoma cells were observed migrating on surfaces with topography (array of posts), coated with adhesive molecules (fibronectin, FN) by Park et al., 2016. Several distinct qualitative behaviors they observed included persistent polarity, oscillation between the cell front and back, and random dynamics. To gain insight into the link between intracellular and ECM signaling, we compared experimental observations to a sequence of mathematical models encoding distinct hypotheses. The successful model required several critical factors. (1) Competition of lamellipodia for limited pools of GTPases. (2) Protrusion / contraction of lamellipodia influence ECM signaling. (3) ECM-mediated activation of Rho. A model combining these elements explains all three cellular behaviors and correctly predicts the results of experimental perturbations. This study yields new insight into how the dynamic interactions between intracellular signaling and the cells environment influence cell behavior.
The phenomenological model for cell shape deformation and cell migration (Chen et.al. 2018; Vermolen and Gefen 2012) is extended with the incorporation of cell traction forces and the evolution of cell equilibrium shapes as a result of cell differentiation. Plastic deformations of the extracellular matrix are modelled using morphoelasticity theory. The resulting partial differential differential equations are solved by the use of the finite element method. The paper treats various biological scenarios that entail cell migration and cell shape evolution. The experimental observations in Mak et.al. (2013), where transmigration of cancer cells through narrow apertures is studied, are reproduced using a Monte Carlo framework.
A theory of fractional kinetics of glial cancer cells is presented. A role of the migration-proliferation dichotomy in the fractional cancer cell dynamics in the outer-invasive zone is discussed an explained in the framework of a continuous time random walk. The main suggested model is based on a construction of a 3D comb model, where the migration-proliferation dichotomy becomes naturally apparent and the outer-invasive zone of glioma cancer is considered as a fractal composite with a fractal dimension $frD<3$.
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