The Impact of Elastic Deformations of the Extracellular Matrix on Cell Migration
- PDF / 918,690 Bytes
- 19 Pages / 439.37 x 666.142 pts Page_size
- 66 Downloads / 166 Views
The Impact of Elastic Deformations of the Extracellular Matrix on Cell Migration A. A. Malik1 · B. Wennberg1 · P. Gerlee1 Received: 26 July 2019 / Accepted: 15 March 2020 / Published online: 4 April 2020 © The Author(s) 2020
Abstract The mechanical properties of the extracellular matrix, in particular its stiffness, are known to impact cell migration. In this paper, we develop a mathematical model of a single cell migrating on an elastic matrix, which accounts for the deformation of the matrix induced by forces exerted by the cell, and investigate how the stiffness impacts the direction and speed of migration. We model a cell in 1D as a nucleus connected to a number of adhesion sites through elastic springs. The cell migrates by randomly updating the position of its adhesion sites. We start by investigating the case where the cell springs are constant, and then go on to assuming that they depend on the matrix stiffness, on matrices of both uniform stiffness as well as those with a stiffness gradient. We find that the assumption that cell springs depend on the substrate stiffness is necessary and sufficient for an efficient durotactic response. We compare simulations to recent experimental observations of human cancer cells exhibiting durotaxis, which show good qualitative agreement. Keywords Durotaxis · Mathematical modeling · Stochastic simulation · Cell migration
1 Introduction Cell migration is essential to many processes such as embryogenesis (Kurosaka and Kashina 2008) and wound healing (Parkin and Cohen 2001), but is also important in many diseases, such as cancer (Wang et al. 2005; Yamaguchi et al. 2005). Two common mechanisms for cell locomotion are “swimming” and “crawling.” The typical example of swimming motion is that of E. Coli. It alternates between moving in a more or less straight path for a random duration of time and tumbling to reorient with
B 1
A. A. Malik [email protected] Department of Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, 412 96 Gothenburg, Sweden
123
49
Page 2 of 19
A. A. Malik et al.
a negligible change in spatial position. The second type of locomotion is crawling, where the cell extends protrusions, formed by the cytoskeleton, a fiber network within the cell consisting of protein filaments. These protrusions adhere to the extracellular matrix, and the cell pulls itself forward. This is the type of motion we consider in this study. It is a cyclic process that can be conceptually described as consisting of four phases (Kurosaka and Kashina 2008). The first is the polarization phase, followed by the protrusion phase, in which the cytoskeleton changes shape by extending a protrusion at the leading edge, which is driven by actin polymerization. The third phase is the attachment phase during which it adheres to the substrate on which it is crawling. The last phase is the retraction phase, where the cell pulls itself forward (Alberts 2017; Kurosaka and Kashina 2008), and adhesion sites at the back end detach. It is known that both the c
Data Loading...
