TY - JOUR
T1 - A theoretical model of collective cell polarization and alignment
AU - He, Shijie
AU - Green, Yoav
AU - Saeidi, Nima
AU - Li, Xiaojun
AU - Fredberg, Jeffrey J.
AU - Ji, Baohua
AU - Pismen, Len M.
N1 - Publisher Copyright:
© 2019 Elsevier Ltd
PY - 2020/4/1
Y1 - 2020/4/1
N2 - Collective cell polarization and alignment play important roles in tissue morphogenesis, wound healing and cancer metastasis. How cells sense the direction and position in these processes, however, has not been fully understood. Here we construct a theoretical model based on describing cell layer as a nemato-elastic medium, by which the cell polarization, cell alignment and cell active contraction are explicitly expressed as functions of components of the nematic order parameter. To determine the order parameter we derive two sets of governing equations, one for the force equilibrium of the system, and the other for the minimization of the system's free energy including the energy of cell polarization and alignment. By solving these coupled governing equations, we can predict the effects of substrate stiffness, geometries of cell layers, external forces and myosin activity on the direction- and position-dependent cell aspect ratio and cell orientation. Moreover, the axisymmetric problem with cells on a ring-like pattern is solved analytically, and the analytical solution for cell aspect ratio are governed by parameter groups which include the stiffness of the cell and the substrate, the strength of myosin activity and the external forces. Our predictions of the cell aspect ratio and orientation are generally comparable to experimental observations. These results show that the pattern of cell polarization is determined by the anisotropic degree of active contractile stress, and suggest a stress-driven polarization mechanism that enables cells to sense their spatial positions to develop direction- and position-dependent behavior. This, in turn, sheds light on the ways to control pattern formation in tissue engineering for potential biomedical applications.
AB - Collective cell polarization and alignment play important roles in tissue morphogenesis, wound healing and cancer metastasis. How cells sense the direction and position in these processes, however, has not been fully understood. Here we construct a theoretical model based on describing cell layer as a nemato-elastic medium, by which the cell polarization, cell alignment and cell active contraction are explicitly expressed as functions of components of the nematic order parameter. To determine the order parameter we derive two sets of governing equations, one for the force equilibrium of the system, and the other for the minimization of the system's free energy including the energy of cell polarization and alignment. By solving these coupled governing equations, we can predict the effects of substrate stiffness, geometries of cell layers, external forces and myosin activity on the direction- and position-dependent cell aspect ratio and cell orientation. Moreover, the axisymmetric problem with cells on a ring-like pattern is solved analytically, and the analytical solution for cell aspect ratio are governed by parameter groups which include the stiffness of the cell and the substrate, the strength of myosin activity and the external forces. Our predictions of the cell aspect ratio and orientation are generally comparable to experimental observations. These results show that the pattern of cell polarization is determined by the anisotropic degree of active contractile stress, and suggest a stress-driven polarization mechanism that enables cells to sense their spatial positions to develop direction- and position-dependent behavior. This, in turn, sheds light on the ways to control pattern formation in tissue engineering for potential biomedical applications.
KW - Cell polarization
KW - Cell-cell interaction
KW - Cell-matrix interaction
KW - Collective cells
UR - http://www.scopus.com/inward/record.url?scp=85077768818&partnerID=8YFLogxK
U2 - 10.1016/j.jmps.2019.103860
DO - 10.1016/j.jmps.2019.103860
M3 - Article
AN - SCOPUS:85077768818
SN - 0022-5096
VL - 137
JO - Journal of the Mechanics and Physics of Solids
JF - Journal of the Mechanics and Physics of Solids
M1 - 103860
ER -