  Controlling growth via cell division is crucial in the development of higher
organisms, and yet the mechanisms through which this is achieved, e.g., in
epithelial tissue, is not yet fully understood. We show that by coupling the
cell cycle oscillator governing cell division to signals that encode
inter-cellular contacts, this phenomenon can be seen as a collective dynamical
transition in a system of coupled oscillators in lattices with changing degree
of disorder. As the distribution of cellular morphological characteristics
become more homogeneous over the course of development, the contact-induced
signals to the cells increase beyond a critical value to trigger coordinated
cessation of oscillations, eventually leading to growth arrest. Our results
suggest that the global phenomenon of growth rate reduction as a tissue
approaches its appropriate size is causally related to the increasingly regular
geometry of local cell-cell contact interfaces.
