  The spatiotemporal coordination and regulation of cell proliferation is
fundamental in many aspects of development and tissue maintenance. Cells have
the ability to adapt their division rates in response to mechanical
constraints, yet we do not fully understand how cell proliferation regulation
impacts cell migration phenomena. Here, we present a minimal continuum model of
cell migration with cell cycle dynamics, which includes density-dependent
effects and hence can account for cell proliferation regulation. By combining
minimal mathematical modelling, Bayesian inference, and recent experimental
data, we quantify the impact of tissue crowding across different cell cycle
stages in epithelial tissue expansion experiments. Our model suggests that
cells sense local density and adapt cell cycle progression in response, during
G1 and the combined S/G2/M phases, providing an explicit relationship between
each cell cycle stage duration and local tissue density, which is consistent
with several experimental observations. Finally, we compare our mathematical
model predictions to different experiments studying cell cycle regulation and
present a quantitative analysis on the impact of density-dependent regulation
on cell migration patterns. Our work presents a systematic approach for
investigating and analysing cell cycle data, providing mechanistic insights
into how individual cells regulate proliferation, based on population-based
experimental measurements.
