Organ growth driven by cell proliferation is an exponential process. As a result, even small variations in proliferation rates, when integrated over a relatively long developmental time, will lead to large differences in size. How organs robustly control their final size despite perturbations in cell proliferation rates throughout development is a long-standing question in biology. Using a mathematical model, we show that in the developing wing of the fruit fly, Drosophila melanogaster , variations in proliferation rates of wing-committed cells are inversely proportional to the duration of cell recruitment, a differentiation process in which a population of undifferentiated cells adopt the wing fate by expressing the selector gene, vestigial . A time-course experiment shows that vestigial-expressing cells increase exponentially while recruitment takes place, but slows down when recruitable cells start to vanish, suggesting that undifferentiated cells may be driving proliferation of wing-committed cells. When this observation is incorporated in our model, we show that the duration of cell recruitment robustly determines a final wing size even when cell proliferation rates of wing-committed cells are perturbed. Finally, we show that this control mechanism fails when perturbations in proliferation rates affect both wing-committed and recruitable cells, providing an experimentally testable hypothesis of our model.
How organs robustly attain a final size despite perturbations in cell growth and proliferation rates is a fundamental question in developmental biology. Since organ growth is an exponential process driven mainly by cell proliferation, even small variations in cell proliferation rates, when integrated over a relatively long time, will lead to large differences in size, unless intrinsic control mechanisms compensate for these variations. Here we use a mathematical model to consider the hypothesis that in the developing wing of Drosophila, cell recruitment, a process in which undifferentiated neighboring cells are incorporated into the wing primordium, determines the time in which growth is arrested in this system. Under this assumption, our model shows that perturbations in proliferation rates of wing-committed cells are compensated by an inversely proportional duration of growth. This mechanism ensures that the final size of the wing is robust in a range of cell proliferation rates. Furthermore, we predict that growth control is lost when fluctuations in cell proliferation affects both wing-committed and recruitable cells. Our model suggests that cell recruitment may act as a temporal controller of growth to buffer fluctuations in cell proliferation rates, offering a solution to a long-standing problem in the field.
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