Modelling cell turnover in a complex tissue during development.

The growth of organs results from proliferation within distinct cellular compartments. Organ development also involves transitions between cell types and variations in cell cycle duration as development progresses, and is regulated by a balance between entry into the compartment, proliferation of cells within the compartment, acquisition of quiescence and exit from that cell state via differentiation or death. While it is important to understand how environmental or genetic alterations can perturb such development, most approaches employed to date are descriptive rather than quantitative. This is because the identification and quantification of such parameters, while tractable in vitro, is challenging in the context of a complex tissue in vivo. Here we present a new framework for determining cell turnover in developing organs in vivo that combines cumulative cell-labelling and quantification of distinct cell-cycle phases without assuming homogeneity of behaviour within that compartment. A mathematical model is given that allows the calculation of cell cycle length in the context of a specific biological example and assesses the uncertainty of this calculation due to incomplete knowledge of cell cycle dynamics. This includes the development of a two population model to quantify possible heterogeneity of cell cycle length within a compartment and estimate the aggregate proliferation rate. These models are demonstrated on data collected from a progenitor cell compartment within the developing mouse kidney, the cap mesenchyme. This tissue was labelled by cumulative infusion, volumetrically quantified across time, and temporally analysed for the proportion of cells undergoing proliferation. By combining the cell cycle length predicted by the model with measurements of total cell population and mitotic rate, this approach facilitates the quantification of exit from this compartment without the need for a direct marker of that event. As a method specifically designed with assumptions appropriate to developing organs we believe this approach will be applicable to a range of developmental systems, facilitating estimations of cell cycle length and compartment behaviour that extend beyond simple comparisons of mitotic rates between normal and perturbed states.