Identifying stem cell numbers and functional heterogeneities during post-embryonic organ growth

Uncovering the number of stem cells necessary to grow an organ has been challenging in most vertebrate systems. Here, we have developed a mathematical model that we use to characterise stem cells in the fish gill, an organ that displays non-exhaustive growth. Our work employs a Markov model, first stochastically simulated via an adapted Gillespie algorithm, and further improved by using probability theory. The stochastic algorithm produces a simulated data set for comparison with experimental data by inspecting quantifiable properties, while the analytical approach skips the step of in silico data generation and goes directly to the quantification, being more abstract and very efficient. By applying the model to a large clonal experimental dataset, we report that a reduced number of stem cells are responsible for growing and maintaining the fish gill. The model also highlights a functional heterogeneity among the stem cells involved, where activation and quiescence phases determine their relative growth contribution. Overall, our work presents an easy-to-apply algorithm to infer the number of stem cells functionally required in a life-long growing system.