How fast are cells dividing: Probabilistic model of continuous labeling assays

Correct estimates of cell proliferation rates are crucial for quantitative models of the development, maintenance and regeneration of tissues. Continuous labeling assays are used to infer proliferation rates in vivo. So far, the experimental and theoretical study of continuous labeling assays focused on the dynamics of the mean labeling-fraction but neglected stochastic effects. To study the dynamics of the labeling-fraction in detail and fully exploit the information hidden in fluctuations, we developed a probabilistic model of continuous labeling assays which incorporates biological variability at different levels, between cells within a tissue sample but also between multiple tissue samples. Using stochastic simulations, we find systematic shifts of the mean-labeling fraction due to variability in cell cycle lengths. Using simulated data as ground truth, we show that current inference methods can give biased proliferation rate estimates with an error of up to 40 %. We derive the analytical solution for the Likelihood of our probabilistic model. We use this solution to infer unbiased proliferation rate estimates in a parameter recovery study. Furthermore, we show that the biological variability on different levels can be disentangled from the fluctuations in the labeling data. We implemented our model and the unbiased parameter estimation method as an open source Python tool and provide an easy to use web service for cell cycle length estimation from continuous labeling assays (https://imc.zih.tu-dresden.de/cellcycle).