Analysis of CFSE time-series data using division-, age- and label-structured population models

Motivation: In vitro and in vivo cell proliferation is often studied using the dye carboxyfluorescein succinimidyl ester (CFSE). The CFSE time-series data provide information about the proliferation history of populations of cells. While the experimental procedures are well established and widely used, the analysis of CFSE time-series data is still challenging. Many available analysis tools do not account for cell age and employ optimization methods that are inefficient (or even unreliable). Results: We present a new model-based analysis method for CFSE time-series data. This method uses a flexible description of proliferating cell populations, namely, a division-, age-and labelstructured population model. Efficient maximum likelihood and Bayesian estimation algorithms are introduced to infer the model parameters and their uncertainties. These methods exploit the forward sensitivity equations of the underlying partial differential equation model for efficient and accurate gradient calculation, thereby improving computational efficiency and reliability compared with alternative approaches and accelerating uncertainty analysis. The performance of the method is assessed by studying a dataset for immune cell proliferation. This revealed the importance of different factors on the proliferation rates of individual cells. Among others, the predominate effect of cell age on the division rate is found, which was not revealed by available computational methods. Availability and implementation: The MATLAB source code implementing the models and algorithms is available from http://janhasenauer.github.io/ShAPE-DALSP/.