Numerical Approaches to Division and Label Structured Population Models

Division and label structured population models (DLSPMs) are a class of partial differential equations (PDEs) that have been used to study intracellular dynamics in dividing cells. DLSPMs have improved the understanding of cell proliferation assays involving measurements such as fluorescent label decay, protein production, and prion aggregate amplification. One limitation in using DLSPMs is the significant computational time required for numerical approximations, especially for models with complex biologically relevant dynamics. Here we develop a novel numerical and theoretical framework involving a recursive formulation for a class of DLSPMs. We develop this framework for a population of dividing cells with an arbitrary functional form describing the intracellular dynamics. We found that, compared to previous methods, our framework is faster and more accurate. We illustrate our approach on three common models for intracellular dynamics and discuss the potential impact of our findings in the context of data-driven methods for parameter estimation.