PDE-constrained optimization for estimating population dynamics over cell cycle from static single cell measurements

Motivation: Understanding how cell cycle responds and adapts dynamically to a broad range of stresses and changes in the cellular environment is crucial for the treatment of various pathologies, including cancer. However, measuring changes in cell cycle progression is experimentally challenging, and model inference computationally expensive. Results: Here, we introduce a computational framework that allows the inference of changes in cell cycle progression from static single-cell measurements. We modeled population dynamics with partial differential equations (PDE), and derive parameter gradients to estimate time- and cell cycle position-dependent progression changes efficiently. Additionally, we show that computing parameter sensitivities for the optimization problem by solving a system of PDEs is computationally feasible and allows efficient and exact estimation of parameters. We showcase our framework by estimating the changes in cell cycle progression in K562 cells treated with Nocodazole and identify an arrest in M-phase transition that matches the expected behavior of microtubule polymerization inhibition. Conclusions: Our results have two major implications: First, this framework can be scaled to high-throughput compound screens, providing a fast, stable, and efficient protocol to generate new insights into changes in cell cycle progression. Second, knowledge of the cell cycle stage- and time-dependent progression function allows transformation from pseudotime to real-time thereby enabling real-time analysis of molecular rates in response to treatments. Availability: MAPiT toolbox (Karsten Kuritz 2020) is available at github: https://github.com/karstenkuritz/MAPiT.