Parameter Identifiability Under Limited Experimental Data in Age-Structured Models of the Cell Cycle

TL;DR

This paper investigates how limited and heterogeneous experimental data affect the ability to identify parameters in age-structured cell cycle models, using analytical methods to determine minimal data requirements for successful model fitting.

Contribution

It introduces an age-structured PDE model with analytical expressions for population observables, assessing data influence on parameter identifiability and proposing identifiable parameter groupings.

Findings

Analytical expressions for balanced exponential growth phase proportions.

Minimal data requirements for successful parameter fitting.

Identification of parameter groupings when parameters are not uniquely identifiable.

Abstract

The mitotic cell cycle governs DNA replication and cell division. The effectiveness of radiotherapy and chemotherapy depends on cell-cycle position, with increased resistance during DNA replication and mitosis. Thus, accurate mathematical models of the cell cycle are essential for understanding and predicting treatment response. However, mathematical modellers often face the problem of a lack of publicly available, sufficiently resolved, time-series datasets for parametrising models. In this work, we consider how the ability to collate population summary measurements across the literature, from different cell lines and/or experimental set ups, affects identifiability of parameters for a cell cycle model. Initially synchronised cell populations gradually desynchronise over successive cycles, converging to balanced exponential growth (BEG) which is characterised by exponential population growth and steady, time-independent phase proportions. These proportions can be obtained from fluorescence-activated cell sorting (FACS) data. The increasing use of the Fluorescent Ubiquitination-based Cell Cycle Indicator (FUCCI) provides higher-resolution information on phase dynamics, such as minimum phase durations and variability. We present an age-structured PDE model in which cell-cycle phase progression follows a delayed gamma distribution. We derive analytical expressions for BEG phase proportions and other FUCCI-observable quantities, and use them to assess how data availability influences parameter identifiability. When parameters are not uniquely identifiable, we determine identifiable parameter groupings, thereby determining the minimum amount of data that must be available for successfully fitting structured population models of the cell cycle.