Developing and applying modelling and Bayesian inference tools for developmental biology

Developmental biology allows us to answer crucial questions about how patterned, polarized cells can organize robustly and repeatably to form living tissues and organisms. Quantitative imaging data is now available that can provide deep insights into developmental processes, but to make best use of these data, we need mathematical and computational models. Linking complex mechanistic models to quantitative experimental data is challenging, but Bayesian inference provides a principled framework for this. Together, mechanistic models can guide hypothesis-driven experiments, while quantitative experimental data can inform modelling through a data- driven framework for inference and testable predictions. However, challenges remain in developing methodological tools to relate mechanistic models to data effectively. We address a number of these challenges in this thesis, and demonstrate the use of such tools in an integrative framework to address hypotheses about the robustness and points of control governing mRNA localization during development. We begin by studying the bottlenecks controlling the regulation of mRNA transport, using a fine-grained stochastic model of transport within a single cell and relate this model to experimental data. We then study this stochastic model in a more general setting and ask how experimental design, such as the sampling frequency of observations via imaging, affects parameter estimation. Summary statistics are frequently used to simplify inference for problems with high-dimensional data. It is not clear how to select and combine summary statistics for approximate Bayesian computation, although much previous work has been done in this area. We address this problem with an adaptive algorithm that aims to maximize the distance between prior and approximate posterior distributions. Finally, we return to our study of mRNA localization by developing a coarse-grained model to address questions about how robustness of mRNA localization is regulated during development. Using a simple differential equation model, we make testable predictions, which demonstrate the surprising robustness of mRNA localization, and subsequently reveal crowding as a mechanism for regulation of this process. Together, the contributions of this work are towards developing modelling and inference tools to enable quantitative hypothesis-driven study of developmental and cell biology.