Speaker
Description
Advances in cellular and tissue biology have enabled robust tracking of large populations of interacting cells while simultaneously collecting detailed, multiplex molecular measurements. In such data-rich settings, mathematical models provide a powerful framework for integrating observations, capturing cellular interactions, and explaining emergent collective behaviours.
A range of approaches link partial differential equation (PDE) models with experimental data, including data-driven methods such as sparse regression and neural networks that infer governing equations and parameter values directly from data, as well as more traditional approaches that estimate parameters for a prescribed PDE model. The latter typically rely on error models that connect experimental measurements to theoretical predictions.
While considerable effort has been devoted to improving these error models, they are typically based on convenient statistical assumptions, most commonly that residuals are Gaussian and uncorrelated, which are unlikely to reflect underlying biological mechanisms. We propose a mechanistic framework for constructing error models by analysing the fluctuations that naturally arise when deriving PDE descriptions from interacting particle systems. By grounding error models in particle-level interactions, this approach aims to produce more realistic parameter estimates and reveal cell–cell interaction mechanisms that may remain hidden under conventional statistical assumptions.
