Computationally efficient mechanism discovery for cell invasion with uncertainty quantification

Abstract

Parameter estimation for mathematical models of biological processes is often difficult and depends significantly on the quality and quantity of available data. We introduce an efficient framework using Gaussian processes to discover mechanisms underlying delay, migration, and proliferation in a cell invasion experiment. Gaussian processes are leveraged with bootstrapping to provide uncertainty quantification for the mechanisms that drive the invasion process. Our frame-work is efficient, parallelisable, and can be applied to other biological problems. We illustrate our methods using a canonical scratch assay experiment, demonstrating how simply we can explore different functional forms and develop and test hypotheses about underlying mechanisms, such as whether delay is present. All code and data to reproduce this work is available at https://github.com/DanielVandH/EquationLearning.jl.1Author summaryIn this work we introduce uncertainty quantification into equation learning methods, such as physics-informed and biologically-informed neural networks. Our framework is efficient and applicable to problems with unknown nonlinear mechanisms that we wish to learn from experiments where only sparse noisy data is available. We demonstrate our methods on a canonical scratch assay experiment from cell biology and show the underlying mechanisms can be learned, providing uncertainty intervals for functional forms and for solutions to partial differential equation models believed to describe the experiment.

Calibration of Agent Based Models for Monophasic and Biphasic Tumour Growth using Approximate Bayesian Computation

“…Mathematical modelling of cancer growth and development has been used to study the dynamical process of cancer cells for many years (Altrock et al, 2015; Beerenwinkel et al, 2015; Barbolosi et al, 2016; Tabassum et al, 2019). Deterministic approaches, such as systems of ordinary differential equations (ODEs) and systems of partial differential equations (PDEs), have been used successfully to model cancer growth (Villasana and Radunskaya, 2003; Yafia, 2011; Tao et al, 2014; Jenner et al, 2020b; Dehingia et al, 2021; Klowss et al, 2022; VandenHeuvel et al, 2022). While insightful, generally these models do not capture the heterogeneity that arises through stochastic processes of tumour growth, or consider the behaviour at an individual cancer cell level (Irurzun-Arana et al, 2020).…”