The Francis Crick Institute London

Mechanistic ordinary differential equation (ODE) models are a powerful tool to study dynamic biological systems. However, their predictive power is constrained by gaps, biases, and inconsistencies in the literature. They typically also require quantitative time-lapse data for training, which is time-consuming to collect. At the same time, machine-learning approaches can capture complex patterns from data, but they are often harder to interpret and typically require large training datasets. Hybrid scientific machine learning (SciML) models offer a promising way to combine the strengths of both approaches by integrating mechanistic models with flexible data-driven modules. 
Despite this promise, the use of SciML in biology remains limited by insufficient infrastructure. Dedicated software is needed because coding end-to-end differentiable workflows for gradient-based training of hybrid models is technically challenging. In addition, model exchange is hindered by the lack of a standardized, reproducible format for specifying SciML training problems, analogous to the PEtab standard for ODE models. To address these challenges, we developed PEtab-SciML, an extension of the PEtab format, and implemented support for it in the state-of-the-art modeling toolboxes PEtab.jl and AMICI. In this seminar, I will introduce the PEtab-SciML format. Using real-data examples, I will show how PEtab-SciML enables the integration of diverse data modalities into dynamic model training; such as learning the kinetic parameters of an ODE model from omics and protein sequence data. I will also show how it supports machine-learning-based black-boxing of complex model components, such as quarantine strength in an SIR model. Finally, I will show how PEtab-SciML enables the use of efficient training strategies, such as curriculum learning, that make SciML models easier to train and apply in practice. 

Specialist species thrive under specific environmental conditions in narrow geographic ranges and are widely recognized as heavily threatened by climate deregulation. Many might rely on both their potential to adapt and to disperse towards a refugium to avoid extinction. It is thus crucial to understand the influence of environmental conditions on the unfolding process of adaptation. I will present a PDE model of the eco-evolutionary dynamics of a specialist species in a two-patch environment with moving optima. The transmission of the adaptive trait across generations is modelled by a non-linear, non-local operator of sexual reproduction. In an asymptotic regime of small variance, I justify that the local trait distributions are well approximatted by Gaussian distributions with fixed variances, which allows to report the analysis on the closed system of moments. Thanks to a separation of time scales between ecology and evolution, I next derive a limit system of moments and analyse its stationary states. In particular, I identify the critical environmental speed for persistence, which reflects how both the existence of a refugium and the cost of dispersal impact extinction patterns. Additionally, the analysis provides key insights regarding the path towards this refugium. I show that there exists a critical environmental speed above which the species crosses a tipping point, resulting into an abrupt habitat switch from its native patch to the refugium. When selection for local adaptation is strong, this habitat switch passes through an evolutionary ‘‘death valley’’ that can promote extinction for lower environmental speeds than the critical one.

Unraveling the intricacies of intracellular signalling through predictive mathematical models holds great promise for advancing precision medicine and enhancing our foundational comprehension of biology. However, navigating the labyrinth of biological mechanisms governing signalling demands a delicate balance between a faithful description of the underlying biology and the practical utility of parsimonious models.
In this talk, I will present methods that enable training of large ordinary differential equation models of intracellular signalling and showcase application of such models to predict sensitivity to anti-cancer drugs. Through illustrative examples, I will demonstrate the application of these models in predicting sensitivity to anti-cancer drugs. A critical reflection on the construction of such models will be offered, exploring the perpetual question of complexity and how intricate these models should be.
Moreover, the talk will explore novel approaches that meld machine learning techniques with mathematical modelling. These approaches aim to harness the benefits of simplistic and unbiased phenomenological models while retaining the interpretability and biological fidelity inherent in mechanistic models.