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Meeting-ID: 280 519 2121
Passwort: 584190

Abstract:

Cell differentiation is a fundamental process in developmental biology which studies how unspecialised stem cells become specialised ones. Modern next-generation sequencing allows for simultaneous measurement of a large number of gene expressions at the single-cell level resulting in large high-dimensional datasets. As a consequence, quantitative methods that provide insights into cell differentiation mechanisms in this high-dimensional gene space are in high demand and, despite the large efforts and tools available, modelling differentiating cells and their time evolution remains a topic of extensive investigation.
 In this talk, I will present our novel method to infer cell trajectories by means of non-linear stochastic differential equations, associated to a quasi-potential landscape, in a reduced yet high-dimensional gene space.
We adopt an agnostic perspective by defining the potential and associated system dynamics using neural networks, within the framework of neural differential equations, which can handle settings where the state space is high-dimensional via efficient and accurate solvers. Moreover, a key benefit of our approach is that the neural network architecture provides flexibility while maintaining an analytical form of the potential function; this can be accessed at no extra computational cost to derive other quantities of interest such as the density law of the system.
Optimisation criteria to find the law of paths of the neural SDE is formulated according to the integrated loss on the path space on a suitable discrepancy measure between the observed data and the ones generated by the simulator model. In particular, we investigate the use of the regularised Wasserstein distance and the expected energy score. Two different modelling frameworks are considered: a time-independent neural potential and a time-dependent extension based on the notion of Doob's H-transform and the addition of neural diffusion bridges.
Finally, applications of our approach are provided for a number of artificial and real-world data examples, particularly on scRNA-seq data on early-stage mouse embryos and on the so-called reprogramming dataset for induced Pluripotent Stem Cells (iPSC).