Pseudodynamics+: Reconstructing Population Dynamics from Time-Resolved Single Cell Landscapes with Physics Informed Neural Networks

Abstract

Single-cell profiling provides snapshots of the heterogeneous states that characterise developmental processes, organ regeneration and progression towards disease in a complex landscape. The underlying trajectories are of pivotal interest, but existing methods for reconstructing cell state trajectories commonly neglect population sizes. However, snapshot experiments make it difficult to interpret cell flux because the observed trajectories are confounded by changes in overall population size. This ambiguity can lead to misinterpreting changes in proliferation or death rates as changes in cellular migration. We introduce pseudodynamics+, a physics-informed neural network framework that solves high-dimensional flow equations on complex, branching landscapes. By integrating single-cell genomics with population dynamics, pseudodynamics+ estimates state- and time-dependent parameters of growth, differentiation, and diffusion. The model recapitulates proliferation bursts during T-cell maturation and, when applied to LARRY-barcoded data, predicts differentiation rates consistent with clonal behaviour. When applied to time-resolved persistent-labelling datasets of in vivo mouse bone marrow haematopoiesis, pseudodynamics+ reconstructs continuous tissue flows with dynamic parameters aligned with known molecular signatures. Notably, simulations revealed a previously unrecognised shift from megakaryocyte-biased to balanced progenitor output, explained by evolving fate preferences of progenitor states, as revealed by simulations leveraging our estimated dynamic parameters. Pseudodynamics+ therefore establishes a population-aware framework for reconstructing single-cell population dynamics and is available at https://github.com/Gottgens-lab/pseudodynamics_plus.