MOTIVATION: Trajectory inference (TI) methods for single-cell snapshots of developmental systems have yielded numerous insights into the gene regulatory networks (GRNs) that control cell differentiation. Many TI algorithms have been proposed for recovering cell trajectories from single samples containing cells spanning a spectrum of differentiation states; however, these methods cannot leverage temporal information when a time course of such diverse samples is available. As interest grows in understanding how the regulation of GRNs changes as an organism ages, current TI theory and methods must be adapted to take advantage of all information in aging time courses of single-cell data. RESULTS: In this paper, we present our novel age-conscious method, global StationaryOT, which exploits the temporal information in aging time courses to simultaneously reconstruct debiased cell trajectories at all ages. We demonstrate that this first-of-its-kind method achieves more accurate, biologically consistent trajectories in synthetic and real biological contexts where data sparsity produces significant noise in the outputs of current TI methods when they are applied to time course samples independently. AVAILABILITY: An open-source Python implementation of global StationaryOT, including documentation and examples, is available at https://github.com/ColeBoyle/global-stationaryOT. The source code, data processing scripts, and processed data for reproducing the results in this paper are archived at https://doi.org/10.5281/zenodo.20723235. The raw hematopoiesis data from Li et al. (The dynamics of hematopoiesis over the human lifespan. Nat Methods 2025;22 422-34.) can be accessed at https://www.ncbi.nlm.nih.gov/geo/query/acc.cgi? acc=GSE189161.

MOTIVATION: Lineage tracing and trajectory inference from single-cell RNA-sequencing data hold tremendous potential for uncovering the genetic programs driving development and disease. Single cell datasets are thought to provide an unbiased view on the diverse cellular architecture of tissues. Sampling bias, however, can skew single cell datasets away from the cellular composition they are meant to represent. RESULTS: We demonstrate a novel form of sampling bias, caused by a statistical phenomenon related to repeated sampling from a growing, heterogeneous population. Relative growth rates of cells influence the probability that they will be sampled in clones observed across multiple time points. We support our probabilistic derivations with a simulation study and an analysis of a real time-course of T-cell development. We find that this bias can impact fate probability predictions, and we explore how to develop trajectory inference methods which are robust to this bias. AVAILABILITY AND IMPLEMENTATION: Source code for the simulated datasets and to create the figures in this manuscript is freely available in python at https://github.com/rbonhamcarter/simulate-clones. A python implementation of the extension of the LineageOT method is freely available at https://github.com/rbonhamcarter/LineageOT/tree/multi-time-clones.

Trajectory inference aims at recovering the dynamics of a population from snapshots of its temporal marginals. To solve this task, a min-entropy estimator relative to the Wiener measure in path space was introduced in [Lavenant et al., 2021], and shown to consistently recover the dynamics of a large class of drift-diffusion processes from the solution of an infinite dimensional convex optimization problem. In this paper, we introduce a grid-free algorithm to compute this estimator. Our method consists in a family of point clouds (one per snapshot) coupled via Schrödinger bridges which evolve with noisy gradient descent. We study the mean-field limit of the dynamics and prove its global convergence to the desired estimator. Overall, this leads to an inference method with end-to-end theoretical guarantees that solves an interpretable model for trajectory inference. We also present how to adapt the method to deal with mass variations, a useful extension when dealing with single cell RNA-sequencing data where cells can branch and die.

Understanding how cells change their identity and behaviour in living systems is an important question in many fields of biology. The problem of inferring cell trajectories from single-cell measurements has been a major topic in the single-cell analysis community, with different methods developed for equilibrium and non-equilibrium systems (e.g. haematopoeisis vs. embryonic development). We show that optimal transport analysis, a technique originally designed for analysing time-courses, may also be applied to infer cellular trajectories from a single snapshot of a population in equilibrium. Therefore, optimal transport provides a unified approach to inferring trajectories that is applicable to both stationary and non-stationary systems. Our method, StationaryOT, is mathematically motivated in a natural way from the hypothesis of a Waddington's epigenetic landscape. We implement StationaryOT as a software package and demonstrate its efficacy in applications to simulated data as well as single-cell data from Arabidopsis thaliana root development.

We propose a new method to estimate Wasserstein distances and optimal transport plans between two probability distributions from samples in high dimension. Unlike plug-in rules that simply replace the true distributions by their empirical counterparts, our method promotes couplings with low transport rank, a new structural assumption that is similar to the nonnegative rank of a matrix. Regularizing based on this assumption leads to drastic improvements on high-dimensional data for various tasks, including domain adaptation in single-cell RNA sequencing data. These findings are supported by a theoretical analysis that indicates that the transport rank is key in overcoming the curse of dimensionality inherent to data-driven optimal transport.

f-divergences are a general class of divergences between probability measures which include as special cases many commonly used divergences in probability, mathematical statistics, and information theory such as Kullback-Leibler divergence, chi-squared divergence, squared Hellinger distance, total variation distance, and so on. In this paper, we study the problem of maximizing or minimizing an f-divergence between two probability measures subject to a finite number of constraints on other f-divergences. We show that these infinite-dimensional optimization problems can all be reduced to optimization problems over small finite dimensional spaces which are tractable. Our results lead to a comprehensive and unified treatment of the problem of obtaining sharp inequalities between f-divergences. We demonstrate that many of the existing results on inequalities between f-divergences can be obtained as special cases of our results. We also improve on some existing non-sharp inequalities.