Optimal transport analysis reveals trajectories in steady-state systems

Cellular proliferation biases clonal lineage tracing and trajectory inference

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.

Gene trajectory inference for single-cell data by optimal transport metrics

Single-cell RNA sequencing has been widely used to investigate cell state transitions and gene dynamics of biological processes. Current strategies to infer the sequential dynamics of genes in a process typically rely on constructing cell pseudotime through cell trajectory inference. However, the presence of concurrent gene processes in the same group of cells and technical noise can obscure the true progression of the processes studied. To address this challenge, we present GeneTrajectory, an approach that identifies trajectories of genes rather than trajectories of cells. Specifically, optimal transport distances are calculated between gene distributions across the cell-cell graph to extract gene programs and define their gene pseudotemporal order. Here we demonstrate that GeneTrajectory accurately extracts progressive gene dynamics in myeloid lineage maturation. Moreover, we show that GeneTrajectory deconvolves key gene programs underlying mouse skin hair follicle dermal condensate differentiation that could not be resolved by cell trajectory approaches. GeneTrajectory facilitates the discovery of gene programs that control the changes and activities of biological processes.

Modeling single cell trajectory using forward-backward stochastic differential equations

Recent advances in single-cell sequencing technology have provided opportunities for mathematical modeling of dynamic developmental processes at the single-cell level, such as inferring developmental trajectories. Optimal transport has emerged as a promising theoretical framework for this task by computing pairings between cells from different time points. However, optimal transport methods have limitations in capturing nonlinear trajectories, as they are static and can only infer linear paths between endpoints. In contrast, stochastic differential equations (SDEs) offer a dynamic and flexible approach that can model non-linear trajectories, including the shape of the path. Nevertheless, existing SDE methods often rely on numerical approximations that can lead to inaccurate inferences, deviating from true trajectories. To address this challenge, we propose a novel approach combining forward-backward stochastic differential equations (FBSDE) with a refined approximation procedure. Our FBSDE model integrates the forward and backward movements of two SDEs in time, aiming to capture the underlying dynamics of single-cell developmental trajectories. Through comprehensive benchmarking on multiple scRNA-seq datasets, we demonstrate the superior performance of FBSDE compared to other methods, highlighting its efficacy in accurately inferring developmental trajectories.

Resolving plant development in space and time with single-cell genomics

Single-cell genomics technologies are ushering in a new research era. In this review, we summarize the benefits and current challenges of using these technologies to probe the transcriptional regulation of plant development. In addition to profiling cells at a single snapshot in time, researchers have recently produced time-resolved datasets to map cell responses to stimuli. Live-imaging and spatial transcriptomic techniques are rapidly being adopted to link a cell's transcriptional profile with its spatial location within a tissue. Combining these technologies is a powerful spatiotemporal approach to investigate cell plasticity and developmental responses that contribute to plant resilience. Although there are hurdles to overcome, we conclude by discussing how single-cell genomics is poised to address developmental questions in the coming years.

Reconstructing growth and dynamic trajectories from single-cell transcriptomics data

Time-series single-cell RNA sequencing (scRNA-seq) datasets provide unprecedented opportunities to learn dynamic processes of cellular systems. Due to the destructive nature of sequencing, it remains challenging to link the scRNA-seq snapshots sampled at different time points. Here we present TIGON, a dynamic, unbalanced optimal transport algorithm that reconstructs dynamic trajectories and population growth simultaneously as well as the underlying gene regulatory network from multiple snapshots. To tackle the high-dimensional optimal transport problem, we introduce a deep learning method using a dimensionless formulation based on the Wasserstein-Fisher-Rao (WFR) distance. TIGON is evaluated on simulated data and compared with existing methods for its robustness and accuracy in predicting cell state transition and cell population growth. Using three scRNA-seq datasets, we show the importance of growth in the temporal inference, TIGON's capability in reconstructing gene expression at unmeasured time points and its applications to temporal gene regulatory networks and cell-cell communication inference.

Learning single-cell perturbation responses using neural optimal transport

Understanding and predicting molecular responses in single cells upon chemical, genetic or mechanical perturbations is a core question in biology. Obtaining single-cell measurements typically requires the cells to be destroyed. This makes learning heterogeneous perturbation responses challenging as we only observe unpaired distributions of perturbed or non-perturbed cells. Here we leverage the theory of optimal transport and the recent advent of input convex neural architectures to present CellOT, a framework for learning the response of individual cells to a given perturbation by mapping these unpaired distributions. CellOT outperforms current methods at predicting single-cell drug responses, as profiled by scRNA-seq and a multiplexed protein-imaging technology. Further, we illustrate that CellOT generalizes well on unseen settings by (1) predicting the scRNA-seq responses of holdout patients with lupus exposed to interferon-β and patients with glioblastoma to panobinostat; (2) inferring lipopolysaccharide responses across different species; and (3) modeling the hematopoietic developmental trajectories of different subpopulations.

Brassinosteroid gene regulatory networks at cellular resolution in the Arabidopsis root

Brassinosteroids are plant steroid hormones that regulate diverse processes, such as cell division and cell elongation, through gene regulatory networks that vary in space and time. By using time series single-cell RNA sequencing to profile brassinosteroid-responsive gene expression specific to different cell types and developmental stages of the Arabidopsis root, we identified the elongating cortex as a site where brassinosteroids trigger a shift from proliferation to elongation associated with increased expression of cell wall-related genes. Our analysis revealed HOMEOBOX FROM ARABIDOPSIS THALIANA 7 (HAT7) and GT-2-LIKE 1 (GTL1) as brassinosteroid-responsive transcription factors that regulate cortex cell elongation. These results establish the cortex as a site of brassinosteroid-mediated growth and unveil a brassinosteroid signaling network regulating the transition from proliferation to elongation, which illuminates aspects of spatiotemporal hormone responses.

RNA velocity unraveled

We perform a thorough analysis of RNA velocity methods, with a view towards understanding the suitability of the various assumptions underlying popular implementations. In addition to providing a self-contained exposition of the underlying mathematics, we undertake simulations and perform controlled experiments on biological datasets to assess workflow sensitivity to parameter choices and underlying biology. Finally, we argue for a more rigorous approach to RNA velocity, and present a framework for Markovian analysis that points to directions for improvement and mitigation of current problems.

A single-cell Arabidopsis root atlas reveals developmental trajectories in wild-type and cell identity mutants

In all multicellular organisms, transcriptional networks orchestrate organ development. The Arabidopsis root, with its simple structure and indeterminate growth, is an ideal model for investigating the spatiotemporal transcriptional signatures underlying developmental trajectories. To map gene expression dynamics across root cell types and developmental time, we built a comprehensive, organ-scale atlas at single-cell resolution. In addition to estimating developmental progressions in pseudotime, we employed the mathematical concept of optimal transport to infer developmental trajectories and identify their underlying regulators. To demonstrate the utility of the atlas to interpret new datasets, we profiled mutants for two key transcriptional regulators at single-cell resolution, shortroot and scarecrow. We report transcriptomic and in vivo evidence for tissue trans-differentiation underlying a mixed cell identity phenotype in scarecrow. Our results support the atlas as a rich community resource for unraveling the transcriptional programs that specify and maintain cell identity to regulate spatiotemporal organ development.

A single-cell Arabidopsis root atlas reveals developmental trajectories in wild-type and cell identity mutants

In all multicellular organisms, transcriptional networks orchestrate organ development. The Arabidopsis root, with its simple structure and indeterminate growth, is an ideal model for investigating the spatiotemporal transcriptional signatures underlying developmental trajectories. To map gene expression dynamics across root cell types and developmental time, we built a comprehensive, organ-scale atlas at single-cell resolution. In addition to estimating developmental progressions in pseudotime, we employed the mathematical concept of optimal transport to infer developmental trajectories and identify their underlying regulators. To demonstrate the utility of the atlas to interpret new datasets, we profiled mutants for two key transcriptional regulators at single-cell resolution, shortroot and scarecrow. We report transcriptomic and in vivo evidence for tissue trans-differentiation underlying a mixed cell identity phenotype in scarecrow. Our results support the atlas as a rich community resource for unraveling the transcriptional programs that specify and maintain cell identity to regulate spatiotemporal organ development.