Fundamental limits on dynamic inference from single-cell snapshots

By Caleb Weinreb, Samuel L. Wolock, B. Tusi, M. Socolovsky, Allon M. Klein. Proceedings of the National Academy of Sciences of the United States of America, 2017

343 citations recorded by the source corpus.

Significance Seeing a snapshot of individuals at different stages of a dynamic process can reveal what the process would look like for a single individual over time. Biologists apply this principle to infer temporal sequences of gene expression states in cells from measurements made at a single moment in time. However, the sparsity and high dimensionality of single-cell data have made inference difficult using formal approaches. Here, we apply recent innovations in spectral graph theory to devise a simple and asymptotically exact algorithm for inferring the unique dynamic solution under defined approximations and apply it to data from bone marrow stem cells. Single-cell expression profiling reveals the molecular states of individual cells with unprecedented detail. Because these methods destroy cells in the process of analysis, they cannot measure how gene expression changes over time. However, some information on dynamics is present in the data: the continuum of molecular states in the population can reflect the trajectory of a typical cell. Many methods for extracting single-cell dynamics from population data have been proposed. However, all such attempts face a common limitation: for any measured distribution of cell states, there are multiple dynamics that could give rise to it, and by extension, multiple possibilities for underlying mechanisms of gene regulation. Here, we describe the aspects of gene expression dynamics that cannot be inferred from a static snapshot alone and identify assumptions necessary to constrain a unique solution for cell dynamics from static snapshots. We translate these constraints into a practical algorithmic approach, population balance analysis (PBA), which makes use of a method from spectral graph theory to solve a class of high-dimensional differential equations. We use simulations to show the strengths and limitations of PBA, and then apply it to single-cell profiles of hematopoietic progenitor cells (HPCs). Cell state predictions from this analysis agree with HPC fate assays reported in several papers over the past two decades. By highlighting the fundamental limits on dynamic inference faced by any method, our framework provides a rigorous basis for dynamic interpretation of a gene expression continuum and clarifies best experimental designs for trajectory reconstruction from static snapshot measurements.

Subfields: Molecular Biology

View Paper: https://www.semanticscholar.org/paper/7c90e55d1c30d08ba33c0b5d6f63a0eb528717b8

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Citations in the corpus

Lineage tracing on transcriptional landscapes links state to fate during differentiation (2018, methodology): “At present, it is unknown how single cells traverse these trajectories, including whether they progress at different rates or even reverse their dynamics (4).”
Graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells (2017, background): “We also note that the approach here does not suﬀer from the problems discussed in [38].”
TrajectoryNet: A Dynamic Optimal Transport Network for Modeling Cellular Dynamics (2020, neutral): “However, these methods can be biased and fail in a number of circumstances (Weinreb et al., 2018; Lederer & La Manno, 2020) and do not take into account experimental time.”
Mapping Transcriptomic Vector Fields of Single Cells (2022, neutral): “We first performed velocity analysis on those datasets using dynamo with default parameters; however, for all three datasets, this resulted in unexpected backward velocity flows from terminal cell types to undiffer- entiated cells, based on cell-type assignments from the original study (Weinreb et a”
Deep Generative Modeling for Single-cell Transcriptomics (2018, methodology): “We use their population balance analysis [57] result as a potential function for di ﬀ erentiation.”