Rxivist logo

Fundamental limits on dynamic inference from single cell snapshots

By Caleb Weinreb, Samuel Wolock, Betsabeh K. Tusi, Merav Socolovsky, Allon M. Klein

Posted 30 Jul 2017
bioRxiv DOI: 10.1101/170118 (published DOI: 10.1073/pnas.1714723115)

Single cell profiling methods are powerful tools for dissecting the molecular states of cells, but the destructive nature of these methods has made it difficult to measure single cell expression over time. When cell dynamics are asynchronous, they can form a continuous manifold in gene expression space whose structure is thought to encode the trajectory of a typical cell. This insight has spurred a proliferation of methods for single cell trajectory discovery that have successfully ordered cell states and identified differentiation branch-points. However, all attempts to infer dynamics from static snapshots of cell state face a common limitation: for any measured distribution of cells in high dimensional state space, there are multiple dynamics that could give rise to it, and by extension, multiple possibilities for underlying mechanisms of gene regulation. Here, we enumerate from first principles the aspects of gene expression dynamics that cannot be inferred from a static snapshot alone, but nonetheless have a profound influence on temporal ordering and fate probabilities of cells. On the basis of these unknowns, we identify assumptions necessary to constrain a unique solution for the dynamics and translate these constraints into a practical algorithmic approach, called Population Balance Analysis (PBA). At its core, PBA invokes a new method based on spectral graph theory for solving a certain class of high dimensional differential equation. We show the strengths and limitations of PBA using simulations and validate its accuracy on single cell profiles of hematopoietic progenitor cells. Altogether, these results provide a rigorous basis for dynamic interpretation of a gene expression continuum, and the pitfalls facing any method of dynamic inference. In doing so they clarify experimental designs to minimize these shortfalls.

Download data

  • Downloaded 2,335 times
  • Download rankings, all-time:
    • Site-wide: 3,256 out of 101,163
    • In systems biology: 82 out of 2,568
  • Year to date:
    • Site-wide: 54,105 out of 101,163
  • Since beginning of last month:
    • Site-wide: 54,722 out of 101,163

Altmetric data

Downloads over time

Distribution of downloads per paper, site-wide


Sign up for the Rxivist weekly newsletter! (Click here for more details.)


  • 20 Oct 2020: Support for sorting preprints using Twitter activity has been removed, at least temporarily, until a new source of social media activity data becomes available.
  • 18 Dec 2019: We're pleased to announce PanLingua, a new tool that enables you to search for machine-translated bioRxiv preprints using more than 100 different languages.
  • 21 May 2019: PLOS Biology has published a community page about Rxivist.org and its design.
  • 10 May 2019: The paper analyzing the Rxivist dataset has been published at eLife.
  • 1 Mar 2019: We now have summary statistics about bioRxiv downloads and submissions.
  • 8 Feb 2019: Data from Altmetric is now available on the Rxivist details page for every preprint. Look for the "donut" under the download metrics.
  • 30 Jan 2019: preLights has featured the Rxivist preprint and written about our findings.
  • 22 Jan 2019: Nature just published an article about Rxivist and our data.
  • 13 Jan 2019: The Rxivist preprint is live!