Dynamic inference of cell developmental complex energy landscape from time series single-cell transcriptomic data

PLoS Comput Biol. 2022 Jan 24;18(1):e1009821. doi: 10.1371/journal.pcbi.1009821. eCollection 2022 Jan.


Time series single-cell RNA sequencing (scRNA-seq) data are emerging. However, dynamic inference of an evolving cell population from time series scRNA-seq data is challenging owing to the stochasticity and nonlinearity of the underlying biological processes. This calls for the development of mathematical models and methods capable of reconstructing cellular dynamic transition processes and uncovering the nonlinear cell-cell interactions. In this study, we present GraphFP, a nonlinear Fokker-Planck equation on graph based model and dynamic inference framework, with the aim of reconstructing the cell state-transition complex potential energy landscape from time series single-cell transcriptomic data. The free energy of our model explicitly takes into account of the cell-cell interactions in a nonlinear quadratic term. We then recast the model inference problem in the form of a dynamic optimal transport framework and solve it efficiently with the adjoint method of optimal control. We evaluated GraphFP on the time series scRNA-seq data set of embryonic murine cerebral cortex development. We illustrated that it 1) reconstructs cell state potential energy, which is a measure of cellular differentiation potency, 2) faithfully charts the probability flows between paired cell states over the dynamic processes of cell differentiation, and 3) accurately quantifies the stochastic dynamics of cell type frequencies on probability simplex in continuous time. We also illustrated that GraphFP is robust in terms of cluster labelling with different resolutions, as well as parameter choices. Meanwhile, GraphFP provides a model-based approach to delineate the cell-cell interactions that drive cell differentiation. GraphFP software is available at https://github.com/QiJiang-QJ/GraphFP.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Animals
  • Cell Differentiation / genetics*
  • Computational Biology
  • Mice
  • RNA-Seq / methods*
  • Single-Cell Analysis / methods*
  • Time Factors
  • Transcriptome / genetics*

Grant support

This work was supported by the Fund to LW from the National Key Research and Development Program of China under Grant 2019YFA0709501. LW and SZ were also supported by the National Natural Science Foundation of China (No. 12071466 to LW and No.11871465 to SZ). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.