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

Abstract

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.

Reconstructing growth and dynamic trajectories from single-cell transcriptomics data

“…While TIGON reconstructs velocity and growth simultaneously, other important factors, such as signals from the microenvironment and communication among cells, may be important to include. Direct incorporation of cell–cell communication in the model remains challenging, particularly, for a large number of interactive cells in the high-dimensional gene expression space 60 , 61 . Applications of cell–cell communication inference methods, such as CellChat 46 or exFINDER 62 , to single-cell gene expression inferred at unmeasured time points by TIGON, can produce dynamic cell–cell communication networks.…”

MDIC3: Matrix decomposition to infer cell-cell communication

“…The cell-cell communications from MDIC3 avoid the effect of unknown L-R pairs and are in line with the biological nature. Similarly, GraphFP, 110 like MDIC3, does not rely on L-R databases in its cell-cell interaction prediction process, and its results also provide an overall perspective. However, GraphFP is designed for predicting cell-cell interactions on the basis of a large amount of dynamic time-series data, making it more suitable for the analysis of time-series data with multiple time points and may be more advantageous when exploring changes in cell-cell interactions at different time points.…”

Inferring structural and dynamical properties of gene networks from data with deep learning

“…( 1 , 15 , 20 )) and data-driven perspective (e.g. ( 18 , 19 , 65 , 66 )). Based on the deterministic system obtained from DNN and the estimated diffusion coefficient, we propose the DNN-PSCA approach, which offers an approach for combining data-driven and model-driven strategy to quantify the energy landscape for gene networks.…”