Quantifying pluripotency landscape of cell differentiation from scRNA-seq data by continuous birth-death process

Tipping points in epithelial-mesenchymal lineages from single-cell transcriptomics data

Understanding cell fate decision-making during complex biological processes is an open challenge that is now aided by high-resolution single-cell sequencing technologies. Specifically, it remains challenging to identify and characterize transition states corresponding to "tipping points" whereby cells commit to new cell states. Here, we present a computational method that takes advantage of single-cell transcriptomics data to infer the stability and gene regulatory networks (GRNs) along cell lineages. Our method uses the unspliced and spliced counts from single-cell RNA sequencing data and cell ordering along lineage trajectories to train an RNA splicing multivariate model, from which cell-state stability along the lineage is inferred based on spectral analysis of the model's Jacobian matrix. Moreover, the model infers the RNA cross-species interactions resulting in GRNs and their variation along the cell lineage. When applied to epithelial-mesenchymal transition in ovarian and lung cancer-derived cell lines, our model predicts a saddle-node transition between the epithelial and mesenchymal states passing through an unstable, intermediate cell state. Furthermore, we show that the underlying GRN controlling epithelial-mesenchymal transition rearranges during the transition, resulting in denser and less modular networks in the intermediate state. Overall, our method represents a flexible tool to study cell lineages with a combination of theory-driven modeling and single-cell transcriptomics data.

A physics-informed neural SDE network for learning cellular dynamics from time-series scRNA-seq data

MOTIVATION

Learning cellular dynamics through reconstruction of the underlying cellular potential energy landscape (aka Waddington landscape) from time-series single-cell RNA sequencing (scRNA-seq) data is a current challenge. Prevailing data-driven computational methods can be hampered by the lack of physical principles to guide learning from complex data, resulting in reduced prediction accuracy and interpretability when applied to infer cell population dynamics.

RESULTS

Here, we propose PI-SDE, a physics-informed neural stochastic differential equation (SDE) framework that combines the Hamilton-Jacobi (HJ) equation and neural SDE to learn cellular dynamics. Grounded in potential energy theory of biological systems, PI-SDE integrates the principle of least action by enforcing the HJ equation when reconstructing cellular potential energy function. This approach not only facilitates accurate predictions, but also improves interpretability, especially in the reconstructed potential energy landscape. Through benchmarking on two real scRNA-seq datasets, we demonstrate the importance of incorporating the HJ regularization term in dynamic inference, especially in predicting gene expression at held-out time points. Meanwhile, the learned potential energy landscape provides biologically interpretable insights into the process of cell differentiation. Our framework enhances model performance, while maintaining robustness and stability.

AVAILABILITY

PI-SDE software is available at https://github.com/QiJiang-QJ/PI-SDE.

SPIDE: A single cell potency inference method based on the local cell-specific network entropy

For a given single cell RNA-seq data, it is critical to pinpoint key cellular stages and quantify cells' differentiation potency along a differentiation pathway in a time course manner. Currently, several methods based on the entropy of gene functions or PPI network have been proposed to solve the problem. Nevertheless, these methods still suffer from the inaccurate interactions and noises originating from scRNA-seq profile. In this study, we proposed a cell potency inference method based on cell-specific network entropy, called SPIDE. SPIDE introduces the local weighted cell-specific network for each cell to maintain cell heterogeneity and calculates the entropy by incorporating gene expression with network structure. In this study, we compared three cell entropy estimation models on eight scRNA-Seq datasets. The results show that SPIDE obtains consistent conclusions with real cell differentiation potency on most datasets. Moreover, SPIDE accurately recovers the continuous changes of potency during cell differentiation and significantly correlates with the stemness of tumor cells in Colorectal cancer. To conclude, our study provides a universal and accurate framework for cell entropy estimation, which deepens our understanding of cell differentiation, the development of diseases and other related biological research.

Rapid and biased evolution of canalization during adaptive divergence revealed by dominance in gene expression variability during Arctic charr early development

Adaptive evolution may be influenced by canalization, the buffering of developmental processes from environmental and genetic perturbations, but how this occurs is poorly understood. Here, we explore how gene expression variability evolves in diverging and hybridizing populations, by focusing on the Arctic charr (Salvelinus alpinus) of Thingvallavatn, a classic case of divergence between feeding habitats. We report distinct profiles of gene expression variance for both coding RNAs and microRNAs between the offspring of two contrasting morphs (benthic/limnetic) and their hybrids reared in common conditions and sampled at two key points of cranial development. Gene expression variance in the hybrids is substantially affected by maternal effects, and many genes show biased expression variance toward the limnetic morph. This suggests that canalization, as inferred by gene expression variance, can rapidly diverge in sympatry through multiple gene pathways, which are associated with dominance patterns possibly biasing evolutionary trajectories and mitigating the effects of hybridization on adaptive evolution.

Accurate Estimation of Single-Cell Differentiation Potency Based on Network Topology and Gene Ontology Information

One important task in single-cell analysis is to quantify the differentiation potential of single cells. Though various single-cell potency measures have been proposed, they are based on individual biological sources, thus not robust and reliable. It is still a challenge to combine multiple sources to generate a relatively reliable and robust measure to estimate differentiation. In this paper, we propose a New Centrality measure with Gene ontology information (NCG) to estimate single-cell potency. NCG is designed by combining network topology property with edge clustering coefficient, and gene function information using gene ontology function similarity scores. NCG distinguishes pluripotent cells from non-pluripotent cells with high accuracy, correctly ranks different cell types by their differentiation potency, tracks changes during the differentiation process, and constructs the lineage trajectory from human myoblasts into skeletal muscle cells. These indicate that NCG is a reliable and robust measure to estimate single-cell potency. NCG is anticipated to be a useful tool for identifying novel stem or progenitor cell phenotypes from single-cell RNA-Seq data. The source codes and datasets are available at https://github.com/Xinzhe-Ni/NCG.

Energy landscape decomposition for cell differentiation with proliferation effect

Complex interactions between genes determine the development and differentiation of cells. We establish a landscape theory for cell differentiation with proliferation effect, in which the developmental process is modeled as a stochastic dynamical system with a birth-death term. We find that two different energy landscapes, denoted U and V, collectively contribute to the establishment of non-equilibrium steady differentiation. The potential U is known as the energy landscape leading to the steady distribution, whose metastable states stand for cell types, while V indicates the differentiation direction from pluripotent to differentiated cells. This interpretation of cell differentiation is different from the previous landscape theory without the proliferation effect. We propose feasible numerical methods and a mean-field approximation for constructing landscapes U and V. Successful applications to typical biological models demonstrate the energy landscape decomposition's validity and reveal biological insights into the considered processes.

Cell identity conversion in liver regeneration after injury

Cell identity conversion in liver injury is the process that mature cells, specifically hepatocytes or cholangiocytes, convert into cells with other identities, which is found to play a pivotal role in liver regeneration. A better characterization of cell identity conversion will not only facilitate the understanding of liver tissue repair but also the development of novel regenerative therapies. In this review, we discuss the latest advances in cell identity conversion during liver regeneration, including conversions between hepatocytes and cholangiocytes and hepatocyte reprogramming to liver progenitor-like cells. To develop a unified description of cellular states in injury-related liver regeneration, we further propose the quantitative approach to explore cell identity conversion based on the Waddington's landscape.

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

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.

Dynamic inference of cell development processes from time series scRNA-seq data is a major challenge. Here, we present GraphFP, a coherent computational framework that simultaneously reconstructs the cell state-transition complex potential energy landscape and infers cell-cell interactions from time series single-cell transcriptomic data. Based on the mathematical framework of nonlinear Fokker-Planck equation on graph, GraphFP models the stochastic dynamics of the cell state/type frequencies on probability simplex in continuous time, where the free energy with a nonlinear quadratic interaction term is employed to characterize cell-cell interactions. We formulate the model inference problem in the form of a dynamic optimal transport framework and solve it efficiently with the celebrated adjoint method. GraphFP allows for 1) reconstructing cell state potential energy, which is a measure of cellular differentiation potency, 2) charting the probability flows between paired cell states over dynamic processes, 3) quantifying the stochastic dynamics of cell type frequencies on probability simplex in continuous time, and 4) delineating cell-cell interactions that drive cell differentiation. We show how GraphFP can be used to faithfully reveal and accurately quantify the cell development processes using the embryonic murine cerebral cortex development time series scRNA-seq dataset.

Dynamics-based data science in biology

With the increasingly accumulated bio-data, dynamics-based data-science has been progressing as an efficient way to reveal mechanisms of dynamical biological processes. We review three applications on detecting the tipping-points of diseases, quantifying cell's potency, and predicting time-series, to show the importance of dynamics-based data-science.

Statistical mechanics meets single-cell biology

Single-cell omics is transforming our understanding of cell biology and disease, yet the systems-level analysis and interpretation of single-cell data faces many challenges. In this Perspective, we describe the impact that fundamental concepts from statistical mechanics, notably entropy, stochastic processes and critical phenomena, are having on single-cell data analysis. We further advocate the need for more bottom-up modelling of single-cell data and to embrace a statistical mechanics analysis paradigm to help attain a deeper understanding of single-cell systems biology.