Dissecting Transition Cells from Single-cell Transcriptome Data through Multiscale Stochastic Dynamics

Abstract

Advances of single-cell technologies allow scrutinizing of heterogeneous cell states, however, analyzing transitions from snap-shot single-cell transcriptome data remains challenging. To investigate cells with transient properties or mixed identities, we present MuTrans, a method based on multiscale reduction technique for the underlying stochastic dynamical systems that prescribes cell-fate transitions. By iteratively unifying transition dynamics across multiple scales, MuTrans constructs the cell-fate dynamical manifold that depicts progression of cell-state transition, and distinguishes meta-stable and transition cells. In addition, MuTrans quantifies the likelihood of all possible transition trajectories between cell states using the coarse-grained transition path theory. Downstream analysis identifies distinct genes that mark the transient states or drive the transitions. Mathematical analysis reveals consistency of the method with the well-established Langevin equation and transition rate theory. Applying MuTrans to datasets collected from five different single-cell experimental platforms and benchmarking with seven existing tools, we show its capability and scalability to robustly unravel complex cell fate dynamics induced by transition cells in systems such as tumor EMT, iPSC differentiation and blood cell differentiation. Overall, our method bridges data-driven and model-based approaches on cell-fate transitions at single-cell resolution.

Unifying deterministic and stochastic ecological dynamics via a landscape-flux approach

“…Some approaches have focused on the zero-noise limit (20)(21)(22)(23) while others have considered the finite stochastic fluctuations (1,(24)(25)(26), but certain mathematical challenges still remain (25,26). Data-driven approaches to landscape changes and transition paths have recently been explored in the microenvironment "ecosystem" of cancer-immune interactions (27)(28)(29)(30). In this study, we highlight a recently developed method for analyzing the global stability and dynamics of both deterministic and stochastic complex systems in a unified framework (4,17,31,32).…”

On the Mathematics of RNA Velocity I: Theoretical Analysis

“…The inner-product scheme is constructed similar to diffusion map [8]. Related idea and methodology has been utilized to analyze the scRNA-seq data analysis [44,55,66]. Given the sample probability density q(x), we define a new kernel…”

“…Specifically, if we choose α = 1, then the transition probability will not depend on the data potential V (x) in the infinite samples limit. This structure opens the way of studying the non-equilibrium steady state and landscape theory for cell developments with scRNA-seq experimental data [65,63,17,44,55,66].…”

“…The partition of the state space can be achieved by the clustering of cells, or by the simultaneous reduction of multi-scale dynamics [13,66]. The coarse-grained transition probability matrix can be indeed calculated analytically instead of through numerical simulations:…”

A dynamical systems treatment of transcriptomic trajectories in hematopoiesis

“…For example, a mathematical model of a pitchfork bifurcation can be fit to scRNA-seq data and yield predictions for developmental perturbations (9), large transcriptomic matrices can be dimensionally reduced to enhance the resolution of bifurcations to precisely determine the genes enabling a cell fate decision (10,11), and well characterized cell-lineage relationships can be used to extract predictive models of gene regulation (12,13). While these studies generally characterize cell fate decisions as bifurcations of an underlying developmental landscape, other studies model cell fate decisions as noise-induced state transitions on non-bifurcating developmental landscapes, by parameterizing cells' dynamics and stochasticity, and use these models to infer lineage relationships and state transition probabilities (14)(15)(16).…”