On the Mathematics of RNA Velocity I: Theoretical Analysis

Li, Tiejun; Shi, Jifan; Wu, Yichong; Zhou, Peijie

doi:10.1101/2020.09.19.304584

Cited by 15 publications

(22 citation statements)

References 68 publications

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“…For instance, the barrier-crossing mechanism is not sufficient to capture the oscillatory processes such as cell cycle (38). Instead of constructing cellcell scale random walk with a pure diffusion-like kernel on transcriptome data, such non-equilibrium process might be accounted for by single-cell RNA velocity (18,45,46), thereafter a multi-scale reduction approach can naturally apply (47). Effective ways in root cell states detection (e.g.…”

Section: Discussionmentioning

confidence: 99%

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

Zhou

Wang

et al. 2021

Preprint

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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.

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Section: Discussionmentioning

confidence: 99%

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

Zhou

Wang

et al. 2021

Preprint

Self Cite

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“…Because velocity can be estimated for each gene in each cell, velocities of all genes in any cell form a high-dimensional vector, with each dimension corresponding to a gene. This high-dimensional velocity vector is often projected into a low-dimensional space for visualization using either pearson or cosine kernels ( Bergen et al, 2020 ; La Manno et al, 2018 ; Li et al, 2020 ) to reveal the direction of cell fate transitions in low-dimensional space via projected velocities.…”

Section: Star+methodsmentioning

confidence: 99%

Mapping transcriptomic vector fields of single cells

Qiu

Zhang

Martin-Rufino

et al. 2022

Cell

232

328

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“…Because velocity can be estimated for each gene in each cell, velocities of all genes in any cell form a high-dimensional vector, with each dimension corresponding to a gene. This high-dimensional velocity vector is often projected into a low-dimensional space for visualization using either pearson or cosine kernels (La Manno et al 2018; Bergen et al 2020; Li et al 2020) to reveal the direction of cell fate transitions in low-dimensional space via projected velocities.…”

Section: Methodsmentioning

confidence: 99%

Mapping Transcriptomic Vector Fields of Single Cells

Qiu

Zhang

Yang

et al. 2019

Preprint

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Understanding how gene expression in single cells progress over time is vital for revealing the mechanisms governing cell fate transitions. RNA velocity, which infers immediate changes in gene expression by comparing levels of new (unspliced) versus mature (spliced) transcripts (La Manno et al. 2018) , represents an important advance to these efforts. A key question remaining is whether it is possible to predict the most probable cell state backward or forward over arbitrary time-scales. To this end, we introduce an inclusive model (termed Dynamo ) capable of predicting cell states over extended time periods, that incorporates promoter state switching, transcription, splicing, translation and RNA/protein degradation by taking advantage of scRNA-seq and the co-assay of transcriptome and proteome. We also implement scSLAM-seq by extending SLAM-seq to plate-based scRNA-seq (Hendriks et al. 2018;Erhard et al. 2019;Cao, Zhou, et al. 2019) and augment the model by explicitly incorporating the metabolic labelling of nascent RNA. We show that through careful design of labelling experiments and an efficient mathematical framework, the entire kinetic behavior of a cell from this model can be robustly and accurately inferred. Aided by the improved framework, we show that it is possible to reconstruct the transcriptomic vector field from sparse and noisy vector samples generated by single cell experiments. The reconstructed vector field further enables global mapping of potential landscapes that reflects the relative stability of a given cell state, and the minimal transition time and most probable paths between any cell states in the state space. This work thus foreshadows the possibility of predicting long-term trajectories of cells during a dynamic process instead of short time velocity estimates. Our methods are implemented as an open source tool, dynamo ( https://github.com/aristoteleo/dynamo-release ).

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On the Mathematics of RNA Velocity I: Theoretical Analysis

Cited by 15 publications

References 68 publications

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

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

Mapping transcriptomic vector fields of single cells

Mapping Transcriptomic Vector Fields of Single Cells

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