Mapping transcriptomic vector fields of single cells

Qiu, Xiaojie; Zhang, Yan; Martin-Rufino, Jorge D.; Weng, Chen; Hosseinzadeh, Shayan; Yang, Dian; Pogson, Angela N; Hein, Marco Y.; Min, Kyung Hoi; Wang, Li; Grody, Emanuelle I.; Shurtleff, Matthew J.; Yuan, Ruoshi; Xu, Shumin; Ma, Yian; Replogle, Joseph M.; Lander, Eric S.; Darmanis, Spyros; Bahar, İvet; Sankaran, Vijay G.; Xing, Jianhua; Weissman, Jonathan S.

doi:10.1016/j.cell.2021.12.045

Cited by 239 publications

(402 citation statements)

References 114 publications

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“…Multidimensional systems can show complex bifurcation patterns ( Rand et al, 2021 ; Kheir Gouda et al, 2019 ). With sufficient single-cell trajectories, one can extend the procedure described in this work and in Qiu et al, 2022 to reconstruct the multi-dimensional vector field and the full governing Fokker-Planck equations directly. The full model will help address questions on the role of noise in CPTs ( Balázsi et al, 2011 ).…”

Section: Discussionmentioning

confidence: 99%

Epithelial-to-mesenchymal transition proceeds through directional destabilization of multidimensional attractor

Wang

Poe

Yang

et al. 2022

eLife

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How a cell changes from one stable phenotype to another one is a fundamental problem in developmental and cell biology. Mathematically a stable phenotype corresponds to a stable attractor in a generally multi-dimensional state space, which needs to be destabilized so the cell relaxes to a new attractor. Two basic mechanisms for destabilizing a stable fixed point, pitchfork and saddle-node bifurcations, have been extensively studied theoretically, however direct experimental investigation at the single cell level remains scarce. Here we performed live cell imaging studies and analyses in the framework of dynamical systems theories on epithelial-to-mesenchymal transition (EMT). While some mechanistic details remain controversial, EMT is a cell phenotypic transition (CPT) process central to development and pathology. Through time-lapse imaging we recorded single cell trajectories of human A549/Vim-RFP cells undergoing EMT induced by different concentrations of exogenous TGF-β in a multi-dimensional cell feature space. The trajectories clustered into two distinct groups, indicating that the transition dynamics proceeds through parallel paths. We then reconstructed the reaction coordinates and the corresponding quasi-potentials from the trajectories. The potentials revealed a plausible mechanism for the emergence of the two paths where the original stable epithelial attractor collides with two saddle points sequentially with increased TGF-β concentration, and relaxes to a new one. Functionally the directional saddle-node bifurcation ensures a CPT proceeds towards a specific cell type, as a mechanistic realization of the canalization idea proposed by Waddington.

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Section: Discussionmentioning

confidence: 99%

Epithelial-to-mesenchymal transition proceeds through directional destabilization of multidimensional attractor

Wang

Poe

Yang

et al. 2022

eLife

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“…To bypass this limitation in a self-consistent way, we implemented a “Boolean” or binary measure of velocity, as motivated by validation in the original manuscript (Sec. 3 in SN2 of [1]), introduced in the context of validating protaccel [4], and implied by resampling β values from a uniform distribution in an investigation of latent landscapes (p. 3 in Supplementary Methods of [13]). Essentially, instead of computing transition probabilities based on the velocity values, we computed them based on signs, bypassing the unit inconsistency.…”

Section: Logic and Methodologymentioning

confidence: 99%

“…As before, the arrows were broadly coherent whether or not they included quantitative information. Finally, as described in Section 1.1, the embedding procedure has previously demonstrated catastrophic failure to capture known dynamics in biological datasets [5, 9, 10, 13, 22]. Therefore, although embeddings are qualitatively appealing, they are unstable, challenging to validate, and harbor intrinsic global- and local-scale pitfalls that arise even in simple scenarios.…”

Section: Prospects and Solutionsmentioning

confidence: 99%

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RNA velocity unraveled

Gorin

Fang

Chari

et al. 2022

Preprint

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We perform a thorough analysis of RNA velocity methods, with a view towards understanding the suitability of the various assumptions underlying popular implementations. In addition to providing a self-contained exposition of the underlying mathematics, we undertake simulations and perform controlled experiments on biological datasets to assess workflow sensitivity to parameter choices and underlying biology. Finally, we argue for a more rigorous approach to RNA velocity, and present a framework for Markovian analysis that points to directions for improvement and mitigation of current problems.

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“…Further, evaluating the generalizability of differential equations is still an open question. Previous approaches have relied on time-resolved scRNA-seq and linear ordinary differential equations (ODEs) to model the dynamics of regulatory networks ( 5 , 6 ). However, linear systems may fail to capture the non-linearity of single-cell dynamics.…”

Section: Introductionmentioning

confidence: 99%

DeepVelo: Single-cell Transcriptomic Deep Velocity Field Learning with Neural Ordinary Differential Equations

Chen

King

Gerstein

et al. 2022

Preprint

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Recent advances in single-cell RNA sequencing technology provided unprecedented opportunities to simultaneously measure the gene expression profile and the transcriptional velocity of individual cells, enabling us to sample gene regulatory network dynamics along developmental trajectories. However, traditional methods have been challenged in offering a fundamental and quantitative explanation of the dynamics as differential equations due to the high dimensionality, sparsity, and complex gene interactions. Here, we present scDVF, a neural-network-based ordinary differential equation that can learn to model single-cell transcriptome dynamics and describe gene expression changes across time at a single-cell resolution. We applied scDVF on multiple published datasets from different technical platforms and demonstrate its utility to 1) formulate transcriptome dynamics of different timescales; 2) measure the instability of individual cell states; and 3) identify developmental driver genes upstream of the signaling cascade. Benchmarking with state-of-the-art vector-field learning methods shows that scDVF can improve representation accuracy by at least 50%. Further, our perturbation studies revealed that single-cell dynamical systems may exhibit properties similar to chaotic systems. In summary, scDVF allows for the data-driven discovery of differential equations that delineate single-cell transcriptome dynamics.

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Mapping transcriptomic vector fields of single cells

Cited by 239 publications

References 114 publications

Epithelial-to-mesenchymal transition proceeds through directional destabilization of multidimensional attractor

Epithelial-to-mesenchymal transition proceeds through directional destabilization of multidimensional attractor

RNA velocity unraveled

DeepVelo: Single-cell Transcriptomic Deep Velocity Field Learning with Neural Ordinary Differential Equations

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