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

Abstract

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.

Comparative single-cell transcriptomes of dose and time dependent epithelial–mesenchymal spectrums

“…This result reveals a transient EMT path that may primarily involve the relatively low expression of both E and M genes. Nonetheless, the enrichment of time data points in the regions of high E-gene activity and M-gene activity suggested a possible alternative transient EMT path (Figure 4B , right) ( 37 , 38 ). We next considered the relationship between these transient paths, particularly the E-low and M-low region, with our alternative M-score.…”

Comparative single-cell transcriptomes of dose and time dependent epithelial-mesenchymal spectrums

“…This result reveals a transient EMT path that may primarily involve the relatively low expression of both E and M genes. Nonetheless, the enrichment of time data points in the regions of high E-gene activity and M-gene activity suggested a possible alternative transient EMT path ( Figure 4B, right ) [23, 24]. We then identified significantly differentially expressed genes across all sixteen segments of the 4 × 4 grid and focused first on known EMT marker genes.…”

Profiling intermediate cell states in high resolution

“…However, it is possible that hybrid cell states can be produced from both continuous and discontinuous transitions in the cell state space ( Moris et al., 2016 ) . This becomes particularly relevant in the case of multistability, as predicted by theory ( Mojtahedi et al., 2016 ) and observed experimentally ( Schuijers et al., 2015 ; Wang et al., 2022 ). Transitions on bistable cell state landscapes can be sharp, discontinuous, and lead to short-term increases in cell state heterogeneity.…”