Epithelialtomesenchymal 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. Epithelialtomesenchymal transition (EMT) is a phenotypic transition process extensively studied recently but mechanistic details remain elusive. Through timelapse imaging we recorded single cell trajectories of human A549/VimRFP cells undergoing EMT induced by different concentrations of TGFβ in a multidimensional cell feature space. The trajectories cluster into two distinct groups, indicating that the transition dynamics proceeds through parallel paths. We then reconstructed the reaction coordinates and corresponding pseudopotentials from the trajectories. The potentials reveal a plausible mechanism for the emergence of the two paths as the original stable epithelial attractor collides with two saddle points sequentially with increased TGFβ concentration, and relaxes to a new one. Functionally the directional saddlenode 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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Author Response:
Reviewer #2 (Public Review):
I think this is a very interesting and timely contribution to the literature. It combines a dynamical systems perspective and single cell data in a very neat and exciting combination in order to identify aspects of the EMT process and dynamics.
This is an ambitious and multifaceted study and draws on a wide range of experimental, data science, and modelling tools and techniques. Overall I really liked the scope and focus of the study. I do believe that there are a few points where the arguments can be tightened and I will focus on those aspects.
General Comments:
In order to capture the dynamics the authors should perhaps engage with the arguments in Cruel and Flandoli (J Dynamics Diff Equations) which prove that additive noise destroys a pitchfork bifurcation. Related to this I …
Author Response:
Reviewer #2 (Public Review):
I think this is a very interesting and timely contribution to the literature. It combines a dynamical systems perspective and single cell data in a very neat and exciting combination in order to identify aspects of the EMT process and dynamics.
This is an ambitious and multifaceted study and draws on a wide range of experimental, data science, and modelling tools and techniques. Overall I really liked the scope and focus of the study. I do believe that there are a few points where the arguments can be tightened and I will focus on those aspects.
General Comments:
In order to capture the dynamics the authors should perhaps engage with the arguments in Cruel and Flandoli (J Dynamics Diff Equations) which prove that additive noise destroys a pitchfork bifurcation. Related to this I think the arguments in PMC3372930 should be considered. They make a case against the pitchfork bifurcation on purely dynamical grounds. In PMID: 27616569 the arguments are not made quite as forceful but this is an excellent background reference. Against this background it is probably not surprising that the dynamics are best explained by saddle node bifurcations.
One potential concern relates to the construction of the Langevin equation. Additive noise is a very specific choice and needs to be clearly justified. It is convenient, but not based on any physical reasoning in this case. We know that multiplicative noise (e.g. in the chemical Langevin equation, or geometric noise) will qualitatively alter the dynamics compared to the deterministic model. Much of the discussion in lines 250260 is therefore limited or restricted to the case of additive noise and this needs to be made explicit. If additive noise is chosen because reaction coordinates can only be easily defined in this framework then this limitation should be specified.
I can see that the simple additive noise makes the integrations in the calculation of the potential 486499 easier, but again the limitations of this approach should be addressed either by pointing them out, or by considering a model with multiplicative noise.
The most intriguing result to my mind is the existence of multiple reaction paths. I would like to see to what extent this is robust to e.g. multiplicative noise and other factors in the analysis.
Thanks for these great points. One point we want to clarify. In our Langevin formulation, we do not assume additive noises, and the corresponding diffusion constant D is also positiondependent, as explained in Materials and Methods (1). In the revised manuscript we added the xdependence of the noise terms to make it clear.
References:
 Scheffer M, et al. (2009) Earlywarning signals for critical transitions. Nature 461(7260):5359.

Evaluation Summary:
This is a multifaceted study of the epithelial to mesenchymal transition (EMT) in live cells. EMT is relevant for cancer, development, and wound healing. The authors were able to discern two possible cell transition path categories without multicolor labeling or other advanced experimental approaches, which could be impactful. The study draws on a wide range of experimental, data science, and modelling tools and techniques.
(This preprint has been reviewed by eLife. We include the public reviews from the reviewers here; the authors also receive private feedback with suggested changes to the manuscript. Reviewer #1, Reviewer #2 and Reviewer #3 agreed to share their name with the authors.)

Reviewer #1 (Public Review):
This manuscript uses computational approaches to study in live cells the epithelial to mesenchymal transition (EMT) , which is relevant for cancer, development, and wound healing. The manuscript's strengths are its powerful combination of interdisciplinary approaches to define cell paths during phenotypic transitions in live cells, with an ability to discern two possible cell transition path categories without multicolor labeling or other advanced experimental approaches, which could be impactful. The manuscript's weaknesses are reading difficulty arising from the complexity of the computational analysis and the uncertainty of the method's applicability to other cell lines, proteins, and cellular transitions. The claims are justified by the data, given this particular set of analysis steps, but the question …
Reviewer #1 (Public Review):
This manuscript uses computational approaches to study in live cells the epithelial to mesenchymal transition (EMT) , which is relevant for cancer, development, and wound healing. The manuscript's strengths are its powerful combination of interdisciplinary approaches to define cell paths during phenotypic transitions in live cells, with an ability to discern two possible cell transition path categories without multicolor labeling or other advanced experimental approaches, which could be impactful. The manuscript's weaknesses are reading difficulty arising from the complexity of the computational analysis and the uncertainty of the method's applicability to other cell lines, proteins, and cellular transitions. The claims are justified by the data, given this particular set of analysis steps, but the question remains if fewer or simpler steps could lead to the same conclusion, or how the methods and findings relate to existing knowledge of bifurcations and cellular phenotypic transitions.

Reviewer #2 (Public Review):
I think this is a very interesting and timely contribution to the literature. It combines a dynamical systems perspective and single cell data in a very neat and exciting combination in order to identify aspects of the EMT process and dynamics.
This is an ambitious and multifaceted study and draws on a wide range of experimental, data science, and modelling tools and techniques. Overall I really liked the scope and focus of the study. I do believe that there are a few points where the arguments can be tightened and I will focus on those aspects.
General Comments:
In order to capture the dynamics the authors should perhaps engage with the arguments in Cruel and Flandoli (J Dynamics Diff Equations) which prove that additive noise destroys a pitchfork bifurcation. Related to this I think the arguments in …
Reviewer #2 (Public Review):
I think this is a very interesting and timely contribution to the literature. It combines a dynamical systems perspective and single cell data in a very neat and exciting combination in order to identify aspects of the EMT process and dynamics.
This is an ambitious and multifaceted study and draws on a wide range of experimental, data science, and modelling tools and techniques. Overall I really liked the scope and focus of the study. I do believe that there are a few points where the arguments can be tightened and I will focus on those aspects.
General Comments:
In order to capture the dynamics the authors should perhaps engage with the arguments in Cruel and Flandoli (J Dynamics Diff Equations) which prove that additive noise destroys a pitchfork bifurcation. Related to this I think the arguments in PMC3372930 should be considered. They make a case against the pitchfork bifurcation on purely dynamical grounds. In PMID: 27616569 the arguments are not made quite as forceful but this is an excellent background reference. Against this background it is probably not surprising that the dynamics are best explained by saddle node bifurcations.
One potential concern relates to the construction of the Langevin equation. Additive noise is a very specific choice and needs to be clearly justified. It is convenient, but not based on any physical reasoning in this case. We know that multiplicative noise (e.g. in the chemical Langevin equation, or geometric noise) will qualitatively alter the dynamics compared to the deterministic model. Much of the discussion in lines 250260 is therefore limited or restricted to the case of additive noise and this needs to be made explicit. If additive noise is chosen because reaction coordinates can only be easily defined in this framework then this limitation should be specified.
I can see that the simple additive noise makes the integrations in the calculation of the potential 486499 easier, but again the limitations of this approach should be addressed either by pointing them out, or by considering a model with multiplicative noise.
The most intriguing result to my mind is the existence of multiple reaction paths. I would like to see to what extent this is robust to e.g. multiplicative noise and other factors in the analysis.

Reviewer #3 (Public Review):
Building upon their established framework that reconstructs the transition pathways between cell phenotypes from timelapse livecell imaging, Dr. Xing and colleagues quantified the epithelialtomesenchymal transition (EMT)  central to development and pathology  in which epithelial cells lose their "fellowship" and begin to migrate and reproduce on their own. They directly demonstrated for the first time that EMT proceeds through two parallel pathways, i.e., the original epithelial state evolves into two metastable states that then gravitate toward the same mesenchymal state. This is an epic work that provides novel insight of EMT and developmental processes, and defines a new, promising direction of systems biology.
The strength/significance of the work lies at the following aspects. First, instead of …
Reviewer #3 (Public Review):
Building upon their established framework that reconstructs the transition pathways between cell phenotypes from timelapse livecell imaging, Dr. Xing and colleagues quantified the epithelialtomesenchymal transition (EMT)  central to development and pathology  in which epithelial cells lose their "fellowship" and begin to migrate and reproduce on their own. They directly demonstrated for the first time that EMT proceeds through two parallel pathways, i.e., the original epithelial state evolves into two metastable states that then gravitate toward the same mesenchymal state. This is an epic work that provides novel insight of EMT and developmental processes, and defines a new, promising direction of systems biology.
The strength/significance of the work lies at the following aspects. First, instead of relying on data mining as commonly practiced in the field, the authors built their quantitative framework with a solid theoretical underpinning and a clear physical perspective. Using deep learning/AI to extract information from imaging, they extended the techniques of transition path sampling  wellestablished in physical chemistry  to reconstruct the reaction coordinates and the associated pseudopotentials characterizing the pathways of cell phenotypic transitions. Second, rather than a few static snapshots, the authors tested their theory with the livecell timelapsed imaging, in which the spatialtemporal correlation intrinsic to the system can be better preserved. This greatly constrains the possible interpretations of data and hence enables more faithful determination of the mechanisms. Last but not the least, the authors present a coherent pipeline with a proven success (in EMT) that is capable of quantitatively characterizing how cells evolve from one phenotype to another in any system, with the potential of mapping out the entire landscape for development. The weakness of this manuscript pertains to the clarity in writing, including but not limited to the theoretical assumption, presentation of methodology, and potential connections with existing experiments. Overall the key conclusion is justified with the data presented.

