In the vicinity of a tipping point, critical transitions occur when small changes in an input condition cause sudden, large, and often irreversible changes in the state of a system. Many natural systems ranging from ecosystems to molecular biosystems are known to exhibit critical transitions in their response to stochastic perturbations. In diseases, an early prediction of upcoming critical transitions from a healthy to a disease state by using early-warning signals is of prime interest due to potential application in forecasting disease onset. Here, we analyze cell-fate transitions between different phenotypes (epithelial, hybrid-epithelial/mesenchymal [E/M], and mesenchymal states) that are implicated in cancer metastasis and chemoresistance. These transitions are mediated by a mutually inhibitory feedback loop—microRNA-200/ZEB—driven by the levels of transcription factor SNAIL. We find that the proximity to tipping points enabling these transitions among different phenotypes can be captured by critical slowing down-based early-warning signals, calculated from the trajectory of ZEB messenger RNA level. Further, the basin stability analysis reveals the unexpectedly large basin of attraction for a hybrid-E/M phenotype. Finally, we identified mechanisms that can potentially elude the transition to a hybrid-E/M phenotype. Overall, our results unravel the early-warning signals that can be used to anticipate upcoming epithelial–hybrid-mesenchymal transitions. With the emerging evidence about the hybrid-E/M phenotype being a key driver of metastasis, drug resistance, and tumor relapse, our results suggest ways to potentially evade these transitions, reducing the fitness of cancer cells and restricting tumor aggressiveness.

The infectious novel coronavirus disease COVID-19 outbreak has been declared as a public health emergency of international concern, and later as an epidemic. To date, this outbreak has infected more than one million people and killed over fifty thousand people across the world. In most countries, the COVID-19 incidence curve rises sharply in a short span of time, suggesting a transition from a disease free (or low-burden disease) equilibrium state to a sustained infected (or high-burden disease) state. Such a transition from one stable state to another state in a relatively short span of time is often termed as a critical transition. Critical transitions can be, in general, successfully forecasted using many statistical measures such as return rate, variance and lag-1 autocorrelation. Here, we report an empirical test of this forecasting on the COVID-19 data sets for nine countries including India, China and the United States. For most of the data sets, an increase in autocorrelation and a decrease in return rate predict the onset of a critical transition. Our analysis suggests two key features in predicting the COVID-19 incidence curve for a specific country: a) the timing of strict social distancing and/or lockdown interventions implemented, and b) the fraction of a nation's population being affected by COVID-19 at the time of implementation of these interventions. Further, using satellite data of nitrogen dioxide which is emitted predominantly as a result of anthropogenic activities, as an indicator of lockdown policy, we find that in countries where the lockdown was implemented early and strictly have been successful in reducing the extent of transmission of the virus. These results hold important implications for designing effective strategies to control the spread of infectious pandemics. CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

The COVID-19 outbreak was first declared an international public health, and it was later deemed a pandemic. In most countries, the COVID-19 incidence curve rises sharply over a short period of time, suggesting a transition from a disease-free (or low-burden disease) equilibrium state to a sustained infected (or high-burden disease) state. Such a transition is often known to exhibit characteristics of "critical slowing down." Critical slowing down can be, in general, successfully detected using many statistical measures, such as variance, lag-1 autocorrelation, density ratio, and skewness. Here, we report an empirical test of this phenomena on the COVID-19 datasets of nine countries, including India, China, and the United States. For most of the datasets, increases in variance and autocorrelation predict the onset of a critical transition. Our analysis suggests two key features in predicting the COVID-19 incidence curve for a specific country: (a) the timing of strict social distancing and/or lockdown interventions implemented and (b) the fraction of a nation's population being affected by COVID-19 at that time. Furthermore, using satellite data of nitrogen dioxide as an indicator of lockdown efficacy, we found that countries where lockdown was implemented early and firmly have been successful in reducing COVID-19 spread. These results are essential for designing effective strategies to control the spread/resurgence of infectious pandemics.

13In the vicinity of a tipping point, critical transitions occur when small changes in an input condition causes 14 sudden, large and often irreversible changes in the state of a system. Many natural systems ranging from 15 ecosystems to molecular biosystems are known to exhibit critical transitions in their response to stochastic 16 perturbations. In diseases, an early prediction of upcoming critical transitions from a healthy to a dis-17 ease state by using early warning signals is of prime interest due to potential application in forecasting 18 disease onset. Here, we analyze cell-fate transitions between different phenotypes (epithelial, hybrid epithe-19 lial/mesenchymal (E/M) and mesenchymal states) that are implicated in cancer metastasis and chemoresis-20 tance. These transitions are mediated by a mutually inhibitory feedback loop microRNA-200/ZEB driven 21 by the levels of transcription factor SNAIL. We find that the proximity to tipping points enabling these 22 transitions among different phenotypes can be captured by critical slowing down based early warning sig-23 nals, calculated from the trajectory of ZEB mRNA level. Further, the basin stability analysis reveals the 24 unexpectedly large basin of attraction for a hybrid E/M phenotype. Finally, we identified mechanisms that 25 can potentially elude the transition to a hybrid E/M phenotype. Overall, our results unravel the early warn- 26 ing signals that can be used to anticipate upcoming epithelial-hybrid-mesenchymal transitions. With the 27 emerging evidence about the hybrid E/M phenotype being a key driver of metastasis, drug resistance, and 28 tumor relapse; our results suggest ways to potentially evade these transitions, reducing the fitness of cancer 29 cells and restricting tumor aggressiveness. 30 Keywords: critical transition | indicators of critical slowing down | alternative stable states | epithelial-31 hybrid-mesenchymal transition | cancer biology 32 1 This article contains supplementary materials. 2 sudipta@iitrpr.ac.in 3 h.levine@northeastern.edu 4 mkjolly@iisc.ac.in 5 parthasharathi@iitrpr.ac.in Significance Statement 33Epithelial-hybrid-mesenchymal transitions play critical roles in cancer metastasis, drug resistance, and tumor 34 relapse. Recent studies have proposed that cells in a hybrid epithelial/mesenchymal phenotype may be more 35 aggressive than those on either end of the spectrum. However, no biomarker to predict upcoming transitions 36 has been identified. Here, we show that critical slowing down based early warning signals can detect sudden 37 transitions among epithelial, hybrid E/M, and mesenchymal phenotypes. Importantly, our results highlight 38 how stable a hybrid E/M phenotype can be, and how can a transition to this state be avoided. Thus, our 39 study provides valuable insights into restricting cellular plasticity en route metastasis. 40 Introduction 41Biological systems often display nonlinear dynamics and emergent complex behavior, and consequent multi-42 stability [1, 2]. This nonlinear behavior in many ...

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