Unifying deterministic and stochastic ecological dynamics via a landscape-flux approach

Xu, Li; Patterson, Denis; Staver, A. Carla; Levin, Simon A.; Wang, Jin

doi:10.1073/pnas.2103779118

Cited by 14 publications

(6 citation statements)

References 53 publications

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“…However, it has become apparent that relying solely on the landscape for the dynamics is true only for equilibrium systems with detailed balance (no net input to or output from the system) but is insufficient for capturing the entire dynamics for the nonequilibrium systems. [7][8][9]17,46,75,76] Our findings in this study of the cell cycle illustrate this point well, as its complex behavior requires the presence of an additional rotational flux. While the landscape contributes to attracting the system into the close oscillation ring valley, it is the flux that drives the coherent oscillation along the cycle path.…”

Section: Discussionsupporting

confidence: 70%

Quantifying Landscape‐Flux via Single‐Cell Transcriptomics Uncovers the Underlying Mechanism of Cell Cycle

Zhu,

Wang

2024

Advanced Science

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Recent developments in single‐cell sequencing technology enable the acquisition of entire transcriptome data. Understanding the underlying mechanism and identifying the driving force of transcriptional regulation governing cell function directly from these data remains challenging. This study reconstructs a continuous vector field of the cell cycle based on discrete single‐cell RNA velocity to quantify the single‐cell global nonequilibrium dynamic landscape‐flux. It reveals that large fluctuations disrupt the global landscape and genetic perturbations alter landscape‐flux, thus identifying key genes in maintaining cell cycle dynamics and predicting associated functional effects. Additionally, it quantifies the fundamental energy cost of the cell cycle initiation and unveils that sustaining the cell cycle requires curl flux and dissipation to maintain the oscillatory phase coherence. This study enables the inference of the cell cycle gene regulatory networks directly from the single‐cell transcriptomic data, including the feedback mechanisms and interaction intensity. This provides a golden opportunity to experimentally verify the landscape‐flux theory and also obtain its associated quantifications. It also offers a unique framework for combining the landscape‐flux theory and single‐cell high‐through sequencing experiments for understanding the underlying mechanisms of the cell cycle and can be extended to other nonequilibrium biological processes, such as differentiation development and disease pathogenesis.

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Section: Discussionsupporting

confidence: 70%

Quantifying Landscape‐Flux via Single‐Cell Transcriptomics Uncovers the Underlying Mechanism of Cell Cycle

Zhu,

Wang

2024

Advanced Science

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“…The escape time from one local stable state to another can also be used as a quantitative measure for global stability. One can estimate the mean exit time from the basin of attraction ( 15 , 29 , 37 , 38 ). We can then obtain the mean first passage time ( M F P T ) for the escape shown as ref.…”

Section: Resultsmentioning

confidence: 99%

Non-equilibrium early-warning signals for critical transitions in ecological systems

Patterson

Levin

et al. 2023

Proc. Natl. Acad. Sci. U.S.A.

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Complex systems can exhibit sudden transitions or regime shifts from one stable state to another, typically referred to as critical transitions. It becomes a great challenge to identify a robust warning sufficiently early that action can be taken to avert a regime shift. We employ landscape-flux theory from nonequilibrium statistical mechanics as a general framework to quantify the global stability of ecological systems and provide warning signals for critical transitions. We quantify the average flux as the nonequilibrium driving force and the dynamical origin of the nonequilibrium transition while the entropy production rate as the nonequilibrium thermodynamic cost and thermodynamic origin of the nonequilibrium transition. Average flux, entropy production, nonequilibrium free energy, and time irreversibility quantified by the difference in cross-correlation functions forward and backward in time can serve as early warning signals for critical transitions much earlier than other conventional predictors. We utilize a classical shallow lake model as an exemplar for our early warning prediction. Our proposed method is general and can be readily applied to assess the resilience of many other ecological systems. The early warning signals proposed here can potentially predict critical transitions earlier than established methods and perhaps even sufficiently early to avert catastrophic shifts.

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“…To obtain a more comprehensive understanding of the overall stability and behavior, people have turned to the concept of landscape, which can describe the global stability of the system. However, it has become apparent that relying solely on the landscape for the dynamics is true only for equilibrium systems with detailed balance (no net input to or output from the system) is insufficient for capturing the entire dynamics for the nonequilibrium systems (7–9, 17, 43, 71, 72). Our findings in this study of the cell cycle illustrate this point well, as its complex behavior requires the presence of an additional rotational flux.…”

Section: Discussionmentioning

confidence: 99%

Quantifying landscape-flux via single-cell transcriptomics uncovers the underlying mechanism of cell cycle

Zhu

Wang

2023

Preprint

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Recent developments of single-cell sequencing technology enabling acquisition of the whole transcriptome data. To uncover the underlying mechanism of cell cycle function from such data, we reconstruct a continuous vector field based on the discrete single-cell RNA velocity to quantify the global non-equilibrium dynamical landscape and flux. We reveal that biological noise can make the global landscape more complex and less predictable. Genetic perturbations alter landscape-flux, thus identify key genes in maintaining cell cycle dynamics and predict the associated effects on cell cycle behaviour. Cell cycle initiation costs energy and sustaining cell cycle requires dissipation to increase oscillatory phase coherence. This approach enables the inference of cell cycle gene regulatory networks directly from single-cell transcriptomic data, including feedback mechanisms. Our study provides a new framework with insights into cell cycle regulation from single-cell transcriptome data and can be extended to other biological processes, such as differentiation-development and disease pathogenesis

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Unifying deterministic and stochastic ecological dynamics via a landscape-flux approach

Cited by 14 publications

References 53 publications

Quantifying Landscape‐Flux via Single‐Cell Transcriptomics Uncovers the Underlying Mechanism of Cell Cycle

Quantifying Landscape‐Flux via Single‐Cell Transcriptomics Uncovers the Underlying Mechanism of Cell Cycle

Non-equilibrium early-warning signals for critical transitions in ecological systems

Quantifying landscape-flux via single-cell transcriptomics uncovers the underlying mechanism of cell cycle

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