ArticleProceedings of the National Academy of Sciences of the United States of America2021
Geometry of gene regulatory dynamics.
Article in Proceedings of the National Academy of Sciences of the United States of America, 2021. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 55 papers.
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Who cites it
55 citing papers in PubMed, 3 citations in OpenAlex.
- Article
- Dynamic Landscape Analysis of cell fate decisions provides predictive models of neural development from single-cell data.PLoS biology · 2026Article
- AbioRxiv : the preprint server for biology · 2026Article
- Gene regulatory networks: from correlative models to causal explanations.Nature reviews. Genetics · 2026Review
- Evolution of phenocopying in a dynamical model of developmental trajectories.PLoS computational biology · 2026Article
- Unifying theories in high-dimensional biophysics: approaches, challenges and opportunities.NPJ systems biology and applications · 2026Article
- Parameter-free representations outperform single-cell foundation models on downstream benchmarks.ArXiv · 2026Article
- Parameter-free representations outperform single-cell foundation models on downstream benchmarks.bioRxiv : the preprint server for biology · 2026Article
- Signals and the shape of developmental landscapes.Proceedings of the National Academy of Sciences of the United States of America · 2026Article
- From static definitions to dynamic landscapes: physiological states in yeast.Frontiers in microbiology · 2026Article
- Generative epigenetic landscapes map the topology and topography of cell fates.Proceedings of the National Academy of Sciences of the United States of America · 2025Article
- Reconstructing Waddington's landscape from data.Proceedings of the National Academy of Sciences of the United States of America · 2025Article
- Beyond metaphor: quantitative reconstruction of Waddington landscape and exploration of cellular behavior.Briefings in bioinformatics · 2025Review
- Searching for physical principles of morphogenesis.Development (Cambridge, England) · 2025Review
- Article
- Dynamical systems of fate and form in development.Seminars in cell & developmental biology · 2025Review
- Dynamical systems theory as an organizing principle for single-cell biology.NPJ systems biology and applications · 2025Review
- Dynamical model and geometric insights in the discontinuity theory of immunity.bioRxiv : the preprint server for biology · 2025Article
- From genes to patterns: five key dynamical systems concepts to decode developmental regulatory mechanisms.Development (Cambridge, England) · 2025Review
- Article
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Authors and funding
5 authors at 5 institutions in 5 countries.
Funding
Abstract
Embryonic development leads to the reproducible and ordered appearance of complexity from egg to adult. The successive differentiation of different cell types that elaborate this complexity results from the activity of gene networks and was likened by Waddington to a flow through a landscape in which valleys represent alternative fates. Geometric methods allow the formal representation of such landscapes and codify the types of behaviors that result from systems of differential equations. Results from Smale and coworkers imply that systems encompassing gene network models can be represented as potential gradients with a Riemann metric, justifying the Waddington metaphor. Here, we extend this representation to include parameter dependence and enumerate all three-way cellular decisions realizable by tuning at most two parameters, which can be generalized to include spatial coordinates in a tissue. All diagrams of cell states vs. model parameters are thereby enumerated. We unify a number of standard models for spatial pattern formation by expressing them in potential form (i.e., as topographic elevation). Turing systems appear nonpotential, yet in suitable variables the dynamics are low dimensional and potential. A time-independent embedding recovers the original variables. Lateral inhibition is described by a saddle point with many unstable directions. A model for the patterning of the
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Registered trials
Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.