Dynamic landscapes and statistical limits on growth during cell fate specification
Phys. Rev. E 111, 064418 – Published 26 June, 2025
DOI: https://doi.org/10.1103/63d2-4wq6
Abstract
The complexity of gene regulatory networks in multicellular organisms makes interpretable low-dimensional models highly desirable. An attractive geometric picture, attributed to Waddington, visualizes the differentiation of a cell into diverse functional types as gradient flow on a dynamic potential landscape. However, it is unclear under what constraints this metaphor is mathematically precise. Here, we consider the controlled growth of a single cell into a population with a target distribution over cell states. Expanding on a connection between stochastic control and optimal transport, we show that growth-maximizing regulatory strategies are described by time-dependent potential landscapes under certain generic growth-control trade-offs. Our analysis leads to a sharp bound on the time it takes for a population to grow to a target distribution with a certain size. We show how the framework can be used to compute regulatory strategies and growth curves in an illustrative model of growth and differentiation. The theory suggests a conceptual link between nonequilibrium thermodynamics, cellular decision-making during fate specification, and transport-based sampling methods from machine learning.
Physics Subject Headings (PhySH)
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This article appears in the following collection:
Statistical Physics Meets Machine Learning - Machine Learning Meets Statistical Physics
The Editors of Physical Review E are pleased to present the Collection on Statistical Physics Meets Machine Learning - Machine Learning Meets Statistical Physics, highlighting research at the intersection of machine learning and statistical physics, on the occasion of the two Statistical Physics Meets Machine Learning and the two Machine Learning Meets Statistical Physics sessions at the 2025 Global Physics Summit. The Collection is being guest edited by David Schwab (CUNY, New York) and Yuhai Tu (IBM Watson Research Center Yorktown Heights, NY). Every article published in this collection underwent a rigorous peer review process, adhering to the same high standards applied to all papers. The Physical Review E editorial team managed the peer review and made all editorial decisions.
