Dynamic landscapes and statistical limits on growth during cell fate specification

TL;DR

This paper develops a mathematical framework linking dynamic potential landscapes to cell fate decisions, providing bounds on growth time and strategies for differentiation under biological constraints.

Contribution

It introduces a novel theory connecting growth-maximizing strategies with time-dependent landscapes, clarifying the mathematical basis of Waddington's landscape metaphor.

Findings

Derived bounds on population growth time to target cell distributions

Proposed a method to compute regulatory strategies and growth curves

Linked nonequilibrium thermodynamics to cellular decision-making

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 biological constraints this metaphor is mathematically precise. Here, we show that growth-maximizing regulatory strategies that guide a single cell to a target distribution of cell types are described by time-dependent potential landscapes under certain generic growth-control tradeoffs. Our analysis leads to a sharp bound on the time it takes for a population to grow to a target distribution of 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 and cellular decision-making during development.