Dynamic landscapes and statistical limits on growth during cell fate specification

Area of Science:

• Systems biology
• Theoretical biology
• Computational biology

Background:

• Gene regulatory networks in multicellular organisms are complex, necessitating interpretable low-dimensional models.
• Waddington's potential landscape metaphor visualizes cell differentiation as gradient flow, but its mathematical precision is debated.

Purpose of the Study:

• To mathematically investigate the constraints under which Waddington's potential landscape metaphor for cell differentiation is precise.
• To model the controlled growth of a single cell into a population with a specific distribution of cell states.

Main Methods:

• Connecting stochastic control theory with optimal transport.
• Analyzing growth-maximizing regulatory strategies under generic growth-control trade-offs.
• Developing a framework to compute regulatory strategies and growth curves.

Main Results:

• Growth-maximizing regulatory strategies can be described by time-dependent potential landscapes.
• A sharp bound is derived for the time required for a population to reach a target distribution and size.
• The framework allows computation of regulatory strategies and growth curves in a model of growth and differentiation.

Conclusions:

• The study provides a mathematically precise framework for Waddington's potential landscape model of cell differentiation.
• It links nonequilibrium thermodynamics, cellular decision-making, and machine learning transport-based sampling methods.
• The findings offer insights into optimizing cell growth and achieving specific cell fate distributions.