Inferring Stochastic Rates from Heterogeneous Snapshots of Particle Positions.

Area of Science:

• Mathematical Biology
• Biophysics
• Cellular Dynamics

Background:

• Imaging techniques offer spatial resolution but destroy temporal dynamics.
• Snapshot data lacks trajectory information but contains demographic insights.
• Partial differential equations (PDEs) model population dynamics but require continuous data.

Purpose of the Study:

• Investigate inferring demographic rates from static snapshots of stochastic particle systems.
• Develop a mathematical framework connecting particle paths to spatial processes for inference.
• Analyze the inverse problem's properties and factors influencing inference quality.

Main Methods:

• Embraced stochastic data nature for mathematical analysis.
• Derived a connection between individual particle paths and Poisson spatial processes.
• Studied inverse problem properties and inference quality factors.

Main Results:

• Established a framework for inferring demographic rates from spatial snapshots.
• Showed cell-to-cell geometric heterogeneity can enhance inference quality in specific regimes.
• Demonstrated the utility of Poisson spatial processes for analyzing static population data.

Conclusions:

• Provides a mathematical foundation for analyzing stochastically evolving populations from static observations.
• Highlights the potential of incorporating cell heterogeneity to improve dynamic rate inference.
• Enables deeper investigation into subcellular spatial patterns of RNA and other molecules.