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Parameter estimation and inference for stochastic reaction-diffusion systems: application to morphogenesis in D.

Michael A Dewar1, Visakan Kadirkamanathan, Manfred Opper

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This study introduces a Bayesian inference method for parameter estimation in stochastic reaction-diffusion systems. The approach quantifies parameter uncertainty, crucial for experimental design in systems biology.

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Area of Science:

  • Systems Biology
  • Computational Biology
  • Biophysics

Background:

  • Reaction-diffusion systems model biological processes like development and signaling.
  • Low molecular counts necessitate stochastic modeling for inherent variability.
  • Parameter estimation for these systems remains a significant challenge.

Purpose of the Study:

  • To develop a Bayesian inference approach for parameter and state estimation in stochastic reaction-diffusion systems.
  • To determine the full posterior distribution of parameters, including expected values and uncertainty.

Main Methods:

  • Bayesian inference framework applied to stochastic reaction-diffusion models.
  • Parameter and state estimation performed simultaneously.
  • Method validated on synthetic data and real biological data (Bicoid diffusion in Drosophila).

Main Results:

  • The Bayesian method successfully estimates parameters and their full posterior distributions.
  • Analysis of Bicoid diffusion data reveals significant variation in parameter inference precision.
  • The ability to infer posterior distributions has implications for experimental design.

Conclusions:

  • Bayesian inference is a feasible and advantageous approach for parameter estimation in stochastic reaction-diffusion systems.
  • Credibility intervals from parameter estimates are valuable for guiding experimental design.
  • Further research is needed to scale the method for larger, more complex systems.