Maximum entropy inference of reaction-diffusion models

Area of Science:

• Complex Systems Modeling
• Theoretical Physics
• Mathematical Biology

Background:

• Reaction-diffusion equations are widely used for modeling complex systems in biology, chemistry, and physics.
• Current models are often phenomenological, necessitating parameter fitting to experimental data.
• There is a need for more robust and data-integrative modeling frameworks.

Purpose of the Study:

• To introduce a novel formalism for constructing reaction-diffusion models based on the principle of maximum entropy.
• To develop a method capable of incorporating diverse experimental data, including ensemble currents and temporal distributions.
• To extend the Schrödinger bridges and maximum caliber frameworks to nonlinear interacting systems.

Main Methods:

• Developed a maximum entropy-based formalism for reaction-diffusion models.
• Extended the Schrödinger bridges and maximum caliber problem frameworks.
• Applied the formalism to nonlinear interacting systems.

Main Results:

• Successfully modeled morphogen evolution in zebrafish fins.
• Accurately predicted the population dynamics of two toad species in Poland.
• Demonstrated the ability to incorporate various experimental data types.

Conclusions:

• The maximum entropy formalism provides a powerful, data-driven approach to reaction-diffusion modeling.
• This novel method enhances the predictive accuracy of complex system models.
• The framework is applicable to diverse scientific domains requiring quantitative modeling.