Quantifying the most probable dynamics of a particle inside a sphere.

Area of Science:

• Biophysics
• Physical Chemistry
• Computational Biology

Background:

• Particle random walk phenomena are observed in various biophysical and physical systems.
• Receptor diffusion dynamics toward cellular membranes are crucial for cellular functions.
• Understanding confined diffusion in spherical geometries is essential for biophysical modeling.

Purpose of the Study:

• To investigate statistically dominant transition dynamics for particles in confined spherical diffusion.
• To quantify the most probable transition time from a spherical center to boundary points.
• To identify the most probable transition pathways to preferential terminal locations on the spherical surface.

Main Methods:

• Developed a computational framework combining stochastic process modeling and deep learning.
• Integrated numerical simulations of stochastic differential equations with neural networks.
• Trained neural networks on the Onsager-Machlup variational principle for entropy-optimized trajectories.

Main Results:

• Quantified the most probable transition times for particles diffusing within spherical boundaries.
• Identified statistically dominant pathways for particle migration from the center to the surface.
• Derived mechanistic insights into the spatiotemporal organization of membrane-bound receptors.

Conclusions:

• The study proposes a predictive framework for receptor spatial distribution influenced by constrained diffusion energetics.
• The computational approach offers a novel method for analyzing complex diffusion dynamics.
• Findings contribute to understanding the energetic basis of receptor organization on cellular membranes.