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

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This study reveals how particles move within spherical spaces, identifying the fastest paths and times for diffusion. This helps predict how membrane-bound receptors organize spatially based on their movement energetics.

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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.