Subdiffusion-limited fractional reaction-subdiffusion equations with affine reactions: Solution, stochastic paths,...

Area of Science:

• Chemical kinetics
• Statistical physics
• Biophysics

Background:

• Normal diffusion is standard for modeling chemical reactions.
• Anomalous subdiffusion is prevalent in cellular environments but lacks canonical reaction models.
• The link between mesoscopic and microscopic models for reaction-subdiffusion is poorly understood.

Purpose of the Study:

• Develop a canonical model for reaction-subdiffusion systems.
• Establish a clear relationship between mesoscopic fractional equations and microscopic Langevin dynamics.
• Apply the model to biological systems often simplified with normal diffusion.

Main Methods:

• Defined the subdiffusion-limited model using mesoscopic equations with fractional derivatives for movement and reaction.
• Showed the fractional system solution relates to a random time change of the integer-order system solution.
• Derived the corresponding microscopic Langevin description and developed a simulation method for stochastic trajectories.

Main Results:

• Established an explicit algebraic relationship between fractional and integer-order solutions in Laplace space.
• Identified precise microscopic conditions for the appropriateness of the mesoscopic model.
• Demonstrated applicability to morphogen gradient formation, fluctuating mobility, and FRAP experiments.

Conclusions:

• The study provides a robust framework for modeling reaction-subdiffusion phenomena.
• This work bridges the gap between mesoscopic and microscopic descriptions in complex systems.
• Offers new modeling approaches for biological processes exhibiting anomalous diffusion.