Redi

Redi simulates reaction-diffusion systems at the mesoscopic scale using a Gillespie-like stochastic model that incorporates variable diffusion coefficients dependent on local concentration, viscosity, and frictional forces.

Key Features:

• Stochastic Simulation Algorithm: Implements a Gillespie-like stochastic simulation algorithm to capture inherent randomness in reaction-diffusion processes.
• Variable Diffusion Coefficients: Represents diffusion coefficients as functions of local concentration, viscosity, and frictional forces to model nonhomogeneous and structured media.
• Spatio-Temporal Dynamics Simulation: Simulates spatio-temporal concentration dynamics and reproduces bicoid protein gradient formation in Drosophila Melanogaster embryos with accuracy within 1% of experimental data.

Scientific Applications:

• Environment-dependent reaction-diffusion systems: Models biochemical systems where diffusion and reaction processes are influenced by local concentration, viscosity, or frictional forces.
• Developmental biology (morphogen distribution): Studies morphogen distribution in embryos, exemplified by bicoid protein gradients in Drosophila Melanogaster.
• Tissue engineering: Applies to tissue engineering scenarios requiring detailed spatial reaction-diffusion modeling.
• Pharmacokinetics: Supports modeling of spatially heterogeneous drug distribution where diffusion varies locally.
• Cellular signaling pathways: Analyzes signaling processes in which spatial heterogeneity affects reaction-diffusion behavior.

Methodology:

Computational methods include semi-linear parabolic partial differential equations with variable diffusion coefficients coupled to a Gillespie-like stochastic simulation algorithm.