Modeling of Phototransduction: Homogenization and Concentrated Capacity for the Heat Equation

Phototransduction is the process by which light, captured by a visual pigment molecule in a photoreceptor cell, generates an electric response. This response is caused by a change of concentrations of certain chemical substances in the cytoplasm of the outer rod segment in the retina of vertebrates.

The basic ideas and results of a work by Andreucci, DiBenedetto and Bisegna are presented. This contains a diffusion model of these substances with suitable Neumann- and Dirichlet boundary data. The complex shape of the outer rod segment leads to a homogenization ansatz with a simultaneous concentration of capacity on the thin surface-like lateral border.