FIG. 3.
Shielded diffusion-limited growth. FA protein forms a diffusion barrier of height ε and surface area s′ = sn, where n is the number of associated proteins, around the mineral cluster. The absorption rate k+ρr per unit surface area of the growth units depends on the local concentration ρr of growth units at the surface of the particle. Dissociation also occurs at rate k− per unit surface area. Neither absorption nor dissociation occurs in the shielded region (red). For ε sufficiently small, ρr ≈ ρε. The concentration ρr is then determined through conservation of flux. Outside of the diffusion layer (of thickness δ ≫ r), the concentration of growth units approaches ρ∞.