Formation of intracellular concentration landscapes by multisite protein modification

Multiple cellular proteins are covalently modified (e.g., phosphorylated/dephosphorylated) at several sites, which leads to diverse signaling activities. Here, we consider a signaling cascade that is activated at the plasma membrane and composed of two-site protein modification cycles, and we focus on the radial profile of the concentration landscapes created by different protein forms in the cytoplasm. We show that under proper conditions, the concentrations of modified proteins generate a series of peaks that propagate into the cell interior. Proteins modified at both sites form activity gradients with long plateaus that abruptly decay at successive locations along the path from the membrane to the nucleus. We demonstrate under what conditions signals generated at the membrane stall in the vicinity of that membrane or propagate into the cell. We derive analytical approximations for the main characteristics of the protein concentration profiles and demonstrate what we believe to be a novel steady-state pattern formation mechanism capable of generating precise spatial guidance for diverse cellular processes.