| Contents |
| In a protein spatio-temporal dynamics in a single cell one can easily arrive to coupled non-linear reaction-diffusion systems defined for the nuclear and cytoplasmic concentrations of species involved in the protein signaling network (for example, by using Michaelis-Menten and Hill kinetics to describe reactions between the species), connected with the so-called Kedem-Katchalsky boundary conditions on the nuclear membrane simulating transport of the species between the compartments. We are particularly interested in spatio-temporal signaling of the p53 protein in response to DNA damage. Among other things, we show that oscillatory patterns (and instabilities) in p53 concentration can be driven by spatial and compartmental representation of processes occurring in a cell, and by a membrane permeability property that can impose physiological delays into protein responses. The semi-implicit Rothe method is used to (constructively) prove existence and uniqueness of non-negative solutions of such reaction-diffusion systems. |
|