A plausible identifiable model of the canonical NF-κB signaling pathway

An overwhelming majority of mathematical models of regulatory pathways, including intensively studied NF- κ B pathway, remains non-identifiable meaning that their parameters may not be determined by existing data. The existing NF- κ B models that are capable to reproduce experimental data, contain non-identifiable parameters, while simplified models with a smaller number of parameters exhibit dynamics that significantly differs from that observed in experiments. Here, we reduce an existing model of the canonical NF- κ B pathway by decreasing the number of equations from 15 to 6 in a way that the resulting model exhibits dynamics closely following that of the original model, both for the nominal and the randomly selected parameters. We carried out the sensitivity-based linear analysis and Monte Carlo-based analysis to demonstrate that the resulting model is structurally and practically identifiable based on a simple TNF stimulation protocol in which 5 model variables are measured. The reduced model is capable to reproduce different types of responses characteristic to regulatory motives controlled by negative feedback loops: nearly-perfect adaptation, damped and sustained oscillations. It can serve as a building block of more comprehensive models of immune responses and cancer, where NF- κ B plays a decisive role. Our approach, although may not be automatically generalized, suggests that other regulatory pathways models can be transformed to identifiable, while retaining their dynamical features.