Negative feedback systems for modelling NF-κB transcription factor oscillatory activity

Low-dimensional negative feedback systems (NFSs) were developed within a signal flow model to describe the oscillatory activities of NF-kappa B caused by interactions with its inhibitor I kappa B alpha. The NFSs were established as 3rd- and 4th-order linear systems containing unperturbed and perturbed negative feedback (NF) loops with constant or time-varying NF strengths and a feed-forward loop. NF-related analytical solutions to the NFSs representing the time courses of NF-kappa B and I kappa B alpha were determined and their exact mathematical relationship was found. The NFS's parameters were determined to fit the experimental time courses of NF-kappa B in TNF-alpha-stimulated embryonic fibroblasts, rela-/- embryonic fibroblasts reconstituted with RelA, C9L cells, GFP-p65 knock-in embryonic fibroblasts and embryogenic fibroblasts lacking I kappa beta and I kappa B epsilon, LPS-stimulated IC-21 macrophages treated or not with DCPA, and anti-IgM-stimulated DT40 B-lymphocytes. The unperturbed and perturbed NFSs describing the above biosystems generated isochronous and non-isochronous solutions, depending on a constant or time-varying NF strength, respectively. The oscillation period of the NF-coupled solutions, the phase difference between them and the time delays in the appearance of cytoplasmic I kappa B alpha after stimulation of NF-kappa B were determined. A significant divergence between the I kappa B alpha solutions to the NFSs and the I kappa B alpha experimental courses led to a rejection of the NF coupling between NF-kappa B and I kappa B alpha in the above biosystems. It was shown that neither the linearity nor the low dimensionality of the NFSs altered the NF relationship and the divergence between the I kappa B alpha solutions to the NFS and I kappa B alpha experimental time courses. Although the NF relationship between I kappa B alpha and NF-kappa B was not confirmed in all the experimental data analyzed, delayed negative feedback was found in some cases.