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-κB caused by interactions with its inhibitor IκBα. 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-κB and IκBα were determined and their exact mathematical relationship was found. The NFS's parameters were determined to fit the experimental time courses of NF-κB in TNF-α-stimulated embryonic fibroblasts, rela-/- embryonic fibroblasts reconstituted with RelA, C9L cells, GFP-p65 knock-in embryonic fibroblasts and embryogenic fibroblasts lacking Iκß and IκBε, 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 IκBα after stimulation of NF-κB were determined. A significant divergence between the IκBα solutions to the NFSs and the IκBα experimental courses led to a rejection of the NF coupling between NF-κB and IκBα 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 IκBα solutions to the NFS and IκBα experimental time courses. Although the NF relationship between IκBα and NF-κB was not confirmed in all the experimental data analyzed, delayed negative feedback was found in some cases.

Chemiluminescent picture of diphenyleneiodonium-inhibited NADPH oxidase: a bimodal process and its logistic-exponential model-based description.

A chemiluminescence (CL) study of diphenyleneiodonium-inhibited NADPH oxidase was performed on a cellular system containing neutrophils stimulated by phorbol myristate acetate, indicating a complex bimodal structure of CL processes corresponding to different stages of the inhibition. The complex structure of these processes was described by a superposition of two logistic-exponential (LE) models, characterizing these processes as bimodal ones. To determine the mechanistic foundation of the LE model-described processes, a generalized form of the second-order dynamic system of CL reactions, the solution to which corresponds to the LE model, was constructed. The diphenyleneiodonium effects on neutrophil NADPH oxidase were separated from the total bimodal CL of the whole measurement system by the use of difference CL processes. These difference processes were also found to be bimodal; thus, inhibitor-induced reduction of CL could be described by a second-order dynamic system. The rate constants and initial concentrations in this dynamic system were determined by the least squares method applied to numerical solutions approximating the difference processes. Using interrelations between the parameters of the dynamic system, cooperative effects in the inhibitor reactions with NADPH oxidase were found and described quantitatively. Other evidences of cooperativity were obtained from integral characteristics of the CL reduction process, i.e. dose-response and progress curves, determined by numerical integration of the LE models constituting the superposition. On this basis, it was also possible to detect a specific binding of the inhibitor to the enzyme. Finally, putative reaction mechanisms suggested by the model obtained were considered and compared with those known at present.

Logistic-exponential model for chemiluminescence kinetics.

A logistic-exponential (LE) model for chemiluminescence (ChL) kinetics was constructed as a superposition of a logistic function, representing the ascending sigmoidal-in-shape phase, and an exponential function representing the descending phase of the ChL time course. The logistic component of the LE model expresses a non-linear autocatalytic reversible reaction counteracting a rise in the ChL which is not considered by a classical two-exponential model of the time course of ChL, whereas the exponential component of the LE model represents a first-order reaction of a ChL decay. The proposed reactions, that underlie the time course of ChL, were shown to form a second-order dynamic system. Main characteristics of the LE model such as the ChL peak value (CL(m)), the peak time (t(m)) and the inflexion points' times (t(i)) were determined as well as the error calculus for the LE model. Moreover, several applications of the LE model to ChL processes generated by both native and perturbed polymorphonuclear granulocytes (PMNs) and red blood cells (RBCs), intoxicated yeast, ferrous ion-treated bull spermatozoa, autoxidising l-3,4-dihydroxyphenylalanine (l-DOPA), or luminol oxidised in the Fenton reaction were made.