The coupled uniform sequential reaction systems (CUSERS) model, which allows for determining the structure of signaling pathways with incomplete information from the temporal patterns of their components, was applied to the experimental records of activities of TLR4 downstream species
IKK and NF-κB in LPS-stimulated wild-type (WT), MyD88-deficient and TRIF-deficient macrophages. New signaling pathways targeting IKK were revealed in MyD88-deficient and TRIF-deficient macrophages, and shown to be described by the coupled systems formed by 3- and 5-component or
5- and 10-component pathways, respectively. By comparing the temporal pattern of IKK in WT macrophages with those in MyD88-deficient and TRIF-deficient macrophages, two new signaling pathways, which were absent in the above defective macrophages, were found and described by a system formed
by coupling 9- and 10-component pathways. As a direct consequence of the above findings, a coupled system composed of six different 3-, 5-, 5-, 9-, 10- and 10-component pathways targeting IKK and describing its temporal pattern, IKK(f), in WT macrophages was constructed. This system
significantly modifies the canonical NF-κB signaling by introducing novel pathways of IKK activation. The expression of nuclear NF-κB in WT macrophages was found to depend on two different signaling pathways and to be modelled by a coupled system composed of 1- and
4-component or 2- and 8-component pathways, in dependence on sampling frequencies used in different experiments. From the three-modal NF-κB(t) temporal pattern in LPS-stimulated WT fibroblasts, three 1-, 12- and 17-component signaling pathways targeting nuclear NF-κB
were determined.
On coupled systems of fractional impulsive differential equations by using a new Caputo-Fabrizio fractional derivative
