The NF-{\kappa}B signaling network plays an important role in many different compartments of the immune system during immune activation. Using a computational model of the NF-{\kappa}B signaling network involving two negative regulators, I{\kappa}B{\alpha} and A20, we performed sensitivity analyses with three different sampling methods and present a ranking of the kinetic rate variables by the strength of their influence on the NF-{\kappa}B signaling response. We also present a classification of temporal response profiles of nuclear NF-{\kappa}B concentration into six clusters, which can be regrouped to three biologically relevant clusters. Lastly, based upon the ranking, we constructed a reduced network of the IKK-NF-{\kappa}B-I{\kappa}B{\alpha}-A20 signal transduction.
NF-κB is a stimulus-responsive pleiotropic transcription activator and plays a significant role in various parts of the immune system during differentiation of immune cells, development of lymphoid organs, and immune activation [1]. Upon stimulation by LPS, TNFα, or UV irradiation, the NF-κB transcriptional activator is shuttled into the nucleus, initiating transcription of target genes responsible for inflammatory cytokines, anti-apoptic molecules, and NF-κB signal termination. NF-κB shuttling between nucleus and cytoplasm is regulated by the IKK-NF-κB-IκBα-A20 signaling module, which consists mainly of four proteins: IκBα, IKK (IκB kinase), A20, and NF-κB [1,2,3,4,5].
Recent computational models of NF-κB signal transduction have greatly enhanced our understanding of the underlying (negative regulation) mechanisms of NF-κB signaling and are being corroborated by experimental measurements. Hoffmann et al. [2] demonstrated that IκBα is responsible for strong negative feedback in NF-κB response which results in oscillatory shuttling of NF-κB transcription activator between cytoplasm and nucleus, whereas IκBβ and IκBε reduce the oscillation magnitudes. Nelson et al [6] reported a groundbreaking observation of sustained oscillations of NF-κB shuttling within a single cell, which drew attention to the possible cellular mechanism and functionality of the oscillatory pattern of NF-κB signaling [6,7,8,9]. In addition to IκB isoforms with their negative regulatory role, A20, a cytoplasmic ubiquitin-modifying enzyme [5] is also required for termination of NF-κB activity, thus limiting TNFαinduced [4] or LPS-induced inflammation [5]. Lipniacki et al. [10,11] modified the NF-κB model of Hoffmann et al. [2,3] by adding A20 as an additional NF-κB activity terminator, and excluding IκBβ and IκBε, thereby successfully reproducing experimentally observed NF-κB signaling response for A20-deficient cells [4].
Sensitivity analysis allows the identification of the most significant kinetic reactions which control the dynamic patterns of NF-κB response, i.e., oscillation of NF-κB shuttling. Ihekwaba et al. [12,13] performed a sensitivity analysis on a simplified version of Hoffmann’s NF-κB signaling model that considers only IκBα, NF-κB, IKK, and their complexes. Due to the computational cost of sampling 64 kinetic rate variables, their sensitivity analysis was limited to a single-variable variation [12] and at most a pairwise modulation of 9 kinetic rate variables presumed to be of high importance [13].
For this paper, we use Lipniacki et al.’s model of the IKK-NFκB-IκBα-A20 signal transduction network [10,11] in Fig. 1. This model includes two negative regulators, IκBα and A20. We performed sensitivity analysis on the network using three different sampling methods: single-variable variation, Orthogonal Array sampling, and Latin Hypercube sampling. The sensitivity analyses of the resulting temporal profiles of nuclear NF-κB response enable an importance ranking of all the kinetic rate variables in the model. We also present a classification of the resulting temporal profiles of nuclear NF-κB concentration into six clusters, which are regrouped further into three biologically relevant clusters. We propose a reduced network of IKK-NFκB-IκBα-A20 signal transduction based on these critical kinetic rate variables.
The NF-κB signaling network model proposed in [10,11] and presented in Fig. 1 involves the kinetics of IKK, NF-κB, A20, IκBα, their complexes, mRNA transcripts of A20 and IκBα, and translocation/shuttling of NF-κB and IκBα between nucleus and cytoplasm. The regulatory module has two activators IKK and NF-κB, and two inhibitors A20 and IκBα. In resting cells, unphosphorylated IκBα binds to NF-κB and sequesters NF-κB in an inactive form, namely IκBα-NF-κB, in the cytoplasm. In the presence of an extracellular stimulus such as by TNF or LPS, IKK is transformed into its active/phosphorylated form and is capable of phosphorylating IκBα, leading to ubiquitinassisted proteolysis of IκBα. As a result of degradation of IκBα, free NF-κB enters the nucleus and upregulates transcription of the two inhibitors IκBα and A20. The newly synthesized IκBα inhibits NF-κB activity by sequestering it in the cytoplasm while A20 negatively regulates IKK activity by transforming IKK into an inactive form, in which IKK is no longer capable of phosphorylating IκBα. As NF-κB, IκBα and their complexes are translocated from cytoplasm to nucleus, their concentrations change by a factor equal to the volume ratio of cytoplasm to nucleus, namely Kv.
The IKK-NF-κB-IκBα-A20 network model in Fig. 1 and Table I is readily translated into a set of ordinary differential equations with 15 dependent variables, 25 kinetic rate variables, and the initial cytoplasmic concentration of NF-κB as an initial condition. The total concentration of NF-κB, summed across all involved complexes, remains constant. Runge-Kutta 4 th order method is used to numerically solve th
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