Signal transduction is a complex process in which a cell converts environmental signals to a series of intracellular biochemical reactions. Diverse cellular stimuli can create a wide variety of transcription factor activities through signal transduction pathways, resulting in differential gene expression that dictates subsequent cellular behaviors. Although a great deal of effort has been made in modeling signal transduction pathways or gene regulatory networks independently, a strategy to link the signaling pathway with downstream gene expression responses seems to be lacking. Thus, a systematic approach is needed to integrate experimental data and theoretical hypotheses, to identify the physiological consequences of environmental stimuli.
Over the past few years, a considerable number of studies have reported various systematic modeling protocols for the reconstruction of large-scale cellular signaling networks [1–8]. Besides the qualitative analysis of the signaling networks, mathematical approaches for the quantitative modeling and simulation of signal transduction pathways have also been developed [9–15]. Most of these quantitative signaling models are kinetic reactions represented by the assemblage of ordinary differential equations (ODE) . The ODEs are designed to simulate dynamic changes throughout continuous but limited time points that define a function of rate changes for one independent variable and one or more of its derivatives with respect to that variable. Given the determined kinetic parameters, such ODE models provide a "forward-engineering" framework to simulate the spatiotemporal dynamics of the system. The time profiles of the target transcription factor activation in response to various stimuli can be obtained by this established approach.
In gene regulatory network modeling, some wet-bench experimental approaches have been used to detect the gene expression and transcriptional activities. Microarray technology is a powerful high-throughput technique enabling biologists to simultaneously measure the expression profile of tens of thousands of genes under prescribed conditions [17, 18]. As for transcriptional activities, the electrophoretic mobility shift assay (EMSA) [19, 20] is an affinity electrophoresis technique that can determine single protein or protein-DNA complex binding activity at a time. However, the ability to broadly assess the activities of transcription factors is still much limited. Therefore, most computational transcription activity and gene regulatory network are reconstructed from genome wide gene expression data.
Such a data-driven approach to gene expression analysis provides systematic information of underlying gene regulatory systems and offers the possibility to infer the dynamics and mechanisms of transcription control by reverse engineering [21–28]. There are two kinds of reverse engineering strategies for modeling gene regulatory networks based on DNA microarray data, namely the "influence" and "physical" approaches . The "influence approach" produces the genetic network that illustrates regulatory influences between RNA transcripts. This strategy can integrate information pertaining to the relationships between regulated genes, protein-protein interactions, and enzyme catalysis to establish network based on transcript profiling data when the expression of certain transcripts is highly correlated. However, influence models are difficult to interpret in the context of location and modification in the cell. The second strategy, known as the "physical approach", seeks to construct a physical interaction model between transcription factors and gene promoters. The transcriptional activities can be often predicted from gene expression data by a sigmoid function . Moreover, factor analysis is another methodology to construct a physical regulation model which is represented as bipartite graph with transcription factors in the first layer and regulated genes in the second layer for reducing the dimensionality of the reverse engineering problem. In previous studies, principal component analysis (PCA) , independent component analysis (ICA) , and network component analysis (NCA)  have been applied to reconstruct transcription factor activities using gene expression profiles. PCA and ICA are traditional dimensionality reduction technologies. The transcription factor activity reconstructed by PCA and ICA is constrained, respectively, to be mutually orthogonal and statistical independent. These statistical assumptions do not match the real biological systems. However, NCA contrasts with traditional PCA and ICA in that it does not make any aforementioned statistical assumptions.
NF-κB is a transcription factor that has long been recognized as the "master switch" in regulating the expression of various cytokines and host response effectors, as well as a wide array of genes to control inflammation, cell survival, apoptosis, and immune defense responses . NF-κB signaling can be initiated from membrane receptors, such as Toll-like receptors, tumor necrosis factor alpha (TNF-α) receptors, and interleukin-1 (IL-1) receptors, either individually or synergistically. In the past few decades, many studies have tried to resolve the complex NF-κB dependent protein-protein and DNA-protein interactions, and significant progress has since been made on modeling signal transduction pathways and gene regulatory networks of the inflammatory response based on both biochemical and microarray data [35–40]. However, a systemic and dynamic view of how external stimuli evoke NF-κB-dependent signal transduction activities to the downstream gene expression still remained unclear.
To overcome this challenge, we proposed a new computational modeling approach by connecting transcription activities derived from the reverse engineering of gene expression profiling to the transcription activities simulated from a forward engineering signaling model, using the NF-κB signaling pathway with the corresponding gene responses as the case study. In this work, the NCA model was applied to reconstruct the regulatory activity of NF-κB using gene expression profile data obtained in response to specific external stimuli . A kinetic model was used to simulate the IKK-NF-κB signaling pathway . By mapping the NF-κB profiles generated from the reverse engineering gene expression profiling data and the ones from the forward simulation, the bridging IKK activities induced by external stimuli were inferred. Features of this inferred signaling process were then confirmed by independent experiments using similar stimuli. This strategy successfully linked the initial signaling pathway with the relevant gene regulatory network. It also successfully inferred and distinguished the corresponding stimuli from gene responses under different inflammation conditions. Taken together, the strategy discussed in the present study can help enhance our understanding of inflammatory responses during the infection process; it is also applicable to other cellular processes.