Interactions of molecules are essential for almost all cellular functions. Genes and proteins seldom carry out their functions in isolation. They operate through a number of interactions with other biomolecules. Molecular interactions in biological pathways and networks are highly dynamic and may be controlled by feedback loops and forward regulation mechanisms as well as interlinks with other cellular hierarchies. They make experimental elucidation and computational analysis of pathways extremely challenging. Mathematical modeling is becoming increasingly important as a tool to capture molecular interactions and dynamics from high-throughput experiments. Biological pathways and networks are often represented graphically. Ordinary differential equations (ODEs) have been commonly used to help explain the kinetic process of association and disassociation among molecules in chemical or biochemical reactions.

Tumor necrosis factor-alpha (TNFα) is a cytokine involved in systematic inflammation and is a member of a group of cytokines that all stimulate the acute phase reaction. Dysregulation and over-production of TNFα have been implicated in the pathogenesis of a wide spectrum of human diseases, e.g. sepsis, diabetes, cancer, osteoporosis, multiple sclerosis and crohns disease. Eliminating TNFα by a specific monoclonal antibody, e.g. infliximab, caused dramatic effects on the phenotype of the diseases, with severe side effects. To find specific ways with least side effects to block or partially block TNFα actions, we need to learn more about the signaling pathways of TNFα. Some research efforts have been shifted from intercellular to intracellular signaling in order to increase the knowledge about the involved cell proteins and to get a better understanding of the molecular dynamics of the TNFα-related pathways, especially the TNFα-NFκB signaling pathway.

Biological cartoons and analytical pathway models have been constructed for the TNFα-NFκB signaling pathway respectively. These models can be used for computer simulation studies in order to get insights on setting various experimental scenarios. The better understanding of diseases makes the drug development more appropriate with minimal side effects [1, 2]. Reliable information about proteins and molecular interactions of the signaling pathway is needed to improve the structure of a pathway model. It has known that several protein purification methods are not capable of detecting protein activities in natural concentration. Because of protein over-expression, non-natural protein complex building can occur [3, 4] which could cause faults in modeling. Although a significant amount of biological and biochemical literature is now available in this research field, some of which examine only small parts of the pathway and sometimes with methods relying on over-expression situations. In this paper, we introduce an integrative approach to analyze experimental TNFα-NFκB signaling pathway model. We built an integrative database that includes mathematical modeling data, literature information as well as biological data. In particular, the modeling data consists of kinetic constants, kinetic equations and initial concentrations for building mathematical ODE models. The biological data includes descriptions of proteins, protein-protein interactions and other information concerning signaling pathways. All information can be retrieved and visualized within our integrative computational framework. The paper is organized as follows: Section 2 provides our methodology and delimitates the modeling of the TNFα-NFκB signaling pathway based on ODE models and the literature information. Section 3 describes the results obtained from our extended TNFα-NFκB signaling pathway model. Section 4 gives our discussion and conclusion of this work.

For signaling pathway modeling, the following problems occur:

• It is not clear, which proteins should be used to set up a stable model basis, which can easily be extended?
• How is the chronology of protein interactions and which proteins build up a complex?
• How fast and long do the proteins interact (this means, what are the kinetic parameters)?

These problems play a major role in modeling the TNFα-NFκB signaling pathway within our framework. The mathematical models described in [23, 25, 31] related to TNFα pathway showed us that these models contain similar proteins and the general dynamics of complex building was almost identical. Among these models we identified the model based on Cho (we referred it as Model A) as the best available model for possible further improvement in order to address pathway modeling problems mentioned previously. Several other possible extensions/improvements for the pathway Model A were also identified depending on research foci and we concluded that three new proteins – TRAF1, FLIP, and MEKK3 – should be included for possible improvement of Model A. The main focus of our work was to model the TNFα- NFκB signaling pathway starting from TNFα receptor to the transcription factor AP1, rather than going into other levels. By including the three new proteins, we derived an initial extended pathway model using our integrated analytical framework as shown in Fig. (3).

Fig. (3) The new TNFα-NFκB pathway model (Model B) includes three new proteins MEKK3 (m32), FLIP (m33) and TRAF1 (m35). Circles (with m and a number) represent various states for protein concentration (i.e. kinetic constants), and directed arrows represent dynamic relations (i.e. kinetic equations). The protein complex TNF/TNFR1/TRADD/RIP1/TRAF2/MEKK3/IKK connects to NFκB is colored red. The new protein complexes are colored magenta, e.g. Caspase8/FLIP (m34), RAF1/Caspase8* (m36) and TRAF2/TRAF1c(m38).

It is worth mentioning that TRAF1 and FLIP were also considered in the mathematical models by Schöberl, Ihekwaba and MEKK3 has been intensively discussed [25, 31]. All proteins contained in the cell proliferation module of the extended pathway model were identified and compared among others via the TAP tagged strategy and the protein-protein interaction connectivity map [32]. We noted that some basic interactions, which were modeled, could not be found in the protein-protein interaction connectivity map (i.e. TNFR1-TRADD, TRADD-FADD, TRADD-RIP, RIP-Caspase8 and RIP-IKK). Since cIAP has not been further examined, the interaction with effector Caspases was not modeled. We resulted with a final ODE pathway model (we referred this final ODE pathway model, Model B).

In Model B, several single proteins like TNFR1, TRADD, RIP1, TRAF2, IKK, IκB and NFκB were identified in the protein-protein interaction connectivity map (Fig. 4). The connectivity map comprises no complexes, only individual proteins. IKK is presented by its subunits IKKα, IKKβ and IKKγ, colored lilac, and IκB is presented by its subunits IkBα, IkBβ and IkBε, colored orange. NFκB’s family members (monomers) are colored red and their precursors are mentioned in the connectivity map, i.e. NFκB1 (p50; precursor: p105), NFκB2 (p52; precursor: p100), p65 (RelA), c-Rel (Rel), and RelB. All these seven proteins in both the Model B and the connectivity map. With limited experimental data, further modeling improvements are very difficult. The incorporated biological and modeling knowledge are retrieved from the knowledgebase and integrated into the extended TNFα-NFκB signaling pathway model within our framework.

Fig. (4) The protein-protein interaction connectivity map (Bouwmeester et al. 2004). The proteins that are colored are modeled in our new TNFα-NFκB signaling pathway model B.

We performed a systematic examination of the TNFα-NFκB signaling pathway by simulating different scenarios to analyze the sensitivity of the Model B with respect to possible changes of the kinetic parameters. The extended TNFa-NFκB signaling pathway model B now including all three new components namely the proteins: MEKK3, FLIP and TRAF1 is indeed quite a stable model. TRAF1 and Caspase8* are reversible from the complex proteins and TRAF1 is irreversibly cleaved and TRAF1c and Caspase8* were yielded. The comparison of the protein concentrations was also performed by plotting the concentrations of the components of other existing mathematical models including model by Cho [24], i.e. Model A, models by Schöberl [31] and Ihekwaba [25] and the new Model B side-by-side. Components, which show extraordinary differences, were examined via further literature investigations. As a result, our extended TNFα-NFκB signaling pathway model B appears to be the most detailed and consistent mathematical model with protein-protein interaction connectivity information incorporated in it.

Complex interactions of intracellular proteins regarding time course and protein concentrations as well as kinetic behaviors cause high variability in biological functions. To bring light to these complex interaction systems inside of cells, we first have to identify the involved proteins and then to model their interactions by means of sufficient techniques. TNFα is a cytokine, which is implicated in the pathogenesis of various human diseases and therefore it has been under intense investigations for better understanding of the exact signal flow.

Objective of this work was to build a new TNFα- NFκB signaling pathway model that allows integration of protein-protein interaction connectivity map. The mathematical models relating to the TNFα-NFκB signaling pathway contained similar proteins and identical concept behind complex building. Bouwmeester et al. [32] published a connectivity map giving a detailed view on protein-protein interactions of the TNFα-NFκB signaling pathway on a physiological protein concentration level and this map was used, compared and studied with our extended mathematical model.

Mathematical models based on Cho [24], Schöberl [31] and Ihekwaba [25] are available in relation to TNFα- NFκB signaling pathway. Improvements of the existing pathway models are very difficult and challenging. The decision to use the mathematical model by Cho (i.e. Model A) as our base model and extending it was based on the facts that it is the most detailed mathematical model available today for TNFα- NFκB signaling starting from TNFα receptor up to the transcription factor AP1. The Schöberl [24] and Ihekwaba [14] models describe signaling from IKK and NFκB level onwards. The Ihekwaba’s model is concentrating more into the details of modeling IKK interactions rather than the TNFα-NFκB signaling.

Having selected Model A for extension, we found out that this model contained several inconsistencies, regarding the “recycling” of particular proteins after protein complex dissociation for TNFα- NFκB signaling pathway as a whole. Model A did not provide valid reasons why they constructed their model in a particular way. We identified some inconsistencies and corrected the model accordingly with information from the protein-protein interaction connectivity map. In the extended Model B these, inconsistencies were abolished. Hence, this extended model can serve as a more consistent mathematical description to reflect TNFα- NFκB signaling pathway. Our overall integrative analytical approach can also be used to more easily compare and study other future models for further modeling improvements as more experimental data become available. In essence, the knowledgebase of our integrative framework will grow accordingly.

Three new proteins – TRAF1, FLIP, and MEKK3 – were included into the extended model B. TRAF1 and FLIP were already considered in the Schöberl model and MEKK3 has also been intensively discussed in the TNFα- NFκB signaling pathway literature. The importance of this protein has also been pointed out by Bouwmeester et al. [32]. The exact localization of MEKK3 in the signaling pathway and the interactions with other proteins are not fully clear at the moment. That is why the actual position in the extended pathway model has to be regarded as a first approximation to nature.

One of the main goals of this work was to use the information of the protein-protein interaction connectivity map to build an improved pathway model. In practice, we found that several protein interactions mentioned in literature could not be found in the connectivity map provided by Bouwmeester et al. [32]. Especially, these were the interactions which are situated in close proximity to the cell membrane. On this regard, the connectivity map just outlines which proteins are parts of the TNFα- NFκB signaling pathway, but does not exactly specify all the occurring interactions between them. To construct a valid mathematical model, it is necessary to have a complete view on the interactions in the signaling pathway. If all the important interactions are revealed, this might require changing the general model structure, as the connectivity map suggests several alternative inhibiting and activating signal flow paths, which have not been modeled yet.

The limitation of experimental data also makes it more challenging to develop a pathway model only for TNFα-NFκB signaling pathway. Information of several sources has to be combined and adapted to fit into one pathway model. Hence, this task makes the possibility of combining models more challenging and interesting. Stochastic mathematical modeling approach is also an interest of our research, and we are currently working on extending a Bayesian probabilistic graphical model framework [21] for TNFα-NFκB signaling pathway. The validation of the structure of TNFα-NFκB signaling pathway by means of experimental data and simulation studies are our on-going work in order to get a more physiologically realistic model. This can be done by incorporating experimental data into the knowledgebase and analyzing the pathway models. It is an iterative interplay between experimental analysis and modeling strategies. Simulation results done on signaling pathways will enable us to interpret the biological system from a global systemic view. This will further increase the understanding of signaling pathways.