Computational Molecular Biology 2016, Vol.6, No.1, 1-20
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to the diversity and complexity of the NFkB pathway researchers are now combining computational-mathematical
modeling with biochemical experimentation to get a clear picture of the components and their interactions in the
pathway. This combined approach not only provides the ins ights of the molecular interactions but also the kinetic
details of the interactions.
However, it is important to note that the effect of a signaling molecule on NF-κB often
strictly depends on the cell type or the micro-environment and that even opposite effects can occur in distinct cell
types.
2.2 Computational modeling of NFkB pathway
A mathematical modeling represents a well-coordinated setting which helps to test different predictions based on
previous biochemical data for the working of a system. Mathematical modeling often leads to finding missing
links in the complex signaling networks. A mathematical model could be simple, describing the features but not
the realistic cascade or it could be detailed providing a comprehensive view of the signaling network. Building a
model requires three steps – Firstly, selecting the components and getting their detailed interaction overview from
previous experimentation data. Secondly, quantifying concentration and strength of the components by selecting
appropriate parameters, defined as the rate constants. Lastly, a mathematical formula has to be deduced for
simulation of the components (Chaplain, 2011). Reaction-network models assume that each molecule in the cell is
uniformly distributed within. This gives rise to ordinary differential equations (ODE) - one equation for each
molecule (Eungdamrong, 2004). As NFkB pathway governs enormous cellular signaling pathways, modulation of
the pathway is of prime importance in drug research studies. The use of computational language in investigating
the complex networking of the NFkB pathway has produced some amazing understanding of its functioning and
its interaction with other components within the cell. As IkB plays a central role in regulating the activities of the
NFkB pathway, it has been the major focus of
in silico
studies in recent years. Unified Modeling Language (UML)
is being used as a basis for the recent computational model systems. We here have mainly focused on
deterministic and stochastic modeling.
Hoffman et al., provided a pioneering model with a deep view of the NFkB signaling pathway describing the
effect of isoforms of IkB (α, β and Є) on NFkB regulation. The model was comprised of 24 ODEs delineating the
concentration fluctuations of NFkB and IkB in cytoplasm and nucleus using genetically reduced systems. It also
contained 30 parameters from previous experimentation data. They explicitly modeled the interaction of NFkB
with IkB and their translocation, the interaction of IKK with the NFkB-IkB complex, degradation rates of IkB and
transcription and translation of IkB isoforms. Their final results demonstrated that the oscillatory dynamics of the
NFkB is dictated by the concentration of two variables, the IKK and IkB. O'Dea et al., built a model using
Hoffman’s model for IKK-IkB-NFkB signaling modulation. They used MATLAB and Excel with extended
equilibration time. Isoforms of IkB were not considered and hence the rate constants for IkBα, IkBβ and IkBЄ
were considered to be similar (Dea et al., 2007). Cheong et al., demonstrated by his modeling studies that the
combinatory action of the three isoforms of IkB mediates the distinction between long and short term stimuli
(Cheong et al., 2008). Kearns et al., demonstrated that during long lasting activity of NFkB, IkBЄ dampens the
oscillations mediated by IkBα (Kearns et al., 2006). Basak et al. built a model to introduce p100 and LPS
induction of IKK mediated IkB degradation (Basak et al., 2007) . Shih et al., demonstrated that IkBδ provides
negative feedback to NFkB during sequential signal induction (Shih et al., 2009). Recently, Alves et al.
demonstrated that IkBЄ provides negative feedback to cRel and RelA to regulate the B-cell expansion (Alves et
al., 2015). Lipniacki et al. modeled IKK, NFkB, IkB and IKK inhibitor in nucleus and cytoplasm using 15 ODEs
or differential equations. Lipniacki et al. combined deterministic as well as stochastic modeling to find that single
TNF-α molecule can induce a massive NFkB induction (Lipniacki et al., 2007). Choudhary et al. demonstrated
that TRAF1 and NIK activity regulates the coupling of canonical and non-canonical NFkB pathway (Choudhary
et al., 2013). Ashall et al. used semi-stochastic modeling approach to determine the NFkB stimulation by TNFα at
various time- intervals (Ashall et al., 2009). Tay et al. used various stochastic models to show the heterogeneity of
NFkB in single cell level (Tay et al., 2010). Pogson et al., used agent based approach to provide a more in-depth
understanding of the NFkB pathway which was not possible by the equation based methods. Their result showed
