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Review
. 2012 Mar;246(1):221-38.
doi: 10.1111/j.1600-065X.2011.01092.x.

Lessons from mathematically modeling the NF-κB pathway

Soumen Basak  1 , Marcelo Behar, Alexander Hoffmann
Affiliations
Review

Lessons from mathematically modeling the NF-κB pathway

Soumen Basak et al. Immunol Rev. 2012 Mar.

Abstract

Mathematical modeling has proved to be a critically important approach in the study of many complex networks and dynamic systems in physics, engineering, chemistry, and biology. The nuclear factor κB (NF-κB) system consists of more than 50 proteins and protein complexes and is both a highly networked and dynamic system. To date, mathematical modeling has only addressed a small fraction of the molecular species and their regulation, but when employed in conjunction with experimental analysis has already led to important insights. Here, we provide a personal account of studying how the NF-κB signaling system functions using mathematical descriptions of the molecular mechanisms. We focus on the insights gained about some of the key regulatory components: the control of the steady state, the signaling dynamics, and signaling crosstalk. We also discuss the biological relevance of these regulatory systems properties.

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Figures

Fig. 1
Fig. 1. The NF-κB signaling system
Schematic of the molecular components that make of the NF-κB signaling system: a family of kinases controls the half-life of a family of inhibitors and protein precursors, thereby regulating the activity of 15 dimers (which consist of 5 monomer combinations) which control gene expression through a degenerate regulatory DNA element.
Fig. 2
Fig. 2. The NF-κB signaling system
(A) Schematic of the molecular interactions contained in a sample kinetic model [version 3.0 (37) and version 3.1 (38)]. Each number indicates a kinetic parameter within an ordinary differential equation. (B) Table of the kinetic parameter classes [contained in (A)] and the type of ordinary differential equation used to describe the molecular interaction. Parameter values were obtained from literature (green), fitted predominantly based on literature data (blue), or fitted predominantly based on new experimental data (red).
Fig. 3
Fig. 3. The Systems Biology approach to elucidate NF-κB signaling
The Systems Biology approach was defined as involving iterative mathematical modeling and experimentation (2). To elucidate NF-κB signaling, a kinetic model was constructed based on literature. Simulations were used to develop hypotheses, and then identify perturbations (such as TNF duration dose–responses) that may test these informatively. Subsequent experimental studies were carried out accordingly, allowing evaluation of the hypothesis, and may demand a refinement or expansion of the kinetic model.
Fig. 4
Fig. 4. Kinetic buffering desensitizes the NF-κB system to metabolic perturbations
(A) Schematic of the key reactions controlling IκB abundance. In resting cell, the short half-life of free IκB necessitates a high synthesis rate (2690 pM/min) to maintain the observed pool of free IκB proteins (51). When the free IκB is stabilized to the same half-life as bound IkB the required synthesis rate is reduced >10-fold (208 pM/min). This alteration defined the virtual IκB-flux mutant. (B) Where as normal cells show a high degree of insensitivity to ribotoxic stress (translational inhibition must be >70% to elicit a response), the IκB flux mutant shows NF-κB activation with >30%, a level achieved by UV and during UPR.
Fig. 5
Fig. 5. Encoding dynamic control of NF-κB in response to TNF and LPS
(A) Schematic of negative feedback regulators involved in shaping NF-κB responses to inflammatory stimuli. The depicted IκBs function is dynamic feedback regulators, whereas A20 provides integral feedback and a rheostat function to limit NF-κB responses. (B) Schematics of the TNF and LPS-responsive NF-κB profiles observed in biochemical experiments in wild-type (red) or specific knockout (blue) cells. In response to TNF, the duration of the first phase of NF-κB activation is determined by the inducibility of IκBα synthesis, whereas dampening of the responses is a function of the inducibility of IκBε. The amplitude of the first phase and duration of the second phase is a function of A20’s abundance. In response to LPS, the duration of NF-κB signaling is a function of the rate at which IκBd is produced. This graphic summary is based on work described and cited in the text.
Fig. 6
Fig. 6. Signaling crosstalk within the NF-κB signaling system: some examples
(A) Dose–response graph of NF-κB to TNF. A prior exposure to IL-1 renders cells less sensitive to subsaturating doses of TNF. This crosstalk effect is mediated in part by A20 (38). (B) Heat map of peak NF-κB activity (color scale) in response to ribotoxic stress signals effecting translational inhibition (x-axis) in cells containing constitutive IKK activity at various values (y-axis; 51). (C) Timecourse of RelA:p50 activation to LTb. Whereas naıve cells only show modest activation of RelA:p50, prior TNF exposure enhances the activation (compare solid and dashed lines) to such an extent that inflammatory target genes are activated as well (not shown here). This priming effect is mediated by IkBd (39).
Fig. 7
Fig. 7. Perspective: accounting for the generation and activation/inactivation of multiple NF-κB dimers
The NF-κB Signaling system may be described in terms of two interconnected networks: the NF-κB network (left) that depicts monomer expression (inducible in green arrows), pre-cursor processing and other regulated steps (blue), and dimer formation (black arrows); and the IκB network which depicts IκB synthesis (green arrows), IκB interactions with NF-κB dimers (black inhibitory connectors), and IκB degradation (blue arrows). Understanding how the kinetic mechanisms in each network combine to control the activity of multiple NF-κB dimers in different cell types remains an important future goal.
Fig. 8
Fig. 8. Perspective: the NF-κB signaling system within the context of upstream, downstream, and coordinated regulatory networks
The NF-κB signaling system receives inputs from signaling modules associated with a variety of receptors that respond to the presence of distinct classes of molecules. These same signaling modules also activate a subset of other signaling systems. The coordinated activities of the effectors of theses signaling systems together determine the cellular response via gene regulatory networks. Understanding how the coordinated activation of multiple signaling systems produce stimulus-appropriate cellular responses remains an important future goal.
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