The Blueprint of Logical Decisions in a NF-κB Signaling System

Abstract

Nearly identical cells can exhibit substantially different responses to the same stimulus that causes phenotype diversity. Such interplay between phenotype diversity and the architecture of regulatory circuits is crucial since it determines the state of a biological cell. Here, we theoretically analyze how the circuit blueprints of NF-κB in cellular environments are formed and their role in determining the cells' metabolic state. The NF-κB is a collective name for a developmental conserved family of five different transcription factors that can form homodimers or heterodimers and often promote DNA looping to reprogram the inflammatory gene response. The NF-κB controls many biological functions, including cellular differentiation, proliferation, migration, and survival. Our model shows that nuclear localization of NF-κB differentially promotes logic operations such as AND, NAND, NOR, and OR in its regulatory network. Through the quantitative thermodynamic model of transcriptional regulation and systematic variation of promoter-enhancer interaction modes, we can account for the origin of various logic gates as formed in the NF-κB system. We further show that the interconversion or switching of logic gates yielded under systematic variations of the stimuli activity and DNA looping parameters. Such computation occurs in regulatory and signaling pathways in individual cells at a molecular scale, which one can exploit to design a biomolecular computer.

Figure 1

Schematic for forming various possible logic gates configurations for the NF-κB system as formed by long-distance TF promoter interaction through DNA looping and by the diffusion of TF to the promoter. (A) H and L indicate the high and low stimuli activities in the table. The symbols E1 and E2 are the two enhancer elements of NF-κB system, namely, IRE, κB sites. The symbol A is the Boolean expression of the corresponding gate operations, and LP is the number of enhancer–promoter loops. (B) Various configurations for AND, OR, NAND, and NOR logical operations. The active configurations are marked with the tick symbols in the figure. Here, we use the purple and green colors cartoon for the protein, IRF, and NF-κB. These two proteins are stimulated by the IFN-β and TNF-α, as shown by the orange and brown color cartoons. The red and light blue cartoons are used to indicate the heterodimeric complex of p300-AP-1 and RNAP molecules. The yellow symbol indicates the facilitated tracking diffusion and translation modes of TFs. (C) Schematic view of various logic gates in parameter space. We show the logic gates as a function of a few controllable parameters such as free energies for the stimuli-induced protein activation, ϵ_{IFN−β/TNF−α}, the strength of DNA loops ϵ_LP and the activities of stimuli, λ_IFN−β and λ_TNF−α. The gradients in the color bars are used to show the gene expression level.

Figure 2

Transition of the various logic gates in the parameter space. Panels A, B, C, and D refer to the population of the active assemblies for the AND, OR, NAND, and NOR logic gates as a function of stimuli activities (λ_TNF−α and λ_IFN−β). Panels E and F are the logic gates switching between AND to OR and NAND to NOR. Note that the switching only happens as the strength of interaction between stimuli and TF (ϵ_L–TF) varies. The switching from OR-AND to NOR-NAND happens through the variation of DNA stiffness parameter (ϵ_LP) as a function of stimuli activities. The color bars show the population of all active configurations formed in the parameter space. The contour maps corresponding to the top view of logic gates transition maps (shown in panels E and F) for OR-AND and NOR-NAND transitions for varying ϵ_L–TF values are shown in Figures 3 and 4, respectively.

Figure 3

Transition of AND-OR logic gates switching as a function stimuli activities. The two-dimensional contours are taken from Figure 2E at a particular value of ϵ_L–TF, shown on each panel’s top. The switching between the two gates is visible from the analysis. The color bars show the population of all active configurations formed in the parameter space.

Figure 4

Switching of NAND to NOR logic gates as a function TNF-α and IFN-β activities. The two-dimensional contours are taken from Figure 2F at a particular value of ϵ_L–TF, shown on each panel’s top. The switching between the two gates is visible from the analysis. The color bars show the population of all active configurations formed in the parameter space.

Figure 5

Behavior space for the complete set of available assembly configurations is plotted as K-L divergence (D_KL): similarity between theoretical model computed output surfaces and the Boolean surfaces obtained from Monte Carlo simulations. The regions are marked for the exclusive AND to OR, and NAND to NOR logic gates in the panels A and B,respectively. The calculations are done by varying degrees of oligomerization (n_H) to explore the robustness of the switching among gates.