Spatio-temporal modelling of the NF-κBNF-κB intracellular signalling pathway: The roles of diffusion, active transport, and cell geometry

The nuclear factor kappa B (NF-κBNF-κB) intracellular signalling pathway is central to many stressful, inflammatory, and innate immune responses. NF-κBNF-κB proteins themselves are transcription factors for hundreds of genes. Experiments have shown that the NF-κBNF-κB pathway can exhibit oscillatory dynamics—a negative feedback loop causes oscillatory nuclear-cytoplasmic translocation of NF-κBNF-κB. Given that cell size and shape are known to influence intracellular signal transduction, we consider a spatio-temporal model of partial differential equations for the NF-κBNF-κB pathway, where we model molecular movement by diffusion and, for several key species including NF-κBNF-κB, by active transport as well.Through numerical simulations we find values for model parameters such that sustained oscillatory dynamics occur. Our spatial profiles and animations bear a striking resemblance to experimental images and movie clips employing fluorescent fusion proteins. We discover that oscillations in nuclear NF-κBNF-κB may occur when active transport is across the nuclear membrane only, or when no species are subject to active transport. However, when active transport is across the nuclear membrane and NF-κBNF-κB is additionally actively transported through the cytoplasm, oscillations are lost. Hence transport mechanisms in a cell will influence its response to activation of its NF-κBNF-κB pathway. We also demonstrate that sustained oscillations in nuclear NF-κBNF-κB are somewhat robust to changes in the shape of the cell, or the shape, location, and size of its nucleus, or the location of ribosomes. Yet if the cell is particularly flat or the nucleus sufficiently small, then oscillations are lost. Thus the geometry of a cell may partly determine its response to NF-κBNF-κB activation.The NF-κBNF-κB pathway is known to be constitutively active in several human cancers. Our spatially explicit modelling approach will allow us, in future work, to investigate targeted drug therapy of tumours.

► The NF-κBNF-κB intracellular signalling pathway exhibits oscillatory behaviour.
► We study a spatio-temporal model which is novel for this pathway.
► We explore the roles of diffusion, active transport, and cell geometry.
► Molecular transport mechanisms and cell geometry determine NF-κBNF-κB dynamics.
► Our spatial profiles and animations match experimental images and movie clips.