Spatio-temporal modelling of intracellular signalling pathways: transcription factors, negative feedback systems, and oscillations

There are many intracellular signalling pathways where the spatial distribution of the molecular species cannot be neglected. One such class of pathways is those involving transcription factors (e.g. Hes 1, p53-Mdm2, NF-κ B, heat-shock proteins) which often exhibit oscillations in both space and time. In this chapter we present a partial differential equation model of the transcription factor, Hes 1. Our model considers the dynamics of Hes 1 in a 2-dimensional cellular domain including a nucleus, cytoplasm and microtubule-organising centre (MTOC). Spatial movement of the molecules (protein, mRNA) is assumed to be by diffusion, and also convection along microtubules. Through numerical simulations we find ranges of values for the model parameters such that sustained oscillatory dynamics occur, consistent with available experimental measurements. In order to bridge the gap between in vivo and in silico experiments we investigate more realistic cell geometries by using an imported image of a real cell as our computational domain.