Mathematical Modelling and Analysis of the Brassinosteroid and\n Gibberellin Signalling Pathways and their Interactions

The plant hormones brassinosteroid (BR) and gibberellin (GA) have important\nroles in a wide range of processes involved in plant growth and development. In\nthis paper we derive and analyse new mathematical models for the BR signalling\npathway and for the crosstalk between the BR and GA signalling pathways. To\nanalyse the effects of spatial heterogeneity of the signalling processes, along\nwith spatially-homogeneous ODE models we derive coupled PDE-ODE systems\nmodelling the temporal and spatial dynamics of molecules involved in the\nsignalling pathways. The values of the parameters in the model for the BR\nsignalling pathway are determined using experimental data on the gene\nexpression of BR biosynthetic enzymes. The stability of steady state solutions\nof our mathematical model, shown for a wide range of parameters, can be related\nto the BR homeostasis. Our results for the crosstalk model suggest that the\ninteraction between transcription factors BZR and DELLA exerts more influence\non the dynamics of the signalling pathways than BZR-mediated biosynthesis of\nGA, suggesting that the interaction between transcription factors may\nconstitute the principal mechanism of the crosstalk between the BR and GA\nsignalling pathways. In general, perturbations in the GA signalling pathway\nhave larger effects on the dynamics of components of the BR signalling pathway\nthan perturbations in the BR signalling pathway on the dynamics of the GA\npathway. The perturbation in the crosstalk mechanism also has a larger effect\non the dynamics of the BR pathway than of the GA pathway. Large changes in the\ndynamics of the GA signalling processes can be observed only in the case where\nthere are disturbances in both the BR signalling pathway and the crosstalk\nmechanism.\n