  The plant hormones brassinosteroid (BR) and gibberellin (GA) have important
roles in a wide range of processes involved in plant growth and development. In
this paper we derive and analyse new mathematical models for the BR signalling
pathway and for the crosstalk between the BR and GA signalling pathways. To
analyse the effects of spatial heterogeneity of the signalling processes, along
with spatially-homogeneous ODE models we derive coupled PDE-ODE systems
modelling the temporal and spatial dynamics of molecules involved in the
signalling pathways. The values of the parameters in the model for the BR
signalling pathway are determined using experimental data on the gene
expression of BR biosynthetic enzymes. The stability of steady state solutions
of our mathematical model, shown for a wide range of parameters, can be related
to the BR homeostasis. Our results for the crosstalk model suggest that the
interaction between transcription factors BZR and DELLA exerts more influence
on the dynamics of the signalling pathways than BZR-mediated biosynthesis of
GA, suggesting that the interaction between transcription factors may
constitute the principal mechanism of the crosstalk between the BR and GA
signalling pathways. In general, perturbations in the GA signalling pathway
have larger effects on the dynamics of components of the BR signalling pathway
than perturbations in the BR signalling pathway on the dynamics of the GA
pathway. The perturbation in the crosstalk mechanism also has a larger effect
on the dynamics of the BR pathway than of the GA pathway. Large changes in the
dynamics of the GA signalling processes can be observed only in the case where
there are disturbances in both the BR signalling pathway and the crosstalk
mechanism.
