The plant hormones brassinosteroid (BR) and gibberellin (GA) have important roles in a wide range of processes involved in plant growth and development. The BR signalling pathway acts by altering the phosphorylation state of its transcription factors BZR1/2, whereas the GA signalling pathway acts by reducing the stability of its transcription factor DELLA. Both signalling pathways include a negative feedback, with high levels of BR causing increased repression of key BR-biosynthetic genes mediated by BZR1/2, and high levels of GA causing decreased stability of DELLA, where DELLA is responsible for activating key genes involved in GA biosynthesis. We derive and analyse new mathematical models for the BR signalling pathway and  the crosstalk between the BR and GA signalling pathways. To analyse the effects of spatial heterogeneity of the signalling processes, along with  ODE models we derive  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. We show that solutions of our models can exhibit oscillatory behaviour depending on the parameters associated with BZR1/2 phosphorylation. Comparison between ODE and PDE-ODE models demonstrates that the spatial heterogeneity in the signalling processes has significant effect only in the case when we have periodic solutions for at least one of the models . Our results for the crosstalk model suggest that the interaction between transcription factors  exerts more influence on the dynamics of the signalling pathways , and that perturbations in the GA signalling pathway have larger effects on the dynamics of components of the BR signalling pathway , apart from in the case when the model for the BR signalling pathway has periodic solutions .
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 .
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The BR signalling pathway acts by altering the phosphorylation state of its transcription factors BZR1/2, whereas the GA signalling pathway acts by reducing the stability of its transcription factor DELLA. Both signalling pathways include a negative feedback, with high levels of BR causing increased repression of key BR-biosynthetic genes mediated by BZR1/2, and high levels of GA causing decreased stability of DELLA, where DELLA is responsible for activating key genes involved in GA biosynthesis. We
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models can exhibit oscillatory behaviour depending on the parameters associated with BZR1/2 phosphorylation. Comparison between ODE and PDE-ODE models demonstrates that the spatial heterogeneity in the signalling processes has significant effect only in the case when we have periodic solutions for at least one of the models
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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,
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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