Methods for Modeling Brassinosteroid-Mediated Signaling in Plant Development

Abstract

Mathematical modeling of biological processes is a useful tool to draw conclusions that are contained in the data, but not directly reachable, as well as to make predictions and select the most efficient follow-up experiments. Here we outline a method to model systems of a few proteins that interact transcriptionally and/or posttranscriptionally, by representing the system as Ordinary Differential Equations and to study the model dynamics and stationary states. We exemplify this method by focusing on the regulation by the brassinosteroid (BR) signaling component BRASSINOSTEROID INSENSITIVE1 ETHYL METHYL SULFONATE SUPPRESSOR1 (BES1) of BRAVO, a quiescence-regulating transcription factor expressed in the quiescent cells of Arabidopsis thaliana roots. The method to extract the stationary states and the dynamics is provided as a Mathematica code and requires basic knowledge of the Mathematica software to be executed.

Mathematical modelling and analysis of the brassinosteroid and gibberellin signalling pathways and their interactions

“…This suggests that interactions between BZR and DELLA exert more influence over the dynamics of the pathways than BZR-mediated biosynthesis of GA and are more likely to be able to promote any effective change in the behaviour of the signalling processes. Numerical results also demonstrated that for all parameter sets where solutions tended to a steady state, the solutions of model (10), (12)- (14) and the averaged over space solutions of model (7), (8), (15)- (19) exhibit similar dynamics, although spatially heterogenous steady-states are obtained for BR and GA concentrations, Fig. 18.…”

“…The BR and GA signalling pathways have a diverse range of effects on plant growth and developmental processes, some of which overlap. To examine the behaviours of these signalling pathways and their interactions we developed mathematical models of the BR signalling pathway, and crosstalk between the BR and GA pathways under assumptions of both spatial homogeneity: models (1) and (10), (12)- (14), and spatial heterogeneity of signalling processes: models (7)-(9) and (7), (8), (15)- (19). Tables 1 and 3 and β z = 10 µM −1 min −1 , γ z = 0.133 min −1 .…”

“…For the case 'BR strongly perturbed ' δ z and ρ z have had their orders of magnitude increased by three, θ z = 41.2µM −1 , all other parameters as in Tables 1 and 3 and β z = 10 µM −1 min −1 , γ z = 0.133 min −1 . Figure 18: The spatial distribution of BR and GA in the cell segment Ω c (solutions of (7), (8), (15)- (19)) at different times, parameter values are as in Tables 1 and 3 and β z = 10 µM −1 min −1 , γ z = 0.133 min −1 . The concentration of BR starts of uniform, and is produced at x = 7.43 µm, the nucleus, leading to the greatest concentration at this point.…”

“…Similar to model (7)- (9), to ensure appropriate units we obtain rescaled relations between boundarylocalised variables in model (15)- (19) and the corresponding variables in model (10), (12)…”

“…from Tables 1 and 3 and β z = 10 µM −1 min −1 , γ z = 0.133 min −1 . System (7), (8), (15)- (19) was solved numerically, and these solutions were averaged over the space and then compared to the solutions of system (10), (12)- (14). The behaviour of the two models was similar for most of the parameter sets considered in section 6.2, see e.g.…”