Mathematical modelling of the floral transition

The floral transition is a developmental process through which some plants commit to flowering and stop producing leaves. This is controlled by changes in gene expression in the shoot apical meristem (SAM). Many of the genes involved are known, but their interactions are usually only studied one by one, or in small sets. While it might be necessary to properly ascertain the existence of regulatory interactions from a biological standpoint, it cannot really provide insight in the functioning of the floral-transition process as a whole. For this reason, a modelling approach has been used to integrate knowledge from multiple studies. Several approaches were applied, starting with ordinary differential equation (ODE) models. It revealed in two cases – one on rice and one on Arabidopsis thaliana – that the currently available data were not sufficient to build data-driven ODE models. The main issues were the low temporal resolution of the time series, the low spatial resolution of the sampling methods used on meristematic tissue, and the lack of gene expression measurements in studies of factors affecting the floral transition. These issues made the available gene expression time series of little use to infer the regulatory mechanisms involved. Therefore, another approach based on qualitative data was investigated. It relies on data extracted from published in situ hybridization (ISH) studies, and Boolean modelling. The ISH data clearly showed that shoot apical meristems (SAM) are not homogeneous and contain multiple spatial domains corresponding to coexisting steady-states of the same regulatory network. Using genetic programming, Boolean models with the right steady-states were successfully generated. Finally, the third modelling approach builds upon one of the generated Boolean models and implements its logic into a 3D tissue of SAM. As Boolean models cannot represent quantitative spatio-temporal phenomena such as passive transport, the model had to be translated into ODEs. This model successfully reproduced the patterning of SAM genes in a static tissue structure. The main biological conclusions of this thesis are that the spatial organization of gene expression in the SAM is a crucial part of the floral transition and of the development of inflorescences, and it is mediated by the transport of mobile proteins and hormones. On the modelling front, this work shows that quantitative ODE models, despite their popularity, cannot be applied to all situations. When the data are insufficient, simpler approaches like Boolean models and ODE models with qualitatively selected parameters can provide suitable alternatives and facilitate large-scale explorations of the space of possible models, due to their low computational cost