Multiscale Modelling to Unravel the Interplay between Morphogen Gradients and Zonation in the Root Meristem of A.thaliana

An intriguing challenge in developmental biology is to understand how organ development is spatially coordinated to form well-structured, patterned complex organisms in a reproducible way. In multicellular organisms, pattern formation is related to the graded distribution and activity of signalling molecules called morphogens: dividing cells exposed to particular concentration thresholds of a morphogen follow a developmental path of cell differentiation, which results in spatio-temporal patterns. Formation, positioning and maintenance of the boundaries between these cell compartments are essential for the correct outcome of the patterning events. The development of animals and plants is based on a similar logic. Both in animal and plant development, a gradient of cell differentiation arises from stem cell niches, where local signals from an organizer coordinate the balance between self-renewal and the generation of daughter cells that differentiate into new tissues. However, in animals, at the completion of development, self-renewal and differentiation is strictly localized to very few stem cells. In contrast, plant post-embryonic development is maintained throughout the plant lifespan by the activity of root meristems, where stem cells are localized and the transition from cell division to cell differentiation is orchestrated to generate distinct developmental zones. In the model plant Arabidopsis thaliana, advanced molecular, genetic and genomic tools are available and root development is arguably the most tractable system. A key role for plant hormones in Arabidopsis root development is well established. Specifically, the phytohormone auxin acts as a morphogen, as its asymmetric distribution within tissues sets positional information that guides cell-type specification, thus patterning and growth. Auxin peculiar carrier-mediated polar transport gives rise to a concentration gradient along the root longitudinal axis, which shapes developmental zones: stem cell niche, division zone and differentiation zone. The formation of an auxin maximum in the stem cell niche is essential to maintain stem cell function. At the boundary between the zones (transition boundary) auxin divisional activity is counteracted by the phytohormone cytokinin, and their dynamic crosstalk is necessary to balance cell division over cell differentiation, in order to set a stable meristem size. Molecular genetic approaches have identified many of the key signals components underlying auxin and cytokinin interaction in the Arabidopsis root, providing qualitative but not quantitative insights into the activity of cytokinin on auxin distribution. Moreover, there are no tools available to make auxin gradients directly visible in living tissues. In order to explain the observed cell-type specific auxin distribution and how cytokinin shapes auxin gradients, I thus adopted a systems biology approach, integrating experimental evidence with mathematical and computational modelling. This approach enables a simplified and formal description of the biological mechanisms at different scales (molecular, subcellular, cellular and supracellular) and allows for theoretical assumptions that could guide future experiments, whose results can feedback into the model. In recent years, several modeling approaches have provided a good qualitative description of auxin transport, but the link between physico-chemical and biological descriptors is still missing and none of the proposed mechanisms unveils the developmental cues that drive the emergence of meristem zonation at the cellular level. During my PhD project, I dissected the problem both by theoretical and computational tools. Mathematical modelling is essential to define explicitly the relationship between physical entities attempting to find an analytical solution to the problem. On the other hand, computational modelling is advantageous in that it provides numerical solution to complex problems through the implementation of powerful algorithms. Therefore, I first developed a one-dimensional analytical and theoretical description based on physico-chemical laws, in order to provide a straightforward condition for auxin maximum formation and a framework for a quantitative assessment. Within this framework, I linked microscopic (cell-based) description to macroscopic (organ-scale) dynamics through a derived auxin diffusivity parameter and through reaction terms. The derivation of a cell-specific equivalent diffusivity allows for a direct link both between parameters and between discrete and continuous formalisms: in the limit of a continuous description, I was able to derive a linear diffusion equation, where all transport components are embedded within the equivalent diffusivity parameter. I was eventually able to estimate an average value for the equivalent diffusion coefficient. Extending the analysis to the organ scale I provided further conditions for the “reflux fountain” of auxin in the meristem. As an ultimate goal, I envision that this formalism could be used as a tool for the estimation of parameters given sensor-derived auxin maps. Moving forward, to investigate the cell-specific interplay between auxin and cytokinin and its effect on meristem size, I developed a two-dimensional computational model combined with a genetic approach. I integrated experimentally derived parameters into a spatial model at cellular resolution that simulates auxin transport within a layout resembling root geometries, tissues and zones. This two-dimensional model provides a mechanistic understanding on how the shape of the auxin graded distribution in the root depends on the hormone cytokinin, which controls both auxin transport and local auxin degradation. The model predicts, as an emerging property, that the dual input of cytokinin results in an auxin minimum at the transition zone. This auxin minimum acts as a positional signal to trigger the transition between dividing and differentiating cells, thereby setting a boundary to control meristem size and root growth.