Modelling hormonal response and development

Abstract

As our knowledge of the complexity of hormone homeostasis, transport, perception, and response increases, and their outputs become less intuitive, modelling is set to become more important. Initial modelling efforts have focused on hormone transport and response pathways. However, we now need to move beyond the network scales and use multicellular and multiscale modelling approaches to predict emergent properties at different scales. Here we review some examples where such approaches have been successful, for example, auxin-cytokinin crosstalk regulating root vascular development or a study of lateral root emergence where an iterative cycle of modelling and experiments lead to the identification of an overlooked role for PIN3. Finally, we discuss some of the remaining biological and technical challenges.

Keywords: hormone signalling; modelling; multiscale modelling; systems biology.

Figure 1

Models of auxin transport in the shoot apex. (A) At the cell level, auxin is actively transported by PIN (efflux) and AUX (influx) proteins, in addition to the natural influx of protonated auxin. Abbreviation: IAAH, indole-3-acetamide hydrolase. The polar localisation of PIN on the membranes is believed to be auxin-dependent, but the exact mechanism is unknown, as indicated by the question mark. Black arrows represent chemical reactions (thickness indicates relative rates). Coloured arrows represent transport of the substance bearing the same colour. (B) Experimental data, which often consists of microscope images of fluorescent reporters for auxin response and/or antibody-based localisation of PIN subcellular distribution (in red), are incorporated into multicellular computational models (C) to make predictions about auxin distribution patterns (denoted in green). In (C) left, white arrows represent PIN polarity, green circles are auxin sources, and blue triangles auxin sinks. In (C) right, white dots mark cells from the central zone. (B) and (C) are reproduced, with permission, from , indicated by (*) and , indicated by (**).

Figure 2

Models of the abscisic acid (ABA) and the gibberellin (GA) hormone signalling network. (A) Model of ABA receptor activation showing the formation of receptor–ABA–PP2C (R–A–P) ternary complexes for the monomeric and the dimeric PYR/PYL/RCAR proteins considered in the modelling study . The dissociation constants (K_d) for the reactions were measured experimentally and used to parameterise the model. Adapted from . (B) The three functional modules of the GA signalling network (perception, response, and biosynthesis) are shown. Perception (yellow box): GA4 first binds to the GID receptor and the complex then interacts with DELLA proteins, leading to the ubiquitination (denoted with a green chain) and degradation of DELLA proteins. Response (green box): GID1, GA20OX, and GA3OX genes are transcriptionally activated by DELLA proteins but repress their own transcription. Biosynthesis (blue box): GA12 is converted to GA15 then to GA24, and finally to GA9 by the GA20ox enzyme. GA9 is then converted to GA4 by the GA3ox enzyme. Hence, DELLA-mediated upregulation of GA biosynthesis transiently elevates the levels of the hormone and the GID1 receptor, leading to DELLA degradation, thus creating a negative feedback loop. Reproduced, with permission, from .

Figure 3

Multiscale models of hormone-regulated root development. (A) Initial models predicted that the current interactions between the known components regulating root vascular patterns were insufficient to correctly predict the expression of AHP6 and other key components in a multiscale model (i) with PIN proteins localised as they have been experimentally observed (ii). However, when an additional inhibitor of cytokinin and the catalytic degradation of microRNA were incorporated into this model, it was able to predict AHP6 response patterns closely resembling those observed experimentally (iii). (B) LAX3 expression is restricted to two cells overlying the LRP (ii). Initial attempts to model this, using three-dimensional cell and tissue geometries, were unable to robustly restrict LAX3 expression to two cells (i). However, by including an auxin efflux carrier into the model (subsequently identified as PIN3) and controlling the order of activation, the model was able to restrict LAX3 activity to just two cortical cells (iii). In both sets of images, the expression of AHP6 or LAX3 is shown as a heat map, with red representing the highest expression. Images reproduced, with permission, from and .