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Plants are sessile organisms and therefore they must adapt their growth and architecture to a changing environment. Understanding how hormones and genes interact to coordinate plant growth in a changing environment is a major challenge in developmental biology. Although a localized auxin concentration maximum in the root tip is important for root development, auxin concentration cannot change independently of multiple interacting hormones and genes. In this review, we discuss the experimental evidence showing that the POLARIS peptide of Arabidopsis plays an important role in hormonal crosstalk and root growth, and review the crosstalk between auxin and other hormones for root growth with and without osmotic stress. Moreover, we discuss that experimental evidence showing that, in root development, hormones and the associated regulatory and target genes form a network, in which relevant genes regulate hormone activities and hormones regulate gene expression. We further discuss how it is increasingly evident that mathematical modeling is a valuable tool for studying hormonal crosstalk. Therefore, a combined experimental and modeling study on hormonal crosstalk is important for elucidating the complexity of root development.

An important question in plant biology is how genes influence the crosstalk between hormones to regulate growth. In this study, we model POLARIS ( PLS ) gene function and crosstalk between auxin, ethylene and cytokinin in Arabidopsis . Experimental evidence suggests that PLS acts on or close to the ethylene receptor ETR1, and a mathematical model describing possible PLS–ethylene pathway interactions is developed, and used to make quantitative predictions about PLS–hormone interactions. Modelling correctly predicts experimental results for the effect of the pls gene mutation on endogenous cytokinin concentration. Modelling also reveals a role for PLS in auxin biosynthesis in addition to a role in auxin transport. The model reproduces available mutants, and with new experimental data provides new insights into how PLS regulates auxin concentration, by controlling the relative contribution of auxin transport and biosynthesis and by integrating auxin, ethylene and cytokinin signalling. Modelling further reveals that a bell‐shaped dose–response relationship between endogenous auxin and root length is established via PLS. This combined modelling and experimental analysis provides new insights into the integration of hormonal signals in plants. Synopsis Hormone signalling systems coordinate plant growth and development through a range of complex interactions. The activities of plant hormones, such as auxin, ethylene and cytokinin, depend on cellular context and exhibit interactions that can be either synergistic or antagonistic. An important question regarding the understanding of those interactions is how genes act on the crosstalk between hormones to regulate plant growth. Previously, we identified the POLARIS ( PLS ) gene of Arabidopsis , which transcribes a short mRNA encoding a 36‐amino acid peptide that is required for correct root growth and vascular development (Casson et al , 2002 ). Experimental evidence shows that there is a link between PLS , ethylene signalling, auxin homeostasis and microtubule cytoskeleton dynamics (Chilley et al , 2006 ). Specifically, mutation of PLS results in an enhanced ethylene‐response phenotype, defective auxin transport and homeostasis, and altered sensitivity to microtubule inhibitors. These defects, along with the short‐root phenotype, are suppressed by genetic and pharmacological inhibition of ethylene action. The expression of PLS is itself repressed by ethylene and induced by auxin. It was also shown that pls mutant roots are hyper‐responsive to exogenous cytokinins and show increased expression of the cytokinin inducible gene ARR5 / IBC6 compared with the wild type (Casson et al , 2002 ). Therefore, PLS may also be required for correct auxin–cytokinin homeostasis to modulate root growth. In this study, we model PLS gene function and crosstalk between auxin, ethylene and cytokinin in Arabidopsis . Experimental evidence suggests that PLS acts on or close to the ethylene receptor ETR1, and a mathematical model describing possible PLS–ethylene pathway interactions is developed, and used to make quantitative predictions about PLS–hormone interactions. Modelling correctly predicts experimental results for the effect of the pls gene mutation on endogenous cytokinin concentration. Modelling also reveals a role for PLS in auxin biosynthesis in addition to a role in auxin transport (Figures 1 and 4 ). The model reproduces available mutants, and with new experimental data provides new insights into how PLS regulates auxin concentration, by controlling the relative contribution of auxin transport and biosynthesis and by integrating auxin, ethylene and cytokinin signalling. Modelling further reveals that a bell‐shaped dose–response relationship between endogenous auxin and root length is established via PLS. In summary, we developed the first hormonal crosstalk model in Arabidopsis and revealed a hormonal crosstalk circuit through PLS and the downstream of ethylene signalling. Our study provides a platform to further integrate hormonal crosstalk in space and time in Arabidopsis . An important question in plant biology is how genes influence the crosstalk between hormones to regulate growth. We have developed the first hormonal crosstalk network in Arabidopsis by iteratively combining modelling with experimental analysis. We have revealed that the POLARIS gene interacts with the ethylene receptor and regulates both auxin transport and biosynthesis. Our modelling analysis has reproduced all known mutants. With new experimental data, it has provided new insights into how the POLARIS gene regulates auxin concentration for root development in Arabidopsis , by controlling the relative contribution of auxin transport and biosynthesis and by integrating auxin, ethylene and cytokinin signalling. Modelling and experimental analysis have revealed that a bell‐shaped dose–response relationship between endogenous auxin and root length is established via POLARIS .