Bayesian uncertainty analysis establishes the link between the parameter space of a complex model of hormonal crosstalk in Arabidopsis root development and experimental measure
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A major challenge in plant developmental biology is to understand how plant growth is coordinated by interacting hormones and genes. To meet this challenge, it is important to formulate a mathematical model. For the mathematical model to best describe the true biological system, it is necessary to understand the parameter space of the model. We develop sequential history matching methodology, using Bayesian emulation, to comprehensively explore the link between subsets of experimental measurements and the model parameter space of a complex hormonal crosstalk model for Arabidopsis root growth. Using 22 trends, the set of acceptable inputs is reduced to 6.1 × 10^-5% of the original space. It is revealed that 5 further trends, for exogenous application of ACC, facilitate an additional reduction of 3 orders of magnitude. Moreover, the final 5 trends, for measurement of the POLARIS gene expression, refocused the set by another 2 orders of magnitude. This indicates that both types of experiments (namely exogenous application of a hormone and measurement of the gene expression) can significantly reduce the set of acceptable parameters. Hence, we provide insight into the constraints placed upon the model structure by, and the biological consequences of, measuring subsets of observations. In particular, we learn about the joint structure of output constraints on the input space. An important example is how different regulatory relationships, such as negative or positive regulation of auxin biosynthesis by cytokinin, affect constraints on the non-implausible parameter space. The link between parameter space and experimental measurements in a complex hormonal crosstalk model for Arabidopsis root growth is established using Bayesian uncertainty analysis. Our approach establishes a novel methodology for understanding the link between experiments, model and parameter space.
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