The genetic and molecular analysis of trichome development in Arabidopsis thaliana has generated a detailed knowledge about the underlying regulatory genes and networks. However, how rapidly these mechanisms diverge during evolution is unknown. To address this problem, we used an unbiased forward genetic approach to identify most genes involved in trichome development in the related crucifer species Arabis alpina. In general, we found most trichome mutant classes known in A. thaliana. We identified orthologous genes of the relevant A. thaliana genes by sequence similarity and synteny and sequenced candidate genes in the A. alpina mutants. While in most cases we found a highly similar genephenotype relationship as known from Arabidopsis, there were also striking differences in the regulation of trichome patterning, differentiation, and morphogenesis. Our analysis of trichome patterning suggests that the formation of two classes of trichomes is regulated differentially by the homeodomain transcription factor AaGL2. Moreover, we show that overexpression of the GL3 basic helix-loop-helix transcription factor in A. alpina leads to the opposite phenotype as described in A. thaliana. Mathematical modeling helps to explain how this nonintuitive behavior can be explained by different ratios of GL3 and GL1 in the two species.Arabis alpina | trichomes | genetic analysis

Highlights d Complex changes in trichome patterning are explained by reduced TTG1 GL3 interaction d Mathematical modeling and data constrainment reveal the network structure d Trichome patterning requires an activator-inhibitor and an activator-diffusion mechanism d Trichome patterning requires two pathways activating longand short-range inhibitors

Trichomes are regularly distributed on the leaves of Arabidopsis thaliana. The gene regulatory network underlying trichome patterning involves more than 15 genes. However, it is possible to explain patterning with only five components. This raises the questions about the function of the additional components and the identification of the core network. In this study, we compare the relative expression of all patterning genes in A. thaliana, A. alpina and C. hirsuta by qPCR analysis and use mathematical modelling to determine the relative importance of patterning genes. As the involved proteins exhibit evolutionary conserved differential complex formation, we reasoned that the genes belonging to the core network should exhibit similar expression ratios in different species. However, we find several striking differences of the relative expression levels. Our analysis of how the network can cope with such differences revealed relevant parameters that we use to predict the relevant molecular adaptations in the three species.

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Uncertainty is ubiquitous in biological systems. These uncertainties can be the result of lack of knowledge or due to a lack of appropriate data. Additionally, the natural variability of biological systems caused by intrinsic noise, e.g. in stochastic gene expression, leads to uncertainties. With the help of numerical simulations the impact of these uncertainties on the model predictions can be assessed, i.e. the impact of the propagation of uncertainty in model parameters on the model response can be quantified. Taking this into account is crucial when the models are used for experimental design, optimization, or decision-making, as model uncertainty can have a significant effect on the accuracy of model predictions. We focus here on spectral methods to quantify prediction uncertainty based on a probabilistic framework. Such methods have a basis in, e.g., computational mathematics, engineering, physics, and fluid dynamics, and, to a lesser extent, systems biology. In this chapter, we highlight the advantages these methods can have for modelling purposes in systems biology and do so by providing a novel and intuitive scheme. By applying the scheme to an array of examples we show its power, especially in challenging situations where slow converge due to high-dimensionality, bifurcations, and spatial discontinuities play a role.