Etienne Farcot

The auxin signalling network translates dynamic input into robust patterning at the shoot apex

The plant hormone auxin is thought to provide positional information for patterning during development. It is still unclear, however, precisely how auxin is distributed across tissues and how the hormone is sensed in space and time. The control of gene expression in response to auxin involves a complex network of over 50 potentially interacting transcriptional activators and repressors, the auxin response factors (ARFs) and Aux/IAAs. Here, we perform a large‐scale analysis of the Aux/IAA‐ARF pathway in the shoot apex of Arabidopsis, where dynamic auxin‐based patterning controls organogenesis. A comprehensive expression map and full interactome uncovered an unexpectedly simple distribution and structure of this pathway in the shoot apex. A mathematical model of the Aux/IAA‐ARF network predicted a strong buffering capacity along with spatial differences in auxin sensitivity. We then tested and confirmed these predictions using a novel auxin signalling sensor that reports input into the signalling pathway, in conjunction with the published DR5 transcriptional output reporter. Our results provide evidence that the auxin signalling network is essential to create robust patterns at the shoot apex.

Cytokinin signalling inhibitory fields provide robustness to phyllotaxis

How biological systems generate reproducible patterns with high precision is a central question in science. The shoot apical meristem (SAM), a specialized tissue producing plant aerial organs, is a developmental system of choice to address this question. Organs are periodically initiated at the SAM at specific spatial positions and this spatiotemporal pattern defines phyllotaxis. Accumulation of the plant hormone auxin triggers organ initiation, whereas auxin depletion around organs generates inhibitory fields that are thought to be sufficient to maintain these patterns and their dynamics. Here we show that another type of hormone-based inhibitory fields, generated directly downstream of auxin by intercellular movement of the cytokinin signalling inhibitor ARABIDOPSIS HISTIDINE PHOSPHOTRANSFER PROTEIN 6 (AHP6), is involved in regulating phyllotactic patterns. We demonstrate that AHP6-based fields establish patterns of cytokinin signalling in the meristem that contribute to the robustness of phyllotaxis by imposing a temporal sequence on organ initiation. Our findings indicate that not one but two distinct hormone-based fields may be required for achieving temporal precision during formation of reiterative structures at the SAM, thus indicating an original mechanism for providing robustness to a dynamic developmental system.

Inference of the Arabidopsis Lateral Root Gene Regulatory Network Suggests a Bifurcation Mechanism That Defines Primordia Flanking and Central Zones

A new correlation algorithm infers the Arabidopsis lateral root gene regulatory network from time-course transcriptomic data and provides mechanistic insight into primordia patterning. A large number of genes involved in lateral root (LR) organogenesis have been identified over the last decade using forward and reverse genetic approaches in Arabidopsis thaliana. Nevertheless, how these genes interact to form a LR regulatory network largely remains to be elucidated. In this study, we developed a time-delay correlation algorithm (TDCor) to infer the gene regulatory network (GRN) controlling LR primordium initiation and patterning in Arabidopsis from a time-series transcriptomic data set. The predicted network topology links the very early-activated genes involved in LR initiation to later expressed cell identity markers through a multistep genetic cascade exhibiting both positive and negative feedback loops. The predictions were tested for the key transcriptional regulator AUXIN RESPONSE FACTOR7 node, and over 70% of its targets were validated experimentally. Intriguingly, the predicted GRN revealed a mutual inhibition between the ARF7 and ARF5 modules that would control an early bifurcation between two cell fates. Analyses of the expression pattern of ARF7 and ARF5 targets suggest that this patterning mechanism controls flanking and central zone specification in Arabidopsis LR primordia.

Epidermal identity is maintained by cell–cell communication via a universally active feedback loop in Arabidopsis thaliana

The transcription factors ARABIDOPSIS THALIANA MERISTEM L1 (ATML1) and PROTODERMAL FACTOR2 (PDF2) are indispensable for epidermal cell-fate specification in Arabidopsis embryos. However, the mechanisms of regulation of these genes, particularly their relationship with cell-cell signalling pathways, although the subject of considerable speculation, remain unclear. Here we demonstrate that the receptor kinase ARABIDOPSIS CRINKLY4 (ACR4) positively affects the expression of ATML1 and PDF2 in seedlings. In contrast, ATML1- and PDF2-containing complexes directly and negatively affect both their own expression and that of ACR4. By modelling the resulting feedback loop, we demonstrate a network structure that is capable of maintaining robust epidermal cell identity post-germination. We show that a second seed-specific signalling pathway involving the subtilase ABNORMAL LEAFSHAPE1 (ALE1) and the receptor kinases GASSHO1 (GSO1) and GASSHO2 (GSO2) acts in parallel to the epidermal loop to control embryonic surface formation via an ATML1/PDF2-independent pathway. Genetic interactions between components of this linear pathway and the epidermal loop suggest that an intact embryo surface is necessary for initiation and/or stabilization of the epidermal loop, specifically during early embryogenesis.

Modelling hormonal response and development

Highlights • Modelling has helped to understand the complex network structure of single hormonal pathways, but has also provided insights into hormone activity at many levels.• We describe how multiple hormones have been incorporated into new models.• We explore future challenges in integrating different models.• We propose that future models need to be more realistic by capturing more geometrical, mechanical as well as biological data.

A Data-Driven Integrative Model of Sepal Primordium Polarity in Arabidopsis

This study presents a new modeling approach allowing diverse types of data to be integrated in a coherent molecular regulatory network model. This was used to analyze sepal primordium development and revealed three previously unreported pathways potentially involved in polarity. Flower patterning is determined by a complex molecular network but how this network functions remains to be elucidated. Here, we develop an integrative modeling approach that assembles heterogeneous data into a biologically coherent model to allow predictions to be made and inconsistencies among the data to be found. We use this approach to study the network underlying sepal development in the young flower of Arabidopsis thaliana. We constructed a digital atlas of gene expression and used it to build a dynamical molecular regulatory network model of sepal primordium development. This led to the construction of a coherent molecular network model for lateral organ polarity that fully recapitulates expression and interaction data. Our model predicts the existence of three novel pathways involving the HD-ZIP III genes and both cytokinin and ARGONAUTE family members. In addition, our model provides predictions on molecular interactions. In a broader context, this approach allows the extraction of biological knowledge from diverse types of data and can be used to study developmental processes in any multicellular organism.

Modeling Regulatory Networks to Understand Plant Development: Small Is Beautiful

We now have unprecedented capability to generate large data sets on the myriad genes and molecular players that regulate plant development. Networks of interactions between systems components can be derived from that data in various ways and can be used to develop mathematical models of various degrees of sophistication. Here, we discuss why, in many cases, it is productive to focus on small networks. We provide a brief and accessible introduction to relevant mathematical and computational approaches to model regulatory networks and discuss examples of small network models that have helped generate new insights into plant biology (where small is beautiful), such as in circadian rhythms, hormone signaling, and tissue patterning. We conclude by outlining some of the key technical and modeling challenges for the future.

A modular analysis of the auxin signalling network.

Auxin is essential for plant development from embryogenesis onwards. Auxin acts in large part through regulation of transcription. The proteins acting in the signalling pathway regulating transcription downstream of auxin have been identified as well as the interactions between these proteins, thus identifying the topology of this network implicating 54 Auxin Response Factor (ARF) and Aux/IAA (IAA) transcriptional regulators. Here, we study the auxin signalling pathway by means of mathematical modeling at the single cell level. We proceed analytically, by considering the role played by five functional modules into which the auxin pathway can be decomposed: the sequestration of ARF by IAA, the transcriptional repression by IAA, the dimer formation amongst ARFs and IAAs, the feedback loop on IAA and the auxin induced degradation of IAA proteins. Focusing on these modules allows assessing their function within the dynamics of auxin signalling. One key outcome of this analysis is that there are both specific and overlapping functions between all the major modules of the signaling pathway. This suggests a combinatorial function of the modules in optimizing the speed and amplitude of auxin-induced transcription. Our work allows identifying potential functions for homo- and hetero-dimerization of transcriptional regulators, with ARF:IAA, IAA:IAA and ARF:ARF dimerization respectively controlling the amplitude, speed and sensitivity of the response and a synergistic effect of the interaction of IAA with transcriptional repressors on these characteristics of the signaling pathway. Finally, we also suggest experiments which might allow disentangling the structure of the auxin signaling pathway and analysing further its function in plants.

Brief paper: A mathematical framework for the control of piecewise-affine models of gene networks

This article introduces results on the control of gene networks, in the context of piecewise-affine models. We propose an extension of this well-documented class of models, where some input variables can affect the main terms of the equations, with a special focus on the case of affine dependence on inputs. Some generic control problems are proposed, which are qualitative, respecting the coarse-grained nature of piecewise-affine models. Piecewise constant feedback laws that solve these control problems are characterized in terms of affine inequalities, and can even be computed explicitly for a subclass of inputs. The latter is characterized by the condition that each state variable of the system is affected by at most one input variable. These general feedback laws are then applied to a two-dimensional example, consisting in two genes inhibiting each other. This example has been observed in real biological systems, and is known to present a bistable switch for some parameter values. Here, the parameters can be controlled, allowing to express feedback laws leading to various behaviours of this system, including bi-stability as well as situations involving a unique global equilibrium.

Limit cycles in piecewise-affine gene network models with multiple interaction loops

In this article, we consider piecewise affine differential equations modelling gene networks. We work with arbitrary decay rates, and under a local hypothesis expressed as an alignment condition of successive focal points. The interaction graph of the system may be rather complex (multiple intricate loops of any sign, multiple thresholds, etc.). Our main result is an alternative theorem showing that if a sequence of region is periodically visited by trajectories, then under our hypotheses, there exists either a unique stable periodic solution, or the origin attracts all trajectories in this sequence of regions. This result extends greatly our previous work on a single negative feedback loop. We give several examples and simulations illustrating different cases.