Mathematical models light up plant signaling

Quantifying Plant Signaling Pathways by Integrating Luminescence-Based Biosensors and Mathematical Modeling

Plants have evolved intricate signaling pathways, which operate as networks governed by feedback to deal with stressors. Nevertheless, the sophisticated molecular mechanisms underlying these routes still need to be comprehended, and experimental validation poses significant challenges and expenses. Consequently, computational hypothesis evaluation gains prominence in understanding plant signaling dynamics. Biosensors are genetically modified to emit light when exposed to a particular hormone, such as abscisic acid (ABA), enabling quantification. We developed computational models to simulate the relationship between ABA concentrations and bioluminescent sensors utilizing the Hill equation and ordinary differential equations (ODEs), aiding better hypothesis development regarding plant signaling. Based on simulation results, the luminescence intensity was recorded for a concentration of 47.646 RLUs for 1.5 μmol, given the specified parameters and model assumptions. This method enhances our understanding of plant signaling pathways at the cellular level, offering significant benefits to the scientific community in a cost-effective manner. The alignment of these computational predictions with experimental results emphasizes the robustness of our approach, providing a cost-effective means to validate mathematical models empirically. The research intended to correlate the bioluminescence of biosensors with plant signaling and its mathematical models for quantified detection of specific plant hormone ABA.

A Compartmental Model for Xylella fastidiosa Diseases with Explicit Vector Seasonal Dynamics

The bacterium Xylella fastidiosa is mainly transmitted by the meadow spittlebug Philaenus spumarius in Europe, where it has caused significant economic damage to olive and almond trees. Understanding the factors that determine disease dynamics in pathosystems that share similarities can help to design control strategies focused on minimizing transmission chains. Here, we introduce a compartmental model for X. fastidiosa-caused diseases in Europe that accounts for the main relevant epidemiological processes, including the seasonal dynamics of P. spumarius. The model was confronted with epidemiological data from the two major outbreaks of X. fastidiosa in Europe, the olive quick disease syndrome in Apulia, Italy, caused by the subspecies pauca, and the almond leaf scorch disease in Mallorca, Spain, caused by subspecies multiplex and fastidiosa. Using a Bayesian inference framework, we show how the model successfully reproduces the general field data in both diseases. In a global sensitivity analysis, the vector-to-plant and plant-to-vector transmission rates, together with the vector removal rate, were the most influential parameters in determining the time of the infectious host population peak, the incidence peak, and the final number of dead hosts. We also used our model to check different vector-based control strategies, showing that a joint strategy focused on increasing the rate of vector removal while lowering the number of annual newborn vectors is optimal for disease control. [Formula: see text] Copyright © 2023 The Author(s). This is an open access article distributed under the CC BY-NC-ND 4.0 International license.

Mathematical Modeling Reveals That Sucrose Regulates Leaf Senescence via Dynamic Sugar Signaling Pathways

Sucrose (Suc) accumulation is one of the key indicators of leaf senescence onset, but little is known about its regulatory role. Here, we found that application of high (120-150 mM) and low levels (60 mM) of Suc to young leaf (YL) and fully expanded leaf (FEL) discs, respectively, decreased chlorophyll content and maximum photosynthetic efficiency. Electrolyte leakage and malondialdehyde levels increased at high Suc concentrations (90-120 mM in YL and 60 and 150 mM in FEL discs). In FEL discs, the senescence-associated gene NtSAG12 showed a gradual increase in expression with increased Suc application; in contrast, in YL discs, NtSAG12 was upregulated with low Suc treatment (60 mM) but downregulated at higher levels of Suc. In YL discs, trehalose-6-phosphate (T6P) accumulated at a low half-maximal effective concentration (EC50) of Suc (1.765 mM). However, T6P levels declined as trehalose 6 phosphate synthase (TPS) content decreased, resulting in the maximum velocity of sucrose non-fermenting-1-related protein kinase (SnRK) and hexokinase (HXK) occurring at higher level of Suc. We therefore speculated that senescence was induced by hexose accumulation. In FEL discs, the EC50 of T6P occurred at a low concentration of Suc (0.9488 mM); T6P levels progressively increased with higher TPS content, which inhibited SnRK activity with a dissociation constant (Kd) of 0.001475 U/g. This confirmed that the T6P-SnRK complex induced senescence in detached FEL discs.

Fifteen compelling open questions in plant cell biology

As scientists, we are at least as excited about the open questions-the things we do not know-as the discoveries. Here, we asked 15 experts to describe the most compelling open questions in plant cell biology. These are their questions: How are organelle identity, domains, and boundaries maintained under the continuous flux of vesicle trafficking and membrane remodeling? Is the plant cortical microtubule cytoskeleton a mechanosensory apparatus? How are the cellular pathways of cell wall synthesis, assembly, modification, and integrity sensing linked in plants? Why do plasmodesmata open and close? Is there retrograde signaling from vacuoles to the nucleus? How do root cells accommodate fungal endosymbionts? What is the role of cell edges in plant morphogenesis? How is the cell division site determined? What are the emergent effects of polyploidy on the biology of the cell, and how are any such "rules" conditioned by cell type? Can mechanical forces trigger new cell fates in plants? How does a single differentiated somatic cell reprogram and gain pluripotency? How does polarity develop de-novo in isolated plant cells? What is the spectrum of cellular functions for membraneless organelles and intrinsically disordered proteins? How do plants deal with internal noise? How does order emerge in cells and propagate to organs and organisms from complex dynamical processes? We hope you find the discussions of these questions thought provoking and inspiring.

Universality in kinetic models of circadian rhythms in [Formula: see text]

Biological evolution has endowed the plant Arabidopsis thaliana with genetically regulated circadian rhythms. A number of authors have published kinetic models for these oscillating chemical reactions based on a network of interacting genes. To investigate the hypothesis that the Arabidopsis circadian dynamical system is poised near a Hopf bifurcation like some other biological oscillators, we varied the kinetic parameters in the models and searched for bifurcations. Finding that each model does exhibit a supercritical Hopf bifurcation, we performed a weakly nonlinear analysis near the bifurcation points to derive the Stuart-Landau amplitude equation. To illustrate a common dynamical structure, we scaled the numerical solutions to the models with the asymptotic solutions to the Stuart-Landau equation to collapse the circadian oscillations onto two universal curves-one for amplitude, and one for frequency. However, some models are close to bifurcation while others are far, some models are post-bifurcation while others are pre-bifurcation, and kinetic parameters that lead to a bifurcation in some models do not lead to a bifurcation in others. Future kinetic modeling can make use of our analysis to ensure models are consistent with each other and with the dynamics of the Arabidopsis circadian rhythm.

Isolation and Functional Characterization of Two SHORT VEGETATIVE PHASE Homologous Genes from Mango

The SHORT VEGETATIVE PHASE (SVP) gene is a transcription factor that integrates flowering signals and plays an important role in the regulation of flowering time in many plants. In this study, two full-length cDNA sequences of SVP homologous genes—MiSVP1 and MiSVP2—were obtained from ‘SiJiMi’ mango. Sequence analysis showed that the MiSVPs had typical MADS-box domains and were highly conserved between each other. The analysis of expression patterns showed that the MiSVPs were expressed during flower development and highly expressed in vegetative tissues, with low expression in flowers/buds. The MiSVPs could responded to low temperature, NaCl, and PEG treatment. Subcellular localization revealed that MiSVP1 and MiSVP2 were localized in the nucleus. Transformation of Arabidopsis revealed that overexpression of MiSVP1 delayed flowering time, overexpression of MiSVP2 accelerated flowering time, and neither MiSVP1 nor MiSVP2 had an effect on the number of rosette leaves. Overexpression of MiSVP1 increased the expression of AtFLC and decreased the expression of AtFT and AtSOC1, and overexpression of MiSVP2 increased the expression levels of AtSOC1 and AtFT and decreased the expression levels of AtFLC. Point-to-point and bimolecular fluorescence complementation (BiFC) assays showed that MiSVP1 and MiSVP2 could interact with SEP1-1, SOC1D, and AP1-2. These results suggest that MiSVP1 and MiSVP2 may play a significant roles in the flowering process of mango.

Novel 3D Imaging Systems for High-Throughput Phenotyping of Plants

The use of 3D plant models for high-throughput phenotyping is increasingly becoming a preferred method for many plant science researchers. Numerous camera-based imaging systems and reconstruction algorithms have been developed for the 3D reconstruction of plants. However, it is still challenging to build an imaging system with high-quality results at a low cost. Useful comparative information for existing imaging systems and their improvements is also limited, making it challenging for researchers to make data-based selections. The objective of this study is to explore the possible solutions to address these issues. We introduce two novel systems for plants of various sizes, as well as a pipeline to generate high-quality 3D point clouds and meshes. The higher accuracy and efficiency of the proposed systems make it a potentially valuable tool for enhancing high-throughput phenotyping by integrating 3D traits for increased resolution and measuring traits that are not amenable to 2D imaging approaches. The study shows that the phenotype traits derived from the 3D models are highly correlated with manually measured phenotypic traits (R2 > 0.91). Moreover, we present a systematic analysis of different settings of the imaging systems and a comparison with the traditional system, which provide recommendations for plant scientists to improve the accuracy of 3D construction. In summary, our proposed imaging systems are suggested for 3D reconstruction of plants. Moreover, the analysis results of the different settings in this paper can be used for designing new customized imaging systems and improving their accuracy.

Multiscale computational models can guide experimentation and targeted measurements for crop improvement

Computational models of plants have identified gaps in our understanding of biological systems, and have revealed ways to optimize cellular processes or organ-level architecture to increase productivity. Thus, computational models are learning tools that help direct experimentation and measurements. Models are simplifications of complex systems, and often simulate specific processes at single scales (e.g. temporal, spatial, organizational, etc.). Consequently, single-scale models are unable to capture the critical cross-scale interactions that result in emergent properties of the system. In this perspective article, we contend that to accurately predict how a plant will respond in an untested environment, it is necessary to integrate mathematical models across biological scales. Computationally mimicking the flow of biological information from the genome to the phenome is an important step in discovering new experimental strategies to improve crops. A key challenge is to connect models across biological, temporal and computational (e.g. CPU versus GPU) scales, and then to visualize and interpret integrated model outputs. We address this challenge by describing the efforts of the international Crops in silico consortium.

Unique and contrasting effects of light and temperature cues on plant transcriptional programs

Plants have adapted to tolerate and survive constantly changing environmental conditions by reprogramming gene expression in response to stress or to drive developmental transitions. Among the many signals that plants perceive, light and temperature are of particular interest due to their intensely fluctuating nature which is combined with a long-term seasonal trend. Whereas specific receptors are key in the light-sensing mechanism, the identity of plant thermosensors for high and low temperatures remains far from fully addressed. This review aims at discussing common as well as divergent characteristics of gene expression regulation in plants, controlled by light and temperature. Light and temperature signaling control the abundance of specific transcription factors, as well as the dynamics of co-transcriptional processes such as RNA polymerase elongation rate and alternative splicing patterns. Additionally, sensing both types of cues modulates gene expression by altering the chromatin landscape and through the induction of long non-coding RNAs (lncRNAs). However, while light sensing is channeled through dedicated receptors, temperature can broadly affect chemical reactions inside plant cells. Thus, direct thermal modifications of the transcriptional machinery add another level of complexity to plant transcriptional regulation. Besides the rapid transcriptome changes that follow perception of environmental signals, plant developmental transitions and acquisition of stress tolerance depend on long-term maintenance of transcriptional states (active or silenced genes). Thus, the rapid transcriptional response to the signal (Phase I) can be distinguished from the long-term memory of the acquired transcriptional state (Phase II - remembering the signal). In this review we discuss recent advances in light and temperature signal perception, integration and memory in Arabidopsis thaliana, focusing on transcriptional regulation and highlighting the contrasting and unique features of each type of cue in the process.

Proteomic analysis of a clavata-like phenotype mutant in Brassica napus

Rapeseed is one of important oil crops in China. Better understanding of the regulation network of main agronomic traits of rapeseed could improve the yielding of rapeseed. In this study, we obtained an influrescence mutant that showed a fusion phenotype, similar with the Arabidopsis clavata-like phenotype, so we named the mutant as Bnclavata-like (Bnclv-like). Phenotype analysis illustrated that abnormal development of the inflorescence meristem (IM) led to the fused-inflorescence phenotype. At the stage of protein abundance, major regulators in metabolic processes, ROS metabolism, and cytoskeleton formation were seen to be altered in this mutant. These results not only revealed the relationship between biological processes and inflorescence meristem development, but also suggest bioengineering strategies for the improved breeding and production of Brassica napus.

Practical steps to digital organism models, from laboratory model species to 'Crops in silico

A recent initiative named 'Crops in silico' proposes that multi-scale models 'have the potential to fill in missing mechanistic details and generate new hypotheses to prioritize directed engineering efforts' in plant science, particularly directed to crop species. To that end, the group called for 'a paradigm shift in plant modelling, from largely isolated efforts to a connected community'. 'Wet' (experimental) research has been especially productive in plant science, since the adoption of Arabidopsis thaliana as a laboratory model species allowed the emergence of an Arabidopsis research community. Parts of this community invested in 'dry' (theoretical) research, under the rubric of Systems Biology. Our past research combined concepts from Systems Biology and crop modelling. Here we outline the approaches that seem most relevant to connected, 'digital organism' initiatives. We illustrate the scale of experimental research required, by collecting the kinetic parameter values that are required for a quantitative, dynamic model of a gene regulatory network. By comparison with the Systems Biology Markup Language (SBML) community, we note computational resources and community structures that will help to realize the potential for plant Systems Biology to connect with a broader crop science community.

A multi-model framework for the Arabidopsis life cycle

Linking our understanding of biological processes at different scales is a major conceptual challenge in biology and aggravated by differences in research methods. Modelling can be a useful approach to consolidating our understanding across traditional research domains. The laboratory model species Arabidopsis is very widely used to study plant growth processes and has also been tested more recently in ecophysiology and population genetics. However, approaches from crop modelling that might link these domains are rarely applied to Arabidopsis. Here, we combine plant growth models with phenology models from ecophysiology, using the agent-based modelling language Chromar. We introduce a simpler Framework Model of vegetative growth for Arabidopsis, FM-lite. By extending this model to include inflorescence and fruit growth and seed dormancy, we present a whole-life-cycle, multi-model FM-life, which allows us to simulate at the population level in various genotype × environment scenarios. Environmental effects on plant growth distinguish between the simulated life history strategies that were compatible with previously described Arabidopsis phenology. Our results simulate reproductive success that is founded on the broad range of physiological processes familiar from crop models and suggest an approach to simulating evolution directly in future.

Plant Virus Epidemiology: Applications and Prospects for Mathematical Modeling and Analysis to Improve Understanding and Disease Control

In recent years, mathematical modeling has increasingly been used to complement experimental and observational studies of biological phenomena across different levels of organization. In this article, we consider the contribution of mathematical models developed using a wide range of techniques and uses to the study of plant virus disease epidemics. Our emphasis is on the extent to which models have contributed to answering biological questions and indeed raised questions related to the epidemiology and ecology of plant viruses and the diseases caused. In some cases, models have led to direct applications in disease control, but arguably their impact is better judged through their influence in guiding research direction and improving understanding across the characteristic spatiotemporal scales of plant virus epidemics. We restrict this article to plant virus diseases for reasons of length and to maintain focus even though we recognize that modeling has played a major and perhaps greater part in the epidemiology of other plant pathogen taxa, including vector-borne bacteria and phytoplasmas.

Mathematical Modeling Approaches in Plant Metabolomics

The experimental analysis of a plant metabolome typically results in a comprehensive and multidimensional data set. To interpret metabolomics data in the context of biochemical regulation and environmental fluctuation, various approaches of mathematical modeling have been developed and have proven useful. In this chapter, a general introduction to mathematical modeling is presented and discussed in context of plant metabolism. A particular focus is laid on the suitability of mathematical approaches to functionally integrate plant metabolomics data in a metabolic network and combine it with other biochemical or physiological parameters.

Process-Based Models of Phenology for Plants and Animals

Phenology is a key aspect of plant and animal life strategies that determines the ability to capture seasonally variable resources. It defines the season and duration of growth and reproduction and paces ecological interactions and ecosystem functions. Phenology models have become a key component of models in agronomy, forestry, ecology, and biogeosciences. Plant and animal process-based phenology models have taken different paths that have so far not crossed. Yet, they share many features because plant and animal annual cycles also share many characteristics, from their stepwise progression, including a resting period, to their dependence on similar environmental factors. We review the strengths and shortcomings of these models and the divergences in modeling approaches for plants and animals, which are mostly due to specificities of the questions they tackle. Finally, we discuss the most promising avenues and the challenges phenology modeling needs to address in the upcoming years.

A quantitative model of the phytochrome-PIF light signalling initiating chloroplast development

The components required for photosynthesis are encoded in two separate genomes, the nuclear and the plastid. To address how synchronization of the two genomes involved can be attained in early light-signalling during chloroplast development we have formulated and experimentally tested a mathematical model simulating light sensing and the following signalling response. The model includes phytochrome B (PhyB), the phytochrome interacting factor 3 (PIF3) and putative regulatory targets of PIF3. Closed expressions of the phyB and PIF3 concentrations after light exposure are derived, which capture the relevant timescales in the response of genes regulated by PIF3. Sequence analysis demonstrated that the promoters of the nuclear genes encoding sigma factors (SIGs) and polymerase-associated proteins (PAPs) required for expression of plastid encoded genes, contain the cis-elements for binding of PIF3. The model suggests a direct link between light inputs via PhyB-PIF3 to the plastid transcription machinery and control over the expression of photosynthesis components both in the nucleus and in the plastids. Using a pluripotent Arabidopsis cell culture in which chloroplasts develop from undifferentiated proplastids following exposure to light, we could experimentally verify that the expression of SIGs and PAPs in response to light follow the calculated expression of a PhyB-PIF3 regulated gene.

Plant Science View on Biohybrid Development

Biohybrid consists of a living organism or cell and at least one engineered component. Designing robot-plant biohybrids is a great challenge: it requires interdisciplinary reconsideration of capabilities intimate specific to the biology of plants. Envisioned advances should improve agricultural/horticultural/social practice and could open new directions in utilization of plants by humans. Proper biohybrid cooperation depends upon effective communication. During evolution, plants developed many ways to communicate with each other, with animals, and with microorganisms. The most notable examples are: the use of phytohormones, rapid long-distance signaling, gravity, and light perception. These processes can now be intentionally re-shaped to establish plant-robot communication. In this article, we focus on plants physiological and molecular processes that could be used in bio-hybrids. We show phototropism and biomechanics as promising ways of effective communication, resulting in an alteration in plant architecture, and discuss the specifics of plants anatomy, physiology and development with regards to the bio-hybrids. Moreover, we discuss ways how robots could influence plants growth and development and present aims, ideas, and realized projects of plant-robot biohybrids.

Reshaping Plant Biology: Qualitative and Quantitative Descriptors for Plant Morphology

An emerging challenge in plant biology is to develop qualitative and quantitative measures to describe the appearance of plants through the integration of mathematics and biology. A major hurdle in developing these metrics is finding common terminology across fields. In this review, we define approaches for analyzing plant geometry, topology, and shape, and provide examples for how these terms have been and can be applied to plants. In leaf morphological quantifications both geometry and shape have been used to gain insight into leaf function and evolution. For the analysis of cell growth and expansion, we highlight the utility of geometric descriptors for understanding sepal and hypocotyl development. For branched structures, we describe how topology has been applied to quantify root system architecture to lend insight into root function. Lastly, we discuss the importance of using morphological descriptors in ecology to assess how communities interact, function, and respond within different environments. This review aims to provide a basic description of the mathematical principles underlying morphological quantifications.

Molecular and genetic control of plant thermomorphogenesis

Temperature is a major factor governing the distribution and seasonal behaviour of plants. Being sessile, plants are highly responsive to small differences in temperature and adjust their growth and development accordingly. The suite of morphological and architectural changes induced by high ambient temperatures, below the heat-stress range, is collectively called thermomorphogenesis. Understanding the molecular genetic circuitries underlying thermomorphogenesis is particularly relevant in the context of climate change, as this knowledge will be key to rational breeding for thermo-tolerant crop varieties. Until recently, the fundamental mechanisms of temperature perception and signalling remained unknown. Our understanding of temperature signalling is now progressing, mainly by exploiting the model plant Arabidopsis thaliana. The transcription factor PHYTOCHROME INTERACTING FACTOR 4 (PIF4) has emerged as a critical player in regulating phytohormone levels and their activity. To control thermomorphogenesis, multiple regulatory circuits are in place to modulate PIF4 levels, activity and downstream mechanisms. Thermomorphogenesis is integrally governed by various light signalling pathways, the circadian clock, epigenetic mechanisms and chromatin-level regulation. In this Review, we summarize recent progress in the field and discuss how the emerging knowledge in Arabidopsis may be transferred to relevant crop systems.

Integrating Hormone- and Micromolecule-Mediated Signaling with Plasmodesmal Communication

Intercellular and supracellular communications through plasmodesmata are involved in vital processes for plant development and physiological responses. Micro- and macromolecules, including hormones, RNA, and proteins, serve as biological information vectors that traffic through the plasmodesmata between cells. Previous studies demonstrated that the plasmodesmata are elaborately regulated, whereby a long queue of multiple signaling molecules forms. However, the mechanism by which these signals are coupled or coordinated in terms of simultaneous transport in a single channel remains a puzzle. In the last few years, several phytohormones that could function as both non-cell-autonomous signals and plasmodesmal regulators have been disclosed. Plasmodesmal regulators such as auxin, salicylic acid, reactive oxygen species, gibberellic acids, chitin, and jasmonic acid could regulate intercellular trafficking by adjusting plasmodesmal permeability. Here, callose, along with β-glucan synthase and β-glucanase, plays a critical role in regulating plasmodesmal permeability. Interestingly, most of the previously identified regulators are capable of diffusing through the plasmodesmata. Given the small sizes of these molecules, the plasmodesmata are prominent intercellular channels that allow diffusion-based movement of those signaling molecules. Obviously, intercellular communication is under the control of a major mechanism, named a feedback loop, at the plasmodesmata, which mediates complicated biological behaviors. Prospective research on the mechanism of coupling micromolecules at the plasmodesmata for developmental signaling and nutrient provision will help us to understand how plants coordinate their development and photosynthetic assimilation, which is important for agriculture.

Illuminating Progress in Phytochrome-Mediated Light Signaling Pathways

Light signals regulate a plethora of plant responses throughout their life cycle, especially the red and far-red regions of the light spectrum perceived by the phytochrome family of photoreceptors. However, the mechanisms by which phytochromes regulate gene expression and downstream responses remain elusive. Several recent studies have unraveled the details on how phytochromes regulate photomorphogenesis. These include the identification of E3 ligases that degrade PHYTOCHROME INTERACTING FACTOR (PIF) proteins, key negative regulators, in response to light, a better view of how phytochromes inhibit another key negative regulator, CONSTITUTIVELY PHOTOMORPHOGENIC 1 (COP1), and an understanding of why plants evolved multiple negative regulators to repress photomorphogenesis in darkness. These advances will surely fuel future research on many unanswered questions that have intrigued plant photobiologists for decades.

SHORT VEGETATIVE PHASE Up-Regulates TEMPRANILLO2 Floral Repressor at Low Ambient Temperatures

Plants integrate day length and ambient temperature to determine the optimal timing for developmental transitions. In Arabidopsis (Arabidopsis thaliana), the floral integrator FLOWERING LOCUS T (FT) and its closest homolog TWIN SISTER OF FT promote flowering in response to their activator CONSTANS under long-day inductive conditions. Low ambient temperature (16°C) delays flowering, even under inductive photoperiods, through repression of FT, revealing the importance of floral repressors acting at low temperatures. Previously, we have reported that the floral repressors TEMPRANILLO (TEM; TEM1 and TEM2) control flowering time through direct regulation of FT at 22°C. Here, we show that tem mutants are less sensitive than the wild type to changes in ambient growth temperature, indicating that TEM genes may play a role in floral repression at 16°C. Moreover, we have found that TEM2 directly represses the expression of FT and TWIN SISTER OF FT at 16°C. In addition, the floral repressor SHORT VEGETATIVE PHASE (SVP) directly regulates TEM2 but not TEM1 expression at 16°C. Flowering time analyses of svp tem mutants indicate that TEM may act in the same genetic pathway as SVP to repress flowering at 22°C but that SVP and TEM are partially independent at 16°C. Thus, TEM2 partially mediates the temperature-dependent function of SVP at low temperatures. Taken together, our results indicate that TEM genes are also able to repress flowering at low ambient temperatures under inductive long-day conditions.

Towards recommendations for metadata and data handling in plant phenotyping

Recent methodological developments in plant phenotyping, as well as the growing importance of its applications in plant science and breeding, are resulting in a fast accumulation of multidimensional data. There is great potential for expediting both discovery and application if these data are made publicly available for analysis. However, collection and storage of phenotypic observations is not yet sufficiently governed by standards that would ensure interoperability among data providers and precisely link specific phenotypes and associated genomic sequence information. This lack of standards is mainly a result of a large variability of phenotyping protocols, the multitude of phenotypic traits that are measured, and the dependence of these traits on the environment. This paper discusses the current situation of standardization in the area of phenomics, points out the problems and shortages, and presents the areas that would benefit from improvement in this field. In addition, the foundations of the work that could revise the situation are proposed, and practical solutions developed by the authors are introduced.

A quantitative and dynamic model of the Arabidopsis flowering time gene regulatory network

Various environmental signals integrate into a network of floral regulatory genes leading to the final decision on when to flower. Although a wealth of qualitative knowledge is available on how flowering time genes regulate each other, only a few studies incorporated this knowledge into predictive models. Such models are invaluable as they enable to investigate how various types of inputs are combined to give a quantitative readout. To investigate the effect of gene expression disturbances on flowering time, we developed a dynamic model for the regulation of flowering time in Arabidopsis thaliana. Model parameters were estimated based on expression time-courses for relevant genes, and a consistent set of flowering times for plants of various genetic backgrounds. Validation was performed by predicting changes in expression level in mutant backgrounds and comparing these predictions with independent expression data, and by comparison of predicted and experimental flowering times for several double mutants. Remarkably, the model predicts that a disturbance in a particular gene has not necessarily the largest impact on directly connected genes. For example, the model predicts that SUPPRESSOR OF OVEREXPRESSION OF CONSTANS (SOC1) mutation has a larger impact on APETALA1 (AP1), which is not directly regulated by SOC1, compared to its effect on LEAFY (LFY) which is under direct control of SOC1. This was confirmed by expression data. Another model prediction involves the importance of cooperativity in the regulation of APETALA1 (AP1) by LFY, a prediction supported by experimental evidence. Concluding, our model for flowering time gene regulation enables to address how different quantitative inputs are combined into one quantitative output, flowering time.

Molecular systems governing leaf growth: from genes to networks

Arabidopsis leaf growth consists of a complex sequence of interconnected events involving cell division and cell expansion, and requiring multiple levels of genetic regulation. With classical genetics, numerous leaf growth regulators have been identified, but the picture is far from complete. With the recent advances made in quantitative phenotyping, the study of the quantitative, dynamic, and multifactorial features of leaf growth is now facilitated. The use of high-throughput phenotyping technologies to study large numbers of natural accessions or mutants, or to screen for the effects of large sets of chemicals will allow for further identification of the additional players that constitute the leaf growth regulatory networks. Only a tight co-ordination between these numerous molecular players can support the formation of a functional organ. The connections between the components of the network and their dynamics can be further disentangled through gene-stacking approaches and ultimately through mathematical modelling. In this review, we describe these different approaches that should help to obtain a holistic image of the molecular regulation of organ growth which is of high interest in view of the increasing needs for plant-derived products.

Quantitative analysis of receptor tyrosine kinase-effector coupling at functionally relevant stimulus levels

A major goal of current signaling research is to develop a quantitative understanding of how receptor activation is coupled to downstream signaling events and to functional cellular responses. Here, we measure how activation of the RET receptor tyrosine kinase on mouse neuroblastoma cells by the neurotrophin artemin (ART) is quantitatively coupled to key downstream effectors. We show that the efficiency of RET coupling to ERK and Akt depends strongly on ART concentration, and it is highest at the low (∼100 pM) ART levels required for neurite outgrowth. Quantitative discrimination between ERK and Akt pathway signaling similarly is highest at this low ART concentration. Stimulation of the cells with 100 pM ART activated RET at the rate of ∼10 molecules/cell/min, leading at 5-10 min to a transient peak of ∼150 phospho-ERK (pERK) molecules and ∼50 pAkt molecules per pRET, after which time the levels of these two signaling effectors fell by 25-50% while the pRET levels continued to slowly rise. Kinetic experiments showed that signaling effectors in different pathways respond to RET activation with different lag times, such that the balance of signal flux among the different pathways evolves over time. Our results illustrate that measurements using high, super-physiological growth factor levels can be misleading about quantitative features of receptor signaling. We propose a quantitative model describing how receptor-effector coupling efficiency links signal amplification to signal sensitization between receptor and effector, thereby providing insight into design principles underlying how receptors and their associated signaling machinery decode an extracellular signal to trigger a functional cellular outcome.

Multiple pathways regulate shoot branching

Shoot branching patterns result from the spatio-temporal regulation of axillary bud outgrowth. Numerous endogenous, developmental and environmental factors are integrated at the bud and plant levels to determine numbers of growing shoots. Multiple pathways that converge to common integrators are most probably involved. We propose several pathways involving not only the classical hormones auxin, cytokinins and strigolactones, but also other signals with a strong influence on shoot branching such as gibberellins, sugars or molecular actors of plant phase transition. We also deal with recent findings about the molecular mechanisms and the pathway involved in the response to shade as an example of an environmental signal controlling branching. We propose the TEOSINTE BRANCHED1, CYCLOIDEA, PCF transcription factor TB1/BRC1 and the polar auxin transport stream in the stem as possible integrators of these pathways. We finally discuss how modeling can help to represent this highly dynamic system by articulating knowledges and hypothesis and calculating the phenotype properties they imply.