Quantitative Plant Biology

Intercellular communication is essential for plant development and responses to biotic and abiotic stress. A key pathway is diffusive exchange of signal molecules and nutrients via plasmodesmata. These cell wall channels connect the cytoplasms of most cells in land plants. Their small size, with a typical diameter of about 50 nm, and complex structure have hindered the quantification plasmodesmata-mediated intercellular diffusion. This measure is essential for disentangling the contributions of diffusive and membrane transporter-mediated movement of molecules that, together, define cell interactions within and across tissues. We compared the two most promising methods to measure plasmodesmata-mediated interface permeability, live-cell microscopy with fluorescent tracer molecules and transmission electron microscopy-based mathematical modeling, to evaluate the potential for obtaining absolute quantitative values. We applied both methods to 29 cell-cell interfaces from nine angiosperm species and found a stronger association between the modelled and experimentally determined interface permeabilities than between the experimentally-determined permeability and any single structural parameter. By feeding the values into a simulation of an artificial Arabidopsis leaf, we illustrate how interface permeabilities can help to predict diffusion patterns of defense-related molecules, such as glucosinolates and transcription factors.

RationaleAnalyses of leaf gas exchange rely on an Ohmic analogy that arrays single stomatal, internal air space, and mesophyll conductances in series. Such models underlie inferences of mesophyll conductance and the relative humidity of leaf airspaces, reported to fall as low as 80%. An unresolved question is whether such Ohmic models are biased with respect to real leaves, whose internal air spaces are chambered at various scales by vasculature. DescriptionTo test whether undersaturation could emerge from modeling artifacts, we compared Ohmic model estimates with true parameter values for a chambered leaf with varying distributions and magnitudes of leaf surface conductance ("patchiness"). Key ResultsDistributions of surface conductance can create large biases in gas exchange calculations. Both apparent unsaturation and internal CO2 gradient inversion can be produced by the evolution of particular distributions of stomatal apertures consistent with a decrease in surface conductance, as might occur under increasing vapor pressure deficit. Main conclusionIn gas exchange experiments, the behaviors of derived quantities defined by simple Ohmic models are highly sensitive to the true partitioning of flux and stomatal apertures across leaf surfaces. We need new methods to disentangle model artifacts from real biological responses.

O_LIEthylene biosynthesis and signaling are pivotal pathways in various plant aging processes, including fruit ripening. Kinetic models can be used to better understand metabolic pathways, but modeling of the ethylene-related pathways is limited and the link between these pathways remains unsolved. C_LIO_LIA transcriptomics-based kinetic model was developed, consisting of ordinary differential equations describing ethylene biosynthesis and signaling pathways in tomato during fruit development, ripening and post-harvest storage. C_LIO_LIThis model was calibrated against a large volume of transcriptomic, proteomic and metabolic data during on-vine ripening of tomato fruit grown in winter and summer. The model was validated using data on off-vine postharvest ripening. The ethylene biosynthesis pathway under different conditions appeared to be largely driven by gene expression levels. C_LIO_LIThe ethylene-regulation of fruit ripening of a heat tolerant tomato grown in different seasons is identical but with quantitative differences at the targeted omics levels. This is reflected by some of the same parameters with distinct values for summer and winter fruit. The current model is the first attempt to model the ethylene signaling pathway starting from gene expression, the various protein - protein interactions, including the link with ethylene production, internal ethylene levels and its receptors. C_LI

Stomatal pores control both leaf gas exchange and are one route for infection of internal plant tissues by many foliar pathogens, setting up the potential for tradeoffs between photosynthesis and defense. Anatomical shifts to lower stomatal density and/or size may also limit pathogen colonization, but such developmental changes could permanently reduce the gas exchange capacity for the life of the leaf. I developed and analyzed a spatially explicit model of pathogen colonization on the leaf as a function of stomatal size and density, anatomical traits which partially determine maximum rates of gas exchange. The model predicts greater stomatal size or density increases the probability of colonization, but the effect is most pronounced when the fraction of leaf surface covered by stomata is low. I also derived scaling relationships between stomatal size and density that preserves a given probability of colonization. These scaling relationships set up a potential anatomical conflict between limiting pathogen colonization and minimizing the fraction of leaf surface covered by stomata. Although a connection between gas exchange and pathogen defense has been suggested empirically, this is the first mathematical model connecting gas exchange and pathogen defense via stomatal anatomy. A limitation of the model is that it does not include variation in innate immunity and stomatal closure in response to pathogens. Nevertheless, the model makes predictions that can be tested with experiments and may explain variation in stomatal anatomy among plants. The model is generalizable to many types of pathogens, but lacks significant biological realism that may be needed for precise predictions.

O_LIInternal water storage is of crucial importance for plants under drought stress, allowing them to temporarily maintain transpiration higher than root-uptake flow, thus potentially keeping a positive carbon balance. A deep understanding of this adaptation is key for predicting the fate of ecosystems subjected to climate change-induced droughts of increasing intensity and duration. C_LIO_LIUsing a minimalistic model, we derive predictions for how environmental drivers (atmospheric demand and soil water availability) interplay with the water storage, creating time lags between the flows in the plant, and granting the plant increased hydraulic safety margin protecting its xylem from embolism. C_LIO_LIWe parametrize our model against transpiration and sap flow measurements in a semi-arid pine forest during seasonal drought. From the parametrized whole-stand traits, we derive a 3.7-hour time lag between transpiration and sap flow, and that 31% of daily transpiration comes directly from the plants internal water storage, both corroborated by the measurements. C_LIO_LIDue to the model simplicity, our results are useful for interpreting, analyzing, and predicting the effects of the internal storage buffering from the individual plant to the ecosystem scale. Because internal storage produces survival-enhancing behavior in sub-daily time scales, it is an indispensable component for modeling ecosystems under drought stress. C_LI

During plant infection, complex metabolic interactions occurs between host and pathogen, including a genuine competition for resources. While the pathogen exploits host nutrients to support its growth and virulence, the plant attempts to restrict pathogen multiplication by limiting nutrient availability or producing antimicrobial compounds. To unravel these trophic interactions, we constructed a genome-scale metabolic model of a complete pathosystem by integrating a multi-organ metabolic model of the plant, a pathogen metabolic model, quantitative measurements, and a mathematical framework based on sequential flux balance analyses (FBAs). This strategy was applied to the Ralstonia pseudosolanacearum-tomato system. For the first time, quantitative fluxes of matter occurring during a plant infection were predicted. The model shows that (i) plant photosynthetic capacity is a stronger constraint than mineral availability for bacterial proliferation, (ii) infection-induced reduction of plant transpiration limits and ultimately halts first plant growth, then pathogen expansion, (iii) stem resource hijacking can enhance bacterial growth but remains secondary, and (iv) pathogen-excreted putrescine is likely reused for the plants needs. This study delivers the first holistic and quantitative representation of trophic interactions within a plant-pathogen system and highlights the central importance of water flow when the infectious agent is a fast-growing, xylem-colonizing bacterium.

Previous phyllotaxis models allowed the initiation of new primordia when a threshold of inhibition potential is reached on the meristem front: their adequacy to botanical reality is only qualitative. We formulated the hypothesis that it is not the value of the inhibition threshold that remains constant as the meristem develops, but the difference of the inhibition thresholds during the initiation of two successive primordia. We were thus able to model with accuracy the sequence of plastochron ratios observed by Williams (1975) on the leaf meristem of flax: an outstanding result. More generally, we have shown that the evolution trajectories of the phyllotaxis modes as a function of the plastochron ratios follow the minima of the potential under decreasing plastochron ratios constraint and bifurcate when the number of these minima increases, thus giving physicochemical foundations to the famous van Iterson diagram. This historical representation of rising phyllotaxis shows the trajectories, but doesnt give the velocity of the movement: our plastochron ratio sequence adds this major dynamical information.

Current global models of vegetation dynamics are largely carbon (C) source-driven, with behaviour primarily determined by the environmental responses of photosynthesis. However, real plants operate as integrated wholes, with feedbacks between sources, such as photosynthesis, and sinks, such as growth, resulting in homeostatic concentrations of metabolites such as sugars. A parsimonious approach to implementing this homeostatic coupling of C sources and sinks in a tree growth model is presented, and its implications for the responses of net photosynthesis and growth to environmental factors and tree size assessed. Hill functions describe inhibition of C sources (net photosynthesis) and activation of sinks (structural growth) as sucrose concentration increases. The model is parameterised for a typical tree growing at a site in the Amazonian rainforest and its qualitative behaviour is found to be consistent with observations. A key outcome is that sinks and sources strongly regulate each other. Hence environmental factors that affect potential net photosynthesis, such as atmospheric CO2, have greatly reduced effects on growth when homeostatic feedbacks from sucrose concentrations are considered. For example, compared with a C-source-only-driven approach (as in most current global models), the response of tree biomass for a tree currently 300 yr old, to increasing atmospheric CO2 projected to the end of this century under a high scenario, is reduced by ca.77%, from +122% to +29%, with net photosynthesis and growth rate responses reduced by a similar amount. Furthermore, in this coupled approach, any direct controls on growth (either environmental or through phenological controls on xylogensis) will influence source activity through the sucrose feedback. For example, a reduction in potential growth through temperature constraints on cell-wall construction increases sucrose concentrations, resulting in a compensating reduction in net photosynthesis. While net photosynthesis controls growth, growth controls net photosynthesis. In addition, we find a strong effect of changing tree allometry on C source-sink relations as the tree grows. Larger trees are less source-limited due to a higher ratio of sapwood area (and hence potential C assimilation rate) to potential growth rate, consistent with the observed decline in growth response to atmospheric CO2 as trees age. We suggest that the implications of including C source-sink coupling in models of vegetation dynamics, such as dynamic global vegetation models, are likely to be profound.

The conversion of supplemental greenhouse light energy into biomass is not always optimal. Recent trends in global energy prices and discussions on climate change highlight the need to reduce our energy footprint associated with the use of supplemental light in greenhouse crop production. This can be achieved by implementing "smart" lighting regimens which in turn rely on a good understanding of how fluctuating light influences photosynthetic physiology. Here, a simple fit-for-purpose dynamic model is presented. It accurately predicts net leaf photosynthesis under natural fluctuating light. It comprises two ordinary differential equations predicting: 1) the total stomatal conductance to CO2 diffusion and 2) the CO2 concentration inside a leaf. It contains elements of the Farquhar-von Caemmerer-Berry model and the successful incorporation of this model suggests that for tomato (Solanum lycopersicum L.), it is sufficient to assume that Rubisco remains activated despite rapid fluctuations in irradiance. Furthermore, predictions of the net photosynthetic rate under both 400ppm and enriched 800ppm ambient CO2 concentrations indicate a strong correlation between the dynamic rate of photosynthesis and the rate of electron transport. Finally, we are able to indicate whether dynamic photosynthesis is Rubisco or electron transport rate limited. Author summaryThe cultivation of greenhouse crops under optimised conditions will become increasingly important, with supplemental lighting playing a vital role. However, converting light energy into plant photosynthesis is not always optimal. A potential venue that may lead to the efficient conversion of light energy involves a model-based implementation of "smart" lighting control strategy. This approach does however necessitate a good understanding of how plants harness light energy under natural fluctuating irradiance. Accordingly, as a first step, we have developed a small leaf-level model that predicts dynamic photosynthesis in natural fluctuating light. It may potentially be used in future supplemental light control applications.

O_LIPlants respond to mechanical stimuli by a rapid increase in cytosolic calcium. The intensity and kinetics of the calcium changes define calcium signatures important for biological responses . In this study, we determine the properties of a calcium permeable force-gated channel localized at the plasma membrane called Rapid Mechanically Activated (RMA). C_LIO_LIUsing patch-clamp and pressure-clamp, we characterized the kinetics of activation and inactivation of RMA channel upon stimulation by pulses of pressure applied onto the plasma membrane. Combining repetitive pressure pulse protocols at different frequencies with modeling, we investigated the channels capacity to transduce high frequency mechanical stimuli. C_LIO_LIRMA channel rapidly activates in response to membrane tension, then it inactivates during prolonged stimulation. Upon repeated stimulations, RMA current amplitude decreases irreversibly indicating that undergoes adaptation. The channel kinetics may be modeled with four chemical states and the model predicts that it behaves as a pass band filter in the 10 Hz - 1 kHz range. C_LIO_LIIn conclusion, due to its activation/inactivation characteristics, RMA channel is a candidate to mediate cytosolic calcium signaling in response to mechano-stimulation. Its adaptation and filtering properties suggest its involvement in the transduction of high frequency mechanical stimulation such as those produced by insects vibrations. C_LI

Mathematical modelling is essential for understanding how complex biological systems respond to genetic, physiological, and environmental changes. Existing approaches, however, often require trade-offs between mechanistic detail, model size, parameter uncertainty, and interpretability. Ordinary differential equation (ODE) models capture biochemical processes with quantitative precision but can demand extensive parameterisation. In contrast, large statistical and machine-learning models rely on substantial datasets and frequently lack mechanistic transparency. Qualitative approaches such as Boolean networks improve scalability but may oversimplify biological behaviour. To address some of these limitations, we present PSoup, an R package that automatically converts knowledge graphs into transparent, parameter-free, qualitative models. PSoup uses algebraic update rules designed around a fixed, biologically interpretable baseline, enabling predictions of relative change across diverse perturbations without requiring kinetic parameters. This design allows PSoup to integrate information across biological scales and from heterogeneous experimental sources. We evaluated PSoup using the well-studied shoot branching network of Bertheloot et al. (2019), which ncorporates hormonal (auxin, strigolactone, cytokinin) and metabolic (sucrose) regulation. Across 78 experimental conditions, PSoup correctly predicted 88.5% of perturbation outcomes, including 89.5% accuracy for unique, biologically consistent comparisons. We further demonstrate how PSoup can distinguish among alternative plausible network topologies, revealing how structural differences influence emergent system behaviour. PSoup offers an intuitive, accessible, and mathematically transparent framework for exploring biological networks. Its capacity to integrate diverse knowledge and test alternative hypotheses positions it as a powerful tool for biological discovery and a valuable complement to existing modelling approaches.

Allometric Models (AMs) play a central role in monitoring and mitigating climate change as they provide accurate estimation of biomass and carbon sequestered by trees from non-destructive, easy to obtain physical measurements. Unfortunately, practitioners spend considerable effort in researching, qualifying and choosing AMs for specific growth conditions. To overcome this situation Chave et al. (2014) developed a pan-tropical AM with equivalent accuracy to local, site-specific AMs. We ameliorate this result by incorporating contextual information pertaining to growth conditions in a Machine Learning (ML) model, eventually achieving a reduction in Mean Average Error (MAE) of -17% as measured on hold-out data. This breakthrough shall have important impact in applications such as national forest inventories, carbon certifications and calibration of satellite based biomass maps to field data. To complete, we propose a principled method to estimate how much additional error one can expect when applying a given AM to shifting conditions and provide a data-driven safety check to practitioners.

Plant growth and development involve the integration of numerous processes, influenced by both endogenous and exogenous factors. At any given time during a plants life cycle, the plant architecture is a readout of this continuous integration. However, untangling the individual factors and processes involved in the plant development and quantifying their influence on the plant developmental process is experimentally challenging. Here we used a combination of computational plant models to help understand experimental findings about how local phloem anatomical features influence the root system architecture. In particular, we simulated the mutual interplay between the root system architecture development and the carbohydrate distribution to provide a plausible mechanistic explanation for several experimental results. Our in silico study highlighted the strong influence of local phloem hydraulics on the root growth rates, growth duration and final length. The model result showed that a higher phloem resistivity leads to shorter roots due to the reduced flow of carbon within the root system. This effect was due to local properties of individual roots, and not linked to any of the pleiotropic effects at the root system level. Our results open the door to a better representation of growth processes in plant computational models.

Plant ecophysiology is founded on a rich body of physical and chemical theory, but it is challenging to connect theory with data in unambiguous, analytically rigorous, and reproducible ways. Custom scripts written in computer programming languages (coding) enable plant ecophysiologists to model plant processes and fit models to data reproducibly using advanced statistical techniques. Since many ecophysiologists lack formal programming education, we have yet to adopt a unified set of coding principles and standards that could make coding easier to learn, use, and modify. We identify eight principles to help in plant ecophysiologists without much programming experience to write resilient code: 1) standardized nomenclature, 2) consistency in style, 3) increased modularity/extensibility for easier editing and understanding, 4) code scalability for application to large datasets, 5) documented contingencies for code maintenance, 6) documentation to facilitate user understanding; 7) extensive tutorials, and 8) unit testing. We illustrate these principles using a new R package, {photosynthesis}, which provides a set of analytical and simulation tools for plant ecophysiology. Our goal with these principles is to advance scientific discovery in plant ecophysiology by making it easier to use code for simulation and data analysis, reproduce results, and rapidly incorporate new biological understanding and analytical tools.

O_LICalcium signals are fundamental for plants and play a crucial role in long-term processes such as growth and development, as well as in rapid responses to environmental stimuli and stress factors. Nevertheless, the mechanisms involved in decoding calcium signal in plants are still largely unclear. C_LIO_LIHere, we have addressed the question of calcium signal decoding in a bottom-up modelling approach. We started with the thermodynamics of Ca2+ binding to a Ca2+ binding protein (CBP), e.g. via EF hands. Remarkably, Ca2+ binding properties of the EF hands do not coincide with the Ca2+ sensitivity of the protein containing these EF hands. C_LIO_LIIn analysing the next levels of complexity, we identified six universal fundamental Ca2+-decoding modules, in which Ca2+ either interacts directly with a target protein (TP) or modulates its activity via a CBP. These modules are the basic units that enable the amplitude and frequency of Ca2+ signals to be decoded. Representatives of these modules are omnipresent in plant cells. They straightforwardly explain the puzzling finding that Ca2+-dependent kinases exhibit different Ca2+-sensitivities when tested with different substrates. C_LIO_LIIn-depth analysis of the properties of the modules provides a fundamental theoretical basis for understanding Ca2+ signal decoding and may contribute to finding the "Rosetta Stone" for Ca2+ signals in plants. C_LI

One of the major puzzles in phyllotaxis is the much higher frequency of Fibonacci spirals compared to other spiral arrangements such as Lucas spirals. We show that spirals are a form of symmetry, in the same way that axial symmetry is a form of symmetry, which explains why they can be the consequence of many different microscopic phenomena. We apply dynamical systems theory to the main types of phyllotaxis. We show that only Fibonacci spirals should exist and that the other spiral modes (including Lucas) are the consequence of developmental errors, such as the dislocation of a pseudo-orthostichy.

Efforts to cope with hunger by breeding highly productive annual crops for rain-fed agriculture in stochastic-rainfall environments have had only minor success, which we attribute to biological constraints that limit the crops yields. We use optimization modelling to interpret experimentally measured transpiration trajectories of wild barley plants following a rain event: the plants first maximized biomass accumulation by employing their maximal transpiration rate, then switched to their minimal transpiration rate to ensure survival until maturity. Thus, breeding plants with lower minimal transpiration rates combined with higher water-use efficiency and maximal transpiration rates could increase expected yields. However, our experimental results indicate that biological constraints impose tradeoffs among maximal and minimal transpiration rates and water-use efficiency. A proposed breeding methodology identifies less biologically constrained cultivar candidates.

The times between appearance of successive leaves or phyllochron characterize the vegetative development of annual plants. Hypothesis testing models, which enables to compare phyllochron between genetic groups or conditions, are usually based on regression of thermal time on the number of leaves, most of the time assuming a constant leaf appearance rate. However these models are both statistically biased and inappropriate in terms of modelling. We propose a stochastic process model in which the emergence of new leaves is considered as successive time-to-events, which provides a flexible and more accurate modelling as well as unbiased testing procedures. The model was applied on an original maize dataset collected in fields for three years on plants originating from two divergent selection experiments for flowering time conducted in two maize inbred lines. We showed that the main differences in phyllochron were not observed between selection populations (Early or Late), but rather between ancestral lines, years of experimentation, and leaf ranks. Our results highlight a strong departure from the assumption of a constant leaf appearance rate in one year that could be related to climate variations, even if the impact of each climatic variables individually was not clearly elucidated.

Using a simple plant growth model based on the logistic equation I re-evaluate how biomass allocation between roots and shoots articulates dynamically with the rate of whole-plant biomass production. Defined by parameters reflecting lumped physiological properties, the model constrains roots and shoots to grow sigmoidally over time. From those temporal patterns detailed trajectories of allocation and growth rate are reconstructed. Sigmoid growth trajectories of roots and shoots are incompatible with the dominant ‘functional equilibrium’ model of adaptive allocation and growth often used to explain plants’ responses to nutrient shortage and defoliation. Anything that changes the differential rates of growth between roots and shoots will automatically change allocation and, unavoidably, change whole-plant growth rate. Biomass allocation and whole-plant growth rate are not independent traits. Allocation and growth rate have no unique relationship to one another but can vary across a wide spectrum of possible relationships. When root-shoot allocation seems to respond to the environment it is likely to be a secondary illusory consequence of other primary responses such as localised root proliferation in soil or leaf expansion within canopy gaps. Changes in root-shoot allocation cannot themselves compensate directly for an impairment of growth rate caused by an external factor such as nutrient shortage or defoliation; therefore, such changes cannot be ‘adaptive’.‘The reasons are so simple they often escape notice.’ (James 2012, p. 6).Competing Interest StatementThe authors have declared no competing interest.View Full Text

Mature plant leaves are a composite of distinct cell types, including epidermal, mesophyll and vascular cells. Notably the proportion of these cells, and the relative transcript concentrations within different cell types may change over time. While gene expression data at a single-cell level can provide cell-type specific expression values, it is often too expensive to perform this on high resolution time series. Although bulk RNA-seq can be performed in a high resolution time series, the RNA-seq in whole leaves measures the average gene expression values across all cell types in each sample. In this study, we combined single cell RNA-seq data with time-series data from whole leaves to infer an atlas of cell type-specific gene expression changes over time for Arabidopsis thaliana. We inferred how relative transcript concentrations of cell types vary across diurnal and developmental time scales. Importantly this analysis revealed three sub-groups of mesophyll cells that have distinct temporal profiles of expression. Finally, we develop tissue-specific gene networks that form a new community resource: An Arabidopsis Leaf Time-Dependent Atlas (AraLeTa), which allows users to extract gene networks that are confirmed by transcription factor binding data and specific to certain cell types, at certain times of day and certain developmental stages, which is available at: https://regulatorynet.shinyapps.io/araleta/.