Quantitative Plant Biology

Plants use light energy to produce ATP and redox equivalents for metabolism. Since during the course of a day plants are exposed to constantly fluctuating light, the supply of ATP and redox equivalents is also fluctuating. Further, if the metabolism cannot use all of the supplied energy, the excess absorbed energy can damage the plant in the form of reactive oxygen species. It is thus reasonable to assume that the metabolism downstream of the energy supply is dynamic and as being capable of dampening sudden spikes in supply is advantageous, it is further reasonable to assume that the immediate downstream metabolism is flexible as well. A flexible metabolism exposed to a fluctuating input is unlikely to be in metabolic steady-state, yet a lot of mathematical models for carbon fixation assume one for the Calvin-Benson-Bassham (CBB) cycle. Here we present an analysis of the validity of this assumption by progressively simplifying an existing model of photosynthesis and carbon fixation.

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.

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

Paul Green hypothesized that growth anisotropy of plant cylindrical organs could be controlled by cell-wall elastic strain. The present study aimed to challenge this hypothesis through a robust experimental and analytical framework. By combining live-cell imaging of C. corallina internodal cells with controlled turgor pressure manipulation, we simultaneously measured, for the first time, both the growth strain rate tensor and the elastic compliance tensor derived from multiaxial mechanical testing in the same cell. Under Greens hypothesis, a significant correlation should be observed between the two tensors in all directions. Our results revealed a moderate yet significant correlation between multiaxial elastic compliances and growth strain rates most pronounced in the axial direction. The ratio of axial-to-radial elastic compliance was significantly correlated with the ratio of radial-to-axial growth strain rates. In contrast, other quantities, such as the radial compliance components or the orientations of the two tensors relative to the cell axis showed no significant correlation. Furthermore the growth strain rate tensor was strongly age-dependent in both magnitude and orientation, unlike the elastic compliance. Finally, analysis of intra-tensor variability revealed that axial and radial components were strongly correlated for both tensors, with a lowered correlation in the principal axis decomposition.

Development and spatial pattern formation are inherently linked. The coordinated determination of cell fates is crucial in any developmental process and requires extensive intercellular communication. Plants cells exchange many molecular signals via the symplasmic pathway, i.e., via plasmodesmata: narrow channels connecting the cytoplasm of neighbouring cells. Regulation of symplasmic transport is vital for normal plant development, and mutations that disrupt this regulation are often embryo or seedling lethal. In many tissues, symplasmic transport of small molecules is diffusion driven, resulting in a non-selective and bidirectional transport, although net directionality could arise from gradients. This has led to the (dogmatic) belief that symplasmic transport can only be detrimental to pattern formation, because signalling molecules cannot be confined, and gradients would fade. Here, we develop a detailed biophysical description of symplasmic transport to explore how plasmodesmata affect gradients in a linear tissue. We then apply the model in more complex tissue contexts, observing and explaining, e.g., that symplasmic transport may result in steeper gradients in the root apical meristem. In conclusion, our model provides a reference framework for estimating the consequences of symplasmic transport and explains how symplasmic transport can contribute to more robust developmental patterning.

New plants organs form by local accumulation of auxin, which is transported by PIN proteins that localize following mechanical stresses. As auxin itself modifies tissue mechanics, a feedback loop between tissue mechanics and auxin patterning unfolds - yet the impact of tissue-wide mechanical coupling on auxin pattern emergence remains unclear. Here, we use a hybrid model composed of a vertex model for plant tissue mechanics, and a compartment model for auxin transport to explore the collective mechanical response of the tissue to auxin patterns and how it feeds back onto auxin transport. We compare a model accounting for a tissue-wide mechanical integration to a model where mechanical stresses are averaged out across the tissue. We show that only tissue-wide mechanical coupling leads to focused auxin spots, which we show to result from the formation of a circumferential stress field around these spots, self-reinforcing PIN polarity and auxin accumulation.

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.

How organisms produce organs with robust shapes and sizes is still an open question. In recent years, the Arabidopsis sepal has been used as a model system to study this question because of its highly reproducible shape and size. One interesting aspect of the sepal is that its epidermis contains cells with very different sizes. Previous reports had qualitatively shown that sepals with more or less giant cells exhibit comparable final size and shape. Here we investigate this question using quantitative approaches. We find that a mixed population of cell size modestly contribute to the normal width of the sepal, but is not essential for its shape robustness. Furthermore, in a mutant with increased cell and organ growth variability, the change in final sepal shape caused by giant cells is exaggerated, but the shape robustness is not affected. This formally demonstrates that sepal shape variability is robust to cell size heterogeneity. Main conclusionA mixed population of cells with varied sizes plays a limited role in ensuring the symmetrical shape of the sepal, and is not essential for sepal shape robustness in Arabidopsis.

Plant morphologies exhibit a wide array of outcomes that have evolved as a consequence adapting to a wide array of ecological pressures. These disparate morphologies have provided a rich field for comparative morphologists, developmental biologists, and geneticists to explore. Ultimately the array of variation observed in nature across different plant species is built on the same functional unit, the phytomer, which is composed of a leaf, a node, and an internode. Sequentially produced phytomers exhibit heteroblasty, that is, a gradual or abrupt change in shape, either due to size changes or changes due to reproductive phase. The progression of shape change over time is often indirectly measured by sampling several stages of plant growth and comparing allometric relationships between shape variables. However, a more precise method is to use an absolute time scale and measure shape change of sequential organs directly. In this study we use such time-dependent measurements to build a general model of organ growth for several Setaria genotypes, for both leaves and internodes. We term this the second-order function-value trait (2FVT) model, because it generalizes individual function-value trait models generated for each organ. This model reduces phenotypic noise by averaging the general trend of ontogeny and provides a quantitative tool to describe where and when phenotypic shifts occur during the ontogenies of different genotypes. The ability to recognize how ontogenetic variation is distributed within equivalent positions of the body plan at the interspecific level can be used as a tool to explore various questions related to growth and form in plants both for comparative morphology and developmental genetics.

Plant development and adaptation are highly dependent on cell morphology and growth. High turgor pressure in plants causes stress on the cell wall, followed by cell extension. In tip-growing cells, the localization of vesicles and cytoskeleton components has been well studied. However, there has been a lack of attention to the spatial profile of mechanical properties, specifically the cell wall elasticity. In this study, we introduce a new surface morphology-based method to measure the elasticity of the cell wall in tip-growing cells. Previous work is based on measurements from the wall meridional outline, a technique that cannot track the elastic deformation of the cell wall experimentally. Instead, we developed a way to infer the bulk modulus distribution from the cell surface by triangulating experimental marker points coming from fluorescent labeling. To justify the use of our protocol in tip-growing cells from the moss Physcomitrium patens, we replicated the experimental noise and moss morphology in simulated cells. In practice, we found that a larger triangulation improved robustness against noise, which agreed with our theoretical study. With multiple cell sampling, we determined that 10 cells were sufficient to recover the elasticity distribution with noise, but only when the elastic stretches were high enough. We then created a dimensionless map of inference error to verify a spatial change of P. patens bulk modulus within two folds. This technique will open the field to more comprehensive measurements of cell wall elasticity, providing a key step in understanding tip cell growth and morphogenesis. Author summaryTip-growing cells can be characterized by their fast growth concentrated at the cells apex. Their growth and morphogenesis are tightly regulated processes involving cell wall addition and rearrangement while the cell wall is under stress originating from the cells internal turgor pressure. We start by studying the cell walls elastic properties, one aspect of the cell growth process. We use a method of marker point tracking across the surface of the tip-growing cell to measure the walls elasticity profile. In this work, we present a parameter sensitivity study of this method on synthetic cells and report our results on experimental moss tip-growing cells. Our results suggest that this inference method can reliably measure a cell wall elasticity gradient under combined geometric and mechanical conditions that create elastic strains within 5% at the tip.

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.

Using conventional statistical approaches there exist powerful methods to classify shapes. Embedded in morphospaces is information that allows us to visualize theoretical leaves. These unmeasured leaves are never considered nor how the negative morphospace can inform us about the forces responsible for shaping leaf morphology. Here, we model leaf shape using an allometric indicator of leaf size, the ratio of vein to blade areas. The borders of the observable morphospace are restricted by constraints and define an orthogonal grid of developmental and evolutionary effects which can predict the shapes of possible grapevine leaves. Leaves in the genus Vitis are found to fully occupy morphospace available to them. From this morphospace we predict the developmental and evolutionary shapes of grapevine leaves that are not only possible, but exist, and argue that rather than explaining leaf shape in terms of discrete nodes or species, that a continuous model is more appropriate.

Plant cell growth depends on turgor pressure, the cell hydrodynamic pressure, which drives expansion of the extracellular matrix (the cell wall). Turgor pressure regulation depends on several physical, chemical and biological factors, including: vacuolar invertases, which modulate osmotic pressure of the cell, aquaporins, which determine the permeability of the plasma membrane to water, cell wall remodeling factors, which determine cell wall extensibility (inverse of effective viscosity), and plasmodesmata, which are membrane-lined channels that allow free movement of water and solutes between cytoplasms of neighbouring cells, like gap junctions in animals. Plasmodesmata permeability varies during plant development and experimental studies have correlated changes in the permeability of plasmodesmal channels to turgor pressure variations. Here we study the role of plasmodesmal permeability in cotton fiber growth, a type of cell that increases in length by at least 3 orders of magnitude in a few weeks. We incorporated plasmodesma-dependent movement of water and solutes into a classical model of plant cell expansion. We performed a sensitivity analysis to changes in values of model parameters and found that plasmodesmal permeability is among the most important factors for building up turgor pressure and expanding cotton fibers. Moreover, we found that non-monotonic behaviors of turgor pressure that have been reported previously in cotton fibers cannot be recovered without accounting for dynamic changes of the parameters used in the model. Altogether, our results suggest an important role for plasmodesmal permeability in the regulation of turgor pressure. Significance StatementThe cotton fiber is among the plant cells with the highest growth rates. In cultivars, a single fiber cell generally reaches a few centimeters in length. How such size is achieved is still poorly understood. In order to tackle this question, we built a comprehensive mathematical model of fiber elongation, considering cell mechanics and water entry into the cell. Model predictions agree with experimental observations, provided that we take into account active opening and closure of plasmodesmata, the nano-channels that connect the fiber with neighboring cells. Because cotton fiber length is a key factor for yarn quality, our work may help understanding the mechanisms behind an important agronomic trait.

Yield of harvestable organs is a complex function of photosynthetic output, and sink-strength and timing of competing carbon sinks. In potato (Solanum tuberosum) the effect of tuber onset timing and post-tuberization canopy senescence on growth dynamics and tuber fresh weight are poorly understood. To advance our understanding we compared above- and belowground traits of wildtype plants (WT) with StSP6A, i.e., tuberigen, knockdown plants (SP6Ai) and developed simple computational models to aid interpretation of results. We find that SP6Ai results in a delay of approximately 2 weeks in tuber onset, yet has a 4-to-5-week delayed canopy senescence. Together this results in a prolonged tuber growth phase, with reduced synchronization in tuber onset and a resulting increased variance in tuber sizes, while overall final tuber fresh weight remains similar. Using a leaf and tuber growth model comparing various leaf senescence mechanisms, we find that resource competition, and not a shared signal for tuberization and senescence, is able to explain how delayed tuberization leads to further delayed senescence. Our results point to a role for resource competition in the correlated timing of tuber onset and canopy senescence, as well as a leading role for StSP6A in tuber onset synchronization and tuber size uniformity. Graphical Abstract O_FIG O_LINKSMALLFIG WIDTH=144 HEIGHT=200 SRC="FIGDIR/small/566204v1_ufig1.gif" ALT="Figure 1"> View larger version (33K): org.highwire.dtl.DTLVardef@a3abf3org.highwire.dtl.DTLVardef@16de607org.highwire.dtl.DTLVardef@18e3a2org.highwire.dtl.DTLVardef@8c7b5_HPS_FORMAT_FIGEXP M_FIG C_FIG

Precise regulation of cell division is central for the formation of complex multicellular organisms and a hallmark of stem cell activity. In plants, due to the absence of cell migration, correct placement of newly produced cell walls during cell division is of eminent importance for generating functional tissues and organs. In particular, during radial growth of plant shoots and roots, concerted cell divisions in the cambium are essential to produce adjacent xylem and phloem tissues in a strictly bidirectional manner. While several intercellular signaling cascades have been identified to instruct tissue organization during radial growth, a role of mechanical forces in guiding cambium stem cell activity has been frequently proposed but, so far, not been functionally investigated on the cellular level. Here, we coupled anatomical analyses with a cell-based vertex model to analyze the role of mechanical stress in radial plant growth at the cell and tissue scale. Simulations based on segmented cellular outlines of radially growing Arabidopsis hypocotyls revealed a distinct stress pattern with circumferential stresses in cambium stem cells which coincided with the orientation of cortical microtubules. Integrating stress patterns as a cue instructing cell division orientation was sufficient for the emergence of typical cambium-derived cell files and agreed with experimental results for stress-related tissue organization in confining mechanical environments. Our work thus underlines the significance of mechanical forces in tissue organization through self-emerging stress patterns during the growth of plant organs.

How much interactivity is there in a seed-seedling transition system? The answer for this question can reveal a key aspect for early plant establishment. Thus, we hypothesize that information entropy is correlated with early plant development because it is directly related to interactions between seed-seed, seed-seedling, and seedling-seedling. To test this hypothesis, we perform an overlapping of classical physiological measurements (embryo protrusion), gene expression in germination sensu stricto, water dynamics in germinating seeds and information theory. For a biological model, we used Solanum lycocarpum A. St.{square}Hil. seeds. This is a Neotropical species with high intra-specific variability in the seed sample. Our finds demonstrate that the dynamic and transient seed-seedling transition system is influenced by the number of individuals (seed or seedling) in the sample, especially at a same physiological stage. In addition, we also discuss that: (i) information entropy enables the quantification of system disturbance relative to individuals in the same physiological stage (seed-seed or seedling-seedling), which may be determinant for embryo growth during germination. (ii) there is possible intraspecific communication in seed-seedling transition systems formed by germinating seeds with the potential to alter the pattern of embryonic development of the sample. In view of this, we suggest the use of information entropy as a tool for studies of biological systems to clarify the phenomenon of mutual stimulation in the germination process.

Plants respond to wounding stress by changing gene expression patterns and inducing jasmonic acid (JA), as well as other plant hormones. This includes activating some specialized metabolism pathways, including the glucosinolate pathways, in the case of Arabidopsis thaliana. We model how these responses are regulated by using machine learning to incorporate putative cis-regulatory elements (pCREs), known transcription factor binding sites from literature, in-vitro DNA affinity purification sequencing (DAP-seq) and DNase I hypersensitive sites to predict gene expression for genes clustered by their wound response using machine learning. We found temporal patterns where regulatory sites and regions of open chromatin differed between clusters of genes up-regulated at early and late wounding time points as well as clusters where JA response was induced relative to clusters where JA response was not induced. Overall, we identified pCREs that improved model predictions of expression clusters over known binding sites. We discovered 4,255 pCREs related to wound response at different time points and 2,569 pCREs related to differences between JA-induced and non-JA induced wound response. In addition, pCREs found to be important at different wounding time points were mapped to the promoters of genes in a glucosinolate biosynthesis pathway indicating regulation of this pathway under wounding stress. Finally, we experimentally validated a predicted cis-regulatory element, CCGCGT, showing that knock-out via CRISPR-Cas9 reduces gene expression in response to wounding.

In Arabidopsis thaliana, the stem cell niche (SCN) within the root apical meristem (RAM) is maintained by an intricate regulatory network that ensures optimal growth and high developmental plasticity. Yet, many aspects of this regulatory network of stem cell quiescence and replenishment are still not fully understood. Here, we investigate the interplay of the key transcription factors (TFs) BRASSINOSTEROID AT VASCULAR AND ORGANIZING CENTRE (BRAVO), PLETHORA 3 (PLT3) and WUSCHEL-RELATED HOMEOBOX 5 (WOX5) involved in SCN maintenance. Phenotypical analysis of mutants involving these TFs uncover their combinatorial regulation of cell fates and divisions in the SCN. Moreover, interaction studies employing fluorescence resonance energy transfer fluorescence lifetime imaging microscopy (FRET-FLIM) in combination with novel analysis methods, allowed us to quantify protein-protein interaction (PPI) affinities as well as higher-order complex formation of these TFs. We integrated our experimental results into a computational model, suggesting that cell type specific profiles of protein complexes and characteristic complex formation, that is also dependent on prion-like domains in PLT3, contribute to the intricate regulation of the SCN. We propose that these unique protein complex signatures could serve as a read-out for cell specificity thereby adding another layer to the sophisticated regulatory network that balances stem cell maintenance and replenishment in the Arabidopsis root.

Reticulate leaf venation, characterized by the presence of loops, is a distinguishing feature of many flowering plants. However, our understanding of both the geometry and the morphogenesis of reticulate vein patterns is far from complete. We show that in the Chinese money plant (Pilea peperomioides), major veins form an approximate Voronoi diagram surrounding secretory pores known as hydathodes. We also propose a mechanistic model based on polar transport of the plant hormone auxin to produce Voronoi patterns. In contrast with classical models where veins directly connect auxin sources to sinks, our model generates veins that bisect the space between adjacent auxin sources, collectively forming loops. The paradigm change offered by this model may open the door to study reticulate vein formation in other species.

Photosynthesis is co-limited by multiple factors depending on the plant and its environment. These include biochemical rate limitations, internal and external water potentials, temperature, irradiance, and carbon dioxide (CO2). Amphistomatous leaves have stomata on both abaxial and adaxial leaf surfaces. This feature is considered an adaptation to alleviate CO2 diffusion limitations in productive environments where other factors are not limiting as the diffusion path length from stomate to chloroplast is effectively halved. Plants can also reduce CO2 limitations through other aspects of optimal stomatal anatomy: stomatal density, distribution, patterning, and size. A number of studies have demonstrated that stomata are overdispersed on a single leaf surface; however, much less is known about stomatal anatomy in amphistomatous leaves, especially the coordination between leaf surfaces, despite their prevelance in nature and near ubiquity among crop species. Here we use novel spatial statistics based on simulations and photosynthesis modeling to test hypotheses about how amphistomatous plants may optimize CO2 limitations in the model angiosperm Arabidopsis thaliana grown in different light environments. We find that 1) stomata are overdispersed, but not ideally dispersed, on both leaf surfaces across all light treatments; 2) abaxial and adaxial leaf surface patterning are independent; and 3) the theoretical improvements to photosynthesis from abaxial-adaxial stomatal coordination are miniscule (<< 1%) across the range of feasible parameter space. However, we also find that 4) stomatal size is correlated with the mesophyll volume that it supplies with CO2, suggesting that plants may optimize CO2 diffusion limitations through alternative pathways other than ideal, uniform stomatal spacing. We discuss the developmental, physical, and evolutionary constraits which may prohibit plants from reaching the theoretical adaptive peak of uniform stomatal spacing and inter-surface stomatal coordination. These findings contribute to our understanding of variation in the anatomy of amphistomatous leaves.