A mathematical model of biofilm growth and spread within plant xylem: Case study of Xylella fastidiosa in olive trees.

Xylem-limited bacterial pathogens cause some of the most destructive plant diseases. Though imposed measures to control these pathogens are generally ineffective, even among susceptible taxa, some hosts can limit bacterial loads and symptom expression. Mechanisms by which this resistance is achieved are poorly understood. In particular, it is still unknown how differences in vascular structure may influence biofilm growth and spread within a host. To address this, we developed a novel theoretical framework to describe biofilm behaviour within xylem vessels, adopting a polymer-based modelling approach. We then parameterised the model to investigate the relevance of xylem vessel diameters on Xylella fastidiosa resistance among olive cultivars. The functionality of all vessels was severely reduced under infection, with hydraulic flow reductions of 2-3 orders of magnitude. However, results suggest wider vessels act as biofilm incubators; allowing biofilms to develop over a long time while still transporting them through the vasculature. By contrast, thinner vessels become blocked much earlier, limiting biofilm spread. Using experimental data on vessel diameter distributions, we were able to determine that a mechanism of resistance in the olive cultivar Leccino is a relatively low abundance of the widest vessels, limiting X. fastidiosa spread.

Transition metal-catalysed carbene- and nitrene transfer to carbon monoxide and isocyanides.

Transition metal-catalysed carbene- and nitrene transfer to the C1-building blocks carbon monoxide and isocyanides provides heteroallenes (i.e. ketenes, isocyanates, ketenimines and carbodiimides). These are versatile and reactive compounds allowing in situ transformation towards numerous functional groups and organic compounds, including heterocycles. Both one-pot and tandem processes have been developed providing valuable synthetic methods for the organic chemistry toolbox. This review discusses all known transition metal-catalysed carbene- and nitrene transfer reactions towards carbon monoxide and isocyanides and in situ transformation of the heteroallenes hereby obtained, with a special focus on the general mechanistic considerations.

Significance of root hairs for plant performance under contrasting field conditions and water deficit.

BACKGROUND AND AIMS: Previous laboratory studies have suggested selection for root hair traits in future crop breeding to improve resource use efficiency and stress tolerance. However, data on the interplay between root hairs and open-field systems, under contrasting soils and climate conditions, are limited. As such, this study aims to experimentally elucidate some of the impacts that root hairs have on plant performance on a field scale. METHODS: A field experiment was set up in Scotland for two consecutive years, under contrasting climate conditions and different soil textures (i.e. clay loam vs. sandy loam). Five barley (Hordeum vulgare) genotypes exhibiting variation in root hair length and density were used in the study. Root hair length, density and rhizosheath weight were measured at several growth stages, as well as shoot biomass, plant water status, shoot phosphorus (P) accumulation and grain yield. KEY RESULTS: Measurements of root hair density, length and its correlation with rhizosheath weight highlighted trait robustness in the field under variable environmental conditions, although significant variations were found between soil textures as the growing season progressed. Root hairs did not confer a notable advantage to barley under optimal conditions, but under soil water deficit root hairs enhanced plant water status and stress tolerance resulting in a less negative leaf water potential and lower leaf abscisic acid concentration, while promoting shoot P accumulation. Furthermore, the presence of root hairs did not decrease yield under optimal conditions, while root hairs enhanced yield stability under drought. CONCLUSIONS: Selecting for beneficial root hair traits can enhance yield stability without diminishing yield potential, overcoming the breeder's dilemma of trying to simultaneously enhance both productivity and resilience. Therefore, the maintenance or enhancement of root hairs can represent a key trait for breeding the next generation of crops for improved drought tolerance in relation to climate change.

Using high resolution X-ray computed tomography to create an image based model of a lymph node.

Lymph nodes are an important part of the immune system. They filter the lymphatic fluid as it is transported from the tissues before being returned to the blood stream. The fluid flow through the nodes influences the behaviour of the immune cells that gather within the nodes and the structure of the node itself. Measuring the fluid flow in lymph nodes experimentally is challenging due to their small size and fragility. In this paper, we present high resolution X-ray computed tomography images of a murine lymph node. The impact of the resulting visualized structures on fluid transport are investigated using an image based model. The high contrast between different structures within the lymph node provided by phase contrast X-ray computed tomography reconstruction results in images that, when related to the permeability of the lymph node tissue, suggest an increased fluid velocity through the interstitial channels in the lymph node tissue. Fluid taking a direct path from the afferent to the efferent lymphatic vessel, through the centre of the node, moved faster than the fluid that flowed around the periphery of the lymph node. This is a possible mechanism for particles being moved into the cortex.

Phase contrast synchrotron radiation computed tomography of muscle spindles in the mouse soleus muscle.

Muscle spindles are skeletal muscle sensory organs involved in the sensation of position and movement of the body. We have explored the capability of phase contrast computed tomography to visualise muscle spindles in murine skeletal muscle. In particular, we have validated the visualisation of nerve fibres through phase contrast computed tomography using light microscopy on stained histological sections. We further present the first three-dimensional visualisation of muscle spindles in mouse soleus skeletal muscle in conjunction with the neurovascular bundle associated with it.

Plant exudates may stabilize or weaken soil depending on species, origin and time.

We hypothesized that plant exudates could either gel or disperse soil depending on their chemical characteristics. Barley (Hordeum vulgare L. cv. Optic) and maize (Zea mays L. cv. Freya) root exudates were collected using an aerated hydroponic method and compared with chia (Salvia hispanica L.) seed exudate, a commonly used root exudate analogue. Sandy loam soil was passed through a 500-µm mesh and treated with each exudate at a concentration of 4.6 mg exudate g-1 dry soil. Two sets of soil samples were prepared. One set of treated soil samples was maintained at 4°C to suppress microbial processes. To characterize the effect of decomposition, the second set of samples was incubated at 16°C for 2 weeks at -30 kPa matric potential. Gas chromatography-mass spectrometry (GC-MS) analysis of the exudates showed that barley had the largest organic acid content and chia the largest content of sugars (polysaccharide-derived or free), and maize was in between barley and chia. Yield stress of amended soil samples was measured by an oscillatory strain sweep test with a cone plate rheometer. When microbial decomposition was suppressed at 4°C, yield stress increased 20-fold for chia seed exudate and twofold for maize root exudate compared with the control, whereas for barley root exudate decreased to half. The yield stress after 2 weeks of incubation compared with soil with suppressed microbial decomposition increased by 85% for barley root exudate, but for chia and maize it decreased by 87 and 54%, respectively. Barley root exudation might therefore disperse soil and this could facilitate nutrient release. The maize root and chia seed exudates gelled soil, which could create a more stable soil structure around roots or seeds. HIGHLIGHTS: Rheological measurements quantified physical behaviour of plant exudates and effect on soil stabilization.Barley root exudates dispersed soil, which could release nutrients and carbon.Maize root and chia seed exudates had a stabilizing effect on soil.Physical engineering of soil in contact with plant roots depends on the nature and origin of exudates.

How changing root system architecture can help tackle a reduction in soil phosphate (P) levels for better plant P acquisition.

The readily available global rock phosphate (P) reserves may run out within the next 50-130 years, causing soils to have a reduced P concentration which will affect plant P uptake. Using a combination of mathematical modelling and experimental data, we investigated potential plant-based options for optimizing crop P uptake in reduced soil P environments. By varying the P concentration within a well-mixed agricultural soil, for high and low P (35.5-12.5 mg L(-1) respectively using Olsen's P index), we investigated branching distributions within a wheat root system that maximize P uptake. Changing the root branching distribution from linear (evenly spaced branches) to strongly exponential (a greater number of branches at the top of the soil) improves P uptake by 142% for low-P soils when root mass is kept constant between simulations. This causes the roots to emerge earlier and mimics topsoil foraging. Manipulating root branching patterns, to maximize P uptake, is not enough on its own to overcome the drop in soil P from high to low P. Further mechanisms have to be considered to fully understand the impact of P reduction on plant development.

Mathematical modelling of the Phloem: the importance of diffusion on sugar transport at osmotic equilibrium.

Plants rely on the conducting vessels of the phloem to transport the products of photosynthesis from the leaves to the roots, or to any other organs, for growth, metabolism, and storage. Transport within the phloem is due to an osmotically-generated pressure gradient and is hence inherently nonlinear. Since convection dominates over diffusion in the main bulk flow, the effects of diffusive transport have generally been neglected by previous authors. However, diffusion is important due to boundary layers that form at the ends of the phloem, and at the leaf-stem and stem-root boundaries. We present a mathematical model of transport which includes the effects of diffusion. We solve the system analytically in the limit of high Münch number which corresponds to osmotic equilibrium and numerically for all parameter values. We find that the bulk solution is dependent on the diffusion-dominated boundary layers. Hence, even for large Péclet number, it is not always correct to neglect diffusion. We consider the cases of passive and active sugar loading and unloading. We show that for active unloading, the solutions diverge with increasing Péclet. For passive unloading, the convergence of the solutions is dependent on the magnitude of loading. Diffusion also permits the modelling of an axial efflux of sugar in the root zone which may be important for the growing root tip and for promoting symbiotic biological interactions in the soil. Therefore, diffusion is an essential mechanism for transport in the phloem and must be included to accurately predict flow.

A mathematical model of water and nutrient transport in xylem vessels of a wheat plant.

At a time of increasing global demand for food, dwindling land and resources, and escalating pressures from climate change, the farming industry is undergoing financial strain, with a need to improve efficiency and crop yields. In order to improve efficiencies in farming, and in fertiliser usage in particular, understanding must be gained of the fertiliser-to-crop-yield pathway. We model one aspect of this pathway; the transport of nutrients within the vascular tissues of a crop plant from roots to leaves. We present a mathematical model of the transport of nutrients within the xylem vessels in response to the evapotranspiration of water. We determine seven different classes of flow, including positive unidirectional flow, which is optimal for nutrient transport from the roots to the leaves; and root multidirectional flow, which is similar to the hydraulic lift process observed in plants. We also investigate the effect of diffusion on nutrient transport and find that diffusion can be significant at the vessel termini especially if there is an axial efflux of nutrient, and at night when transpiration is minimal. Models such as these can then be coupled to whole-plant models to be used for optimisation of nutrient delivery scenarios.

A 3D image-based modelling approach for understanding spatiotemporal processes in phosphorus fertiliser dissolution, soil buffering and uptake by plant roots.

Phosphorus (P) is a key yield-limiting nutrient for crops, but the main source of P fertiliser is finite. Therefore, efficient fertilisation is crucial. Optimal P application requires understanding of the dynamic processes affecting P availability to plants, including fertiliser dissolution rate and soil buffer power. However, standard soil testing methods sample at fixed time points, preventing a mechanistic understanding of P uptake variability. We used image-based modelling to investigate the effects of fertiliser dissolution rate and soil buffer power on P uptake by wheat roots imaged using X-ray CT. We modelled uptake based on 1-day, 1-week, and 14-week dissolution of a fixed quantity of total P for two common soil buffer powers. We found rapid fertiliser dissolution increased short-term root uptake, but total uptake from 1-week matched 1-day dissolution. We quantified the large effects root system architecture had on P uptake, finding that there were trade-offs between total P uptake and uptake per unit root length, representing a carbon investment/phosphorus uptake balance. These results provide a starting point for predictive modelling of uptake from different P fertilisers in different soils. With the addition of further X-ray CT image datasets and a wider range of conditions, our simulation approach could be developed further for rapid trialling of fertiliser-soil combinations to inform field-scale trials or management.

Impact of root hairs on microscale soil physical properties in the field.

Aims: Recent laboratory studies revealed that root hairs may alter soil physical behaviour, influencing soil porosity and water retention on the small scale. However, the results are not consistent, and it is not known if structural changes at the small-scale have impacts at larger scales. Therefore, we evaluated the potential effects of root hairs on soil hydro-mechanical properties in the field using rhizosphere-scale physical measurements. Methods: Changes in soil water retention properties as well as mechanical and hydraulic characteristics were monitored in both silt loam and sandy loam soils. Measurements were taken from plant establishment to harvesting in field trials, comparing three barley genotypes representing distinct phenotypic categories in relation to root hair length. Soil hardness and elasticity were measured using a 3-mm-diameter spherical indenter, while water sorptivity and repellency were measured using a miniaturized infiltrometer with a 0.4-mm tip radius. Results: Over the growing season, plants induced changes in the soil water retention properties, with the plant available water increasing by 21%. Both soil hardness (P = 0.031) and elasticity (P = 0.048) decreased significantly in the presence of root hairs in silt loam soil, by 50% and 36%, respectively. Root hairs also led to significantly smaller water repellency (P = 0.007) in sandy loam soil vegetated with the hairy genotype (-49%) compared to the hairless mutant. Conclusions: Breeding of cash crops for improved soil conditions could be achieved by selecting root phenotypes that ameliorate soil physical properties and therefore contribute to increased soil health. Supplementary Information: The online version contains supplementary material available at 10.1007/s11104-022-05530-1.

A dual porosity model of nutrient uptake by root hairs.

• The importance of root hairs in the uptake of sparingly soluble nutrients is understood qualitatively, but not quantitatively, and this limits efforts to breed plants tolerant of nutrient-deficient soils. • Here, we develop a mathematical model of nutrient uptake by root hairs allowing for hair geometry and the details of nutrient transport through soil, including diffusion within and between soil particles. We give illustrative results for phosphate uptake. • Compared with conventional 'single porosity' models, this 'dual porosity' model predicts greater root uptake because more nutrient is available by slow release from within soil particles. Also the effect of soil moisture is less important with the dual porosity model because the effective volume available for diffusion in the soil is larger, and the predicted effects of hair length and density are different. • Consistent with experimental observations, with the dual porosity model, increases in hair length give greater increases in uptake than increases in hair density per unit main root length. The effect of hair density is less in dry soil because the minimum concentration in solution for net influx is reached more rapidly. The effect of hair length is much less sensitive to soil moisture.

Quantifying citrate-enhanced phosphate root uptake using microdialysis.

AIMS: Organic acid exudation by plant roots is thought to promote phosphate (P) solubilisation and bioavailability in soils with poorly available nutrients. Here we describe a new combined experimental (microdialysis) and modelling approach to quantify citrate-enhanced P desorption and its importance for root P uptake. METHODS: To mimic the rhizosphere, microdialysis probes were placed in soil and perfused with citrate solutions (0.1, 1.0 and 10 mM) and the amount of P recovered from soil used to quantify rhizosphere P availability. Parameters in a mathematical model describing probe P uptake, citrate exudation, P movement and citrate-enhanced desorption were fit to the experimental data. These parameters were used in a model of a root which exuded citrate and absorbed P. The importance of soil citrate-P mobilisation for root P uptake was then quantified using this model. RESULTS: A plant needs to exude citrate at a rate of 0.73 µmol cm-1 of root h-1 to see a significant increase in P absorption. Microdialysis probes with citrate in the perfusate were shown to absorb similar quantities of P to an exuding root. CONCLUSION: A single root exuding citrate at a typical rate (4.3 × 10-5 µmol m-1 of root h-1) did not contribute significantly to P uptake. Microdialysis probes show promise for measuring rhizosphere processes when calibration experiments and mathematical modelling are used to decouple microdialysis and rhizosphere mechanisms.

Precipitation-optimised targeting of nitrogen fertilisers in a model maize cropping system.

Typically, half of the nitrogen (N) fertiliser applied to agricultural fields is lost to the wider environment. This inefficiency is driven by soil processes such as denitrification, volatilisation, surface run-off and leaching. Rainfall plays an important role in regulating these processes, ultimately governing when and where N fertiliser moves in soil and its susceptibility to gaseous loss. The interaction between rainfall, plant N uptake and N losses, however, remains poorly understood. In this study we use numerical modelling to predict the optimal N fertilisation strategy with respect to rainfall patterns and offer mechanistic explanations to the resultant differences in optimal times of fertiliser application. We developed a modelling framework that describes water and N transport in soil over a growing season and assesses nitrogen use efficiency (NUE) of split fertilisations within the context of different rainfall patterns. We used ninety rainfall patterns to determine their impact on optimal N fertilisation times. We considered the effects of root growth, root N uptake, microbial transformation of N and the effect of soil water saturation and flow on N movement in the soil profile. On average, we show that weather-optimised fertilisation strategies could improve crop N uptake by 20% compared to the mean uptake. In drier years, weather-optimising N applications improved the efficiency of crop N recovery by 35%. Further analysis shows that maximum plant N uptake is greatest under drier conditions due to reduced leaching, but it is harder to find the maximum due to low N mobility. The model could capture contrasting trends in NUE seen in previous arable cropping field trials. Furthermore, the model predicted that the variability in NUE seen in the field could be associated with precipitation-driven differences in N leaching and mobility. In conclusion, our results show that NUE in cropping systems could be significantly enhanced by synchronising fertiliser timings with both crop N demand and local weather patterns.

A dynamic model of nutrient uptake by root hairs.

Root hairs are known to be important in the uptake of sparingly soluble nutrients by plants, but quantitative understanding of their role in this is weak. This limits, for example, the breeding of more nutrient-efficient crop genotypes. We developed a mathematical model of nutrient transport and uptake in the root hair zone of single roots growing in soil or solution culture. Accounting for root hair geometry explicitly, we derived effective equations for the cumulative effect of root hair surfaces on uptake using the method of homogenization. Analysis of the model shows that, depending on the morphological and physiological properties of the root hairs, one of three different effective models applies. They describe situations where: (1) a concentration gradient dynamically develops within the root hair zone; (2) the effect of root hair uptake is negligibly small; or (3) phosphate in the root hair zone is taken up instantaneously. Furthermore, we show that the influence of root hairs on rates of phosphate uptake is one order of magnitude greater in soil than solution culture. The model provides a basis for quantifying the importance of root hair morphological and physiological properties in overall uptake, in order to design and interpret experiments in different circumstances.

Mechanisms of root reinforcement in soils: an experimental methodology using four-dimensional X-ray computed tomography and digital volume correlation.

Vegetation on railway or highway slopes can improve slope stability through the generation of soil pore water suctions by plant transpiration and mechanical soil reinforcement by the roots. To incorporate the enhanced shearing resistance and stiffness of root-reinforced soils in stability calculations, it is necessary to understand and quantify its effectiveness. This requires integrated and sophisticated experimental and multi-scale modelling approaches to develop an understanding of the processes at different length scales, from individual root-soil interaction through to full soil-profile or slope scale. One of the challenges with multi-scale models is ensuring that they sufficiently closely represent real behaviour. This requires calibration against detailed high-quality and data-rich experiments. This study presents a novel experimental methodology, which combines in situ direct shear loading of a willow root-reinforced soil with X-ray computed tomography to capture the three-dimensional chronology of soil and root deformation within the shear zone. Digital volume correlation (DVC) analysis was applied to the computed tomography dataset to obtain full-field three-dimensional displacement and strain information. This paper demonstrates the feasibility and discusses the challenges associated with DVC experiments on root-reinforced soils.

Significance of root hairs at the field scale - modelling root water and phosphorus uptake under different field conditions.

BACKGROUND AND AIMS: Root hairs play a significant role in phosphorus (P) extraction at the pore scale. However, their importance at the field scale remains poorly understood. METHODS: This study uses a continuum model to explore the impact of root hairs on the large-scale uptake of P, comparing root hair influence under different agricultural scenarios. High vs low and constant vs decaying P concentrations down the soil profile are considered, along with early vs late precipitation scenarios. RESULTS: Simulation results suggest root hairs accounted for 50% of total P uptake by plants. Furthermore, a delayed initiation time of precipitation potentially limits the P uptake rate by over 50% depending on the growth period. Despite the large differences in the uptake rate, changes in the soil P concentration in the domain due to root solute uptake remains marginal when considering a single growth season. However, over the duration of 6 years, simulation results showed that noticeable differences arise over time. CONCLUSION: Root hairs are critical to P capture, with uptake efficiency potentially enhanced by coordinating irrigation with P application during earlier growth stages of crops.

Image-based quantification of soil microbial dead zones induced by nitrogen fertilization.

Microbial communities in agricultural soils underpin many ecosystem services including the maintenance of soil structure, food production, water purification and carbon storage. However, the impact of fertilization on the health of microbial communities is not well understood. This study investigates the spatial and temporal dynamics of nitrogen (N) transport away from a fertilizer granule with pore scale resolution. Specifically, we examined how soil structure and moisture content influence fertilizer derived N movement through the soil pore network and the subsequent impact of on soil microbial communities. We develop a mathematical model to describe N transport and reactions in soil at the pore-scale. Using X-ray Computed Tomography scans, we reconstructed a microscale description of a soil-pore geometry as a computational mesh. Solving two-phase water/air model produced pore-scale water distributions at 15, 30 and 70% water-filled pore volume. The N-speciation model considered ammonium (NH4+), nitrate (NO3-) and dissolved organic N (DON), and included N immobilization, ammonification and nitrification processes, as well as diffusion in soil solution. We simulated the dissolution of a fertilizer pellet and a pore scale N cycle at three different water saturations. To aid interpretation of the model results, microbial activity at a range of N concentrations was measured. The model showed that the diffusion and concentration of N in water films is critically dependent upon soil moisture and N species. We predict that the maximum NH4+ and NO3- concentrations in soil solution around the pellet under dry conditions are in the order of 1 × 103 and 1 × 104 mol m-3 respectively, and under wet conditions 2 × 102 and 1 × 103 mol m-3, respectively. Supporting experimental evidence suggests that these concentrations would be sufficient to reduce microbial activity in the short-term in the zone immediately around the fertilizer pellet (ranging from 0.9 to 3.8 mm), causing a major loss of soil biological functioning. This model demonstrates the importance of pore-scale processes in regulating N movement and their interactions with the soil microbiome.

Surface tension, rheology and hydrophobicity of rhizodeposits and seed mucilage influence soil water retention and hysteresis.

AIMS: Rhizodeposits collected from hydroponic solutions with roots of maize and barley, and seed mucilage washed from chia, were added to soil to measure their impact on water retention and hysteresis in a sandy loam soil at a range of concentrations. We test the hypothesis that the effect of plant exudates and mucilages on hydraulic properties of soils depends on their physicochemical characteristics and origin. METHODS: Surface tension and viscosity of the exudate solutions were measured using the Du Noüy ring method and a cone-plate rheometer, respectively. The contact angle of water on exudate treated soil was measured with the sessile drop method. Water retention and hysteresis were measured by equilibrating soil samples, treated with exudates and mucilages at 0.46 and 4.6 mg g-1 concentration, on dialysis tubing filled with polyethylene glycol (PEG) solution of known osmotic potential. RESULTS: Surface tension decreased and viscosity increased with increasing concentration of the exudates and mucilage in solutions. Change in surface tension and viscosity was greatest for chia seed exudate and least for barley root exudate. Contact angle increased with increasing maize root and chia seed exudate concentration in soil, but not barley root. Chia seed mucilage and maize root rhizodeposits enhanced soil water retention and increased hysteresis index, whereas barley root rhizodeposits decreased soil water retention and the hysteresis effect. The impact of exudates and mucilages on soil water retention almost ceased when approaching wilting point at -1500 kPa matric potential. CONCLUSIONS: Barley rhizodeposits behaved as surfactants, drying the rhizosphere at smaller suctions. Chia seed mucilage and maize root rhizodeposits behaved as hydrogels that hold more water in the rhizosphere, but with slower rewetting and greater hysteresis.

Growth model for arbuscular mycorrhizal fungi.

In order to quantify the contribution of arbuscular mycorrhizal (AM) fungi to plant phosphorus nutrition, the development and extent of the external fungal mycelium and its nutrient uptake capacity are of particular importance. We develop and analyse a model of the growth of AM fungi associated with plant roots, suitable for describing mechanistically the effects of the fungi on solute uptake by plants. The model describes the development and distribution of the fungal mycelium in soil in terms of the creation and death of hyphae, tip-tip and tip-hypha anastomosis, and the nature of the root-fungus interface. It is calibrated and corroborated using published experimental data for hyphal length densities at different distances away from root surfaces. A good agreement between measured and simulated values was found for three fungal species with different morphologies: Scutellospora calospora (Nicol. & Gerd.) Walker & Sanders; Glomus sp.; and Acaulospora laevis Gerdemann & Trappe associated with Trifolium subterraneum L. The model and findings are expected to contribute to the quantification of the role of AM fungi in plant mineral nutrition and the interpretation of different foraging strategies among fungal species.