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Chloroplasts movement within mesophyll cells in C4 plants is hypothesized to enhance the CO2 concentrating mechanism, but this is difficult to verify experimentally. A three-dimensional (3D) leaf model can help analyse how chloroplast movement influences the operation of the CO2 concentrating mechanism. The first volumetric reaction–diffusion model of C4 photosynthesis that incorporates detailed 3D leaf anatomy, light propagation, ATP and NADPH production, and CO2, O2 and bicarbonate concentration driven by diffusional and assimilation/emission processes was developed. It was implemented for maize leaves to simulate various chloroplast movement scenarios within mesophyll cells: the movement of all mesophyll chloroplasts towards bundle sheath cells (aggregative movement) and movement of only those of interveinal mesophyll cells towards bundle sheath cells (avoidance movement). Light absorbed by bundle sheath chloroplasts relative to mesophyll chloroplasts increased in both cases. Avoidance movement decreased light absorption by mesophyll chloroplasts considerably. Consequently, total ATP and NADPH production and net photosynthetic rate increased for aggregative movement and decreased for avoidance movement compared with the default case of no chloroplast movement at high light intensities. Leakiness increased in both chloroplast movement scenarios due to the imbalance in energy production and demand in mesophyll and bundle sheath cells. These results suggest the need to design strategies for coordinated increases in electron transport and Rubisco activities for an efficient CO2 concentrating mechanism at very high light intensities.

We combined a virtual leaf tissue generator and a microscale model of gas diffusion. With this tool, we demonstrated that light-saturated photosynthesis could be improved by altering cell growth and development factors., Computational tools that allow in silico analysis of the role of cell growth and division on photosynthesis are scarce. We present a freely available tool that combines a virtual leaf tissue generator and a two-dimensional microscale model of gas transport during C3 photosynthesis. A total of 270 mesophyll geometries were generated with varying degrees of growth anisotropy, growth extent, and extent of schizogenous airspace formation in the palisade mesophyll. The anatomical properties of the virtual leaf tissue and microscopic cross-sections of actual leaf tissue of tomato (Solanum lycopersicum L.) were statistically compared. Model equations for transport of CO2 in the liquid phase of the leaf tissue were discretized over the geometries. The virtual leaf tissue generator produced a leaf anatomy of tomato that was statistically similar to real tomato leaf tissue. The response of photosynthesis to intercellular CO2 predicted by a model that used the virtual leaf tissue geometry compared well with measured values. The results indicate that the light-saturated rate of photosynthesis was influenced by interactive effects of extent and directionality of cell growth and degree of airspace formation through the exposed surface of mesophyll per leaf area. The tool could be used further in investigations of improving photosynthesis and gas exchange in relation to cell growth and leaf anatomy.

Methods using gas exchange measurements to estimate respiration in the light (day respiration Rd ) make implicit assumptions about reassimilation of (photo)respired CO2 ; however, this reassimilation depends on the positions of mitochondria. We used a reaction-diffusion model without making these assumptions to analyse datasets on gas exchange, chlorophyll fluorescence and anatomy for tomato leaves. We investigated how Rd values obtained by the Kok and the Yin methods are affected by these assumptions and how those by the Laisk method are affected by the positions of mitochondria. The Kok method always underestimated Rd . Estimates of Rd by the Yin method and by the reaction-diffusion model agreed only for nonphotorespiratory conditions. Both the Yin and Kok methods ignore reassimilation of (photo)respired CO2 , and thus underestimated Rd for photorespiratory conditions, but this was less so in the Yin than in the Kok method. Estimates by the Laisk method were affected by assumed positions of mitochondria. It did not work if mitochondria were in the cytosol between the plasmamembrane and the chloroplast envelope. However, mitochondria were found to be most likely between the tonoplast and chloroplasts. Our reaction-diffusion model effectively estimates Rd , enlightens the dependence of Rd estimates on reassimilation and clarifies (dis)advantages of existing methods. ispartof: NEW PHYTOLOGIST vol:223 issue:2 pages:619-631 ispartof: location:England status: published

Summary Methods using gas exchange measurements to estimate respiration in the light (day respiration Rd) make implicit assumptions about reassimilation of (photo)respired CO 2; however, this reassimilation depends on the positions of mitochondria.We used a reaction‐diffusion model without making these assumptions to analyse datasets on gas exchange, chlorophyll fluorescence and anatomy for tomato leaves. We investigated how Rd values obtained by the Kok and the Yin methods are affected by these assumptions and how those by the Laisk method are affected by the positions of mitochondria.The Kok method always underestimated Rd. Estimates of Rd by the Yin method and by the reaction‐diffusion model agreed only for nonphotorespiratory conditions. Both the Yin and Kok methods ignore reassimilation of (photo)respired CO 2, and thus underestimated Rd for photorespiratory conditions, but this was less so in the Yin than in the Kok method. Estimates by the Laisk method were affected by assumed positions of mitochondria. It did not work if mitochondria were in the cytosol between the plasmamembrane and the chloroplast envelope. However, mitochondria were found to be most likely between the tonoplast and chloroplasts.Our reaction‐diffusion model effectively estimates Rd, enlightens the dependence of Rd estimates on reassimilation and clarifies (dis)advantages of existing methods.

We present a combined three-dimensional (3-D) model of light propagation, CO2 diffusion and photosynthesis in tomato (Solanum lycopersicum L.) leaves. The model incorporates a geometrical representation of the actual leaf microstructure that we obtained with synchrotron radiation X-ray laminography, and was evaluated using measurements of gas exchange and leaf optical properties. The combination of the 3-D microstructure of leaf tissue and chloroplast movement induced by changes in light intensity affects the simulated CO2 transport within the leaf. The model predicts extensive reassimilation of CO2 produced by respiration and photorespiration. Simulations also suggest that carbonic anhydrase could enhance photosynthesis at low CO2 levels but had little impact on photosynthesis at high CO2 levels. The model confirms that scaling of photosynthetic capacity with absorbed light would improve efficiency of CO2 fixation in the leaf, especially at low light intensity.

C4 plants such as maize (Zea mays L.), sugarcane (Saccharum officinarum L.) and sorghum [Sorghum bicolor (L.) Moench.] photosynthesize at a high rate due to a CO2 concentration mechanism (CCM) that accumulates CO2 to saturating concentrations around the carboxylation site of ribulose-1,5-bisphosphate carboxylase/oxygenase (Rubisco). Transport of CO2 inside a leaf and, therefore, the CCM, is affected by leaf microstructure. Gas transport models with a realistic leaf microstructure help to assess the significance of anatomical features of C4 plants quantitatively for effective CCM. One- and two-dimensional gas transport models, when applied to analyze the gas diffusion in leaves, understate the three-dimensional nature. Here, we present the first 3D reaction-diffusion model for photosynthesis of a C4 leaf. Equations of CO2 transport and bicarbonate diffusion combined with a biochemical model of C4 photosynthesis were discretized over the 3D geometry of a maize leaf tissue. The model could describe the trends in responses of photosynthesis to light and CO2. The CO2 profile in the leaf microstructure was highly heterogeneous. The model suggests that rapid diffusion of CO2 to mesophyll cytosol is essential to achieve a high rate of photosynthesis.

A multiphase pore scale network model was developed to describe mass transfer in apple fruit. The 3D microscale geometry of the tissue was reconstructed from synchrotron radiation tomography images. Individual cells and pores were identified using a watershed segmentation procedure on a Euclidean distance map of the tissue microstructure. Further morphological characteristics of each individual pore, including its volume, connections to the neighbors and the connected area between the pore and its neighbors, were determined. The tissue was represented by a network of nodes (simplified individual pores and cells) that were interconnected by tubes. The transport of the respiratory gases O2 and CO2 between two nodes was modelled using diffusion laws and irreversible thermodynamics, while respiration was taken into account in the individual cellular nodes. A numerical procedure was applied to simulate the gas transport within the discrete network and to compute the local diffusivities of the links in the network. The predicted overall gas diffusivities compared well to experimental data and results computed from a microscale continuum model, thereby validating the pore scale network model. This approach is a computationally attractive alternative to a continuum multiphase approach for modelling gas transport in fruit.

The mechanism of photosynthesis in C4 crops depends on the archetypal Kranz-anatomy. To examine how the leaf anatomy, as altered by nitrogen supply and leaf age, affects the bundle sheath conductance (gbs), maize (Zea mays L.) plants were grown under three contrasting nitrogen levels. Combined gas exchange and chlorophyll fluorescence measurements were done on fully grown leaves at two leaf ages. The measured data were analysed using a biochemical model of C4 photosynthesis to estimate gbs. The leaf microstructure and ultrastructure were quantified using images obtained from micro-computed tomography and microscopy. There was a strong positive correlation between gbs and leaf nitrogen content (LNC) while old leaves had lower gbs than young leaves. Leaf thickness, bundle sheath cell wall thickness and surface area of bundle sheath cells per unit leaf area (Sb) correlated well with gbs although they were not significantly affected by LNC. As a result, the increase of gbs with LNC was little explained by the alteration of leaf anatomy. In contrast, the combined effect of LNC and leaf age on Sb was responsible for differences in gbs between young leaves and old leaves. Future investigations should consider changes at the level of plasmodesmata and membranes along the CO2 leakage pathway to unravel LNC and age effects further. publisher: Elsevier articletitle: Impact of anatomical traits of maize (Zea mays L.) leaf as affected by nitrogen supply and leaf age on bundle sheath conductance journaltitle: Plant Science articlelink: http://dx.doi.org/10.1016/j.plantsci.2016.07.013 content_type: article copyright: © 2016 Elsevier Ireland Ltd. All rights reserved. ispartof: Plant Science vol:252 pages:205-214 ispartof: location:Ireland status: published

One way to increase potential crop yield could be increasing mesophyll conductance g

Exchange of CO2 in tomato (Solanum lycopersicum L.) leaves was modelled using combined gas diffusion and photosynthesis kinetics in a real 3-D geometric representation of the cellular microstructure, obtained by synchrotron radiation X-ray microtomography. The microscale model for gas exchange accounted for diffusive mass transport of CO2 in the intercellular space (pores), the cell wall network and the intracellular liquid of cells. The photosynthesis kinetics described by the extended Farquhar, von Caemmerer & Berry model were coupled to the gas exchange inside the mesophyll cells. The coupled model was validated by means of gas exchange and chlorophyll fluorescence measurements. The model provides detailed insight into the mechanisms of gas exchange and insight into the effects of changes in ambient CO2 concentration or photon flux density on stomatal and mesophyll conductance. The resistance to diffusion of CO2 from the intercellular air spaces within the leaf through the mesophyll to the sites of carboxylation during photosynthesis depended on the 3-D microstructure of leaf tissue. The model represents an important step forward to study CO2 diffusion coupled to photosynthesis at the leaf tissue level, taking into account its actual 3-D microstructure.

A cell growth algorithm for virtual leaf tissue generation is presented based on the biomechanics of plant cells in tissues. The algorithm can account for typical differences in epidermal layers, palisade mesophyll layer and spongy mesophyll layer which have characteristic differences in the shape of cells, arrangement of cells and void fractions present in each layer. The cell is considered as a closed thin walled structure, maintained in tension by turgor pressure. The cell walls are modelled as linear elastic elements which obey Hooke's law. A Voronoi tessellation was used to generate the initial topology of the cells in the spongy mesophyll layer. Then two layers of brick structured cells are added to the top of it to represent the palisade mesophyll and upper epidermis and a single layer is added at bottom of the Voronoi tessellation to represent the lower epidermal layer. Intercellular air spaces are generated by separating the Voronoi cells along the edges starting from where three Voronoi cells are in contact (schizogenous origin) and/or by deleting some of the Voronoi cells (lysigenous origin). Cell expansion then results from turgor pressure acting on the yielding cell wall material. To find the sequence of positions of each vertex and thus the shape of the tissue with time, a system of differential equations for the positions and velocities of each vertex is established and solved using the ordinary differential equation solver in MatLab. Statistical comparison of the cellular characteristics with 2D cross-sectional slices of real leaf tissue of tomato is excellent. The virtual tissues can be used to systematically study effects of leaf structure on water and gas exchange.

One way to increase potential crop yield could be increasing mesophyll conductance gm. This variable determines the difference between the CO2 partial pressure in the intercellular air spaces (Ci) and that near Rubisco (Cc). Various methods can determine gm from gas exchange measurements, often combined with measurements of chlorophyll fluorescence or carbon isotope discrimination. gm lumps all biochemical and physical factors that cause the difference between Cc and Ci. gm appears to vary with Ci. This variability indicates that gm does not satisfy the physical definition of a conductance according to Fick's first law and is thus an apparent parameter. Uncertainty about the mechanisms that determine gm can be limited to some extent by using analytical models that partition gm into separate conductances. Such models are still only capable of describing the CO2 diffusion pathway to a limited extent, as they make implicit assumptions about the position of mitochondria in the cells, which affect the re-assimilation of (photo)respired CO2. Alternatively, reaction-diffusion models may be used. Rather than quantifying gm, these models explicitly account for factors that affect the efficiency of CO2 transport in the mesophyll. These models provide a better mechanistic description of the CO2 diffusion pathways than mesophyll conductance models. Therefore, we argue that reaction-diffusion models should be used as an alternative to mesophyll conductance models, in case the aim of such a study is to identify traits that can be improved to increase gm.

CO2 exchange in leaves of maize (Zea mays L.) was examined using a microscale model of combined gas diffusion and C4 photosynthesis kinetics at the leaf tissue level. Based on a generalized scheme of photosynthesis in NADP-malic enzyme type C4 plants, the model accounted for CO2 diffusion in a leaf tissue, CO2 hydration and assimilation in mesophyll cells, CO2 release from decarboxylation of C4 acids, CO2 fixation in bundle sheath cells and CO2 retro-diffusion from bundle sheath cells. The transport equations were solved over a realistic 2-D geometry of the Kranz anatomy obtained from light microscopy images. The predicted responses of photosynthesis rate to changes in ambient CO2 and irradiance compared well with those obtained from gas exchange measurements. A sensitivity analysis showed that the CO2 permeability of the mesophyll-bundle sheath and airspace-mesophyll interfaces strongly affected the rate of photosynthesis and bundle sheath conductance. Carbonic anhydrase influenced the rate of photosynthesis, especially at low intercellular CO2 levels. In addition, the suberin layer at the exposed surface of the bundle sheath cells was found beneficial in reducing the retro-diffusion. The model may serve as a tool to investigate CO2 diffusion further in relation to the Kranz anatomy in C4 plants. publisher: Elsevier articletitle: A two-dimensional microscale model of gas exchange during photosynthesis in maize (Zea mays L.) leaves journaltitle: Plant Science articlelink: http://dx.doi.org/10.1016/j.plantsci.2016.02.003 content_type: article copyright: Copyright © 2016 Elsevier Ireland Ltd. All rights reserved. ispartof: PLANT SCIENCE vol:246 pages:37-51 ispartof: location:Ireland status: published

The CO2 concentration near Rubisco and, therefore, the rate of CO2 assimilation, is influenced by both leaf anatomical factors and biochemical processes. Leaf anatomical structures act as physical barriers for CO2 transport. Biochemical processes add or remove CO2 along its diffusion pathway through mesophyll. We combined a model that quantifies the diffusive resistance for CO2 using anatomical properties, a model that partitions this resistance and an extended version of the Farquhar-von Caemmerer-Berry model. We parametrized the model by gas exchange, chlorophyll fluorescence and leaf anatomical measurements from three tomato cultivars. There was generally a good agreement between the predicted and measured light and CO2 response curves. We did a sensitivity analysis to assess how the rate of CO2 assimilation responds to changes in various leaf anatomical properties. Next, we conducted a similar analysis for assumed diffusive properties and curvature factors. Some variables (diffusion pathway length in stroma, diffusion coefficient of the stroma, curvature factors) substantially affected the predicted CO2 assimilation. We recommend more research on the measurements of these variables and on the development of 2-D and 3-D gas diffusion models, since these do not require the diffusion pathway length in the stroma as predefined parameter. publisher: Elsevier articletitle: Modelling the relationship between CO2 assimilation and leaf anatomical properties in tomato leaves journaltitle: Plant Science articlelink: http://dx.doi.org/10.1016/j.plantsci.2015.06.022 content_type: article copyright: Copyright © 2015 Elsevier Ireland Ltd. All rights reserved. ispartof: Plant Science vol:238 pages:297-311 ispartof: location:Ireland status: published

We present a combined three-dimensional (3-D) model of light propagation, CO2 diffusion and photosynthesis in tomato (Solanum lycopersicum L.) leaves. The model incorporates a geometrical representation of the actual leaf microstructure that we obtained with synchrotron radiation X-ray laminography, and was evaluated using measurements of gas exchange and leaf optical properties. The combination of the 3-D microstructure of leaf tissue and chloroplast movement induced by changes in light intensity affects the simulated CO2 transport within the leaf. The model predicts extensive reassimilation of CO2 produced by respiration and photorespiration. Simulations also suggest that carbonic anhydrase could enhance photosynthesis at low CO2 levels but had little impact on photosynthesis at high CO2 levels. The model confirms that scaling of photosynthetic capacity with absorbed light would improve efficiency of CO2 fixation in the leaf, especially at low light intensity.