Using a reaction-diffusion model to estimate day respiration and reassimilation of (photo)respired CO2 in leaves.

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.

Localization of (photo)respiration and CO2 re-assimilation in tomato leaves investigated with a reaction-diffusion model.

The rate of photosynthesis depends on the CO2 partial pressure near Rubisco, Cc, which is commonly calculated by models using the overall mesophyll resistance. Such models do not explain the difference between the CO2 level in the intercellular air space and Cc mechanistically. This problem can be overcome by reaction-diffusion models for CO2 transport, production and fixation in leaves. However, most reaction-diffusion models are complex and unattractive for procedures that require a large number of runs, like parameter optimisation. This study provides a simpler reaction-diffusion model. It is parameterized by both leaf physiological and leaf anatomical data. The anatomical data consisted of the thickness of the cell wall, cytosol and stroma, and the area ratios of mesophyll exposed to the intercellular air space to leaf surfaces and exposed chloroplast to exposed mesophyll surfaces. The model was used directly to estimate photosynthetic parameters from a subset of the measured light and CO2 response curves; the remaining data were used for validation. The model predicted light and CO2 response curves reasonably well for 15 days old tomato (cv. Admiro) leaves, if (photo)respiratory CO2 release was assumed to take place in the inner cytosol or in the gaps between the chloroplasts. The model was also used to calculate the fraction of CO2 produced by (photo)respiration that is re-assimilated in the stroma, and this fraction ranged from 56 to 76%. In future research, the model should be further validated to better understand how the re-assimilation of (photo)respired CO2 is affected by environmental conditions and physiological parameters.

Mesophyll conductance and reaction-diffusion models for CO2 transport in C3 leaves; needs, opportunities and challenges.

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.

Modelling the relationship between CO2 assimilation and leaf anatomical properties in tomato leaves.

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.

Genotype effects on internal gas gradients in apple fruit.

A permeation-diffusion-reaction model was applied to study gas exchange of apple fruit (Kanzi, Jonagold, and Braeburn) as effected by morphology and respiratory metabolism. The gas exchange properties and respiration parameters of the fruit organ tissues were measured. The actual internal tissue geometry of the fruit was reconstructed from digital fruit images and the model was solved over this geometry using the finite element method. The model was validated based on measurements of internal gas concentrations and the gas flux of the fruit to its environment. Both measurements and an in silico study revealed that gradients of metabolic gases exist in apple fruit, depending on diffusion properties and respiration of the different cultivars. Macroscale simulation confirmed that Jonagold has large potential for controlled atmosphere (CA) storage while low diffusion properties of cortex tissue in Braeburn indicated a risk of storage disorder development. Kanzi had less O(2) anoxia at CA storage compared with Braeburn.

A model for gas transport in pear fruit at multiple scales.

A two-dimensional multiscale gas exchange model was developed to evaluate the effect of ambient conditions, fruit size, and maturity on intracellular O(2) and CO(2) concentrations in pear fruit via computational analysis. The model consists of interconnected submodels that describe the gas exchange at the macroscopic scale of the fruit and the microscopic scale of the cells. The multiscale model resulted in a comprehensive description of gas exchange at different scales. The macroscale model was used to describe the gas exchange of the fruit under controlled atmosphere conditions while corresponding intracellular concentrations of microstructure tissue were computed from the microscale. Ripening of the fruit increased the risk of physiological disorders, since increased respiration resulted in anoxia in the fruit centre even under typical storage conditions.

A continuum model for metabolic gas exchange in pear fruit.

Exchange of O(2) and CO(2) of plants with their environment is essential for metabolic processes such as photosynthesis and respiration. In some fruits such as pears, which are typically stored under a controlled atmosphere with reduced O(2) and increased CO(2) levels to extend their commercial storage life, anoxia may occur, eventually leading to physiological disorders. In this manuscript we have developed a mathematical model to predict the internal gas concentrations, including permeation, diffusion, and respiration and fermentation kinetics. Pear fruit has been selected as a case study. The model has been used to perform in silico experiments to evaluate the effect of, for example, fruit size or ambient gas concentration on internal O(2) and CO(2) levels. The model incorporates the actual shape of the fruit and was solved using fluid dynamics software. Environmental conditions such as temperature and gas composition have a large effect on the internal distribution of oxygen and carbon dioxide in fruit. Also, the fruit size has a considerable effect on local metabolic gas concentrations; hence, depending on the size, local anaerobic conditions may result, which eventually may lead to physiological disorders. The model developed in this manuscript is to our knowledge the most comprehensive model to date to simulate gas exchange in plant tissue. It can be used to evaluate the effect of environmental stresses on fruit via in silico experiments and may lead to commercial applications involving long-term storage of fruit under controlled atmospheres.

A permeation-diffusion-reaction model of gas transport in cellular tissue of plant materials.

Gas transport in fruit tissue is governed by both diffusion and permeation. The latter phenomenon is caused by overall pressure gradients which may develop due to the large difference in O(2) and CO(2) diffusivity during controlled atmosphere storage of the fruit. A measurement set-up for tissue permeation based on unsteady-state gas exchange was developed. The gas permeability of pear tissue was determined based on an analytical gas transport model. The overall gas transport in pear tissue samples was validated using a finite element model describing simultaneous O(2), CO(2), and N(2) gas transport, taking into account O(2) consumption and CO(2) production due to respiration. The results showed that the model described the experimentally determined permeability of N(2) very well. The average experimentally determined values for permeation of skin, cortex samples, and the vascular bundle samples were (2.17+/-1.71)x10(-19) m(2), (2.35+/-1.96)x10(-19) m(2), and (4.51+/-3.12)x10(-17) m(2), respectively. The permeation-diffusion-reaction model can be applied to study gas transport in intact pears in relation to product quality.