Microscale mechanisms of gas exchange in fruit tissue

Authors

  • Q. T. Ho,

    1. Flanders Center of Postharvest Technology, BIOSYST-MeBioS, Katholieke Universiteit Leuven, Willem de Croylaan 42, B-3001 Leuven, Belgium;
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  • P. Verboven,

    1. Flanders Center of Postharvest Technology, BIOSYST-MeBioS, Katholieke Universiteit Leuven, Willem de Croylaan 42, B-3001 Leuven, Belgium;
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  • H. K. Mebatsion,

    1. Flanders Center of Postharvest Technology, BIOSYST-MeBioS, Katholieke Universiteit Leuven, Willem de Croylaan 42, B-3001 Leuven, Belgium;
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  • B. E. Verlinden,

    1. Flanders Center of Postharvest Technology, BIOSYST-MeBioS, Katholieke Universiteit Leuven, Willem de Croylaan 42, B-3001 Leuven, Belgium;
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  • S. Vandewalle,

    1. Scientific Computing Research Group, Computer Science Dept., Katholieke Universiteit Leuven, Celestijnenlaan 200A, B-3001 Leuven, Belgium
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  • B. M. Nicolaï

    1. Flanders Center of Postharvest Technology, BIOSYST-MeBioS, Katholieke Universiteit Leuven, Willem de Croylaan 42, B-3001 Leuven, Belgium;
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Author for correspondence:
Bart Nicolaï
Tel: +32 16 32 23 75
Fax:+32 16 32 29 55
Email: bart.nicolai@biw.kuleuven.be

Summary

  • • Gas-filled intercellular spaces are considered the predominant pathways for gas transport through bulky plant organs such as fruit. Here, we introduce a methodology that combines a geometrical model of the tissue microstructure with mathematical equations to describe gas exchange mechanisms involved in fruit respiration.
  • • Pear (Pyrus communis) was chosen as a model system. The two-dimensional microstructure of cortex tissue was modelled based on light microscopy images. The transport of O2 and CO2 in the intercellular space, cell wall network and cytoplasm was modelled using diffusion laws, irreversible thermodynamics and enzyme kinetics.
  • • In silico analysis showed that O2 transport mainly occurred through intercellular spaces and less through the intracellular liquid, while CO2 was transported at equal rates in both phases. Simulations indicated that biological variation of the apparent diffusivity appears to be caused by the random distribution of cells and intercellular spaces in tissue. Temperature does not affect modelled gas exchange properties; it rather acts on the respiration metabolism.
  • • This modelling approach provides, for the first time, detailed information about gas exchange mechanisms at the microscopic scale in bulky plant organs, such as fruit, and can be used to study conditions of anoxia.

Introduction

Diffusion barriers have been shown to restrict fluxes of O2 and CO2 to cells in bulky plant organs such as roots, tubers, stems, inflorescences, seeds and fruit (Sinclair & Goudriaan, 1981; Drew, 1997; Geigenberger et al., 2000; Seymour, 2001; Van Dongen et al., 2003; Armstrong et al., 2006). Restricted fluxes of respiratory gases may lead to anoxia, eventually resulting in cell death (Malik et al., 2003; Franck et al., 2007). Differences in gas exchange properties of plant organs have been observed in response to a wide range of factors covering nutrient availability, water status, environmental conditions, development stage, cultivar and crop management (Malik et al., 2003; Armstrong et al., 2006; Ho et al., 2006a). Knowledge of gas exchange mechanisms would be very valuable to guide commercial storage practices for stored fruits, such as pears, since disorders under controlled atmosphere related to fermentation are a prime cause of concern (Franck et al., 2007). The intercellular free space is believed to affect gas exchange in the fruit tissue greatly (Raven, 1996, Armstrong et al., 2006), as it provides a low resistance pathway for gas supply. At the fruit tissue level, the hypothesis is that O2 is transported through the intercellular space and subsequently permeates through the cellular membrane to the cytoplasm. Finally, the O2 diffuses within the cytoplasm into the mitochondria. Through respiration, O2 is reduced to water and CO2 is produced. CO2 essentially follows the reversed path. However, the air volume fraction of fruit such as pear is smaller than 10% of the fruit volume (Schotsmans et al., 2002). Further, the solubility of CO2 in water is higher than that of O2 and the magnitude of the CO2 concentration in the liquid phase is comparable to its concentration in air; therefore, the exchange mechanisms of the two gases may be significantly different. The relative importance of intra- and intercellular gas exchange rates and metabolic reaction rates has not yet been quantified.

Gas exchange in fruit and other bulky storage organs has been described macroscopically with Fick's laws (Burg & Burg, 1965, Cameron & Yang, 1982; Lammertyn et al., 2001a; Schotsmans et al., 2003; Ho et al., 2006a,b). Typically, the gas exchange at the microscale is not modelled explicitly; instead a macroscopic diffusion equation is used containing empirical apparent diffusivities that implicitly incorporate the microscale topology (Wood et al., 2002, Ho et al., 2006b). This averaging procedure essentially hides the microscale phenomena that are essential to understanding gas exchange. A microscale model of gas exchange in fruit tissue is therefore essential. Microscale exchange of CO2 in leaves has been investigated using theoretical models (Vesala et al., 1996, Aalto & Juurola, 2002). However, O2 transport, which is essential to respiration processes in fruit was not addressed, and the geometrical model was relatively crude compared with the actual irregular microstructure of the tissue.

Mass transport of a component gas occurs in both the gas phase of the intercellular space and the liquid phase of the cytoplasm. Gas exchange between the intercellular space and the cell can be described by gas permeation through the plasma membrane (Nobel, 1991). Gas equilibrium between the gas and liquid phase follows Henry's law (Lide, 1999). CO2 transport is complicated by the fact that there is hydration of CO2 into inline image. Moreover, the equilibrium between soluble forms of CO2 in the liquid phase is affected by the cytoplasmatic and vacuolar pH (Bown, 1985; Boron, 2004). Transport of CO2 in biological liquids in the form of dissolved CO2 and inline image was discussed for blood and mammal tissue by Geers & Gros (2000). A recent review by Teskey et al. (2008) indicates that the high CO2 storage capacity through hydration and dissociation of CO2 to other forms in the liquid phase can affect CO2 exchange considerably. Hydration and dissociation of CO2 to other forms in the liquid phase have not yet been investigated quantitatively in relation to CO2 transport in plant tissue.

In this manuscript, a new approach for the detailed study of O2 and CO2 exchange through the intercellular spaces, cell wall and cytoplasm of cells in fruit tissue is introduced, using a microscale model and pear as a model system. The objectives were: (i) to verify the applicability of the microscale model of gas transport at the tissue level based on measured gas exchange rates and gas concentration profiles in intact fruit; and (ii) to quantify the pathways of gas exchange in relation to the microstructure of fruit tissue.

Materials and Methods

Materials

Pears (Pyrus communis L. cv. ‘Conference’) were harvested on 20 August 2007 at the pre-climacteric stage at the Fruitteeltcentrum (Rillaar, Belgium), cooled and stored according to commercial protocols for a period of 21 d at −0.5°C preceding controlled atmosphere (CA) storage (2.5 kPa O2, 0.7 kPa CO2 at −0.5°C) until they were used for the experiments.

Gas concentration profiles in intact fruit

The O2 concentration in the centre of intact pear fruit was measured with fluorescent optical probes (Foxy-18G probe with overcoat, Ocean Optics, Duiven, the Netherlands) by inserting the probe along the equatorial radial direction at about 31 mm depth towards the centre of the fruit after calibration in water with dissolved O2 at different concentrations. Afterwards, a second calibration was performed to correct for sensor drift (Ho et al., 2006a). The sensor uses fluorescence quenching of a rhutenium complex by O2, which diffuses in a dye covering the tip of the fibreoptic probe.

Macroscale continuum model

The equations that describe gas transport and respiration kinetics were volumed-averaged to derive a continuum model (macroscale) (Wood et al., 2002; Ho et al., 2006b). For the continuum model, it was assumed that gas transport in plant materials was macroscopically approximated by Fick's law of diffusion, including the consumption and production of metabolic active gases resulting from respiration and fermentation, and characterized by apparent diffusivities of tissue (Lammertyn et al., 2003; Ho et al., 2008). Overall macroscopic gas concentration gradients were calculated by dividing the difference in concentration just beneath the skin and in the core of the fruit by its major radius.

Characteristic gas exchange rates in tissue samples

Overall gas diffusion rates through fruit tissue samples of 1–2 mm thickness were measured by the method described by Ho et al. (2006a). The results are given in terms of the apparent diffusivity (m2 s−1), that is, the rate (mol s−1 m−2) expressed per unit thickness (m) and per unit concentration difference (mol m−3) over the sample slice. Therefore, this value is assumed to be characteristic of the particular tissue regardless of the concentration gradient and the sample thickness.

Construction of a 2D geometric model of pear cortex tissue

Light microscopic images of cortex parenchyma tissue of pear (Pyrus communis cv. ‘Conference’) were used as a basis for 2D geometric model (see Mebatsion et al., 2006a for more details about sample preparation and microscopy). Geometric models (Fig. 1) were constructed from the images using an ellipse tessellation algorithm (Mebatsion et al., 2006b). More details are provided in the Supporting Information, Text S1.

Figure 1.

Light microscopic image of pear tissue versus geometrical model using the ellipse tessellation algorithm. (a) Original light microscopic image of pear tissue; (b) ellipse tessellation geometry; (c) transmission electron microscopic image of pear cortex tissue for cell wall thickness determination; (d) detail of tissue structure model.

Microscale gas exchange model

The microscale model for gas exchange included mass transport of the respiratory gases in the intercellular space (pore), the cell wall network, through the cell membrane into the cytoplasm. Respiration was taken into account. We have supposed that the size of the pores and channels connecting the pores (equivalent diameter of about 18 µm for pear, Verboven et al., 2008) is large compared with the mean free path of molecular motions, which is typically 0.07 µm for N2 at 20°C and 105 Pa (Leuning, 1983). Therefore, microscale diffusion was considered to be mainly through Fickian instead of Knudsen diffusion.

O2 transport model  Microscale diffusion was assumed to dominate transport through each of the compartments and was described by Fick's second law, with the characteristic diffusion coefficient inline image (Eqn 1). Respiration was incorporated into the model as a source term inline image.

image(Eqn 1)

where all symbols are listed in Appendix A1.

Redgwell et al. (1997) assumed that the cell wall of fruit was a porous network of cellulose and hemicellulose, and swelling of the cell wall during fruit ripening was associated with movement of water into the voids of the cell wall network by solubilized pectin. In such a case, the resistance would be high. However, no data are available as yet to support this hypothesis. In this study, the cell wall was assumed to be a porous material with air voids. It was therefore assumed that in the intercellular space and the cell wall network, O2 diffuses through the gas phase, while in the cytoplasm it diffuses through the liquid phase. This assumption is discussed later on. The relationship between the O2 concentration in the gas phase inline image and that in the liquid phase inline image is given by Henry's law:

image(Eqn 2)

In the intercellular space and the cell wall network, the respiration inline image is zero, while in the intracellular liquid phase this term is the consumption rate of O2. Michaelis–Menten kinetics were used as a phenomenological model to describe the O2 consumption rate of cell protoplasts (Lammertyn et al., 2001b):

image(Eqn 3)

The cell membrane is essentially a phospholipid bilayer. Passive gas transfer across the cell membrane occurs according to Fick's first law as a consequence of a concentration difference over the membrane. The flux inline image (mol m−2 s−1) through the membrane was equal to:

image(Eqn 4)

CO2 transport model (lumped CO2 transport model)  Transport of CO2 was considered to be transported by means of diffusion through the intercellular space, the cell walls and the cytoplasm. For pores and cell walls, the following equation was used:

image(Eqn 5)

Similar to O2, transport of CO2 in the cell wall was assumed to occur in the gas phase.

The model for CO2 transport in the cytoplasm was more complex because of the various equilibria of CO2 in the liquid phase. The cytoplasmic pH of plant cells appears to be fairly constant and c. 7 despite metabolic processes which generate or consume H+ and despite the wide variation in the external pH (Smith & Raven, 1979; Roberts et al., 1982). The pH in the vacuole is lower as a result of the large pool of organic acids. Therefore, dissociation of inline image to H+ and inline image was neglected in both the cytoplasm and the vacuole. The diffusivity of H+ is high (9.3 × 10−9 m2 s−1; Lide, 1999) so that within the cytoplasm or vacuole the pH can be assumed constant and uniform in this model. The model of CO2 transport in the liquid phase was, therefore:

image( Eqn 6)
image( Eqn 7)

Details of hydration and dissociation of CO2 species in liquid phase are reported in Text S4. The latter two terms of Eqns 6 and 7 represent the forward and backward conversion rate of CO2 to inline image, respectively. The equation for production rate of CO2 in the cytoplasm accounts for both oxidative and fermentative respiration (Peppelenbos et al., 1996).

image(Eqn 8)

The first term on the right-hand side indicates the oxidative CO2 production rate resulting from consumption of O2; and the second term represents anoxic conditions in the cell where the oxidative respiration process is inhibited and replaced by a fermentation pathway.

Similar to O2 transport, the flux inline image (mol m−2 s−1) through the membrane was written as

image(Eqn 9)

The relationship between the equilibrium CO2 concentrations in the gas and liquid phases was again assumed to be described by Henry's law:

image(Eqn 10)

Physical properties and respiration parameters of pores, cell walls and cells  The values and sources of the material properties and respiration parameters are listed in Table 1. The inline image at O2 saturation (2.26 × 10−4 mol m−3 s−1 at 20°C, Ho et al., 2006b) was converted to inline image by dividing it by the porosity of the tissue. inline image (mol m−3) was set equal to 3 µm (3 × 10−3 mol m−3) (Lammertyn et al., 2001b). inline image at the cellular scale was not found in the literature. However, this fermentative process is completely inhibited when the oxidative respiration is at saturation. In this study, microscale gas exchange was simulated at high O2 concentration and fermentation could thus be omitted. The rq,ox was assumed to be equal to unity for the ideal oxidative respiration of hexoses (Andrich et al., 2006).

Table 1.  Physical parameters of microscale gas transport model (bracketed numbers are references; see footnotes) (see Appendix for symbol definitions)
Model parametersO2 microscale modelCO2 microscale model
Diffusivity
 Pore
image
1.6 × 10−5 m2 s−1 at 20°C (1)
image
1.6 × 10−5 m2 s−1 at 20°C (1)
1.39 × 10−5 m2 s−1 at 0°C (1) 1.39 × 10−5 m2 s−1 at 0°C (1)
 Cell
image
2.01 × 10−9 m2 s−1 at 20°C (1)
image
1.67 × 10−9 m2 s−1 at 20°C (1)
1.07 × 10−9 m2 s−1 at 0°C (1) 0.95 × 10−9 m2 s−1 at 0°C (1)
 Cell wall
image
4.25 × 10−9 m2 s−1
image
5.23 × 10−9 m2 s−1
image
1.17 × 10−9 m2 s−1 (4)
Cell wall thicknessLw0.73 µmLw0.73 µm
Membrane permeabilityLmem6–10 nm (2)
image
2.91 × 10−9 m2 s−1 (3) 
image
3.63 × 10−2 m s1 a
image
3.5 × 10−3 m s−1 (8)
 
image
5.6 × 10−6 m s−1 (9)
Henry's constant
image
1.37 × 10−2 mol m−3 kPa−1 at 20°C (1)
image
0.3876 mol m−3 kPa−1 at 20°C (1)
2.11 × 10−2 mol m−3 kPa−1 at 0°C (1)0.673 mol m−3 kPa−1 at 0°C (1)
CO2 reaction rate constant K10.039 s−1 (5)
 K223 s−1 (5)
 K2.5  × 10−4 mol l−1 (5)
Respiration rate constant
image
–2.26 × 10−4 mol m−3 s−1 (6)rq,ox1
image
3 × 10−3 mol m−3 (7)  
image
(80.2 ± 12.3) kJ mol−1  

The diffusivity of both O2 and CO2 in the cell wall was estimated by fitting the calculated apparent diffusivity of a representative sample of tissue to experimental diffusivity data available in our laboratory (Ho et al., 2006a), using a nonlinear least-squares estimation procedure in Matlab (The Mathworks, Inc., Natick, MA, USA). The resulting values were equal to 4.25 × 10−9 m2 s−1 and 5.23 × 10−9 m2 s−1 for inline image and inline image, respectively (Table 1). While the protoplast typically has a pH of c. 7, the vacuolar pH is below 5. In this model it was assumed that the protoplast and vacuole could be represented by a single liquid phase with an average pH of 5. The validity of this approach is shown in Text S5 and S6.

In silico study of gas exchange

The geometry model was imported into Comsol Multiphysics vs 3.3 (Comsol AB, Stockholm, Sweden) for numerical computation of the gas exchange using the model equations outlined earlier. The geometric model was therefore meshed into 267 863 quadratic elements that were triangular in shape. The nonlinear coupled model Eqns (1)–(10) were discretized over this mesh using the finite element method. A direct solver was applied for solving the resulting set of ordinary differential equations model with accuracy threshold less than 10−6. The program was run on a node of 4 GB of RAM (Opteron 250, Duo core Opteron 275) of the High Performance Computer (HPC, AMD Opteron cluster) of K. U. Leuven (Leuven, Belgium). The computing time was around 15 min for each steady-state simulation.

Apparent diffusivity of pear cortex tissue

In silico analysis was carried out to compare microscale gas exchange in pear fruit tissue with the measured gas exchange rates through tissue slices of 4.19 × 10−4 m. At the top of the computational domain, the overall macroscopic gas flux were applied at the position (r = 0.0212 m) where the overall gradient was equal to the actual local gradient (Table 3a; at the bottom the local gas concentration at the same position was applied to ensure realistic conditions (inline image mol m−3 and inline image mol m−3)). The other two lateral boundaries were defined to be insulated. The macroscopic apparent diffusivity of component i (i is O2 or CO2) in cortex tissue Di,tissue (m2 s−1) was then computed from:

Table 3.  (a) Simulated concentration gradients in the fruit, macroscale vs microscale (inline image and inline image (kPa
mm−1) are O2 and CO2 concentration gradients in tissue); (b) macroscopic apparent diffusivities of O2 and CO2 in pear parenchyma tissue (inline image and inline image
(m2 s−1) are the O2 and CO2 apparent diffusivity of tissue) (bracketed numbers are references; see footnotes)
 (a) Concentration gradients in the pear cortex
T (°C)inline image (kPa mm−1)inline image (kPa mm−1)
Macroscale20
 0
0.39
0.14
0.18
0.02
Microscale20
 0
0.38
0.27
0.3
0.03
 (b) Macroscopic apparent diffusivity
T (°C)inline image (m2 s−1)inline image (m2 s−1)
  1. The values reported for the microscale model are average simulated values for nine different tissue geometries.

  2. ± 95% confidence limits.

  3. References: 1, Ho et al. (2006a); 2, Schotsmans et al. (2003); 3, present experiment.

Microscale20(3.54 ± 0.68) × 10−10(3.13 ± 0.59) × 10−9
 0(3.23 ± 0.63) × 10−10(2.83 ± 0.45)  × 10−9
Measurement20(2.87 ± 0.45) × 10−10 (1)(2.6 ± 0.36) × 10−9 (1)
12(4.3 ± 1.7) × 10−10 (2)(1.73 ± 1.15) × 10−9 (2)
20(5.63 ± 3.09) × 10−10 (3)(5.32 ± 1.43) × 10−9 (3)
image(Eqn 11)

Note that when respiration takes place, the flux Ji,total is not constant. To save computing time, we neglected the respiration term in the gas transport equations for calculating the apparent diffusivity. We validated this approach by carrying out a transient simulation with the model including respiration in which we changed the boundary condition from fixed partial pressure to impermeable and by comparing the microscale O2 and CO2 partial pressure time profiles at the bottom with those obtained with a macroscale continuum model.

A sensitivity analysis was performed to study how sensitive the apparent diffusivity was with respect to small changes in model parameters (more details in Text S2 and S3, Table S1).

Results

Gas concentration gradients in pear fruit

Table 2 shows that the O2 concentration in the pear core was considerably lower than that of the ambient atmosphere. This implies the existence of large O2 concentration gradients from the surface to the core of fruit. The higher the temperature, the lower the measured core O2 concentration (Table 2). The macroscopic gradients of O2 concentration inside the fruit were confirmed by the macroscale model of Ho et al. (2008). The calculated O2 profiles from the surface to the centre along the radial direction at different temperatures are given in Fig. 2a. A sharp gradient occurs in the skin layers as a result of their high resistance to gas exchange (Ho et al., 2006a). The calculated O2 concentration decreases parabolically towards the centre. At high ambient temperatures, the O2 partial pressure in the pear core approaches 0 kPa.

Table 2.  Comparison of measured O2 concentration in the centre of pear fruit with simulated values
T (°C)ExperimentSimulation, Ho et al. (2008)
  1. ± SE of nine different pears.

012.2 ± 4.915.5
105.02 ± 6.3 2.5
200.5 ± 1.58 0
Figure 2.

(a) O2 concentration profile along the radial direction of pear fruit predicted by the continuum gas exchange simulation (model of Ho et al., 2008). Solid line, dashed line and dashed-dotted line indicate the profiles at 0, 10 and 20°C, respectively. (b, c) Apparent O2 and CO2 diffusivity of pear cortex tissue versus void fraction (porosity), respectively.

Table 3a also compares the simulated macroscopic gas concentration gradients in the pear cortex with those obtained from the microscale model presented here. A good agreement was found at all temperatures for O2 as well as CO2. Similar O2 concentration gradients were also found in plant seeds (Rolletschek et al., 2003, 2004).

Microscopic gas concentration profiles

The equilibrium 2D O2 profile shows that the O2 concentration is low inside the cells (Fig. 3b) compared with the intercellular spaces (Fig. 3a). There was less than one order of magnitude difference in O2 concentration between the gas and liquid phases. This is because O2 has a low solubility in the cell (Henry's constant for O2 at 20°C is 1.37 × 10−2  mol m−3 kPa−1) and the O2 diffusivity in air is about 104 times that in water. Transfer of O2 occurred mostly in the gas phase through the pores and the cell wall networks. The corresponding microscale fluxes are given in Fig. 4. Gas exchange through the tissue was very heterogeneous. The resistance of the pore and cell wall network with respect to O2 transport (reciprocal to the diffusion coefficient) is lower than that of intracellular O2 transport. Therefore, much more gas diffuses through the pore and cell wall network than through the cytoplasm.

Figure 3.

Simulated respiratory gas concentration (mol m−3) in pear cortex tissue at steady state, taking into account intracellular respiration. At the top of the computational domain, the overall macroscopic gas flux was applied at the position (r = 0.0212 m) where the overall gradient was equal to the actual local gradient (Table 3a); at the bottom, the local gas concentration at the same position was applied to ensure realistic conditions (inline image mol m−3 and inline image mol m−3). The lateral sides of the sample were assumed to be impermeable. Temperature
was set to 20°C. (a) O2 concentration in the gas phase (mol m−3); (b) intracellular O2 concentration (mol m−3); (c) CO2 concentration in the gas phase (mol m−3); (d) intracellular CO2 concentration (mol m−3).

Figure 4.

Total O2 (a) and CO2 (b) flux through tissue in the microscale model for the simulations with the conditions applied in Fig. 3. The colour bar indicates the normal flux on a logarithmic scale (log10(flux)) (flux units are mol m−2 s−1).

The CO2 concentration profiles are shown in Fig. 3c,d. The results indicate a relatively high CO2 concentration in the cytoplasm, because CO2 has a high solubility in the cell (Henry's constant for CO2 at 20°C is 3.876 × 10−1 mol m−3 kPa−1). As a result, the CO2 concentration in the gas and liquid phases have the same order of magnitude.

The ratios of cytoplasmic to gas phase flux were 0.3 and 1.41 for O2 and CO2, respectively. In contrast to O2, CO2 transfer occurs not only in the gas phase, through the pores and the cell wall network, but also through the intracellular liquid phase.

Apparent O2 and CO2 diffusivity

The apparent O2 and CO2 diffusivities of the microscopic samples were calculated to be compared with previously published data (Ho et al., 2006a). Mean values of apparent diffusivity and corresponding 95% confidence interval of nine different tissue microstructures in the pear cortex are given in Table 3b. The resulting apparent O2 and CO2 diffusivities from microscale simulations are clearly very variable. The mean apparent diffusivity of O2 at 20°C was (3.54 ± 0.68) × 10−10 m2 s−1, while the experimental values were (2.87 ± 0.45) × 10−10 m2 s−1, as reported by Ho et al. (2006a). These values are quite small and may be explained by the small void fraction of pear cortex tissue (5–15%). The effect of void fraction on apparent diffusivity of both gases is plotted in Fig. 2b,c.

Simulations with the CO2 microscale model using the lumped intracellular pH = 5 and the model using different pH in protoplast and vacuole are shown in the Text S5 and S6, Table S2. The apparent CO2 diffusivity of the tissue in both cases was almost the same. The estimated apparent diffusivity of CO2 was (3.13 ± 0.59) × 10−9 m2 s−1 at 20°C, while the experimental values were (2.6 ± 0.36) × 10−9 m2 s−1, as reported by Ho et al. (2006a). The measured apparent CO2 diffusivity was one order of magnitude larger than that of O2. The microscale model confirms this observation.

In silico analysis showed that temperature does not have a large effect on the gas exchange properties. The mean apparent diffusivities of O2 and CO2 were (3.54 ± 0.68) × 10−10 and (3.13 ± 0.59) × 10−9 × 10−9 m2 s−1 at 20°C, while the tissue diffusivities were (3.23 ± 0.63) × 10−10 and (2.83 ± 0.45) × 10−9 m2 s−1 at 0°C. The predicted activation energies for the apparent O2 and CO2 diffusivities were (3.09 ± 7.36) and (3.20 ± 6.51) kJ mol−1. The effect of temperature on the apparent O2 and CO2 diffusivities was not statistically significant. Temperature mainly affects the intracellular respiration rates.

Discussion

Microscale model vs macroscale model

The obtained simulation results suggest for the first time that the local gas concentration profiles are very different from those obtained from previous macroscopic apparent diffusivity models (Lammertyn et al., 2003; Ho et al., 2006b, 2008). The microscale model predicts a significantly lower O2 concentration in the cytoplasm than in the intercellular space (the mean ratio of O2 concentration in the cytoplasm to O2 concentration in the intercellular space is around 3.3 × 10−2). The simulation results of microscale fluxes in Fig. 4 indicate that gas transport through the microstructure is much more heterogeneous – the ratio of the mean O2 flux in cytoplasm to the O2 flux in gas phase was around 0.3, indicating that O2 was mainly transported in the gas phase; for CO2 this ratio was 1.41. This corresponds well to the difference in apparent gas diffusivity observed by various authors (Ho et al., 2006a).

As a consequence, a continuum model which does not include the microscale structure of the tissue is not capable of predicting local phenomena such as anoxia at the cellular level, which may have important physiological consequences at certain external conditions.

Importance of the cell wall

The cell wall diffusion model of respiratory gases assumed that the cell wall is a porous structure containing interconnected air spaces (Fig. 3). As a consequence of this assumption in the model, calculated fluxes through cell walls were relatively high. In fact, cell walls acted as channels connecting the larger pores in the tissue, thereby creating a void network structure that facilitates gas exchange. A network structure with strong connectivity has indeed been observed in other plant fruit (Kuroki et al., 2004; Mendoza et al., 2007), but was only recently confirmed in pear (Verboven et al., 2008). If the cell wall structure was assumed to be saturated with liquid, the flux decreased drastically (results not shown). The measured apparent O2 diffusivity of the tissue could not then be predicted by the microscale model (1.02 × 10−10 vs 3.5 × 10−10 m2 s−1 in reality). Therefore, the results reported here indicate that either the cell wall acts as an important gas diffusion channel, or the interconnectivity resulting from the 3D microstructure is considerably larger than expected from the 2D microscopic images. The latter is currently investigated by the authors based on measurements of Verboven et al. (2008).

Redgwell et al. (1997) reported that swelling of the cell wall during fruit ripening was assumed to be associated with movement of water into voids of the cell wall network by solubilized pectin. Hence, the resultant increase of the resistance to gas exchange could be attributed to anoxia, eventually resulting in cell death at the final stage of ripening.

Transport of CO2 in the intracellular compartments

The overall CO2 transport in the liquid phase is the sum of the diffusion of dissolved CO2 and CO2 bound as inline image. The contribution of inline image to CO2 transport was first described by Longmuir et al. (1966). Gros & Moll (1974) and Gros et al. (1976) have shown that facilitated CO2 diffusion involves a flux of H+ equivalent to that of inline image, a fact that tallies with hydration of CO2 producing equal amounts of H+ and inline image. In a liquid system, CO2 diffusion can be facilitated by inline image diffusion with rapid conversion of CO2 into inline image and H+. It was assumed that the pH of the cytoplasm of plant tissues, cells and protoplasts was maintained constant irrespective of accumulation or extrusion of respiratory CO2. The cytoplasmic pH of plant cells appears fairly constant despite metabolic processes, which generate or consume H+, and despite wide variation in the external pH (Smith & Raven, 1979). Boron (2004) reported that a high buffering capacity of intracellular liquid for regulation of intracellular pH leads to a constant pH with regard to acid loading or extruding. The pH of fruit juices is typically about 5, indicating high concentrations of dissociated and undissociated organic acids in the vacuole (Smith & Raven, 1979). The pH of the cytoplasm was found to be equal to 7 (Kurkdjian et al., 1978). Roberts et al. (1981, 1982) reported cytoplasmic and vacuolar pH values of maize root tips of c. 7.2–7.5 and 5.5–5.6, respectively. The pH of pear juice in this study was c. 5. Assuming a cytoplasmic pH of 7 and applying a mass balance for protons in the cytoplasm and vacuole to match the juice pH resulted in a vacuolar pH of c. 4.82. Simulations of CO2 transport with the model including a vacuole (Text S6, Fig. S1) showed that there was no difference in apparent CO2 diffusion compared with the model without vacuole but with an intracellular pH of 5 (see Table S2). This latter model was considerably more efficient in terms of computation time.

Biological variation of apparent diffusivities

Measurement of apparent diffusivity of pear tissue showed that there was high variation of values among samples (Schotsmans et al., 2003; Ho et al., 2006a). We believe that this is mainly the result of microstructure variations. Simulations with different tissue structures in this study showed that differences in porosity, connectivity and cell distribution affected the gas exchange in the tissue to a large extent. An increase of porosity resulted in an increase of apparent diffusivities of the tissue predicted by microscale model simulation (Fig. 2b,c). The macroscopically observed variation in gas diffusivities was therefore, for the first time, linked to the irregular microstructure of the tissue.

Anoxia and core disorders in bulky plant organs

Respiration is the main reason for lower O2 concentrations in fruit and it is affected by the development stage of fruit (Wills et al., 1998). During the growth stage (the period of cell division and enlargement), respiration decreases and reaches a minimum. Anoxia is thus not likely to occur in favourable growth conditions in well-managed orchards. Moreover, photosynthesis may elevate internal O2 concentration. In fact, in seeds, embryo photosynthesis has been shown to elevate the internal O2 concentration up to approximately 50% of atmospheric values (Rolletschek et al., 2003). At the end of the maturation stage, the fruit is detached from the tree, while it remains metabolically active. Fruit ripening then occurs; it is the ensemble of changes taking place in the later stages of maturation and the beginning of senescence with a marked rise in respiratory activity. In this period the fruit are most prone to anoxic stress, depending on specific conditions. We have shown here that temperature has a very small effect on gas exchange properties of the fruit cortex, while it has a large effect on respiration (Ho et al., 2008). As a result, gas concentration gradients in the pear cortex at 0°C were much smaller than at 20°C. The gradients are such that in the core of pears, the lowest O2 concentrations are found, and they are lower for larger fruit (Ho et al., 2008). We found a very low O2 partial pressure in the core of harvested and stored pears at 20°C and normal air O2 concentrations. These critical internal concentrations of O2 have also been observed in other plant organs (roots, rhizomes, seeds, coleoptiles), under normal air O2, and were shown to lead to the development and growth of the anaerobic core in roots (Saglio et al., 1984; Drew, 1992).

When the exposure of pears to low O2 is limited in time to a few hours (e.g. during a hot day at the end of summer), cells may survive. Direct cell damage in plant organs as a result of limited fermentative energy supply during the O2 stress period can be prevented for periods up to 15 h in some cases (Drew, 1997). However, anoxia reduces the amount of detoxification enzymes against harmful reactive O2 species, which are produced as by-products of aerobic metabolism (Drew, 1997; Purvis, 1997; Moller, 2001; Apel & Hirt, 2004). Re-entry of O2 then leads to unrecoverable cell damage. In practice, it is recommended to start cooling immediately after harvest, but to wait at least 3 wk before applying low O2 conditions (Franck et al., 2007). The current results show that this procedure may indeed prevent extremely low O2 concentrations in the core of the fruit and thus also decrease the concentration of harmful reactive O2 species in the pear core (Purvis, 1997, 2001).

Core disorder does regularly develop in stored harvested fruit at low temperature and gas conditions of 2.5 kPa O2 and 0.7 kPa CO2 (Franck et al., 2007). The occurrence depends on the season and currently cannot be predicted. The optimal gas conditions for storage are well established by dedicated storage experiments over several growth seasons (Franck et al., 2007), and should normally not lead to storage disorders. The respiration activity is brought to a minimum, and anoxic conditions are unlikely even with the high resistance to gas exchange of the pear cortex. A multiscale analysis combining the macroscale model to calculate average O2 concentration profiles in the parenchyma near the core of a representative fruit, 0.232 kPa, and the microscale model to compute the corresponding intracellular concentration was conducted. The resulting average minimal intracellular O2 concentration in the nine tissue samples of 4.79 ± 0.01 µm was well above the known estimates of Km for cytochrome oxidase and alternate oxidase in isolated plant mitochondria: 0.14 and 1.7 µm, respectively (Millar et al., 1994; Drew, 1997). While inhibition of respiration at these storage conditions is rapid, ATP formation through oxidative phosphorylation is therefore not inhibited and secured by the normal respiration pathway. On the other hand, recent tomographic studies on pear tissues using synchrotron radiation X-rays have shown that cells may be clustered very tightly in regions close to the vascular xylem vessels, without any aerated gas spaces (Verboven et al., 2008). In such regions, the apparent O2 diffusivity may drop markedly with decreasing void fraction, increasing the risk of insufficient O2 supply to cells.

Conclusions

A microscale model for O2 and CO2 exchange through the intercellular spaces, cell wall and cytoplasm of cells in the pear cortex added a new and important level of detail to existing gas exchange models for plants. Under a range of prevailing concentrations of O2 and temperature, the microscale model produced correct tissue gas fluxes in bulky storage organs such as fruit. In silico analysis revealed that the local gas concentration profiles and fluxes are very different. Our simulations predict that the O2 exchange occurs mainly through the intercellular space, the cell wall network and less so through the intracellular liquid, whereas CO2 exchange occurs at similar rates through each of these phases. The biological variation of the apparent diffusivity of gases in tissue was related to the naturally random distribution of cells and pores in the cortex tissue. Hypoxia and anoxia can now be readily investigated at the cellular level in intact fruit, combining our macroscale and microscale models in a multiscale analysis.

Further advances require that 3D modelling of gas exchange in the microstructure of the tissue is attempted to explain the effect of interconnectivity and tissue anisotropy on the macroscopic gas transport properties of tissue. Indeed, the 2D results are only valid assuming cell walls are interconnecting pathways for gas exchange through the pores.

Acknowledgements

Financial support by the Flanders Fund for Scientific Research (FWO-Vlaanderen) (project G.0603.08), IWT project (IWT-050633) and the K. U. Leuven (OT 04/31, IRO PhD scholarship for Q. T. Ho) is gratefully acknowledged.

Appendix

A1 Nomenclature

inline imageCO2 concentration (mol m−3)

inline imageEquilibrium CO2 concentration in liquid phase of outer membrane (mol m−3)

inline imageinline image concentration (mol m−3)

inline image O2 concentration (mol m−3)

inline image Equilibrium O2 concentration in liquid phase of outer membrane (mol m−3)

inline image CO2 diffusivity (m2 s−1)

inline image CO2 apparent diffusivity of tissue (m2 s−1)

inline imageinline imagediffusivity (m2 s−1)

Dj,tissue Macroscopic apparent diffusivity of component j (m2 s−1)

inline imageO2 diffusivity (m2 s−1)

inline image O2 diffusivity through cell membrane (m2 s−1)

inline image O2 apparent diffusivity of tissue (m2 s−1)

inline imageActivation energy of O2 consumption (kJ mol−1)

inline image O2 permeability through cell membrane (m s−1)

inline image CO2 permeability through cell membrane (m s−1)

inline imageinline image permeability through cell membrane (m s−1)

inline image Henry's constant for O2 (mol m−3 kPa−1)

inline imageHenry's constant for CO2 (mol m−3 kPa−1)

[H+]H+ concentration (mol l−1)

inline imageThe flux of CO2 (mol m−2 s−1)

Ji,total Total flux of component i (mol m−2 s−1)

inline imageThe flux of O2 (mol m−2 s−1)

k1 CO2 hydration velocity constant (s−1)

k2 CO2 dehydration velocity constant (s−1)

K Acid dissociation constant for H2CO3 (mol l−1)

inline image Michaelis–Menten constant of O2 inhibition on fermentative CO2 production (mol m−3).

inline image Michaelis–Menten constant for O2 consumption (mol m−3)

Lmem Thickness of cell membrane (m)

Ltissue Thickness of tissue (m)

Lw Thickness of cell wall (m)

rq,oxRespiration quotient

R Universal gas constant (8.314 J mol−1 K−1)

inline image O2 consumption in liquid cell (mol m−3 s−1)

inline image O2 consumption of tissue (mol m−3 s−1)

inline image CO2 consumption in liquid cell (mol m−3 s−1)

inline imageRelative sensitivity of the predicted inline image with respect to parameter P

T Temperature (K)

t Time (s)

inline imageMaximal fermentative CO2 production rate of the intracellular cellular liquid phase (mol m−3 s−1).

inline image Maximal O2 consumption rate in liquid phase (mol m−3 s−1)

Greek symbols

∇ Gradient operator (m−1)

Pi,tissue Concentration gradient of gas i in tissue (kPa mm−1)

Δ Difference

Subcripts

g Gas phase

i O2 or CO2

l Liquid phase

w Cell wall

Ancillary