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Upgrading the Measurement of Membrane Hydraulic Conductivity and the Osmotically Inactive Volume of Protoplasts for Evaluating the Freshness of Postharvest Leafy Vegetables

Shinichiro Kuroki1, Mai Tanaka1, Hiromichi Itoh1, Kohei Nakano2, Itaru Sotome3,*

Published in Journal of the ASABE 65(1): 189-196 (doi: 10.13031/ja.14755). Copyright 2022 American Society of Agricultural and Biological Engineers.

1 Graduate School of Agricultural Science, Kobe University, Kobe, Japan.

2 United Graduate School of Agricultural Science, Gifu University, Gifu, Japan.

3 Graduate School of Agricultural and Life Sciences, University of Tokyo, Tokyo, Japan.

* Correspondence:

The authors have paid for open access for this article. This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License https://creative

Submitted for review on 15 July 2021 as manuscript number ITSC 14755; approved for publication as a Research Article by the Information Technology, Sensors, & Control Systems Community of ASABE on 13 December 2021.


Abstract. Membrane water permeability is of great importance to better understand the mechanism of water loss; however, its correct understanding and measurement is still an issue. We proposed and tested the efficacy of a numerical analytic approach for the simultaneous determination of the hydraulic conductivity (Lp) and relative osmotically inactive volume (b) of protoplasts isolated from spinach mesophyll tissue. The new approach revealed that the osmotically inactive volume was neither proportional nor constant to the protoplast size and differed for each protoplast. Usage of individually determined b for the computation provided the best fitting performance for determining the Lp, whereas collective b decreased the accuracy of regression and resulted in the underestimation of Lp. Our approach also has the advantage of a shorter period of hyperosmotic challenge, and as such, is suitable for observing fragile protoplasts. We found a gradual reduction in b and a linear increase in Lp during four days of storage at 20°C, likely due to degradation of internal components and dysfunction of the cell membrane, respectively. We also discuss the potential need to consider tissue specificity and possible damage by protoplast isolation to conduct shelf-life research of leafy vegetables.

Keywords.Mesophyll protoplast, Nonosmotic volume, Numerical determination, Spinacia oleracea, Water loss, Water permeability.

Water loss in vegetables not only reduces the fresh appearance of the produce due to reduction of turgor pressure but also depletes its nutritional and textural qualities (Kader, 2002; Lee and Kader, 2000; Paull, 1999), thereby reducing its marketability, particularly in the case of postharvest leafy vegetables. Sotome et al. (2001) used barley seed leaves as a model material and postulated that water migration within the tissue, i.e., water leakage from the symplast to the apoplast, was the main cause of reduction in turgor pressure and successive wilting. Microscale water transport is also of great importance from the food processing aspect to understand cell and tissue deformation due to osmotic dehydration (Mayor et al., 2008) and drying (Ramos et al., 2004).

Because transmembrane water transport is a rate-limiting step for water movement both into and out of cells (Nobel, 2020), the cell membrane hydraulic conductivity coefficient (Lp) is one of the vital parameters describing water loss from produce. Fanta et al. (2014) demonstrated that Lp had the largest influence on the water transport and deformation of pear fruit during dehydration, suggesting the crucial significance of correct understanding and measurement of Lp. The Lp describes either water permeability or mechanical filtration capacity when applying the difference in osmotic pressure inside and outside the cell. Governing equations of the change in cell volume associated with water migration across the cell membrane are shown as equations 1 and 2 and are rewritten as equation 3 using van’t Hoff’s law and the assumption that the cell is spherical (Kedem and Katchalsky, 1958; Sotome et al., 2004):





V = cell volume (m3)

t = time (s)

A = surface area of the cell (m2)

pe = extracellular osmolarity (Pa)

pi = intracellular osmolarity (Pa)

p = number pi

= sum of extracellular molar fractions of solutes that cannot cross the cell membrane

= sum of intracellular molar fractions of solutes that cannot cross the cell membrane

R = gas constant (8.314 Pa m3 mol-1 K-1)

T = temperature (K)

vw = molar volume of water (18 × 10-6 m3 mol-1)

V8 = volume of the cell existing in equilibrium with the extracellular solution (m3)

Vb = osmotically inactive volume of the cell (m3).

The Vb is assumed to consist of cell solids (e.g., organelles and cytoskeleton), hydrate (including the osmotically unresponsive water compartment; Fullerton et al., 2006), and other cell contents (e.g., starch grains and lipid drops) that are certainly not available for transport across the semipermeable cell membrane (Bryant and Wolfe, 1992). The osmotically inactive volume is of interest because it is a quantitatively determined cell constant and, hence, may afford an index to the progression of certain events within the cell (Shapiro, 1948). As seen from equation 3, it is necessary to know the value of Vb to calculate the Lp.

The Vb or the relative osmotically inactive volume (b = Vb/V(0)) are often estimated indirectly by the y-axis intercept of the regression line in the Boyle-van’t Hoff (BVH) plot, which shows a relationship between the cell volumes against the reciprocal of the osmolarities of the solutions (Liu et al., 1995). However, this method of determining the Vb invariably involves an estimate error derived from the cell size distribution (Higgins and Karlsson, 2008), leading to uncertainty in determining the Lp (Higgins and Karlsson, 2010). Moreover, using the BVH plot to estimate Vb necessitates assuming that Vb is either proportional to the cell size (in the case of plotting the normalized cell volume) or constant irrespective of cell size (in the case of plotting the actual cell volume). There are strong doubts concerning whether these assumptions are reasonable for the mesophyll protoplasts because the leaf should have biological dispersion. Inappropriate estimations of Vb will introduce uncertainty into determinations of Lp, possibly resulting in misunderstandings of water transport phenomena during water loss and dehydration, and in turn, postharvest physiology and engineering.

To arrive at the most definite values of Lp and Vb, we propose a numerical analytic approach for the simultaneous determination of Lp and Vb from the cell volume change during the osmotic challenge. This approach also constitutes a direct measurement of the Vb of each cell. Therefore, our aim was to compare and evaluate the accuracy and precision of the Lp calculated from two methods: one from Vb determined numerically using the proposed approach, and the other from an indirectly obtained Vb through a fixed b via BVH plot. In addition, we studied the changes in Lp and Vb during four days of storage and discuss the potential of evaluating changes in produce freshness from the variations of both parameters.

Materials and Methods

Cultivating and Storage Conditions

One week after germination (table 1), 19 spinach plants (Spinacia oleracea L., ‘Orai’) were cultivated hydroponically in growth cabinets for six weeks (Koitotron FR-535A, Koito Kogyo Co. Ltd.). The harvested plants were stored for up to four days in a dark environment in an acryl chamber at 20°C and 99% RH. Storage of four days or less is important to maintain the apparent marketability of the leaves. It is difficult to isolate protoplasts from visibly degraded leaves.

Table 1. Cultivating conditions of spinach leaves.
Raising SeedlingsPlanting
Temperature (?)21.2 ±1.221.1 ±1.2
Humidity (% RH)71.9 ±13.0 (uncontrolled)
Light/dark period (h/h)11/13
Photosynthetic photon flux
density (µmol m-2 s-1)
64.12 ±5.78323.32 ±17.85
Nutrient solutionTap waterHalf-strength
of Otsuka A

Protoplast Isolation Protocol

We modified the protoplast isolation protocol of Shatil-Cohen et al. (2014) and Danon (2014). Apart from enzymatic digestion of the cell wall, all processes were carried out at 20? in a temperature-controlled room. We used a cork borer (20.5 mm diameter) and excised three leaf disks from the third or the fourth leaf of each spinach plant, avoiding the midrib and lateral veins. The epidermides of leaf discs on the abaxial side were removed with vinyl tape, and damaged cells were washed off using a 0.5 mol L-1 mannitol solution. The treated leaf disks were soaked immediately in a petri dish in an enzyme solution comprising cell and protoplast washing [so-called CPW (Frearson et al., 1973)] salt solution, 0.5 mol L-1 mannitol, 1.0% (w/v) cellulase Onozuka RS (Yakult Pharmaceutical Industry Co. Ltd.), 0.1% (w/v) pectolyase Y-23 (Kyowa Kasei Co. Ltd.), and 5 mmol L-1 2-(N-Morpholino) ethanesulfonic acid (MES, Nakalai Tesque Inc.). We closed the lid with parafilm and incubated the disks for 1 h by floating the dish in a water bath set to 28? (TR-2AR, As One Co. Ltd.), after which we removed the enzyme by transferring the disks to a drop of 0.5 mol L-1 mannitol and CPW solution. Subsequently, the disks were further moved to another drop of 0.4 mol L-1 mannitol and CPW solution and then shaken gently using forceps to release the protoplasts. The collected protoplasts were deposited very slowly onto 0.5 mol L-1 sucrose solution and centrifuged for 1 min at 72×g (MX-300, Tomy Seiko Co. Ltd.). Finally, we retrieved the living protoplasts from a thin cushion at the surface of the sucrose solution, which suspension was used to measure hydraulic conductivity.

Two-Laminar-Flows Method

Figure 1 shows the experimental apparatus used for microscopic measurement of the osmotic response of protoplasts. We measured the Lp using the two-laminar-flows method (Sotome et al., 2004), as this method has several advantages: the extracellular osmotic pressure can be changed instantaneously by replacing the solution surrounding the protoplasts; the moment of this replacement can be determined precisely; the effect of the unstirred layer around the cell can be obliterated; and the protoplast is fixed on a membrane filter (TMTP04700, Isopore, Merck KGaA) inside a microchannel, which enables stable measurement of the protoplast volume during microscopic observation without need to adjust the field of view. We took the protoplast suspension up into a microsyringe (MS-X05, Ito Co.) and inserted it into the two-laminar-flows cell. The protoplasts were initially surrounded by a 0.4 mol L-1 mannitol solution for about 1 min so that the osmotic pressure inside the protoplasts would be in equilibrium with the solution. We then applied external osmotic pressure by immediate replacement with a 0.6 mol L-1 mannitol solution, causing the intracellular water to flow out and the protoplasts to shrink. The volumes of the protoplasts were recorded by a digital microscope (DMBA300, Shimadzu Rika Co.) with a long working distance objective lens (EPLE-50, Sigmakoki Co. Ltd.). The scaling factor was 13.483 pixels per µm2. Still images were captured automatically for 250 s with 10 s intervals and saved as bitmap files on a computer disk using software (Motic Images Plus2.3S, Shimadzu Rika Co.). We calculated the protoplast volumes from the horizontal projection area of protoplasts extracted using ImageJ software (U.S. National Institutes of Health) from the acquired images. When the difference in osmolarity is too small, the change in protoplast volume may be smaller than the resolution of microscopic observation. The osmolarity difference we gave (0.4 to 0.6 mol L-1) decreases the protoplast radius by 7.2% to 12.6% when the b range is 0% to 40% (fig. 2), which provides adequate experimental conditions to measure volume changes accurately.

Figure 1. Experimental apparatus for microscopic observation of the osmotic response of protoplasts. The inset shows a magnified photograph of a two-laminar-flows cell on the microscope stage.
Figure 2. Expected change in protoplast radius against osmotic challenge.
Table 2. Parameter setup for numerical analysis in conventional and newly proposed approaches.

Membrane Hydraulic Conductivity and Osmotically Inactive Volume

The Lp was determined by fitting the protoplast volumes recorded during the osmotic challenge to equation 3. The Vb was determined simultaneously with Lp using the new approach developed in this study. Conversely, Vb was calculated via BVH plot using the conventional method. We used the Levenberg-Marquardt optimization scheme (Press et al., 1992) to seek the optimal parameter values that maximize the adjusted R2 with the Fit ODE application (ver. 1.3) in OriginPro (ver. 2021, OriginLab Co.). Table 2 shows the setup of the parameters in the conventional and newly proposed approaches. The initial protoplast volume, V(0), was the volume in equilibrium with the 0.4 mol L-1 mannitol solution and can be handled as a known parameter. However, in both cases, V(0) was treated as an unknown parameter to prevent any inevitable error in measuring V(0) from causing a noticeable error in the determination of Lp, as recommended by Sotome et al. (2004). In the conventional approach, the osmotically inactive fraction (b) of spinach mesophyll cells at 0.4 mol L-1 mannitol solution was set as 0%, 10%, 20%, 30%, and 40% of the initial protoplast volume. These fixed b values covered the range reported using extrapolation of the regression line of the BVH plot in previous studies regarding mesophyll protoplasts (Sommer et al., 2007; Sotome et al., 2004). The V8 was calculated subsequently by substituting ?is(0) and Vb into equation 2. Conversely, in the new approach, V8 was set as one of the unknown parameters, and Vb was calculated by substituting ?is(0), V(0), and V8 into equation 2. The b value is calculated by dividing Vb by V(0), which are both numerically determined, meaning that the proposed approach computes b for each protoplast, whereas in the conventional approach, b is assumed to be the same for all protoplasts.


Comparison of Computing Methods

We used the data for the leaves just after harvesting to assess the fitting accuracy of the volume response function in the conventional and proposed computing methods. Figure 3 shows the volume changes over time for three typical spinach mesophyll protoplasts during the hyperosmotic challenge. We normalized the volumes on the basis of each initial volume in the 0.4 mol L-1 mannitol solution. Faster decay of volumes implies a greater magnitude of Lp. Curve-fitting features differed between the conventional and proposed approaches, particularly when there was a large difference between the fixed and the numerically determined b. The samples had diverse relative final volumes in equilibrium with the 0.6 mol L-1 mannitol solution, demonstrating that b was not the same for all samples. The b that was determined numerically using the proposed approach ranged from 1.9% to 56.3% (fig. 4), demonstrating that Vb was neither proportional to V0 nor constant, irrespective of cell size. Thus, b is neither constant nor inversely proportional to the third power of the diameter (b = 6Vbp-1d-3).

Figure 3. Volume changes over time for three typical spinach mesophyll protoplasts during the hyperosmotic challenge. Dashed and solid lines represent nonlinear regression curves using the conventional and proposed approaches, respectively. The dotted line indicates the relative final volume when assuming the osmotically inactive fraction (b) to be 10%. The numerically determined b for the circle, triangle, and square symbols was 1.9%, 11.1%, and 32.9%, respectively.
Figure 4. Distribution of numerically determined osmotically inactive fraction (b). The dotted line represents the constant b (10% in this case), i.e., the osmotically inactive volume (Vb) is proportional to cell size. The dashed line depicts one example of the diameter dependency of b when assuming a constant Vb irrespective of cell size, i.e., all protoplasts have the same Vb of mean size protoplasts, which is 50 µm in this case. Under this assumption, b would be inversely proportional to the third power of the diameter (b = 6Vbp-1d–3).
Figure 5. Difference in RMSE between conventional and proposed approaches against the fixed osmotically inactive fraction (b). Differences were calculated by subtracting the RMSE in the proposed approach from the RMSE in the conventional approach (?RMSE = RMSEconv - RMSEproposed). Bars indicate standard errors of the mean. Numbers below the plots denote the probabilities of a one-tailed paired t-test.

An assumption of the fixed osmotically inactive fraction in the conventional approach was detrimental to the fitting accuracy and the computation of Lp. The fitting accuracy in root mean square error (RMSE) with nonlinear least-squares regression in the conventional and proposed approaches is shown in figure 5. A one-tailed paired t-test showed that the RMSE of the proposed approach was significantly smaller than that of the conventional approach: the p-values at the 10% intervals of b were, respectively, 1.5 × 10-4, 1.5 × 10-3, 2.4 × 10-4, 3.1 × 10-4, and 2.6 × 10-4, showing that the fitting performance obtained using the proposed approach was superior to that achieved using the conventional approach. We generated a BVH plot using the numerically determined V0 and V8 values with the proposed approach because both volumes estimated with good fitting accuracy are reasonable estimates of protoplast volumes in equilibrium with the 0.4 and 0.6 mol L-1 mannitol solutions (fig. 6). The estimated b (0.267 ±0.293) obtained via the BVH plot provided the minimum RMSE in the analysis using the fixed b at 10% intervals. Nevertheless, the RMSE calculated with the proposed approach was significantly smaller (p = 6.5 × 10-5 by a one-tailed paired t-test). Samples whose final volume did not converge to the volume calculated from fixed b produced increments of RMSE. The farther b was from the mean, the larger the RMSE became. This reduction in fitting performance resulted in underestimation of Lp, as shown in figure 7. The plots featured a convex shape. The farther b was from the mean, the smaller the Lp was, and the greater the deviation was. The Lp values computed from poor RMSEs varied widely and were unreliable.

Figure 6. Boyle-van’t Hoff plot for spinach mesophyll protoplast generated from numerically determined protoplast volume in equilibrium with the 0.4 and 0.6 mol L-1 mannitol solutions. The osmotically inactive fraction (b), which is the y-axis intercept of the linear regression line, was estimated at 0.267 ±0.293.
Figure 7. Plot of difference between cell membrane hydraulic conductivity (Lp,) obtained with the conventional and proposed approaches (?Lp = Lpconv - Lpproposed) against the fixed osmotically inactive fraction (b). Differences were calculated by subtracting Lp in the proposed approach from that in the conventional approach. Bars indicate standard errors of the mean. Numbers above the plots denote the probabilities of a two-tailed paired t-test.

Temporal Changes in Hydraulic Conductivity and Osmotically Inactive Volume

The proposed approach offered the significantly smallest RMSE, enabling us to conduct definitive analyses to compute the three unknown parameters (V8, Vb, and Lp). The temporal changes in Lp and b at two-day intervals are shown in figure 8. The adjusted R2 values for all computations of these parameters exceeded 0.909. Linear regression analysis for Lp showed a positive slope of 7.8 ±3.4 fm s-1 Pa-1 d-1 with p = 2.5 × 10-2, whereas that for b showed a negative slope of -0.02 ±0.01 d-1 with p = 6.4 × 10-2. The correlation between Lp and b was poor, and the difference between slopes (-70.0 ±45.3 fm s-1 Pa-1) was insignificant (p = 1.3 × 10-1; fig. 9). The weight loss of spinach leaves during four days of storage was 2.82% ±0.83%, and visible deterioration was not observed.

Figure 8. Changes in Lp (open circles) and Vb (closed circles) during storage in the dark at 20?. Bars indicate standard errors of the mean (n = 22, 10, and 16 for 0, 2, and 4 days after harvest, respectively). The slopes of univariate linear regression were 7.8 ±3.4 fm s-1 Pa-1 d-1 (p = 2.5 × 10-2) for Lp and -0.02 ±0.01 d-1 (p = 6.4 × 10-2) for Vb.


This study demonstrated the limitation of assuming that all cells have the same osmotically inactive fraction in measuring membrane hydraulic conductivity. Several studies that measured the osmotic water permeability of individual protoplasts either with or without considering the osmotically inactive fractions are shown in table 3. The current study showed that ignoring Vb or assuming Vb to be proportional to cell size, i.e., b = 0% to 40%, impaired the fitting accuracy, resulting in an underestimation of Lp. Although the case that Vb was constant irrespective of cell size was not shown, the deviation between Vb under such an assumption and that of individual protoplasts will, likewise, be a source of fitting error that reduces the accuracy of estimating Lp. To the best of our knowledge, Sommer et al. (2007) were the first to propose an approach for considering the osmotically inactive volume, and consequently its fraction, against the initial protoplast volume when calculating membrane hydraulic conductivity. Although Sommer et al. (2007) did not mention fitting accuracies such as RMSE and adjusted R2, they showed that disregarding b underestimated the membrane water permeability, and the BVH plot gave b values different from those calculated from the respective protoplast, which is in line with our findings. The b values of mesophyll cells pronouncedly varied, suggesting that the diversity of b should be considered when using stopped-flow light scattering (van Heeswijk and van Os, 1986; Wang et al., 2020) and dielectric property measurement (Higgins and Karlsson, 2008; Ishikawa et al., 1997), which determine the collective Lp of many cells.

Figure 9. Relationship between Lp and b. Square, circle, and triangle symbols denote 0, 2, and 4 days after storage, respectively. The slope of univariate linear regression was -70.0 ±45.3 fm s-1 Pa-1 (p = 1.3 × 10-1). A 95% confidence interval does not cover the distribution.
Table 3. Summary of studies on osmotic water permeability (Pos). Hydraulic conductivity is converted using Pos = LpRT/vw.
in ?es
MethodA in ModelPos vs. APos
(µm s-1)
flows method in
Varies with
Independent13.5 ±1.10.10 ±0.10,
BVH plot
S. oleracea, leaf mesophyllSotome et al.
9.7 ±0.80.12 ±0.03,
BVH plot
H. vulgare, cotyledon
10.4 ±4.90.23 ±0.14,
S. oleracea, leaf mesophyllThis study
of volume
Independent5.75 ±2.890.27 ±0.13,
N. tabacum, leaf mesophyllSommer et al.
8.15 ±6.040.32 ±0.11,
A. thaliana, leaf mesophyll
Varies with
Independent360 ±110ImplicitR. sativus, rootMurai-Hatano and
Kuwagata (2007)
Inversely with A340 ±100Implicit
Parallel to A3.01 to 21.61IgnoredZ. mays, BMS cells Moshelion et al.
Digital micro-
fluidic chip
Independent1 to 75IgnoredA. thaliana, leaf mesophyllKumar et al.

The proposed approach also offers the practical advantage of measuring Lp and b. The approach of Sommer et al. (2007) entails measuring protoplast volume that has reached the final steady-state under osmotic challenge, meaning that it requires sufficient time for the observation. Their method is also characterized as a successive way of determining the water permeability of the membrane, i.e., a quasi-simultaneous method of measuring the osmotically inactive volume and water permeability. Conversely, our approach does not require the protoplasts to reach osmotic equilibrium with the extracellular solution, and it searches numerically for the optimal hydraulic conductivity and osmotically inactive volume that represent the raw volume change observed. The long duration of observation has both good and bad impacts. An example of a good impact is that it is possible to acquire the final volume of the osmotic challenge, which may improve regression accuracy for the osmotically inactive volume and membrane water permeability; on the other hand, the frequency of incomputable data increases due to the bursting and disappearance of protoplasts. We faced a problem similar to that of Sommer et al. (2007) in that protoplasts occasionally burst in the late phase of observation (>200 s). The light used for microscopic observation may affect the integrity of the protoplasts. Too little time for the observation provides only the initial linear phase of volume change, known as the “initial rate” approach (Ramahaleo et al., 1999), which results in underestimation of the membrane water permeability (Moshelion et al., 2004; Sommer et al., 2007). We infer a trade-off relationship between the duration of observation of the protoplast volume change and the reliability of determining the parameters. Our approach is probably appropriate for observing fragile protoplasts, as the acquired data cover the first abrupt volume change and the subsequent gradual volume changes before reaching the plateau, which enables simultaneous determination of Lp and b with high accuracy from a rather short duration of observation.

The b values differ according to the cell type (animal or plant), tissue, and organ. For leaves, b was reported to be 8.4% ±4.2% and 14.6% ±4.5% for non-acclimated and acclimated rye leaves (Dowgert and Steponkus, 1984), 12% ±3.2% for barley leaves (Sotome et al., 2004), 27% ±13% for tobacco leaves, and 32% ±11% for Arabidopsis leaves (Sommer et al., 2007). For spinach, b was 22.4% ±1.27% in the chloroplast grana (Williams and Meryman, 1970) and 9.9% ±9.5% in mesophyll cells (Sotome et al., 2004). In this study, the mean b and its variation (23% ±14%) were higher and greater than previously obtained by Sotome et al. (2004). The differences in b among grana, mesophyll cells, and each study imply that the number of chloroplasts in the protoplast affects both the mean and the variation of b, which may differ according to variety, cultivating history, leaf age, and the composition ratio of palisade and sponge tissue. Gutiérrez-Rodríguez et al. (2013) reported that nitrogen fertilization affected the textural, compositional (including chlorophyll concentration), and anatomical properties of hydroponically grown spinach leaves, which in turn, was related to their shelf life. We cannot compare the differences in variety and cultivating conditions in hydroculture, such as nitrogen fertilization and lighting, between our study and previous studies; however, at least, our findings provide one example of evidence that biological variation derived from such differences in preharvest conditions affects b and its distribution within the leaf tissue. In addition, when the leaf’s abaxial surface, without epidermis, is immersed in an enzyme solution, the first protoplasts released are from spongy tissue (Nagata, 1977). As described in the Materials and Methods section, the first protoplasts isolated remained in the enzymatic solution and were discarded for this analysis; thus, the protoplasts gathered were likely all derived from palisade tissue. Therefore, the distribution of b that we observed was the distribution of b in palisade tissue, and the decrease in b with time that we found can be regarded as a decrease in cell solids, the release of hydrating water, and the loss of other cell contents in palisade tissue. The b value potentially allows evaluation of the quality and freshness deterioration during storage, although the distributed nature of b imposes a sensitivity limitation.

Oshita et al. (2006) reported that Lp increased linearly from one day after storage at 20?, whereas Lp was maintained during five days of storage at 2?. Our result for Lp showed a similar increasing tendency during storage at 20? and, as such, indicated membrane deterioration and dysfunction during storage. However, the question of how to evaluate quantitative values remains. The mean Lp values during four days of storage at 20? ranged from 120 to 250 fm s-1 Pa-1 for Oshita et al. (2006) and from 70 to 101 fm s-1 Pa-1 in this study. The former Lp values were calculated from the fixed b, and the latter values were calculated using the approach proposed herein. Therefore, the underestimation of Lp using fixed b, as clarified in this study, cannot explain the difference in magnitude between the two studies. The difference might be related to the protoplast isolation procedure, the cell-wall digestion time, the centrifugal force applied in removing enzymes, and whether or not density gradient centrifugation is applied. Protoplast isolation is a stress-inducing procedure that damages protoplasts and induces cell lysis (Davey et al., 2005; Papadakis and Roubelakis-Angelakis, 2002; Papadakis et al., 2001), implying that Lp varies with not only quality deterioration but also with the protoplast isolation protocol. In further research, minimizing damage during protoplast isolation should be taken into account for more correct understanding of the water permeability of cell membranes and for evaluating the quality and freshness of leafy vegetables. Another consideration for further research is the difference in the observed tissues. Oshita et al. (2006) collected mesophyll protoplasts that included both palisade and spongy tissue, whereas we probably used protoplasts that were derived only from palisade tissue. Further studies using protoplasts derived only from spongy or palisade tissue or using samples stored at low temperatures and under a controlled atmosphere will provide tissue-specific Lp and b values and their changes during storage and distribution, contributing to better understanding of the water loss and storability of postharvest leafy vegetables.


A numerical analytic approach for the simultaneous determination of the hydraulic conductivity (Lp) and the osmotically inactive volume (b) of plant cells has been developed. Our proposed approach has shown that the relative osmotically inactive fraction differed among protoplasts derived from the palisade tissue of spinach leaves. The use of the BVH plot-based representative or averaged value reduced the accuracy of regression, leading to underestimation of Lp. Our approach also has the advantage of measuring Lp and b simultaneously with high accuracy during a relatively short period of osmotic challenge. A storage test at 20? attested to a hitherto unknown gradual reduction in b and a known increment in Lp during storage. These changes were likely related to quality deterioration of the palisade tissue due to degradation of internal components and the easy loss of intracellular water, and therefore can provide a novel and fundamental insight into the water loss and shelf-life of postharvest produce.


This work was supported by JSPS KAKENHI (Grant Nos. 25292155, 15K07666, 351, and 18H02304). Our deepfelt thanks to the members who have belonged to our lab for their willingness to try anything while we figured out how to write up this work. Mention of trade names or commercial products in this publication is solely for the purpose of providing specific information and does not imply recommendation or endorsement by Kobe University, Gifu University, or the University of Tokyo.


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