ORIGINAL PAPER

Evaluation of Models for Spinach Respiratory MetabolismUnder Low Oxygen Atmospheres

Soraya Saenmuang & Muhammad Imran Al-Haq &

Himani Chamila Samarakoon & Yoshio Makino &

Yoshinori Kawagoe & Seiichi Oshita

Received: 23 August 2010 /Accepted: 22 December 2010# Springer Science+Business Media, LLC 2011

Abstract Anaerobic respiration is a major problem thatcauses the deterioration of fresh produce packaged underlow O2 atmospheres. The problem becomes more severeand causes high losses in the packages handling at ambientconditions, especially in developing countries. In designingmodified atmosphere packaging, the risk of anaerobicdevelopment greatly depends upon the accuracy of respira-tion rate prediction; therefore, the respiration rate model fora particular produce has to be identified. In this study,different atmospheric storage conditions in a closed systemwere realized to examine the adaptability of respiration ratemodels for spinach storage under low O2 at an expectedambient temperature of 25 °C. Six models were applied andit was found that, for aerobic conditions, the respiration ratecould be described with a constant respiratory quotient bythree models, viz., (a) Michaelis–Menten model withoutinhibition, (b) Michaelis–Menten model with uncompetitiveinhibition, and (c) Langmuir adsorption model, whereasthree other models, viz. (d) Michaelis–Menten model withcompetitive inhibition, (e) Michaelis–Menten model withnoncompetitive inhibition, and (f) Michaelis–Menten withmixed inhibition could not be fitted. Among the threesuccessful models, the Michaelis–Menten with uncompet-itive inhibition was found to be the most suitable model forpractical applications in developing countries where cold-

chain systems are lacking. This model can be applied forthe prediction of gas composition and optimize the pack-ages, particularly to ensure the aerobic respiration.

Keywords Inhibition .Michaelis–Menten .Modeling .

Respiration rate . Spinach

Introduction

Respiration is an important metabolic process causing thedeterioration of fruits and vegetables after harvest. Ingeneral, for avoiding the higher temperature resulting inthe higher respiration rate, the cold storage and cold-chaindistribution have been recommended. However, the post-harvest losses due to poor postharvest handling techniques,mainly poor temperature management, are still high,especially in tropical countries where the temperature ishigh all year-round and where the refrigeration facilities arenot available. In developing countries, the losses couldrange from 15% to as high as 50% of the production (FAO2009). Not only the lack of the facilities but also improperhandling prior to cold storage cause various problems(Nunes and Emond 2003).

Spinach is one of the highly perishable vegetables thathas a high respiration rate and is susceptible to deteriorationat high temperature. The shelf-life of spinach is approxi-mately 10–14 days at its optimum temperature of 0 °C andis estimated to be less than 8, 6, and 4 days at 4 °C, 10 °C,and 20 °C, respectively (Pandrangi and LaBorde 2004).Modified atmosphere packaging involving low O2 is atechnique that effectively decreases the spinach respirationand consequently diminishes the deteriorations. However,the drawback of low O2 packages is that a shift fromaerobic respiration to anaerobic respiration or fermentation

S. Saenmuang :M. I. Al-Haq :H. C. Samarakoon :Y. Makino :Y. Kawagoe : S. Oshita (*)Laboratory of Bioprocess Engineering, Department of Biologicaland Environmental Engineering, Graduate School of Agriculturaland Life Sciences, The University of Tokyo,Yayoi 1-1-1, Bunkyo-ku,Tokyo 113-8657, Japane-mail: aoshita@mail.ecc.u-tokyo.ac.jp

Food Bioprocess TechnolDOI 10.1007/s11947-010-0503-5

when the O2 concentration becomes lower than lower O2

limit and leads to undesirable reactions. Ko et al. (1996)reported that the O2 level in the spinach packaged at 0 °Cand 5 °C must be maintained at higher than 0.4% in orderto avoid the deterioration due to fermentation. As highrespiration rate at high temperature causes rapid depletionof O2, this problem becomes a major cause of the loss ofpackages handled at ambient temperature. From thisstandpoint, respiration rate modeling is required to designand optimize the packages conditions at an expectedhandling without any cooling systems in developingcountries.

Several models have been proposed for the predictionof respiration rate as a function of the temperature and/orgas composition, based on either empirical relations orfundamental theories (Andrich et al. 1991; Banks et al.1993; Bhande et al. 2008; Cameron et al. 1989; Dadzie etal. 1996; Emond et al. 1993; Fishman et al. 1996; Fonsecaet al. 2002; Lee et al. 1991; Lencki et al. 2004; Makino etal. 1996; Peppelenbos and Leven 1996; Ravindra andGoswami 2008; Talasila et al. 1992; Yang and Chinnan1988). Those models have successfully been applied to avariety of fruits and vegetables. However, there is nomodel applicable to all produce exposed to ambienttemperature. Since the use of an improper model can haveno benefits or even place the packages at risk because ofpoor predictive data, the suitable model and specificparameters for individual produce are still needed to beidentified and quantified.

To our knowledge, no models have been established todescribe changes in respiratory metabolism of spinach,especially when stored at high temperature as 25 °C. Thepresent study was not done to formulate any new model forspinach but to examine six previously published respirationrate models that had been used for various agriculturalproducts and to identify the most suitable model(s) that can

be used for spinach stored under low O2 concentrations atan expected ambient temperature of 25 °C. If such a modelcan be identified, then it can be applied for optimizingspinach handling in the developing countries, where thereare many concerns about the distribution chain at ambienttemperature.

Materials and Methods

Sample Preparation

Spinach plants (Spinacia oleracea L.), purchased a dayafter harvest from Tsukiji wholesale market, Tokyo, Japan,were used. Uniform size of spinach plants was carefullyselected, weighed, and stored in a storage chamber with aninside volume of 14.69 l (Fig. 1).

Seven initial conditions were used in a closed system toexamine the dynamic change of gas compositions andrespiration rate (Table 1). In the first four conditions,similar amount of spinach samples, 240±30 g, were placedin the storage chambers. The pressures inside the storagechambers were reduced by evacuating the headspace gasuntil O2 concentration reached to 18%, 17%, 15%, and13% v/v, and then 100% humidified nitrogen gas wasintroduced to recover the inside pressures to an atmosphericpressure. In these conditions, the initial amounts of O2 perunit mass of spinach were 454.6, 502.6, 378.9, and280.4 mmol kg−1 for 18%, 17%, 15%, and 13% initial O2

concentrations, respectively. For the other three conditions,different amounts of spinach, about 210, 400, and 500 g,were placed in the storage chambers and closed withoutreducing the initial O2 concentration; thus, the initial O2

concentrations were approximately the same as the normalatmosphere or 21% O2 concentration, but the void volumesor initial amounts of O2 per unit mass of spinach were

Fig. 1 The storage chamber andits various components

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different, i.e., 601.8, 298.7, and 236.8 mmol kg−1 for 210,400, and 500 g spinach, respectively.

In each storage chamber, a circulating fan was installed inorder to establish a uniform storage atmosphere. The fan wasoperated for 5 min before each headspace gas sampling forgas concentration measurements. The pressure–temperaturesensor (Thermo recorder RS-12P, ESPEC MIC Corp., Japan)was also placed inside the chamber for measuring the pressureand temperature during the storage period. The measuredtemperature and pressure were used for calculating the actualgas concentrations. The storage chambers at all conditionswere kept in an incubator, controlled at 25 °C for 77 h. Theexperiment was run twice for each storage condition and themean values presented.

Gas Concentration Measurement

During spinach storage, the gas composition inside theseven storage chambers was measured to determine therespiration rate and estimate the models’ parameters. Forthe respiration rate determination, 0.5 ml of headspacegas inside the storage chambers of all conditions wastaken at intervals through the sampling port at the top ofthe storage chambers (Fig. 1). The gas samples wereanalyzed for O2 and CO2 concentrations (in volume/volume percentage) using a gas chromatograph (Molecularsieve-5A column and Gas chromatopack 54 column,Shimadzu Corp., Japan) and were then converted to actualgas concentrations (millimoles per liter) by the Ideal gaslaw, where the void volume was the chamber volumesubtracted by an approximate volume of the spinach. Dueto the high water content of spinach sample, the spinachdensity was estimated to be the water density, i.e., 1 kg l−1,and the spinach volume was approximately the spinachmass.

To estimate the models’ parameter, a large amount of gasconcentration data is needed for ensuring the reliability ofrespiration rate determination and minimizing the risk ofoverfitting due to insufficient number of data points. Taking

many samples of the headspace gas for gas concentrationsmeasurement could affect the pressure and gas concentrationsinside the storage chamber. Therefore, to overcome thisproblem, an optical sensor (21 G Foxy-R sensor withMFPF100-1 multi-frequency phase fluorometer, Ocean optics,Inc., USA) was used for measuring the O2 concentration. Theadvantage of the optical sensor is that it can be used forcontinuous measurement of gas concentration without theheadspace gas consumption (Neethirajan et al. 2009).

The measurement principle of the optical sensor is basedon photoluminescence quenching using a ruthenium com-pound. The system is composed of an exciting source withmulti-frequency phase fluorometer, an optical sensor, anoptical fiber, and a temperature probe. In the operation, theexciting source sends excitation light, at about 475 nm, viathe optical fiber to the ruthenium compound which istrapped in the sol–gel matrix at the tip of the sensor. Whenexcited, the ruthenium complex fluoresces, emitting energyat about 650 nm. If the excited ruthenium complexencounters the O2 molecule, the excess energy quenchesthe fluorescent signal. The quenching time relating to theO2 concentration is then measured by a multi-frequencyphase fluorometer. Parallel with the O2 concentrationmeasurement, the temperature was measured to compensatefor any change in temperature.

Among the seven storage conditions (Table 1), the21% initial O2 concentration with amount of O2 per unitmass of spinach 298.7 mmol kg−1 (condition no. 6) wasselected for estimating the models’ parameters because athigh initial O2 concentration with moderate amount ofstored spinach, the concentrations of O2 and CO2 weresupposed to be varied in a wide range in this condition. Inthe selected condition, the optical sensor was usedconcurrently with the gas chromatograph for continuouslymeasuring the O2 concentration. The concentration outputfrom the optical sensor was recorded every 10 s along withthe O2 concentration measuring by the gas chromatographat the given intervals. The corrected O2 concentrationevery 10 s was determined from the correction factor

Condition no. Initial O2 concentration (%) Sample mass (g) Initial amount of O2 per unitmass of spinach (mmol kg−1)

1 13 240±30 280.4

2 15 240±30 378.9

3 17 240±30 502.6

4 18 240±30 454.6

5 21 210 601.8

6 21 400 298.7

7 21 500 236.8

Table 1 The initial conditionsused to determine modelparameters

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obtained by the correlation between the O2 concentrations(volume/volume percentage) measured with the gas chro-matograph and the concentration output obtained by theoptical sensor. The actual O2 concentration in millimolesper liter then was calculated from the corrected O2

concentration using the Ideal gas law.

Respiration Rate and Respiratory Quotient Determination

The respiration rates were determined by the rate of O2

consumption (RO2) and CO2 production (RCO2) that werecalculated by each gas concentration change per unit time(t) and sample mass (W) between two measurements. Theequations are given as followings:

RO2 ¼CO2ð Þt � CO2ð ÞtþΔt

Δt

� �V

Wð1Þ

RCO2 ¼CCO2ð ÞtþΔt � CCO2ð Þt

Δt

� �V

Wð2Þ

where RO2=O2 consumption rate (millimoles per kilo-gram per hour), RCO2=CO2 production rate (millimolesper kilogram per hour), CO2=O2 concentration (milli-moles per liter), CCO2 =CO2 concentration (millimoles perliter), t=storage time (hours), Δt= time difference be-tween two gas measurements (hours), V=void volume ofa storage chamber (liters), and W=spinach sample mass(kilograms).

The respiratory quotient (RQ) value was calculated fromthe ratio of the CO2 production and O2 consumption ratesand then was analyzed by the analysis of variance and theDuncan’s multiple range test (STATISTICAVersion 8 Trial,StatSoft, Inc., Tulsa, OK, USA) to examine the influence of

the initial conditions and the time period. The respirationrates and RQ value were reported as a function of storagetime, where in this case, the storage time referred to amidpoint of each time interval between two measurementsof the gas concentrations (t+Δt/2).

Modeling

The respiration rate models in the literature are eitherempirical best fitted or theoretical-based models. Due to thelimitation of the empirical models that the introducedparameters cannot be related to a specific physiologicalprocess, therefore only the theoretical-based models wereexamined. The six respiration rate models (Table 2) basedon enzyme kinetics and adsorption theories (Fonseca et al.2002; Lee et al. 1991; Makino et al. 1996; Peppelenbos andLeven 1996) were applied to the experimental data basedon the following assumptions:

1. Spinach and the headspace gas temperatures wereequal, and the temperature was constant throughoutthe storage period.

2. The dissolved CO2 in the spinach tissue was negligible.3. As the ratio of surface area to volume of spinach was

large, the resistance of gases exchange between spinachleaves and its environment was considered to beneglected. Most of the exchanged gases, hence, werein the headspace (Fonseca et al. 2002).

4. The O2 levels in the headspace were high enough tomaintain the oxidative CO2 production without fermen-tation development.

5. RQ value was constant.

A pictorial presentation of the models used in this study(only models 1 to 4) is presented in Fig. 2.

No. Model name Parameters R2

1 Michaelis–Menten without inhibition Rmax 5.74 mmol kg−1 h−1 0.955K 1.19 mmol l−1

2 Michaelis–Menten with Rmax 5.74 mmol kg−1 h−1 0.989competitive inhibition of CO2 K 1.19 mmol l−1

Kc 19,591.47 mmol l−1

3 Michaelis–Menten with Rmax 6.11 mmol kg−1 h−1 0.989uncompetitive inhibition of CO2 K 0.86 mmol l−1

Ku 18.11 mmol l−1

4 Michaelis–Menten with Could not be estimatednoncompetitive inhibition of CO2

5 Michaelis–Menten with Could not be estimatedmixed inhibition of CO2

6 Langmuir adsorption a 1.16 l mmol−1 0.989b 6.11 mmol kg−1 h−1

i 0.06 l mmol−1

Table 2 Estimated parametersfor each model

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Model 1: the Michaelis–Menten Model Without Inhibition

The Michaelis–Menten model is based on one limitingenzyme reaction in which O2 is a substrate. The course ofthe reaction involves the formation of enzyme–substrate

and enzyme–product complexes as shown in Fig. 2a. TheO2 consumption rate is given by Eq. 3.

RO2 ¼RmaxCO2

K þ CO2

ð3Þ

Fig. 2 Pictorial illustration ofmodel nos. 1 to 4: a Michaelis–Menten model without inhibi-tion (model 1), b Michaelis–Menten model with competitiveinhibition (model 2), c Michae-lis–Menten model with uncom-petitive inhibition (model 3),and d Michaelis–Menten modelwith noncompetitive inhibition(model 4)

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where Rmax=maximum O2 consumption rate (millimolesper kilogram per hour) and K=Michaelis–Menten constant(millimoles per liter).

Model 2: the Michaelis–Menten Model with CompetitiveInhibition of CO2

The CO2 is considered to be an inhibitor of the respiratoryreaction. The competitive inhibition occurred when theinhibitor and the substrate compete for binding to the sameactive site of an enzyme. The formation of an enzyme–inhibitor complex causes the reduction in the number offree enzyme available for the substrate binding (Fig. 2b).The O2 consumption rate is given as Eq. 4.

RO2 ¼RmaxCO2

K 1þ CCO2=Kcð Þ þ CO2

ð4Þ

where Kc=competitive inhibition constant (millimoles perliter).

Model 3: the Michaelis–Menten Model with UncompetitiveInhibition of CO2

In uncompetitive inhibition, the inhibitor binds with thecomplex form of the enzyme and the substrate to form anenzyme–substrate–inhibitor complex, a dead-end complexwhich cannot form the product (Fig. 2c). The O2 consump-tion rate is given by Eq. 5.

RO2 ¼RmaxCO2

K þ CO2 1þ CCO2=Kuð Þ ð5Þ

where Ku=uncompetitive inhibition constant (millimolesper liter).

Model 4: the Michaelis–Menten Modelwith Noncompetitive Inhibition of CO2

In noncompetitive inhibition, the inhibitor can bind withboth the enzyme and the enzyme–substrate complex withidentical affinities. The bindings are at the site other thanthe active site; hence, the active site is unaffected and theenzyme–inhibitor complex can bind with the substrate(Fig. 2d). However, the enzyme–substrate–inhibitor com-plex is unable to proceed to give a product. The O2

consumption rate is given by Eq. 6.

RO2 ¼RmaxCO2

K þ CO2ð Þ 1þ CCO2=Knð Þ ð6Þ

where Kn=noncompetitive inhibition constant (millimolesper liter).

Model 5: the Michaelis–Menten Model with MixedInhibition of CO2

The mixed inhibition occurs when the inhibitor canbind with either the enzyme or the enzyme–substratecomplex, but the affinities for these two forms ofenzyme are different. The O2 consumption rate is givenas Eq. 7.

RO2 ¼RmaxCO2

K 1þ CCO2=Kcð Þ þ CO2 1þ CCO2=Kuð Þ ð7Þ

Model 6: the Langmuir Adsorption Model

This model is based on the adsorption theory thatconsiders the controlling mechanism to be the adsorptionof an O2 molecule at the active site of an enzyme. TheCO2 acts as an inhibitor as it indirectly reduces desorptionof O2 molecules that had already adsorbed at the activesite of enzyme. The O2 consumption rate is expressed asEq. 8.

RO2 ¼abCO2

1þ aCO2 þ aiCO2CCO2

ð8Þ

where a=Langmuir constant (liters per millimole), b=Langmuir maximum O2 consumption rate (millimoles perkilogram per hour), and i=Langmuir inhibition constant(liters per millimole).

The CO2 production rate based on those six models wereassumed to be a function of O2 consumption rate with aconstant RQ. The rate is expressed as follows:

RCO2 ¼ RQ � RO2 ð9Þ

Parameters Estimation

To calculate the dataset for estimating the models’parameters, i.e., O2 consumption rate, O2 concentration,and CO2 concentration, the O2 concentration at the 21%initial O2 concentration with amount of O2 per unit mass ofspinach 298.7 mmol kg−1 (condition no. 6) obtained fromthe optical sensor was used.

The O2 consumption rate was calculated by Eq. 10,calculated every 4-h time interval. The optical sensorrecorded the data every 10 s to obtain a more reliableslope; however, the values at the time interval of every 4 hof the storage time were used to find m.

RO2 ¼ mV

Wð10Þ

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where m=slope of linear fitting of the O2 concentration vs.storage time (

ΔCO2Δt , where Δt=4 h).

The CO2 concentration was calculated from the CO2

production rate, where the CO2 production rate wasdetermined by multiplying the obtained O2 consumptionrate with the calculated RQ value (Eq. 9) from the gasconcentrations measured by the gas chromatograph. The O2

consumption rate, O2 concentration, and CO2 concentrationwere then used to estimate each model parameters (Eqs. 3to 8) using non-linear regression (STATISTICAVer. 8 Trial,StatSoft, Inc., Tulsa, OK, USA).

Model Validation

The estimated values of the model parameters and thecalculated value of RQ were used to simulate the O2 andCO2 concentration change with time at the other six storageconditions (condition nos. 1 to 5 and 7). The model wassolved by the finite difference method using a forwarddifference with a 1-min running time interval (MATLABR2007b, The MathWorks, Inc., Natick, MA, USA).

The simulated O2 and CO2 concentrations were evalu-ated by comparing to the experimental data. Because theaccuracy of O2 concentration prediction is crucial forensuring aerobic respiration in a package, the simulatedO2 concentration was evaluated by two parameters: rootmean square error (RMSE; Abdel-Nour et al. 2009; Uchinoet al. 2004) and mean relative percentage deviation ofmodulus (E; Bhande et al. 2008). The lower values ofRMSE and E indicate better agreement between thesimulated and the experimental data. The E values below10% indicate very good agreement whereas the valuesbetween 10% and 20% indicate reasonable agreement(Bhande et al. 2008). The RMSE and E values werecalculated as followings:

RMSE ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPNi¼1

Cexp;i � Cpre;i

� �2N

vuuutð11Þ

E ¼ 100

N

XNi¼1

Cexp;i � Cpre;i

�� ��Cexp;i

ð12Þ

where RMSE=root mean square error (millimoles perliter), E=mean relative percentage deviation of modulus(percent), Cexp,i=experimental gas concentration (milli-moles per liter), Cpre,i=predicted or simulated gas concen-tration (millimoles per liter), and N=number of gasconcentration data point.

Results

Respiration Rate

The respiration rates determined by the O2 consumptionrate and CO2 production rate at different initial O2

concentrations, i.e., 13%, 15%, 17%, and 18% are shownin Fig. 3. No clear dependence of respiration rate on initialO2 concentrations was observed until 65 h of storage, but itappears that respiration rates tended to decrease withstorage time, except in the case of 18% initial O2. The O2

consumption rates ranged from 4.4 to 2.0 mmol kg−1 h−1,and the CO2 production rates ranged from 3.5 to1.8 mmol kg−1 h−1 during the storage.

The respiration rates at 21% initial O2 concentration withdifferent void volumes or initial amounts of O2 per unitmass of spinach, i.e., 236.8, 298.7, and 601.8 mmol kg−1

are shown in Fig. 4. In these conditions, the O2 consump-tion rates ranged from 5.1 to 0.1 mmol kg−1 h−1, and theCO2 production rates ranged from 4.3 to 0.5 mmol kg−1 h−1

during the storage. The decrease of respiration rates withstorage time became greater when the initial amount of O2

Fig. 3 The respiration rates of spinach leaves during storage in a14.69-l chamber with different initial O2 concentrations: a O2

consumption rate and b CO2 production rate. Initial O2 atmospheresand ratio of O2 to mass of leaves were (O2, millimoles per kilogram):black circle 13%, 280.4; white circle 15%, 378.9; black triangle 17%,502.6; and white square 18%, 454.6

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per unit mass of spinach was smaller (Fig. 4). Although aclear influence of initial O2 concentration was not observedamong 13%, 15%, 17%, and 18% initial O2 concentration,the initial respiration rate under these conditions were lowerin comparison with the 21% initial O2 concentration (Figs. 3and 4).

Respiratory Quotient

The RQ values normally range from 0.7 to 1.3 for aerobicrespiration and values higher than 1 indicate fermentation(Kader and Saltveit 2003). RQ values corresponding todifferent initial conditions and storage time are shown inFig. 5. The treatments having RQ values higher than 1.3 areshown in Fig. 5a, where the treatments that remained withinthe aerobic conditions are shown in Fig. 5b.

At 21% O2 with 236.8 mmol kg−1 (Fig. 5a), the RQbecame higher than 1.3 after 60 h of storage when the O2

concentration reached 0.8 mmol l−1 and increased sharplywhen O2 concentration dropped to 0.6 mmol l−1 at 65 h(Table 3). This indicated fermentation after 60 h of storage,and the lower O2 limit to maintain aerobic respiration couldbe estimated to be 0.8–0.6 mmol l−1 (corresponding to 2.0–1.5%). The fermentation was evident with off-flavor anddamaged tissue observed after the end of storage under thiscondition. In contrast, the condition of the same initial O2

concentration but higher amount of O2 per unit mass ofspinach (21%, 298.7 mmol kg−1) did not result in tissuedeterioration (Fig. 6).

For the other conditions, there were non-significantdifferences among the RQ values except in the case of21% O2 with 601.8 mmol kg−1 at 2 h after the storage (p>0.01). From Fig. 5, it could be thought that there wasaerobic respiration with a constant RQ throughout thestorage time for these conditions (condition nos. 1 to 6).The mean RQ for these conditions was 0.8±0.2.

Parameters Estimation

The dataset of O2 consumption rate with different O2 andCO2 concentrations used to estimate the models’ parame-ters is shown in Fig. 7. Some data points were omittedbecause of the large deviation, and in total, 15 data pointswere used for the parameters estimation.

From the six applied models, the parameters of only fourmodels could be estimated, i.e., Michaelis–Menten withoutinhibition (model 1), Michaelis–Menten with competitiveinhibition (model 2), Michaelis–Menten with uncompetitiveinhibition (model 3), and Langmuir adsorption (model 6).These models gave good fits with determination coeffi-cients (R2) higher than 0.95. However, the extremely large

Fig. 5 The RQ values of spinach leaves during storage in a 14.69-l chamber with different initial conditions as a function of storagetime. Initial O2 atmospheres and ratio of O2 to mass of leaves were(O2, millimoles per kilogram): black circle 13%, 280.4; white circle15%, 378.9; black triangle 17%, 502.6; white square 18%, 454.6;black square 21%, 236.8; white triangle 21%, 298.7; and whitediamond 21%, 601.8

Fig. 4 The respiration rates of spinach leaves during storage in a14.69-l chamber with different amounts of O2 per unit mass ofspinach: a O2 consumption rate and b CO2 production rate. Initial O2

atmospheres and ratio of O2 to mass of leaves were (O2, millimolesper kilogram): black square 21%, 236.8; white triangle 21%, 298.7;and white circle 21%, 601.8

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value of competitive inhibition (Kc) indicated that thecompetitive inhibition was not involved, and hence, model2 was not considered. The model parameters for eachmodel are given in Table 2.

Considering the three models (model 1, model 3, andmodel 6), the two inhibition models (model 3 and model 6)gave slightly better fitting results (higher R2) than themodel without inhibition (model 1), suggesting that theinhibition models could be better applied. Because theLangmuir adsorption model is a simplified mathematicalform of the uncompetitive inhibition model and the modelswere developed from different point of views (Makino et al.1996; Hertog 2001), the uncompetitive inhibition model(model 3) was selected for predicting gas concentrations.

Model Validation

The estimated values of the uncompetitive inhibition modelparameters (Table 2) with the mean RQ of 0.8 were used tosimulate the gas concentrations change during storage at thedifferent storage conditions. The simulated results areshown with solid lines in Fig. 8 together with experimentaldata plotted with different symbols. The RMSE and Evalues were calculated during the aerobic conditions. In thecase of 21% O2 with 236.8 mmol kg−1 (and in whichfermentation occurred 60 h after storage), the E and RMSEwere calculated only up to the point where conditionsremained aerobic, i.e., observed O2 concentrations werehigher than the lower O2 limit of 0.8 mmol l−1.

The simulated results showed fairly good agreements tothe experimental data for both O2 and CO2 concentrations.The RMSE and E values for O2 concentration are given inTable 4. The RMSE and E values ranged from 0.09 to0.99 mmol l−1 and 5.1% to 22.4%, respectively.

Discussion

The present study was done to examine six respiration ratemodels used for various agricultural products and to

identify the most suitable model(s) that could be used forspinach stored under low O2 concentrations at an expectedambient temperature of 25 °C. Different initial conditionswere used to determine the respiration rate. Evaluation ofthe obtained data showed that not only the initial O2

concentration but also the initial amount of O2 per unitmass of spinach strongly influenced the dynamic change ofgas compositions and consequently the respiration rate. Thedepletion of O2 with time caused a decrease in therespiration rate for all the storage conditions (Figs. 3 and4), and the respiration rate was especially decreased morerapidly in the case of a lower void volume or lower amountof O2 per unit mass of spinach (Fig. 4). It could be due tothe rapid depletion of O2 and/or due to the inhibition effectof higher accumulated CO2 (Fig. 8). During the 3 days ofstorage at the 21% initial O2 concentration (Fig. 4b), theCO2 production rates ranged from 4.0 to 2.7, 4.3 to 1.8, and4.2 to 0.5 mmol kg−1 h−1 for amounts of O2 per unit massof spinach 601.8, 298.7, and 236.8 mmol kg−1, respectively.However, in the study on baby spinach carried out byAllende et al. (2004), the CO2 production rates ranged from

Fig. 6 Spinach leaves after 77 h of storage in a 14.69-l chamber withdifferent initial O2 atmospheres and ratio of O2 to mass of leaves: a21%, 298.7 mmol kg−1 and b 21%, 236.8 mmol kg−1

Condition O2 (mmol l−1)a CO2 (mmol l−1)a RQ

% O2 mmol kg−1

13 280.4 1.1 3.6 0.89±0.04

15 378.9 2.9 2.6 0.81±0.02

17 502.6 4.2 2.3 0.84±0.00

18 454.6 3.2 3.3 0.81±0.00

21 601.8 4.5 3.6 0.68±0.15

21 298.7 1.2 6.8 0.99±0.02

21 236.8 0.6 7.4 8.55±0.38

Table 3 The RQ values fordifferent initial conditions andstorage time of 65 h

Lower O2 limit to maintainaerobic respiration was0.8–0.6 mmol l−1

a O2 and CO2 concentrations wereobtained by interpolation betweentwo measurements of each gasconcentration

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0.7 to 0.5 mmol kg−1 h−1 for 12 days of storage under 21%initial O2 and super atmospheric initial O2 at 5 °C. It showsthat the respiration rate was dramatically decreased with timein the present study because of high storage temperaturetogether with a low amount of O2 per unit mass of spinach.

Based on the respiration rate results obtained, it issuggested that to realize the suitable atmospheric conditionsand respiration rate, the initial O2 concentration should bedesigned in relation to the amount of the spinach packaged,especially at a high temperature of 25 °C. At low initial O2

concentrations together with a large void volume seemsbeneficial since the low initial O2 concentrations decreasedthe respiration rate (Fig. 3) and with the large void volume,the O2 levels did not change as much over the storage time.Hence, the level of O2 that induces fermentation would bereached at a slower rate. Nonetheless, the large void volumeof a package is not preferable for commercial distribution.The most appropriate condition could be the 21% initial O2

concentration with low void volumes (amount of O2 perunit mass of spinach lower than 601.8 mmol kg−1). Theinitial respiration rate was higher in such conditions, withlow void volume, and it will cause the rapid decrease of O2

and increase of CO2 levels. Consequently, the remarkabledecrease of respiration rate can be obtained (Fig. 4). Theaccumulated CO2 higher than 10% (corresponding to4.0 mmol l−1) also significantly reduced the aerobicmesophilic bacterial growth (Allende et al. 2004). More-over, the use of ambient air as the packaging gas isobviously the most economical option. However, the rapiddepletion of O2 can result in the storage atmosphere fallingbelow the lower O2 limit and thus leading to fermentativemetabolism sooner (Lakakul et al. 1999). At the very lowvoid volume (21% initial O2 with 236.8 mmol kg−1),fermentation occurred after 60 h of storage as observed bythe increase of the RQ (Fig. 5a) and the presence ofdamaged tissue (Fig. 6b). This void volume is suitable foran expected duration of less than 60 h, but the void volumeshould be higher if an expected duration is longer.

Therefore, to achieve the ultimate respiratory suppressionwithout fermentation development, the amount of spinachwithin the package has to be designed for a specific targetstorage duration. Among the studied conditions, the amountof O2 per unit mass of spinach 298.7 mmol kg−1 would be

Fig. 7 Changes in O2 and CO2 and the O2 consumption rate in a14.69-l chamber loaded with spinach leaves in an initial O2

concentration of 21% and an initial amount of O2 per unit mass ofspinach 298.7 mmol kg−1: black triangle O2 concentration, whitecircle CO2 concentration, and white square O2 consumption rate

Fig. 8 Actual and simulated O2 and CO2 concentrations duringstorage for 80 h at 25 °C in packs loaded with spinach leaves and withdifferent initial O2 atmospheres: a 13% O2, 280.4 mmol kg−1; b 15%O2, 378.9 mmol kg−1; c 17% O2, 502.6 mmol kg−1; d 18% O2,454.6 mmol kg−1; e 21% O2, 601.8 mmol kg−1; and f 21% O2,236.8 mmol kg−1: black triangle O2 concentration, white circle CO2

concentration, black line simulated O2 concentration, and gray linesimulated CO2 concentration. Equation 5 was used to calculate thesimulated O2 and CO2 concentrations

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the most appropriate condition over the storage period of80 h (Fig. 4).

The lower O2 limit needed to maintain aerobic respira-tion is generally determined by the RQ breakpoint, i.e., thelower limit is the O2 concentration that causes the RQ toincrease when the O2 concentration further decreased (Granand Beaudry 1993; Peppolenbos and Oosterhaven 1996).The lower O2 limit was 0.2–0.4% for spinach storage at0–5 °C when the CO2 concentration was lower than 0.1%(Ko et al. 1996). However, the lower O2 limit can increasewith the increase either in temperature or CO2 concentra-tion (Beaudry and Gran 1993; Lakakul et al. 1999). In thepresent study, the lower O2 limit was 0.8–0.6 mmol l−1

(corresponding to 2.0–1.5%) for spinach storage at atemperature of 25 °C and CO2 concentration of7.4 mmol l−1 (corresponding to 18%; Table 3). Thissuggested that the lower O2 limit has to be identified forparticular storage conditions. The value of 0.8–0.6 mmol l−1 O2 concentration can be used as a criterionin avoiding fermentation under passive modified atmo-sphere packaging conditions using an initial 21% O2

concentration or lower at 25 °C.With regard to estimation of the models’ parameters, a

good fit was obtained by the Michaelis–Menten modelwithout inhibition (model 1) indicating that the respirationrate was not affected by the CO2 concentration (Table 2).However, the inhibition models (model 3 and model 6) alsofitted well with the experimental data suggesting that theCO2 produced suppressed the respiration (Table 2). Thereason why the two types of model (models with inhibitionand without inhibition) fitted well would be the differentialCO2 concentrations within the storage period. That is, CO2

concentration was observed to be very low (about 1.4% or0.6 mmol l−1 at 2 h) but became very high (about 18.2% or7.2 mmol l−1 at 66 h; Fig. 7).

The influence of CO2 on respiration rate inhibition wasreported to be effective at the levels higher than 5% invarious fresh produces (Peppelenbos and Leven 1996;Kader and Ke 1994; O’ Hare et al. 2000; Fonseca et al.2002) and 10–30% in the case of spinach (Akimoto et al.1996). In the present study, the CO2 level became higherthan 10% (corresponding to 4.0 mmol l−1) after 30 h ofstorage for the condition of 298.7 mmol kg−1 at 21% initialO2 (Fig. 7). Thus, it could be thought that the inhibitioneffect was not observed in the initial period of storage andbecame prominent in the latter period of storage. Thisexplanation was supported by the relatively high ofuncompetitive inhibition constant (Ku) and the small valueof Langmuir inhibition constant (i).

In the present study, the inhibition models (model 3 andmodel 6) gave higher R2 values than the model withoutinhibition (model 1; Table 2), suggesting that the inhibitionmodels could be better applied to spinach under the studied

conditions. Practically, when the initial condition of anormal air atmosphere is applied, the CO2 level willbecome higher than 10% after a certain storage period. Inthis case, the model is required to cover the reaction withand without inhibition. Additionally, with a small voidvolume of a package which is usually desirable forcommercial distribution, the concentration of CO2 in thepackage would reach a high level in a short time. Theinfluence of accumulated CO2 hence would be crucial.Therefore, the inhibition models selected here would be thesuitable models for the prediction of respiration rate and gascomposition in a spinach package.

The respiration rate was well described by the twoinhibition models, the Michaelis–Menten with uncompeti-tive inhibition (model 3) and the Langmuir adsorptionmodel (model 6). These models gave the same fit (R2), butthey are different in interpretation. However, the uncom-petitive inhibition model was selected because its theoret-ical base is more widely accepted and reasonably appliedwith as simpler explanation.

Based on the fact that the respiratory process concernsseveral enzyme reactions, Peppelenbos and Leven (1996)suggested that among the five types of Michaelis–Mentenmodels, the mixed inhibition model (model 5) is the mostclosely related to what is actually occurring in plant tissuessince it considered two inhibition approaches, i.e., thebinding of the inhibitor with free enzyme and enzyme–substrate complex. For the reason of simplicity, thenoncompetitive inhibition model (model 4) that consideredsimilar intensity of the two inhibition approaches wasrecommended by them. However, in the present study, themixed inhibition and the noncompetitive inhibition couldnot be applied. Besides, the results suggested that thecompetitive inhibition (in which the inhibitor binds withfree enzyme) was not involved.

The reason of the difference in the models adaptabilityresults could be the system used in the previous study.Peppelenbos and Leven (1996) used a flow system to

Table 4 The RMSE and E values for O2 concentration at differentstorage conditions

Condition RMSE (mmol l−1) E (%)

% O2 mmol kg−1

13 280.4 0.31 20.3

15 378.9 0.90 22.4

17 502.6 0.99 17.6

18 454.6 0.56 12.4

21 601.8 0.27 4.5

21 236.8 0.09a 5.1a

a Calculated from the experimental O2 concentrations≥0.8 mmol l−1

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determine the respiration rate whereas a closed system wasused in the present study. However, a more probable reasonis that the inhibition mechanism is dependent on theparticular produce and uncompetitive inhibition is the mostsuitable model to describe the respiratory mechanism ofspinach.

The simulated results using the Michaelis–Mentenmodel with uncompetitive inhibition (model 3) showedreasonably good agreements to the experimental gascompositions. The difference of agreements betweensimulated and experimental data appeared in the series ofresults in Fig. 8 and the values of RMSE and E (Table 4)was probably due to the different harvest seasons of spinachused in the each condition. Conte et al. (2008) reported thatthey could not highlight any significant difference amongthe growing cycles of spinach in terms of respiration rate.However, in the study by Conte et al. (2008), the spinachrespiration rate was determined within an hour after aharvest whereas in the present study, experiment wasstarted a day after the harvest and involved commercialhandling and transport that might have affected thephysiological properties of the spinach. The E value washigher than satisfactory level of 20% (Bhande et al. 2008)in case of 13% and 15% initial O2 concentrations; however,the small RMSE of 0.31 and 0.90 mmol l−1 indicated anacceptable agreement. The average RMSE and E values forthe overall dataset of the six storage conditions were0.61 mmol l−1 and 15.4%, respectively. This suggestedadequacy of the model and parameters to describe therespiration rate and predict the O2 concentration at aerobiccondition of O2 concentration higher than the lower O2

limit of 0.8 mmol l−1.In practice, the change of gas compositions in a package

relies on the respiration of the packaged produce and alsothe transfer of gas through packaging film materials. Sincethe present study was conducted in a closed system thatgenerated more severe conditions (greater O2 depletion)than those in commercial film packages where filmpermeability is concerned, the selected model will still beapplicable for the prediction of gas composition in pack-ages, particularly to ensure aerobic respiration.

Conclusions

For aerobic conditions, prediction of spinach respirationrate was described with a constant RQ by the Michaelis–Menten model without inhibition, the Michaelis–Mentenmodel with uncompetitive inhibition, and the Langmuiradsorption model. Among these models, the Michaelis–Menten with uncompetitive inhibition was found to bemore generic and suitable for practical applications as it canbe applied in extensive range of CO2 concentrations and an

extensive range of initial O2 concentrations. The modelsuccessfully predicted the O2 concentration with the RMSEof 0.61 mmol l−1 and the E of 15.4%. The prediction willbe useful for optimizing spinach packages concerning withdistribution at ambient conditions. In addition, the modelwill furnish the primary information for further studiesconcerning with the respiratory metabolism of spinach andother leafy vegetables.

To realize the suitable atmospheric condition, the initialO2 concentration should be designed in relation to amountof the spinach packaged. Among the studied conditions, theuse of ambient air with moderate amount of spinachpackaged (21% initial O2 with O2 per unit mass of spinach298.7 mmol kg−1) was found to be the most appropriatecondition for spinach at 25 °C as it effectively decreasedthe respiration rate without fermentation development overthe storage period. This condition can serve for the storageof spinach in an economical way, especially in thedeveloping countries where cold-chain and expensive gasmodification facilities are not available.

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