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Postharvest Biology and Technology 41 (2006) 260–265

Modeling the influence of temperature and relative humidity onrespiration rate of prickly pear cactus cladodes

Juan Carlos Guevara a, Elhadi M. Yahia b,∗, Randolph M. Beaudry c, Luis Cedeno d

a Departamento de Alimentos y Biotecnologıa, Mexico, D.F., Mexicob Human Nutrition Program, Faculty of Natural Sciences, Universidad Autonoma de Queretaro, Queretaro, Qro. 76010, Mexico

c Department of Horticulture, Michigan State University, East Lansing, MI 48824-1325, USAd UNICAT, Facultad de Quımica, UNAM, Mexico, D.F., Mexico

Received 3 May 2005; accepted 22 April 2006

bstract

Respiration rate (RO2 ) of prickly pear cactus cladodes (Opuntia spp.) was measured as a function of four temperature (T) and six relativeumidity (RH) combinations for O2 partial pressures between 15 and 0.8 kPa, which were considered to support aerobic respiration. The ratef respiration (RO2 ) was determined based on O2 depletion of the atmosphere in sealed containers containing 1 kg of cladodes. The O2 partialressure declined linearly over time and the slopes of the fitted lines were used to calculate the rate of O2 uptake. The rate of O2 consumptionncreased with increasing temperature and decreased with increasing RH. The respiratory rate at 25 ◦C was approximately 30–40 times higherhan at 5 ◦C. The respiratory rate at 65% RH was between 30 and 90% greater than at 90% RH, depending on the temperature. Data for ln(RO2 )or each RH level were regressed against the inverse of the temperature (K−1) to determine Arrhenius constants and calculate the apparent

−1

a of respiration for the six RH conditions. The Ea was similar for each RH level, varying between a low of 113 to a high of 131 kJ mol .he following equation having an r2 of 0.95 was developed describing respiration as a function of RH and temperature (◦C) using only fouronstants: ln(R) = (−0.1985 + 50.96 × (

1273.15+T

)) × RH + 67.64 − 18430 × (1

273.15+T

).

2006 Published by Elsevier B.V.

rature;

fieMtkcta

ha

eywords: Opuntia ficus-indica; Modified atmosphere; Respiration; Tempe

. Introduction

The main causes of prickly pear cactus cladode spoilagere attributed to microbial contamination and physiologi-al changes; these processes limit postharvest shelf life topproximately 7 d for cladodes with thorns and 2 d forladodes with thorns removed (Guevara et al., 2001, 2003).odified atmosphere packaging (MAP) can inhibit posthar-

est spoilage and has been shown to extend the cactus cladodehelf-life up to 30 d at 5 ◦C (Guevara et al., 2001, 2003).ptimum ranges for O2 and CO2 concentrations can be deter-

ined from physicochemical analysis and/or sensory tests,

nce appropriate limiting quality features are defined. Onceptimum storage conditions are defined, needed package and

∗ Corresponding author. Tel.: +52 442 2281416; fax: +52 442 2281416.E-mail address: yahia@uaq.mx (E.M. Yahia).

tdOvaw

925-5214/$ – see front matter © 2006 Published by Elsevier B.V.oi:10.1016/j.postharvbio.2006.04.012

Relative humidity

lm characteristics or features may be derived (Hayakawat al., 1975; Lee et al., 1991; Zhu et al., 2002). DesigningAP systems, especially those that compensate for tempera-

ure changes during the postharvest holding period, requiresnowledge of product (respiration rate, optimum gases con-entration during storage), package (surface area and filmhickness and permeability), and storage conditions (temper-ture and relative humidity).

It is well recognized that the respiratory demand of fresh,arvested products is a function of temperature, oxygen avail-bility, and in some cases, CO2 concentration. Typically, lowemperatures, low O2 levels, and high CO2 levels cause aecrease in enzymatic activity, thus, reducing the uptake of

2 and the production of CO2. However, although waterapor loss is associated with the dissipation of respiratorynd sensible heat, especially in leafy tissues, the impact ofater vapor in the external atmosphere on respiratory activity

J.C. Guevara et al. / Postharvest Biology a

Nomenclature

Ea activation energy (kJ mol−1)R respiration rate (�L kg−1 s−1)RH relative humidity (%)t time (h)T temperature (◦C or K)

hhe(2Shbe

pi(saasnth

aalr

2

2

mwws

2

(R4d

dswcCu(ctocg0warTorOwwihbc

2

taopafaloab�ltAts

3

3

V free volume (L)W fruit weight (kg)

as been little studied (Yahia et al., 2005). Different equationsave been developed to correlate respiration rate with differ-nt storage parameters such as O2 and CO2 concentrationsSong et al., 1992; Gong and Corey, 1994; Jacxsens et al.,000; Hong and Kim, 2001; Mahajan and Goswami, 2001;alvador et al., 2002), but to our knowledge, the impact of theumidity of the storage environment on respiration has noteen described mathematically (Guevara et al., 2006; Yahiat al., 2005).

A convenient way to measure respiration is to seal thelant product in containers and monitor gas concentrationsn that container. Yang and Chinnan (1988), Cameron et al.1989), and Talasila et al. (1992) used closed systems to mea-ure and model respiratory activity under various temperaturend atmospheric conditions. The closed system provides thedditional benefit of permitting humidity modification usingalt solutions within the sealed respiratory chamber. To date,o study has been performed to describe the aerobic respira-ory activity of prickly pear cactus cladodes as a function ofumidity and temperature.

The objectives of the present work are to measure theerobic respiration rate of prickly pear cactus cladodes asfunction of T and RH within a range of non-limiting O2

evels and to develop a mathematical function describing thatelationship for prickly pear cactus cladodes.

. Materials and methods

.1. Product

Prickly pear cactus (Opuntia spp.) cladodes (approxi-ately 40 d from formation of flower buds on the cladodes)ere obtained from a local market in Queretaro, Mexico, andere immediately brought to the laboratory and selected by

ize, uniformity and freedom from defects.

.2. Measurements of gas partial pressures

Oxygen uptake was monitored using a closed system

Haggar et al., 1992; Lee, 1987; Song et al., 1992) at 65–90%H (at 5% RH intervals) and at 5, 14, 20 and 25 ◦C. Sealed,-L glass jars equipped with sampling ports (one per con-ition), each one with approximately 1 kg of cactus clado-

o6fi

nd Technology 41 (2006) 260–265 261

es and 25 mL of different saturated saline solutions. Thealine solutions were used to produce different RH; chambersere equilibrated for 12 h before each assay in temperature-

ontrolled rooms (Morillon et al., 2000; Multon et al., 1991).hanges in O2 and CO2 levels were monitored periodicallysing a NITEC portable O2/CO2 gas analyzer, model GA-20Nitec Inc., Cincinnati, OH) in a configuration that recir-ulated headspace gasses. The entrance and exit ports ofhe analyzer were connected to the entrance and exit portsf the glass jars, and therefore the air sample was flowingontinuously between the jar and the analyzer. The oxy-en sensor consisted of an electrochemical gas cell with a–100 kPa range and a ±0.5 kPa accuracy. The CO2 sensoras a non-scattering infrared sensor with a 0–100 kPa range

nd a ±0.2 kPa accuracy. Sampling was terminated when O2eached 1.5 kPa or CO2 levels exceeded 20 kPa, respectively.he data for the decline in the headspace oxygen as a functionf holding period were fit to a linear function to determine theate of oxygen uptake for each of the 24 T/RH combinations.nly data considered to be a result of aerobic respirationere used; some initial data points, apparently associatedith the adjustment of the measuring system, were not used

n the analysis. Data for CO2 accumulation in the chambereadspace were not used for calculating respiratory activityecause of concerns regarding the solubility of CO2 in theladodes and, to a lesser extent, in the salt solutions.

.3. Mathematical development

Once O2 uptake rates were determined, the data wereransformed using the natural logarithm to normalize vari-nce and to more evenly weight the data across the rangef temperatures and thereby improve fit at the lower tem-eratures. The natural logarithm of respiration was regressedgainst relative humidity using linear curves for each of theour holding temperatures. Intercept and slope constants forll four curves were regressed against temperature and fittedines were used to create a model for all the data as a functionf T (◦C) and RH (%). Respiratory data were un-transformednd reported as �L kg−1 S−1. The following equation cane used to convert volumetric data to mass data at 20 ◦C:g CO2 kg−1 S−1 = (�L CO2 kg−1 S−1) × 1.84. The natural

ogarithm of the respiratory data was also regressed againsthe inverse of T (K−1) for each of the six RH to determinerrhenius constants including the apparent energy of activa-

ion, Ea. Statistical analysis was done using statistical analysisoftware for PC (Excel, Microsoft Corp.).

. Results and discussion

.1. Effect of O2 on respiration rate

The rate of O2 uptake declined linearly with time for eachf the 24 T/RH combinations of 5, 14, 20, and 25 ◦C and5%, 70%, 75%, 80%, 85%, and 90% RH (Fig. 1). The r2 fortted linear lines ranged from a low of 0.98 to a high of 0.99

262 J.C. Guevara et al. / Postharvest Biology a

Fig. 1. Changes in headspace oxygen partial pressure (kPa) as a function ofd(

(Caathie

Huomopacte

aatottstc6CabmvaCitw

3.2. Description by mathematical model

TVt

R

677889

SIr

A

ifferent temperatures and relative humidity: (�) 65% RH, (�) 70% RH,�) 75% RH, (♦) 80% RH, (�) 85% RH and (©) 90% RH.

Table 1). For all temperatures tested, the changes in O2 (andO2) profiles for 85 and 90% RH were not different from onenother, but differed markedly for depletion profiles for 65%nd 70% RH. Linear changes in O2 partial pressure agree withhe expected pattern of a linear decline for many products

eld in closed containers under aerobic conditions includ-ng tomato (Lycopersicum esculentum Mill.) by Cameront al. (1989), fresh green onions (Allium fistulosum L.) by t

able 1alues for slope (m), intercept (b) and r2 for linear best fit curves fitted to data in

emperature/relative humidity combinations; the slope (O2 uptake) units are in �L k

H (%) Temperature (◦C)

5 14

m b r2 m b r2

5 1.17 12.4 0.99 11.4 12.5 0.990 1.17 13.7 0.99 10.1 12.3 0.995 1.14 14.4 0.99 8.29 12.0 0.980 1.09 15.1 0.99 7.21 12.0 0.995 0.84 14.1 0.99 6.66 11.9 0.995 0.89 15.0 0.99 6.94 12.1 0.99

Constants for best fit lines fitted to above slope da

lope −0.01409 −0.1939ntercept 2.142 23.472 0.79 0.88

lso, linear best fit values (slope, intercept, and r2) for O2 uptake data in columns r

nd Technology 41 (2006) 260–265

ong and Kim (2001), and for different horticultural prod-cts by Jacxsens et al. (2000). Non-linearity in the declinef the atmospheric O2 level can be indicative of develop-entally dependent changes in the aerobic respiratory rate

r the suppression of respiratory activity due to limiting O2artial pressures. Several models have described O2 uptakes a function of O2 including partial pressures in the rangeapable of inhibiting the terminal oxidases in the electronransport pathway (Hayakawa et al., 1975; Mannapperumat al., 1989; Cameron et al., 1994).

Even as the O2 partial pressures in this study did notpparently impact O2 depletion rate, the CO2 levels, whichccumulated to partial pressures between 15 and 18 kPa byhe conclusion of the study, also seemed to have had no impactn the O2 content of the containers. Data for CO2 inhibi-ion of respiration in prickly pear cactus cladodes are not inhe literature and, in fact, there is little to support a univer-al inhibition of CO2 on O2 uptake. Beaudry (1993) foundhat CO2 did not reduce O2 uptake of blueberry (Vacciniumorymbosum L.) fruit even at partial pressures from 20 to0 kPa CO2. Peppelenbos et al. (1993) noted little effect ofO2 on O2 uptake by mushrooms (Agaricus bisporus L.),nd no effect of <20 kPa CO2 on O2 uptake was also notedy Joles et al. (1993) for several fruit. Kubo et al. (1990)easured the impact of CO2 on O2 uptake for 18 fruit and

egetables, several of which had no response or experiencedn increase in O2 consumption. They suggested that highO2 levels decreased or increased the respiration rate via its

mpact on ethylene biology. A more thorough exploration ofhe response of prickly pear respiration in response to CO2ill be needed to conclusively demonstrate the impact.

The slope of the linear equations (Table 1) applied tohe O2 depletion curves yielded respiratory rates for the 24

Fig. 1 for container oxygen as a function of holding time at 24 differentg−1 s−1

20 25

m b r2 m b r2

27.8 14.6 0.98 51.1 13.3 0.9925.8 14.5 0.98 39.0 12.8 0.9916.7 13.2 0.99 33.9 12.7 0.9915.2 13.6 0.99 29.0 12.1 0.9815.3 13.6 0.99 28.2 12.6 0.9914.8 13.5 0.99 26.9 12.7 0.99

ta

−0.5598 −0.904062.66 104.7

0.79 0.85

egressed against relative humidity for each of the four temperatures.

J.C. Guevara et al. / Postharvest Biology and Technology 41 (2006) 260–265 263

Table 2To the left, natural logarithm of oxygen uptake of prickly pear cladodes in Table 1 for 24 different relative humidity/temperature combinations

RH (%) T−1 (K−1) Arrhenius constants

0.00360 0.00348 0.00341 0.00335 Slope Intercept r2 Ea

65 0.159 2.44 3.33 3.93 −15743 56.9 0.98 13170 0.157 2.32 3.25 3.66 −14832 53.7 0.97 12375 0.130 2.12 2.81 3.52 −13940 50.4 0.98 11680 0.0845 1.98 2.72 3.37 −13573 49.0 0.99 11385 −0.177 1.90 2.73 3.34 −14632 52.6 0.98 12290 −0.118 1.94 2.69 3.29 −14163 50.9 0.98 118

A R) data regressed against the inverse temperatures (K) for each of the six humidityl .

Tdimot(tiatwTiidTTwtvarrclRuf(ucm

Ft(

e

l

woo

TL

SIr

A

lso, to the right, linear best fit constants for r2, intercept, and slope for ln(evels, by row. Units for the apparent energy of activation (Ea) are kJ mol−1

/RH combinations. RO2 increased with T, but, at each T,eclined with an increasing RH (Table 1). O2 consumptionncreased 7- to 10-fold between 5 and 14 ◦C, and approxi-

ately 5-fold between 14 and 25 ◦C, which may be a resultf a shift in physiological factors limiting metabolism in cac-us cladodes. Similar results were obtained by Jacxsens et al.2000) for broccoli florets. The extent of change in respira-ion with RH differed somewhat for the four T regimes; thencrease in respiration was approximately 30%, 60%, 90%,nd 90% for 5, 14, 20 and 25 ◦C, respectively. Curves fittedo respiratory data revealed that the increase in respirationith declining RH was roughly linear for each T (Table 1).he slopes for these fitted lines declined, and the intercepts

ncreased, with increasing T. The relatively regular changen intercept and slope with temperature enabled fitting theseata to linear curves; one describing the change in slope with, and the other describing the change in the intercept with(data not shown). When these equations were combinedith the equation for changing respiration with humidity,

hey yielded a close fit between experimental and predictedalues (r2 = 0.97), however, the predictive curves were notccurate at the lowest temperature (data not shown). For thiseason, the data were transformed using the natural log of theespiratory data and the inverse of temperature (K) as indi-ated in Table 2 to provide greater statistical weighting to theower temperature data. Equations regressing ln(R02) againstH for each temperature resulted in four lines with r2 val-es ranging between 0.78 and 0.90 (Table 3). The constantsor these lines were found to vary with temperature linearly

Table 3, right portion). Weighting the respiratory rates bysing the natural logarithm eliminated the problem of inac-uracy at the lowest temperature, while lowering the fit onlyarginally (r2 = 0.95, Fig. 2) and resulted in the following

pt

t

able 3inear best fit constants (slope, intercept, and r2) for ln(R) data in Table 3 regressed

T−1 (K−1)

0.00360 0.00348 0.00341

lope −0.01391 −0.0222 −0.0275ntercept 1.117 3.837 5.0532 0.78 0.89 0.80

lso, to the right, constants for lines fitted to the slope and intercept constants, by r

ig. 2. The Arrhenius model applied to the Vm for oxygen, obtained fromhe power function: (�) 65% RH, (�) 70% RH, (�) 75% RH, (♦) 80% RH,�) 85% RH and (©) 90% RH.

quation:

n(R) =(

−0.1985 + 50.96 ×(

1

273.15 + T

))× RH

+ 67.64 − 18430 ×(

1

273.15 + T

)

here T is temperature in ◦C. Using this equation, the ratef O2 uptake can be reasonably well predicted across a rangef temperatures and relative humidity. To our knowledge, no

revious study has integrated the effect of RH and tempera-ure in a predictive model.

The Arrhenius equation is typically applied to describehe T dependence of different biological reactions, and,

against relative humidity for each temperature

Change in constants with 1/T

0.00335 Slope Intercept r2

−0.0248 50.96 −18430 0.815.440 0.953 67.64 0.960.90

ow.

264 J.C. Guevara et al. / Postharvest Biology a

Fht×

lnaKstaisRiplr

icpHpaal

4

dsa

l

avebic

R

B

C

C

C

G

G

G

G

H

H

H

J

J

K

L

ig. 3. Actual vs. predicted oxygen uptake for prickly pear cladodeseld at 24 combinations of temperature and relative humidity. Equa-ion for modeled respiration = exp((−0.1985 + 50.96 × (1/(273.15 + T)))

RH + 67.638–18430 × (1/(273.15 + T))).

ike the Q10, has been used to model the T responsive-ess of respiration of fresh horticultural crops (Cameron etl., 1995). The values of ln(R) regressed against T−1 (T inelvin) yielded essentially linear relationships with similar

lopes (Fig. 3). There was no indication that the slope ofhe Arrhenius relationship varied with RH (Table 2). Thepparent activation energy (Ea) of the six relationships var-ed between 113 and 131 kJ mol−1 and is a function of thelope of the Arrhenius relationship (slope = −Ea/R, where= 0.0083144 kJ mol−1 K−1). The average Ea was approx-

mately 120 kJ mol−1, which is relatively high compared toublished values of 95, 55, 60, and 60 kJ mol−1 for broccoli,ettuce, blueberry, and strawberry (Fragaria × ananassa L.),espectively (Cameron et al., 1995).

The relation of ln(RO2 ) and T−1 (T in Kelvin) for exper-mental values may not be fully linear; there may be ahange in the slope at 14 ◦C, but additional temperatureoints would be needed to verify changing slope (Fig. 3).aggar et al. (1992) and Song et al. (1992) observed a similarhenomenon. Cameron et al. (1994) also reported a higherpparent Ea at lower temperature; they also noted that thepparent Ea increased 1.5- to 2-fold as oxygen increased fromevels that limited respiration to non-limiting levels.

. Conclusions

The natural log of the oxygen consumption rate wasescribed by a linear model dependent on RH in which thelope and constant were linear relationships with temperatures follows:( (

1))

n(R) = −0.1985 + 50.96 ×273.15 + T

× RH

+ 67.64 − 18430 ×(

1

273.15 + T

)L

M

nd Technology 41 (2006) 260–265

nd by Arrhenius equations for each humidity level, whicharied linearly with the inverse of temperature (K). Param-ters from the respiration model and kinetic data maye used in designing effective packaging models for per-shable horticultural products such as prickly pear cactusladodes.

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