Respiration kinetic of mango (Mangifera indica L.) as function of storage temperature

Cinética de respiración de mango (Mangifera indica L.) como función de la temperatura de almacenamiento

Respiration of cut mango (Mangifera Indica L.) cv. Tommy Atkins was studied using the closed system method at three temperatures (4, 20 and 35 °C). Two models were used to estimate the gas concentration, which were adjusted through non-lineal regression algorisms using Matlab R2011a software. Three mathematic models, a model based on Michaelis-Menten's enzymatic kinetics, and two models based on regression analysis, in one of which a saturation equation was included as a new proposal in this field, were set to predict the substrate respiration rate. Results made evident the positive effect of temperature on mango respiration rate. The model with the best adjustment to mango respiration rate was Michaelis-Menten's with an adjusted correlation coefficient of 0.9811 and 0.9747 for CO2 and O2 respectively, with a relative mean error lower than 10%.

Se estudió la respiración del mango cortado (Mangifera Indica L.), cv. Tommy Atkins, utilizando el método de sistema cerrado, a tres temperaturas (4, 20 y 35 °C). Se usaron dos modelos para estimar la concentración de gas, los cuales se ajustaron a través de algoritmos de regresión no lineal usando el software Matlab R2011a. Se ajustaron tres modelos matemáticos para predecir la tasa de respiración del sustrato. Un modelo basado en la cinética enzimática de Michaelis-Menten, y dos modelos basados en análisis de regresión, en uno de los cuales se incluyó una ecuación de saturación como una nueva propuesta en este campo. Los resultados evidenciaron el efecto positivo que tiene la temperatura sobre la tasa de respiración del mango. El modelo que mejor ajuste entregó para la velocidad de respiración del mango fue el modelo de Michaelis-Menten con un coeficiente de correlación ajustado de 0.9811 y 0.9747 para CO2 y O2, respectivamente, con un error medio relativo inferior al 10%.

DOI: https://doi.org/10.15446/rfna.v69n2.59143

Camilo Agudelo¹, Caludia Restrepo² and José Edgar Zapata¹

¹ Facultad de Ciencias Farmacéuticas y Alimentarias. Universidad de Antioquia. Calle 67 No. 53-108. Box Air 1226, Medellín, Colombia. <jedgar_4@yahoo.es>
² Instituto de Ciencia y Tecnología Alimentaria (Foundation INTAL). Carrera 50G No. 12 Sur-91, Itagüí, Colombia.

Received: March 7, 2016; Accepted: July 13, 2016

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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ABSTRACT
Respiration of cut mango (Mangifera Indica L.) cv. Tommy Atkins was studied using the closed system method at three temperatures (4, 20 and 35 °C). Two models were used to estimate the gas concentration, which were adjusted through non-lineal regression algorisms using Matlab R2011a software. Three mathematic models, a model based on Michaelis-Menten's enzymatic kinetics, and two models based on regression analysis, in one of which a saturation equation was included as a new proposal in this field, were set to predict the substrate respiration rate. Results made evident the positive effect of temperature on mango respiration rate. The model with the best adjustment to mango respiration rate was Michaelis-Menten's with an adjusted correlation coefficient of 0.9811 and 0.9747 for CO₂ and O₂ respectively, with a relative mean error lower than 10%.

Key words: Shelf life, Ripeness, Respiratory process

RESUMEN
Se estudió la respiración del mango cortado (Mangifera Indica L.), cv. Tommy Atkins, utilizando el método de sistema cerrado, a tres temperaturas (4, 20 y 35 °C). Se usaron dos modelos para estimar la concentración de gas, los cuales se ajustaron a través de algoritmos de regresión no lineal usando el software Matlab R2011a. Se ajustaron tres modelos matemáticos para predecir la tasa de respiración del sustrato. Un modelo basado en la cinética enzimática de Michaelis-Menten, y dos modelos basados en análisis de regresión, en uno de los cuales se incluyó una ecuación de saturación como una nueva propuesta en este campo. Los resultados evidenciaron el efecto positivo que tiene la temperatura sobre la tasa de respiración del mango. El modelo que mejor ajuste entregó para la velocidad de respiración del mango fue el modelo de Michaelis-Menten con un coeficiente de correlación ajustado de 0.9811 y 0.9747 para CO₂ y O₂, respectivamente, con un error medio relativo inferior al 10%.

Palabras claves: Vida útil, Madurez, Proceso respiratorio

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Mango (M. indica L.) is one of the most popular subtropical fruits (Souza et al., 2015), because of its high economical value (Sellamuthu et al., 2013), attractive color, delicious taste, rich aroma, exotic flavor, and high nutritional value. Furthermore mango is a rich source of carotenoids and provides high contents of ascorbic acid and phenolic compounds (Shahnawaz et al., 2012; Liu et al., 2013).

In general, fruits and vegetables stay metabolically active after harvest, period during which anabolic processes such as photosynthesis, flavor synthesis, fermentation and other cell wall degraders happen (Heydari et al., 2010). Respiration is of particular interest in postharvest technologies because it is associated to fruit and vegetable quality (Nicolaï et al., 2005). Respiration rate is an indicator of the metabolic level, as high rate respiration is associated with short shelf life (Lurie and Crisosto, 2005), and its control may be an effective mean to regulate the metabolism in general, this is why it is important to extend these products shelf life (Kan et al., 2010). This process changes according to species, variety, storage temperature and vegetable physiological state (Nicolaï et al., 2009). All chemical reactions during ripeness are delayed by low temperatures, these are some of the factors affecting quality and deterioration of fruits and vegetables during storage (Nicolaï et al., 2009) besides the effect on fungi, bacteria and insect growing (Nicolaï et al., 2005).

On the other hand, respiration rate may be reduced by changing the atmosphere around the food, which may also delay associated deterioration reactions, extending fruit and vegetable product shelf life (Luo et al., 2011; Selcuk and Erkan, 2015). For instance, a drop on O₂ concentration results in a reduction of the metabolism of broccoli, carrot, pear, tomato (Nicolaï et al., 2005) and papaya (Zapata et al., 2004) among others. CO₂ may act as respiration suppressor in vegetables such as apples, broccoli (Nicolaï et al., 2005), mango (Ravindra and Goswami, 2008) and banana (Bhande et al., 2008), while it does not present any inhibitory effect in onions, lettuce and spinach (Nicolaï et al., 2005). Oxygen negative effects occur because reactive oxygen accumulation damages the integrity of mitochondrial membrane, resulting at the end in an irreversible mitochondrial dysfunction, which is believed to be the main cause of ageing in different kinds of organisms among which postharvest fruits are (Qin et al., 2009).

Respiratory process modeling is an important step in designing and selecting packaging and storing systems of fruit and vegetable products as it is the case of modified atmosphere packaging (Ravindra and Goswami, 2008). Then again, works oriented to assess this kind of parameters in fruit and vegetables, and in particular cut products, are rare. Accepting respiratory process modeling with all implicated factors in enzyme reaction would be highly complex and little practical, the usual strategy has been to develop empiric models for each product with controlled variable functions such as temperature or gas concentration (Guevara et al., 2006; Rai and Paul, 2007; Bhande et al., 2008).

The shelf life of minimally processed (cut) products is, then again, particularly important because it is one of the major growing sectors in food retail market (Robles-Sánchez et al., 2013), although the freshly cut mango still has a very limited offer in the world market (Souza et al., 2015). Nevertheless, the popularity of tropical fruits in the most important world markets, is an excellent opportunity for the introduction of fresh-cut mango (Siddiq et al., 2013). Yet, fresh-cut processing induces chemical and biochemical changes as well as increases product respiration rate leading to a reduction of shelf life (Azarakhsh et al., 2014). Therefore, the current work goal is to assess different models to predict respiration rate and gas concentrations of cut mango cv. Tommy Atkins variety at three different temperatures in a closed system.

MATERIALS AND METHODS

Raw material preparation
Mango (Mangifera indica L.) fruits cv. Tommy Atkins in physiological ripe state determined by Colombian technical norm NTC 5210 (ICONTEC, 2003) were used. These were bought in Central Minorista in the city of Medellín, to which they were brought from the southwest of the department of Antioquia. They were washed with alkaline detergent and disinfected with a solution at 100 ppm of sodium hypochlorite (Ngarmsak et al., 2005). They were cut in 0.5 cm edge cubes, leaving seed and epidermis aside, samples were taken to determine pH (ICONTEC, 1991), soluble solids (ICONTEC, 1999), and acidity contents expressed as citric acid percentage (ICONTEC, 1991).

Respiration experimental calculation
Respiration rate was determined to the mango in a closed system (Ravindra and Goswami, 2008), which consisted in subjecting 150 g of the product deposited in a 4,000 mL capacity airtight recipient to atmospheric conditions of 20.94 % O₂, 78.08 % N₂, and 0.03 % CO₂.

Three temperatures were set out in 4, 20 and 35 °C using an oven with temperature control (Binder, Germany). O₂ consumption and CO₂ production were measured by a PBI Dansensor Check Point O₂/CO₂ analyzer (Dansensor, Denmark). Each assay was performed twice.

Expressions (1) and (2) were used to calculate respiration rate, these had already been used in products such as pepper (Artés-Hernández et al., 2010), mango (Ravindra and Goswami, 2008), and banana (Bhande et al., 2008).

Where R_O2 and R_CO2 are the respiration rates (mL kg-1 h-1), [O₂] and [CO₂] are oxygen and carbon dioxide concentrations, t is time (h), Δt is the time between the two measures of the respective gas, V is the free volume in the respiration chamber (mL), and W is the cut fruit mass (kg).

Models for the gas behavior
The following models were used to estimate the gas concentration by a regression made with Matlab R2011a software, finding the model coefficients for all treatments.

Model 1. A model is proposed to estimate the experimental data of the O₂ and CO₂ concentrations by a growing reason expression or saturation equation (Chapra and Canale, 2007), as indicated in equations (3) and (4), adjusting them to CO₂ kinetic production and O₂ consumption, respectively.

Where a and b are model parameters, and t is time (h).

Model 2. The model used by Bhande et al. (2008) in banana, and Ravindra and Goswami (2008) in mango cv. Amrapali, was also assessed. Equations (5) and (6) are used in this one adjusting O₂ and CO₂ concentrations in time function.

Where a' and b' are model parameters and t is time (h).

Respiration models
Respiration rate for CO₂ (RCO2) and O₂ (RO2) was calculated by three different methodologies:

Equations (3), (4), (5) and (6) were derived, as derivatives of model 1and model 2, respectively.

Respiration rate was calculated with model 1 and model 2 derivatives, replacing them in equations (7) and (8), as follows:

To obtain the cut mango respiration rate in the described conditions, a model based on Michaelis-Menten's kinetic equation was used, using enzymatic kinetic noncompetitive inhibition principles, where CO₂ is supposed to react to an enzyme-substrate complex (Artés-Hernández et al., 2010; Ravindra and Goswami, 2008; Bhande et al., 2008). Equation (9) expresses this mechanism for the respiration process in terms of O₂ consumption and CO₂ production rate. This kind of model presented a significant adjustment in the calculation of mango (Ravindra and Goswami, 2008), banana (Bhande et al., 2008), pepper (Artés-Hernández et al., 2010) and other fruit (Fonseca et al., 2002) respiratory activity.

Arrhenius's equation
Temperature effect on O₂ consumption and CO₂ production rate was assessed by Arrhenius's equation (Iqbal et al., 2009; Waghmare et al., 2013).

Where RGas is O₂ consumption and CO₂ production rate (mL kg-1h-1), Rp is respiration pre-exponential factor,Ea is the activation energy (J mol-1), R is the gas universal constant (8,314 J mol-1 K-1), and Tabs is the absolute temperature in K.

Relative standard deviation
Respiration rates predicted from the different models were contrasted with the experimental respiration rate, equations (1) and (2) by relative standard deviation, equation (12).

Where E is the relative standard deviation module (%), N is the respiration data point number, Rexp is the experimental respiration rate (mL kg-1 h-1), and Rpred is the predicted respiration rate (mL kg-1 h-1). A good adjustment is defined with E<10 % (Ravindra and Goswami, 2008).

RESULTS AND DISCUSION

The physicochemical parameters to fresh mango were pH 3.4, °Bx 9.5 and acidity 1.05% as citric acid. Experimental data of the O₂ consumption and CO₂ production at different temperatures are shown in figure 1. The nonlinear drop on O₂ concentration in the conditions of the current work matches the pattern expected from other climacteric products kept in sealed containers (Ravindra and Goswami, 2008; Hagger et al., 1992; Jacxsens et al., 1999; Guevara et al., 2006) and agrees with the hypothesis of saturation equation (model 1), as this type of equations start assuming that the system is saturated with CO₂ and O₂ consumed until exhaustion (Chapra and Canale, 2007). It is observed that a rise in temperature also raises the gradient of the graph for the gas behavior, consequently the respiration rate increases as it happens with the papaya (Zapata et al., 2004), banana (Bhande et al., 2008), and mango cv. Amrapali (Ravindra and Goswami, 2008). This is due to that the rate of the enzymatic reactions grows exponentially with the rise of the temperature (Lee et al., 1996). Low temperatures reduce respiration rate, O₂ consumption, CO₂ and ethylene production. As the tissues react to the latter (Mendoza et al., 2016), in order for maturity to occur, the needs of ethylene and the time of exposure are higher at low temperatures (Kader, 1994).

Models 1 and 2 parameters
Table 1 shows the values of the coefficients a and b for equations (3), (4), (5) and (6) with their respective correlation coefficients (R2), obtained for the three temperatures assessed in the closed system. Model 1 presented an excellent adjustment to the data in the three assessed temperatures, while model 2 had a very poor adjustment to the data at 4 °C. Model 2 coefficients presented a high variability with temperature compared with model 1; it can be seen that parameter b is more influenced with temperature than coefficient a in both.

Respiration kinetics
Table 2 presents Michaelis-Menten's model parameters, with their corresponding adjusted correlation coefficient (R2). A good adjustment of the experimental data with such model for R_CO2 and R_O2 is observed.

Table 2 data analysis based on the form of equation (9), allows to observe the effect gases have on the rate of CO₂ production and O₂ consumption. These effects are more noticeable at low CO₂ and high O₂ concentrations, at 20 and 35 °C. Km and Ki values indicate CO₂ production rate is more sensible to the concentration of both gases than O₂ consumption rate, due to both constants are lower for the CO₂ production than O₂ consumption expressions. On the other hand, low Km values indicate the significant effect of O₂ concentration on respiration rates in terms of CO₂ as well as O₂. While relatively high Ki values indicate that CO₂ concentration does not have such as significant effect on respiration rates. Nevertheless, the effect this gas has on respiration rate, given the adjust the model shows, cannot be denied. Besides, it is known that very high CO₂ and very low O₂ concentrations may cause respiration to change from aerobic to anaerobic, causing the creation of fermentation products such as acetaldehyde and ethanol (Angós et al., 2008).

Figure 2 shows that CO₂ experimental consumption rate (R_CO2) has a starting value at 4 °C of 5.09 mL kg-1 h-1, compared to the same gas experimental rate at 20 °C of 59.21 mL kg-1 h-1, and at 35 °C it is of 110.76 mL kg-1 h-1. This difference is due to reduction of temperature becomes into a reduction of the rate at which parameter such as respiration, texture and microbial growth change; this is why the organoleptic and physiological characteristics of mango stored at 4 °C did not present significant change in odor, texture and flavor.

Reduction of temperature not only reduces ethylene production, but also the response rate of tissues to such gas; therefore, the more the temperature drops, the higher exposure time required by the metabolic cycle to start at a certain ethylene concentration is (Mendoza et al., 2016). Associated to this the temperature affect R_O2, as can be seen in figure 3.

Table 3 shows the R_CO2 and R_O2 average value predicted for the three temperatures with Michaelis-Menten's equation, models 1 and 2, being noncompetitive inhibition Michaelis-Menten's equation the best model. Figures 2 and 3 show graphic behavior of experimental respiration and the one predicted by the models in terms of R_CO2 and R_O2.

The model proposed (Model 1) is the second that best adjusts to O₂ consumption and CO₂ production, and also to the prediction of R_CO2 and R_O2, being relevant at 4 °C (Figure 2 (A) for CO₂ and Figure 3 (A) for O₂); while at 20 °C and 35 °C the proposed model and the one in the literature present the same values predicted of R_CO2 and R_O2. A cell change due to the incapacity of the enzymes associated to mitochondrial membranes to metabolize glycolysis products may happen at these low temperatures (Kader, 1994) therefore, model 2 may not give a good adjustment.

Relative standard deviation values of each one of the models are shown in table 4. Michaelis-Menten's kinetic model obtained an excellent adjustment for the experimental value with E<10% in the different temperatures, while the model reported in literature had the least fitting, except for R_CO2 and R_O2 in refrigeration temperature; this is due to this model adjustment expressed in the R2 in table 1 is not adequate for this condition. Model 2, reported by Bhande et al. (2008) and Ravindra and Goswami (2008), could be useful in temperatures higher to 4 °C, but does not present good adjustment.

Table 5 shows Arrhenius type equation parameters, activation energy and pre-exponential factor for O₂ consumption and CO₂ production rates of the experimental data, proposed model 1 and Michaelis-Menten's equation. Activation energy values of each gas are very alike between experimental data and Michaelis-Menten's, evidencing a good adjustment of this equation to the sensitivity of the reaction to temperature; besides, activation energy values are between normal values, from 29 to 93 kJ mol-1 for fruit (Benítez et al., 2012). Certain effects could be observed in some cut mango pieces due to cold sensitive reactions generating a brown color, beginning around the vascular bundles, because of the polyphenol-oxidase action on the phenolics released out of the vacuole after freezing (Lee et al., 1996; Blanco-Díaz et al., 2016).

The descending form of the gradient in figures 2 and 3 indicates an inverse relationship between respiration rate and shelf life, which is due to O₂ reduces and CO₂ increases in an airtight container, consequently with what is observed in figure 1. It is also known that respiration rate decreases with CO₂ rising and O₂ dropping due to the first is a product of the reaction and the second is a reactive in it, as can be seen in the general reaction for respiration (Devanesan et al., 2011):

Consequently and accordingly to Le Chatelier's principle, when increasing the concentration of a product or reducing the concentration of a reactive, the chemical reaction rate reduces.

CONCLUSIONS

Noncompetitive inhibition Michaelis-Menten's kinetic equation presented better results in the prediction of the respiration rate in contrast with others two models.

Models 1 and 2 are useful to predict gas concentration but do not predict the respiration rates.

Temperature was an influencing factor in O2 consumption and CO2 production of the cut mango determining a better preservation at 4 °C.

AKNOWLEDGMENTS

The authors of the current work thank the Comité para el Desarrollo de la Investigación (CODI) in the Universidad de Antioquia, for the financial support through the Estrategia de Sostenibilidad 2014-2015. Also to the Fundación INTAL for lending its facilities.

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