Mathematical Modeling of Respiration Rate of Mango (Magnifera indica) 

Respiration is a process of oxidative breakdown of organic matter present in the cells such as starch, sugars, acids, fats, proteins into simpler molecules such as carbon dioxide and water along with concurrent production of energy and other molecules which can be used by the cell for synthetic reactions (Wills et al., 1989). Though it is necessary to maintain the metabolic process, it hastens senescence which is undesirable for shelf life extension. The extent of respiration can be measured by determining the amount of substrate loss, oxygen consumed, carbon dioxide liberated, heat produced and energy evolved (Pantastico et al., 1975). Respiration of climacteric fruits plays a major role in determining their shelf-life.
        
Mango has a very special place in diet low in fats, cholesterol and high in calories. Being a tropical climacteric fruit, keeping quality of mango as a whole fruit for long time is not feasible due to its poor shelf life quality. Due to these reasons, surplus production in peak season cannot be taken quickly enough to market and export zones resulting in 25 to 40 per cent of post harvest loss from harvest to consumption stage (FAO, 2003).
        
Hence, knowledge on respiration rate of Mango will pave a way for Modified Atmosphere Storage of the fruits for enhanced shelf life.
        
The principle behind modified atmosphere packaging is reduction in respiration rates of fruits by modifying the gas composition of the storage atmosphere and thus enhancing the shelf life of the fruits. If the availability of oxygen is restricted, the rate of respiration could be slowed down; thereby quality of the commodities is preserved with enhancement of shelf life (Labuza and Breene, 1989). The appropriate atmosphere is made to evolve within the storage chamber by the respiration of the produce and maintaining that atmosphere by selective permeability of the gases (Ratti et al., 1998; Zagory and Kader, 1988).

The study was conducted on three varieties of mango viz., Mulgoa, Banganapallai and Neelum. The freshly harvested mangoes of commercial (90 per cent) maturity were procured from a nearby farm at Anamalai area of Coimbatore district. The fruits of uniform size were selected and washed in tap water to remove latex, soil particles, floral remains etc and shade dried. The Experimental design is given in Table 1.
 

 
Measurement of respiration rate
 
Known quantities of fruits were kept under air tight condition in the plastic container fitted with a silicon septum (for sampling of gases). The samples were kept at three different storage temperatures viz., Room Temperature, 25°C and 14°C for measurement of respiration rates. The samples were treated with fungicide before keeping them inside the container. The mass of each fruit was weighed individually and volume of fruits were determined by employing water displacement method (Mohsenin, 1980). The free volume of the container was determined by deducting the fruit volume from the total container volume. Every day three gas samples (replications) of 5 ml volume were drawn from the chamber through silicon rubber septum using needle and the oxygen concentration was found out using MAP analyzer (Make: PBI Dansensor Model: Checkmate). The MAP analyser is shown in Plate 1.
        
The respiration rate was calculated by the change in oxygen concentration with time when the commodity was stored in a closed chamber (Cameron et al., 1989) using the following formulae.

 
               ..........(Eqn. 2.1)

 
where,   r     -   respiration rate, mg O₂ kg^-1h^-1
              Co₂-   O₂ concentration inside the chamber, mg l^-1

                    -   change in oxygen concentration over time dt
 
               t        -      time, h
              V_f   -   free volume of the chamber, l
              m_s       -      mass of the stored produce, kg
 
        
The average of three values of oxygen concentration was used to determine the respiration rate.  

Modeling the respiration rate
 
The respiration rate of a commodity is assumed as a function of oxygen concentration at a determined temperature and the respiration rate was modeled based on enzyme kinetic reactions as per Michaelis- Menten type of equation (Ratti et al., 1996) as follows

                                                                                                 
                                                                                .......(Eqn. 2.2)

where,
       r            -  respiration rate, mg O₂ kg^-1h^-1
       Co₂       -  concentration of oxygen inside the container,per cent
‘a’ and ‘b’     -   constants
        
The model (Eqn 3.2) was fitted to the experimental data and the respiration rate was plotted as a function of oxygen concentration. The constants ‘a’ and ‘b’ were obtained using non-linear regression in Sigmaplot 8.0 software.

The respiration rates (RR) of the three varieties of mango stored in three different temperatures viz., were determined experimentally as per the procedure described in the Section 2.1 and the values of respiration rates were used in the mathematical model (Eqn. 2.2) and the value of constants ‘a’ and ‘b’ were obtained and presented in Table 2. The actual and predicted respiration rate values for different mango varieties are presented in Table  to Table 5. From the Table, it is obvious that as the time proceeded both the actual and predicted respiration rate values decreased with oxygen concentration as well as with storage temperature. Among the mango varieties chosen for the study, Neelum showed higher respiration rate at ambient and 24°C storage. Mulgoa showed almost same respiration rate during ambient storage as that of Neelum but the values under 14°C was found to be higher among the three varieties. In all the storage temperatures, Banganapalli had minimum respiration rate values.
 

 

 

 

        
The decrease in oxygen concentration with storage temperature is in accordance with the results of Wen et al., (2006), who observed the same trend for two different varieties of mango. This may be due to less metabolic activities at lower temperatures and oxygen concentration which resulted in reduction of respiration rates. Similar observations were recorded by Bhande et al., (2008) for banana and Iqbal et al., (2009) for shredded carrot slices.

The respiration rates of the mango stored in three different temperatures were determined experimentally and also predicted Respiration rates decreased with oxygen concentration as well as with temperature. Among the mango varieties chosen for the study, Neelum showed higher respiration rates at ambient and 24°C storage whereas Mulgoa had higher respiration rates at 14°C. In all the storage temperatures, Banganapalli had minimum respiration rate values. The development of the mathematical model for the prediction of respiration rates were found be useful for further reference.