Modeling respiration rates of Ipomoea batatas (sweet potato) under hermetic storage system

Abstract

The sweet potato respiration rate versus gas composition was mathematically modeled, as required to design an effective modified atmosphere packaging (MAP) system. Storage tests of sweet potato were conducted at 15–30 °C. The O₂ and CO₂ concentrations were measured over time in a closed system. The respiration rate was estimated to be a derivative of the quadratic function of gas concentration over time and decreased with decreasing O₂ and increasing CO₂. The model of the uncompetitive inhibition enzyme reaction rate fitted well with the experimental results. The temperature dependency of the equation parameters (V_m, K_m, and K_i) followed the Arrhenius relationships. The use of the proposed models to simulate the respiration rates as a function of temperature revealed less temperature dependence in low O₂ and high CO₂ concentrations. This gas composition, more desirable in practice, also agreed with the typical gas composition of MAP.

Introduction

Sweet potato is the world’s seventh most important tropical tuber crop. Sweet potatoes are widely cultivated because they are highly adaptable to the environment, have a high yield, and require a low amount of fertilizer (Horton et al., 1989; Ray and Ravi, 2005). However, many losses occur if the proper environment is not maintained during the post-harvest process (Mtunda et al., 2001; Ray and Ravi, 2005; Rees et al., 2001). Although many studies exist on the storage and curing of sweet potatoes, to reduce the crop losses (Padda and Picha, 2007; Picha, 1987; Ray et al., 1994; Sowley and Oduro, 2002), studies on packaging to extend the market life of sweet potatoes have been limited.

Currently, most sweet potatoes are packaged in a corrugated box (Chakraborty et al., 2017), where they experience rapid respiration and transpiration, leading to an inadequate storage environment, especially at very high humidity inside the box. This environment causes quality deterioration, such as spoilage, mold production, and spotting phenomenon (Ray and Ravi, 2005). Therefore, it is necessary to develop packaging to extend the market life of sweet potatoes. Modified atmosphere packaging (MAP) is one approach to reduce the loss of fresh produce. The MAP method maintains the quality of fresh produce for a long time, by controlling the respiration rate. Mainly temperature, and oxygen (O₂) and carbon dioxide (CO₂) concentrations affect the respiration of fresh produce. The design of MAP system for fresh produce relies on mathematical models that describe the relationship between respiration rate as a function of both gas composition and temperature.

Aerobic respiration is an oxidative breakdown process in which organic matter is decomposed into simple substances, such as CO₂ and water, to release energy (Fonseca et al., 2002). After harvesting, various substrates in fresh produce may be used by aerobic respiration, resulting in loss of taste, quality, and food value (Fonseca et al., 2002). In general, fresh produce have a reduced respiration rate in gas compositions of low O₂, and high CO₂ concentrations at low temperature. The reason is that the enzyme activity is reduced, and the oxidation reaction of the organic substrate is inhibited. As a result, fresh produce stored under low temperature, and low O₂ and high CO₂ conditions have a longer post-harvest life than when stored at room temperature (Lee et al., 1991). Potato (Gunes and Lee, 2006), carrot (Lee et al., 1994), onion (Kwon and Lee, 1995), bellflower (Kwon and Lee, 1994), garlic (Lee and Lee, 1996) and other fresh produce (Beaudry, 2000) have low respiration rates in low O₂ and high CO₂ gas composition at low temperature.

Several methods have been developed to model the respiration rate of fresh produce as a function of the gas composition (O₂, CO₂). The typical techniques for measuring the respiration rate of fresh produce are the open system and closed system (Yam and Lee, 1995). The open system approach involves placing the fresh produce in a barrier container, such as a glass bottle, and measuring the gas concentration while flowing gas of known composition through the inlet at a predetermined flow rate. The respiration rate is determined, by considering the difference in gas concentration at the inlet and the outlet, the flow rate, and the weight (Yam and Lee, 1995). The closed system is the most common procedure for measuring respiration rate, and it involves placing the fresh produce in a closed container and measuring the change in gas concentration over time. The respiration rate can be obtained by considering the rate of change of gas concentration per unit time, the free volume, and weight (Lee, 2007). Several regression equations are used to derive the rate of gas concentration change. The simplest equation expresses the respiration rate of the tomato, as the slope between two points of the measured gas concentration (Henig and Gilbert, 1975). Other best-fitted equations include polynomial functions that require many adjustable coefficients (Gong and Corey, 1994; Yang and Chinnan, 1988) and exponential functions (Beaudry et al., 1992; Emond et al., 1993).

The respiration models based on the principle of enzyme kinetics have already been proposed. Most notable for modeling respiration rates is the Michaelis–Menten type equation (Lee et al., 1991), which provides a brief description of respiration on the assumption that the diffusion and dissolution of O₂ and CO₂ in plant tissues regulates the catalytic reaction caused by the allosteric enzymes (Bhande et al., 2008; McLaughlin and O’Berine, 1999). The effect of CO₂ on respiration can be expressed in three ways: uncompetitive inhibition, which is the most used model in fresh produce, competitive inhibition, and non-competitive inhibition (Fonseca et al., 2002; Lee et al., 1991). Assuming that it serves as a respiration inhibitor, CO₂ can be seen as an uncompetitive inhibitor that binds only to the enzyme–substrate complex, without binding to the enzyme (Lee et al., 1991; Mahajan and Goswami, 2001; McLaughlin and O’Berine, 1999). However, if the respiration mechanism changes from aerobic to anaerobic, this model is not valid (Mahajan and Goswami, 2001). It is also difficult to predict the effect of temperature on uncompetitive inhibition models. Therefore, the temperature is used as an independent variable, by using the Arrhenius equation to predict the respiration rate under various storage conditions (Exama et al., 1993; Mahajan and Goswami, 2001).

Hence, the current study modeled the respiration rate using the uncompetitive inhibitory enzyme kinetic equation at the storage and distribution temperature range of sweet potato. Also, the temperature dependence of respiration was confirmed, based on the Arrhenius equation.

Materials and methods

Raw materials

Sweet potato used in this study was Hogammi, a Korean variety, which was harvested in Korea in October 2017. Sweet potato was cured at 34 °C and 80% relative humidity (RH) for 3 days, and then stored at 13 °C and 80% RH for 2 months before use. Sweet potatoes without scratches and weighing 140–180 g, were selected, washed and then used in the experiment. The proximate composition (%, g/100 g) of the sweet potato, which was measured according to the AOAC method (AOAC, 1975), were as follows: moisture content 59.5 ± 0.43 (mean ± standard deviation, n = 3), carbohydrate 37.95 ± 0.25, total sugar 9.95 ± 0.13, crude fiber 3.5 ± 0.05, crude protein 1.32 ± 0.09, ash 1.08 ± 0.09, crude fat 0.15 ± 0.05.

Storage test

A closed system was employed, using an airtight acrylic box of 210 × 210 × 160 mm, installed in a low-temperature incubator (HB-103SP, Hanbaek Sci. Tech. Co., Bucheon, Korea). Sweet potatoes of 0.6 kg were stored at 15, 20, 25, and 30 °C. The storage test was not performed at < 15 °C where the respiration rate of sweet potato increases, due to chilling injury (James, 1973; Picha, 1987; Ray and Ravi, 2005).

In-line sampling and analysis of gases

A system of gas in-line sampling was constructed to inject gas samples from the acrylic box into a gas chromatograph. The gas injection system consisted of a digital flow controller (KRO-4001S, Line Tech. Co., Seoul, Korea), a mass flow controller (M3030 V, Line Tech. Co.), and a diaphragm vacuum pump (PM17659-86, KNF Co., Seoul, Korea). In addition, a sampling connector was installed, to allow gas samples to escape from the acrylic box to the sampling pump. The sampling connector was equipped with a filter, to ensure airtightness and remove foreign matter. Gas samples in the acrylic box were injected into the gas chromatograph at 5 mL min⁻¹, for 40 s per interval.

The gas chromatograph (Agilent, USA) was equipped with a thermal conductivity detector. A combination of a molecular sieve 5A column and a capillary Porabond Q column (CP7429, Agilent) were used for the chromatographic separation. The oven temperature and the detector temperature were 35 and 100 °C, respectively. The carrier gas was helium, and the flow rate was 50 mL min⁻¹. The analysis was repeated three times, and the average gas composition was calculated. The measurement was not done below 3% O₂, because the enzyme reaction rate model used in this study is only valid for aerobic respiration (Lee, 2007).

Respiration rate

The equations used to model the respiration rate are shown in Table 1. Equations 1 and 2 describe the respiration rates through the uncompetitive inhibition mechanism of the enzyme reaction rate equation. Both equations were linearized, as demonstrated in Eqs. 3 and 4.

Table 1.

Equations used in mathematical modeling of sweet potato respiration rate

Model	Equation	Equation number
Uncompetitive inhibition enzyme kinetics and linearizing uncompetitive inhibition enzyme kinetics (Lee et al., 1991)	${\text{R}}_{{\text{O}}_2}=\frac{{\text{V}}_{\text{m}\left({\text{O}}_2\right)}\left[{\text{O}}_2\right]}{{\text{K}}_{\text{m}\left({\text{O}}_2\right)}+\left(1+\left[{\text{CO}}_2\right]/{\text{K}}_{\text{i}\left({\text{O}}_2\right)}\right)\left[{\text{O}}_2\right]}$	1
	${\text{R}}_{{\text{CO}}_2}=\frac{{\text{V}}_{\text{m}\left({\text{CO}}_2\right)}\left[{\text{O}}_2\right]}{{\text{K}}_{\text{m}\left({\text{CO}}_2\right)}+\left(1+\left[{\text{CO}}_2\right]/{\text{K}}_{\text{i}\left({\text{CO}}_2\right)}\right)\left[{\text{O}}_2\right]}$	2
	$\frac{1}{{\text{R}}_{{\text{O}}_2}}=\frac{1}{{\text{V}}_{\text{m}\left({\text{O}}_2\right)}}+\frac{{\text{K}}_{\text{m}\left({\text{O}}_2\right)}}{{\text{V}}_{\text{m}\left({\text{O}}_2\right)}}\frac{1}{\left[{\text{O}}_2\right]}+\frac{1}{{\text{K}}_{\text{i}\left({\text{O}}_2\right)}{\text{V}}_{\text{m}\left({\text{O}}_2\right)}}\left[{\text{CO}}_2\right]$	3
	$\frac{1}{{\text{R}}_{{\text{CO}}_2}}=\frac{1}{{\text{V}}_{\text{m}\left({\text{CO}}_2\right)}}+\frac{{\text{K}}_{\text{m}\left({\text{CO}}_2\right)}}{{\text{V}}_{\text{m}\left({\text{CO}}_2\right)}}\frac{1}{\left[{\text{O}}_2\right]}+\frac{1}{{\text{K}}_{\text{i}\left({\text{CO}}_2\right)}{\text{V}}_{\text{m}\left({\text{CO}}_2\right)}}\left[{\text{CO}}_2\right]$	4
Arrhenius equation linearizing Arrhenius equation (Mahajan and Goswami, 2001)	${\text{R}}_{\text{m}}=\text{A}·exp\left[\frac{-{\text{E}}_{\text{a}}}{\text{R}\times \text{T}}\right]$	5
	$ln{\text{R}}_{\text{m}}=\frac{-{\text{E}}_{\text{a}}}{\text{R}}\frac{1}{\text{T}}+ln\text{A}$	6
The gradients of respiration rates based on linear functions (Mahajan and Goswami, 2001)	${\text{R}}_{{\text{O}}_2}=\left[\frac{\left[{\text{O}}_2{]}_{\text{t}}-\right[{\text{O}}_2{]}_{\text{t}+1}}{\mathrm{\Delta }\text{t}}\right]\times \frac{\text{V}}{\text{W}\times 100}$	7
	${\text{R}}_{{\text{CO}}_2}=\left[\frac{\left[{\text{CO}}_2{]}_{\text{t}+1}-\right[{\text{CO}}_2{]}_{\text{t}}}{\mathrm{\Delta }\text{t}}\right]\times \frac{\text{V}}{\text{W}\times 100}$	8
Quadratic functions and the derivatives of respiration rates (Gong and Corey, 1994)	$\left[{\text{O}}_2\right]={\text{a}}_1{\text{t}}^2+{\text{a}}_2\text{t}+{\text{a}}_3$	9
	$\left[{\text{CO}}_2\right]={\text{b}}_1{\text{t}}^2+{\text{b}}_2\text{t}+{\text{b}}_3$	10
	${\text{R}}_{{\text{O}}_2}=\frac{\text{d}\left[{\text{O}}_2\right]}{\text{dt}}\times \frac{\text{V}}{\text{W}\times 100}=\frac{\left(2{\text{a}}_1\text{t}+{\text{a}}_2\right)\times \text{V}}{\left(\text{W}\times 100\right)}$	11
	${\text{R}}_{{\text{CO}}_2}=\frac{\text{d}\left[{\text{CO}}_2\right]}{\text{dt}}\times \frac{\text{V}}{\text{W}\times 100}=\frac{\left(2{\text{b}}_1\text{t}+{\text{b}}_2\right)\times \text{V}}{\left(\text{W}\times 100\right)}$	12
Mean relative deviation modulus (Lomauro et al., 1985)	$\text{MRD}\left(\text{\%}\right)=\left[\sum _{\text{n}=1}^{\text{n}}\frac{{\text{R}}_{exp}-{\text{R}}_{\text{pre}}}{{\text{R}}_{exp}}\right]\times \frac{100}{\text{N}}$	13

Temperature dependency

The relationships between the respiration model parameters and the storage temperature were expressed, using the Arrhenius equation (Eq. 5), which was linearized, as shown in Eq. 6.

Mathematical modeling of respiration rates

The respiration rates were modeled as a function of the gas composition, using the linearized equations of the uncompetitive inhibition enzyme reaction rate (Eqs. 3 and 4). The modeling procedures were as follows: (1) the regression equations (Eqs. 9 and 10) were determined from the experimental data of gas composition over time; (2) the dependent variable (i.e., the respiration rates) was estimated to be the derivatives of the regression equations (Eqs. 9 and 10); (3) finally, Eqs. 3 and 4 were determined by multiple linear regression analysis.

The model parameters were modeled as a function of temperature, using the linearized Arrhenius equation (Eq. 6). The parameters (V_m, K_m, and K_i) of the uncompetitive enzyme reaction rate model obtained at different temperatures were estimated by linear and non-linear regression analyses (Eqs. 3, 4 and Eqs. 1, 2, respectively). Primarily estimated parameter values from the linear regression were used as the initial values in the non-linear regression. The linearized models (Eqs. 3 and 4) are invalid to obtain the regression coefficients of V_m, K_m, and K_i with standard errors.

Statistical analysis

Linear and non-linear regression analyses were performed using SAS (SAS, Inc., IL, USA). Non-linear least square (Gauss–Newton algorithm) method was used in the non-linear regression (Lai et al., 2017).

Results and discussion

Respiration rates of O₂ and CO₂

Figure 1 shows the changes in O₂ and CO₂ concentrations during respiration over time, for each storage temperature. The respiration rate was calculated as the rate of gas concentration change for O₂ consumption and CO₂ evolution, respectively. The rates were calculated as the change in gas concentration divided by the time interval between two data points (Eqs. 7 and 8). In addition, a mathematical function was applied to all the data points, using regression analysis. In this study, the 2nd polynomial function (Eqs. 9 and 10) was used to obtain the differential values (Ahn and Lee, 2004; Gong and Corey, 1994).

Fig. 1.

Changes in oxygen and carbon dioxide concentration during respiration of sweet potatoes stored in a closed chamber at different temperatures (filled square: 15 °C, filled diamond: 20 °C, filled circle: 25 °C, filled triangle: 30 °C). dashed line: trend lines of 2nd polynomial regression equations with determination coefficients. Error bars represent standard deviations (n = 3)

Although not illustrated, the respiration rates of the linear slopes between two data points and the 2nd polynomial derivatives decreased over time under all isothermal conditions. These two kinds of respiration rates demonstrated fairly high agreement, according to the mean relative deviation modulus (Eq. 13) of less than 10% (Table 2) (Lomauro et al., 1985). The 2nd polynomial function was finally adopted to calculate the respiration rates (Eqs. 11 and 12), thereby producing continuous rather than discrete data.

Table 2.

Agreement between two different respiration rates: slopes between two data points and derivatives of 2nd polynomials according to mean relative deviation modulus (MRD, Eq. 13)

Temp. (°C)	MRD (%) for respiration rate (${\text{R}}_{{\text{O}}_2}$)	MRD (%) for respiration rate (${\text{R}}_{{\text{CO}}_2}$)
30	5.91a	6.12
25	6.11	6.52
20	6.10	5.41
15	5.75	2.87

^aThe higher the MRD, the lower the agreement

The respiration rate decreased with the decrease in O₂ concentration and increase in CO₂ concentration, indicating that sweet potatoes could be controlled by the O₂ and CO₂ concentrations, like any other crops of MAP applications.

Determination of respiration model parameters

The respiration parameters (V_m, K_m, and K_i) were estimated by multiple linear and non-linear regression analyses with Eqs. 3, 4 and Eqs. 1, 2, respectively (Table 3). In this case, only the non-linear regression could provide the standard error of the parameter estimates, a measure of the accuracy of predictions. The primarily estimated parameters from the linear regression was used as the initial values in the non-linear regression analysis. The non-linear regression could provide the standard errors of each parameter, and also resulted in the higher coefficients of determination. This indicates that the non-linear regression was more beneficial than the conventional linear regression employed in this field. But the tendency in the temperature effect on the parameters was the same for both methods. The maximum respiration rate, V_m, increased at higher temperatures. At all temperatures, K_m values were smaller than K_i, where K_m and K_i denote the constants alleviating respiration suppression by O₂ consumption and CO₂ evolution, respectively (Eqs. 3 and 4). Accordingly, the effect of O₂ consumption on respiration suppression was found to be greater for sweet potato than the effect of CO₂ evolution. Meanwhile, a greater CO₂ than O₂ permeability is characteristic of most plastic films used in MAP, so CO₂ discharge becomes faster than O₂ influx. This situation would be favorable to respiration suppression because the O₂ concentration could be modified to be low to a greater extent than CO₂ concentration to be high. Also, according to ${\text{K}}_{\text{m},\left({\text{O}}_2\right)}$ < ${\text{K}}_{\text{m},\left({\text{CO}}_2\right)}$, the, the respiration suppression by O₂ consumption was greater for O₂ consumption than CO₂ evolution (Ahn and Lee, 2004; Kubo et al., 1996).

Table 3.

Model parameters (V_m, K_m, and K_i) of uncompetitive inhibition enzyme reaction equations in the linear and non-linear forms (Eqs. 3, 4 and Eqs. 1, 2, respectively) from regression analysis

	Temp. (°C)	By linear regression				By non-linear regression
		Vm (mL kg−1 h−1)	Km (%O2)	Ki (%CO2)	R2	Vm (mL kg−1 h−1)	Km (%O2)	Ki (%CO2)	R2
O2	15	31.9a	1.88	24.9	0.93	31.7 ± 0.13**b	2.26 ± 0.07**	30.5 ± 0.98**	0.95
	20	51.1	3.37	19.6	0.95	50.2 ± 0.31**	3.94 ± 0.13**	28.2 ± 1.21**	0.96
	25	75.8	4.10	18.9	0.96	74.7 ± 0.56**	4.89 ± 0.16**	27.8 ± 1.47**	0.98
	30	101.6	5.23	16.7	0.98	101.8 ± 0.91**	6.07 ± 0.21**	25.9 ± 1.73**	0.98
CO2	15	31.6	3.91	19.2	0.95	31.5 ± 0.19**	4.77 ± 0.14**	26.7 ± 1.01**	0.96
	20	46.5	4.59	18.8	0.96	46.1 ± 0.31**	5.49 ± 0.16**	24.1 ± 1.24**	0.97
	25	67.8	6.17	18.5	0.97	67.2 ± 0.51**	7.13 ± 0.19**	23.1 ± 1.52**	0.98
	30	99.7	7.55	17.9	0.97	99.2 ± 0.83**	8.79 ± 0.24**	22.4 ± 1.81**	0.96

**Significant at p < 0.01

^aWithout standard errors because V_m, K_m, and K_i are not directly the regression coefficients of Eqs. 3 and 4

^bWith standard errors

As temperature increased, K_m increased, and K_i decreased. From the increase of K_m, it was found that the effect of O₂ increased as the temperature rose, and from the decrease of K_i, the influence of CO₂ as the temperature rose relatively decreased. These findings indicated that care should be taken to design the film in MAP so that O₂ is not depleted by respiration when the temperature rises. Sweet persimmon (Ahn and Lee, 2004), SAPOTA (Dash et al., 2007), etc. was reported to have similar temperature dependency properties. The temperature-dependent functions of predicting the respiration rate model parameters were modeled by the Arrhenius equation, of which parameters are shown in Table 4.

Table 4.

Model parameters (E_a, lnA) of Arrhenius equations of V_m, K_m, and K_i in the linear form (Eq. 6) from regression analysis

	Ea (J mol−1)	lnA	R2
O2
Vm (mL kg−1 h−1)	56.12 ± 3.44a	26.94 ± 1.40	0.99
Km (%O2)	− 47.28 ± 9.39	− 18.02 ± 3.83	0.93
Ki (%CO2)	17.80 ± 9.39	10.23 ± 1.65	0.91
CO2
Vm (mL kg−1 h−1)	55.40 ± 0.58	26.60 ± 0.24	0.99
Km (%O2)	− 32.99 ± 9.39	− 11.75 ± 0.97	0.99
Ki (%CO2)	3.11 ± 0.25	4.19 ± 0.10	0.98

^aWith standard errors

Application of respiration rate prediction model: temperature dependency

In MAP design, the packaging materials and their thickness that can maintain optimal gas composition consistently are determined, according to a mass balance between respiration and gas transfer from the atmosphere. Food packages experience various temperatures in the actual field, necessitating the analysis of the respiration rate with temperature. If the temperature dependence is large, it may be difficult to maintain the optimum gas composition, due to a change in the respiration rate under fixed packaging conditions. By using the predictive model equations, the respiration rates at different gas compositions and temperatures were mathematically simulated (Table 5). The tested gas composition ranged from the atmospheric to relatively low O₂ and high CO₂, including the common optimal MAP for fresh produce. The typical temperature dependence was observed, where the respiration rate decreased with the decrease in temperature. In order to quantify the temperature dependence, the Arrhenius activation energy (E_a) was calculated, by applying the Arrhenius equation. The larger the E_a (Table 5), the greater the temperature dependence. The temperature dependence was desirably the lowest at gas composition (3% O₂ and 15% CO₂), which is close to optimum gas composition because the temperature dependency of gas composition is minimum at the lowest E_a. The lower temperature dependence means that MAP designed at a given temperature would properly work even at different temperatures. It is very common that the temperature is not uniform in food storage and distribution sites.

Table 5.

Model parameter of Arrhenius equations of the calculated sweet potato respiration rates (${\text{R}}_{{\text{O}}_2}$ and ${\text{R}}_{{\text{CO}}_2}$) at different gas compositions and temperatures by Eqs. 1 and 2

Gas composition		Temp. (°C)	${\text{R}}_{{\text{O}}_2}$ (mL kg−1 h−1)	${\text{Ea}}_{{\text{O}}_2}$ (J mol−1)	R2	${\text{R}}_{{\text{CO}}_2}$ (mL kg−1 h−1)	${\text{Ea}}_{{\text{CO}}_2}$ (J mol−1)	R2
O2 (%)	CO2 (%)
20	0.5	15	28.70	49.23 ± 3.11a	0.99	25.89	48.47 ± 0.59	0.99
		20	42.81			37.01
		25	61.53			50.79
		30	78.68			70.91
15	5	15	24.11	46.08 ± 2.90	0.99	20.79	47.60 ± 5.92	0.99
		20	34.54			29.57
		25	49.25			40.33
		30	61.66			55.93
10	8	15	21.18	43.08 ± 2.77	0.99	17.49	45.69 ± 0.73	0.99
		20	29.29			24.66
		25	41.31			33.09
		30	50.76			45.29
5	12	15	17.21	37.75 ± 2.65	0.99	13.13	41.63 ± 1.07	0.98
		20	22.36			18.18
		25	30.85			23.53
		30	36.76			31.35
3	15	15	14.34	33.40 ± 2.69	0.98	10.25	38.31 ± 1.35	0.99
		20	17.70			13.96
		25	23.96			17.54
		30	27.91			22.90

^aWith standard errors

In conclusion, the modeling of respiration rates should precede MAP design. Current studies on MAP of sweet potato are limited. In this work, sweet potato was found to be one of the after-ripening produce applicable to MAP, because the respiration rates of sweet potatoes in an airtight acrylic box showed to decrease as O₂ concentration decreased and CO₂ concentration increased. The respiration rate of sweet potato was modeled using the uncompetitive inhibition enzyme kinetic model. The Arrhenius equation was also used to determine the effect of temperature on the respiration rate model parameters.

Analysis of the developed model parameters revealed the O₂ consumption had a greater impact on respiration suppression than that of CO₂ evolution, at all temperatures. In MAP, the CO₂ permeability of package films is generally higher than the O₂ permeability, which would favor respiration suppression because O₂ concentration could be modified to be low to a greater extent than CO₂ concentration to be high.

From the mathematical simulation created using the proposed models of respiration rate as a function of temperature, the temperature dependence was the lowest for the gas composition with the lowest O₂ and the highest CO₂, which is close to an optimum gas composition for MAP. This finding indicated that the gas composition changes the least with the temperature at the optimum gas composition, which should be desirable.

List of symbols

${\text{R}}_{{\text{O}}_2}$

O₂ consumption respiration rate (mL kg⁻¹ h⁻¹)

${\text{R}}_{{\text{CO}}_2}$

CO₂ evolution respiration rate (mL kg⁻¹ h⁻¹)

${\text{V}}_{\text{m},\left({\text{O}}_2\right)}$

Maximum respiration rate for O₂ consumption (mL kg⁻¹ h⁻¹)

${\text{V}}_{\text{m},\left({\text{CO}}_2\right)}$

Maximum respiration rate for CO₂ evolution (mL kg⁻¹ h⁻¹)

${\text{K}}_{\text{m},\left({\text{O}}_2\right)}$

Michaelis–Menten constant for O₂ consumption (%O₂)

${\text{K}}_{\text{m},\left({\text{CO}}_2\right)}$

Michaelis–Menten constant for CO₂ evolution (%O₂)

${\text{K}}_{\text{i},\left({\text{O}}_2\right)}$

Inhibition constant for O₂ consumption (%CO₂)

${\text{K}}_{\text{i},\left({\text{CO}}_2\right)}$

Inhibition constant for CO₂ evolution (%CO₂)

$\left[{\text{O}}_2\right]$

O₂ concentration (%O₂)

$\left[{\text{CO}}_2\right]$

CO₂ concentration (%CO₂)

${\text{R}}_{\text{m}}$

Model parameter of Michaelis–Menten equation

E_a

Arrhenius activation energy

R

Universal gas constant (8.314 kJ mol⁻¹)

T

Absolute temperature (K)

V

Free volume of respiration chamber (mL)

W

Weight of sweet potatoes (g)

a

Regression coefficient

b

Regression coefficient

MRD

Mean relative deviation modulus (%)

R_exp

Experimental respiration rate (mL kg⁻¹ h⁻¹)

R_pre

Predicted respiration rate (mL kg⁻¹ h⁻¹)

N

Number of respiration data points

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.