Modeling Respiration Rate of Strawberry (cv. San Andreas) for Modified Atmosphere Packaging Design

Figures & data

Table 1  RRO2 values ± standard deviation and RRO2 reduction percentage values (when temperature was decreased from 23 to 10°C) for each of the initial gaseous compositions assayed

Gas mixture		RRO2 (ml kg^−1 h^−1)
O2 (% v/v)	CO2 (% v/v)	10°C	19°C	23°C	RRO2 reduction percentage (%)
24.7 ± 0.9	0.00 ± 0.02	18.6 ± 2.69 a	46.8 ± 3.30 b	67.6 ± 2.25 c	72.5
22.3 ± 1.9	11.2 ± 0.66	16.2 ± 1.59 a	42.2 ± 3.00 b	70.4 ± 0.67 c	77.0
20.2 ± 1.6	0.00 ± 0.01	16.2 ± 2.33 a	46.0 ± 4.93 b	74.7 ± 3.94 c	78.3
15.6 ± 0.5	0.00 ± 0.01	16.6 ± 2.05 a	42.4 ± 0.302 b	72.4 ± 4.74 c	77.1
8.80 ± 0.5	5.00 ± 0.18	15.8 ± 0.49 a	26.7 ± 2.15 b	65.8 ± 0.50 c	76.0
2.60 ± 0.1	5.30 ± 0.47	15.3 ± 3.56 a	16.6 ± 4.74 a	62.1 ± 4.17 b	75.4
2.30 ± 0.1	12.5 ± 0.64	8.45 ± 4.71 a	12.6 ± 4.69 a	45.6 ± 0.69 b	81.5

Different letters in the same row indicate significant differences according to LSD Fisher test (p < 0.05).

Table 2  Analysis of variance table for respiration rate (RRO2) at 10, 19, and 23°C

Source of variation	Sums of squares	Degrees of freedom	Mean squares	F	p-Value
10°C
Gas composition	119.39	6	19.9	2.79	0.1029
Error	49.96	7	7.14
Total	169.35	13
19°C
Gas composition	2409.62	5	481.92	39.43	<0.0001
Error	97.77	8	12.22
Total	2507.39	13
23°C
Gas composition	1130.91	5	226.18	27.05	0.0002
Error	58.54	7	8.36
Total	1189.45	12

Figure 1  Experimental O₂ consumption rate (RRO2) as a function of O₂ concentration, for the three temperatures assayed. Vertical bars represent standard deviation.

Table 3  Models tested on respiration rate data

Model	Description	Equation
I	No CO2 inhibition
II	Competitive CO2 inhibition
III	Uncompetitive CO2 inhibition
IV	Non–competitive CO2 inhibition
V	Competitive–uncompetitive CO2 inhibition

See text for nomenclature details.

Table 4  Model parameters for five combined Michaelis-Menten–Arrhenius models

Model	R^2	A (ml kg^−1 h^−1)	Ea (kJ mol^−1)	Km (%)	Ki (%)	Kj (%)	Kn (%)
I	0.91	1.6E+13	64.2	1.9	—	—	—
II	0.91	3.5E+13	66.1	1.9	1.2E+12	—	—
III	0.91	1.1E+14	68.8	1.9	—	3.4E+14	—
IV	0.91	1.0E+14	68.7	1.8	—	—	8.2E+13
V	0.91	3.2E+13	65.9	1.8	2.9E+13	3.4E+13	—

Figure 2  RRO2 variation with temperature and O₂ concentration. Surface plot represents model RRO2 values.

Figure 3  Experimental and model O₂ and CO₂ concentration evolution inside modified atmosphere packages of strawberries throughout 80 h storage in increasing temperature conditions.

Table

A	Pre–exponential factor (ml kg^−1 h^−1)
cO2	O2 concentration (%)
cCO2	CO2 concentration (%)
Ea	Activation energy (kJ mol^−1)
Ki	Michaelis–Menten competitive inhibition constant (%)
Kj	Michaelis–Menten uncompetitive inhibition constant (%)
Km	Michaelis–Menten constant (%)
Kn	Michaelis–Menten non-competitive inhibition constant (%)
m	Product mass (kg)
R	Ideal gas constant (8.314 J mol^−1 K^−1)
RRCO2	CO2 production rate per unit mass (ml kg^−1 h^−1)
RRO2	O2 consumption rate per unit mass (ml kg^−1 h^−1)
RQ	Respiration quotient
t	Time (h)
T	Temperature (K)
Vfree	Free reactor volume (m^3)