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

  • Seo Hyeon Han
  • Han Dong Jang
  • Seung Ju LeeEmail author


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 (Vm, Km, and Ki) 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.


Sweet potato Respiration rate Kinetic modeling Temperature dependency 

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)


Model parameter of Michaelis–Menten equation


Arrhenius activation energy


Universal gas constant (8.314 kJ mol−1)


Absolute temperature (K)


Free volume of respiration chamber (mL)


Weight of sweet potatoes (g)


Regression coefficient


Regression coefficient


Mean relative deviation modulus (%)


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


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


Number of respiration data points



This research was supported by the Ministry of Agriculture, Food and Rural Affairs (No. S-2018-A0436-00004), Republic of Korea.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© The Korean Society of Food Science and Technology 2019

Authors and Affiliations

  1. 1.Department of Food Science and BiotechnologyDongguk University-SeoulGoyangKorea

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