Ethylene production,respiration and gas exchange modelling in modified atmosphere packaging for banana fruits

A mathematical model was developed from experimental measurements to describe the evolution of the O₂, CO₂ and ethylene in a modified atmosphere packaging system for Cavendish bananas. The respiration and ethylene production in the fruits were experimentally obtained from a closed system method and then represented by Michaelis–Menten equations of enzyme kinetics. The gas transfer through the packaging was described by a Fick's diffusion equation, and the temperature dependence was represented based on the Arrhenius law. The model was validated by packaging the fruit in perforated bags of polypropylene and low density polyethylene at 12 °C for a period of 8 days. With the developed model it was possible to satisfactorily describe the experimental evolution of the gas content in the headspace of the packages, obtaining coefficients of determination (R²) of 0.93 for the O₂ levels, 0.90–0.91 for the CO₂ levels, and 0.89–0.93 for the ethylene levels.     

Analytical solution of amperometric enzymatic reactions based on Homotopy perturbation method

Electrochemical polymerization is a simple and direct technique often employed for immobilizing redox enzymes at an electrode surface. Besides these, it allows precise control over the amount, spatial distribution and orientation of the enzymes. Analytical expressions pertaining to the immobilization of enzyme by electrochemical polymerization on the electrode surface were obtained by Homotopy perturbation method (HPM). This expression further distinguishes the product of the enzyme reaction at the electrode surface from those occurring alongside the polymer employed for immobilization. These analytical results are compared with the available limiting case results and they are found to be in good agreement.     

Modelling perforated mediated modified atmospheric packaging of capsicum

Perforation of a film would otherwise have a low permeability is an alternative to obtain optimum oxygen and carbon dioxide concentration in modified atmosphere packages. In present study, gas exchange was studied through a macroperforated packet containing capsicum having different number of holes, 1–4, of diameter 0.3 mm at temperatures of 5 and 25 °C. A model combining the Michaelis–Menten kinetics to describe the respiration rate of the product with mass transfer equation to describe the gas transfer across the package provided a good fit to the experimental data. Its applicability was further validated in a dynamic test, subjecting a package to a variable temperature programme simulating conditions in distribution chains. Model showed good agreement between predicted and observed values for both storage conditions with constant temperatures and variable temperature conditions of distribution chain, as mean relative deviation modulus (E) value was <10%.     

Modelling the effect of superatmospheric oxygen concentrations on in vitro mushroom PPO activity

The kinetics of polyphenol oxidase (PPO, EC 1.14.18.1) with respect to oxygen concentrations from 5 to 100% using chlorogenic acid (CGA) as substrate was examined. In vitro mushroom PPO activity was determined by measuring the consumption of oxygen during the oxidation reaction. A differential Michaelis–Menten model was fitted to the obtained total depletion curves. The product concentration as well as the concentration of oxygen had a clear inhibitory effect on the reaction rate. However, the inhibitory effect of oxygen was more evident at low product concentration. A linear mixed inhibition model that considered both the product (oxidised CGA) and oxygen as inhibitors was developed. A model with the product as a competitive inhibitor and oxygen as an uncompetitive inhibitor was the most appropriate to explain the reaction kinetics. The values of the inhibition constants calculated from the model were 0.0032 mmol L⁻¹ for K_m (Michaelis–Menten constant related to oxygen), 0.023 mmol L⁻¹ for K_mc (constant for competitive inhibition due to the product), 1.630 mmol L⁻¹ for K_mu (constant for uncompetitive inhibition due to oxygen) and 1.77 × 10⁻⁴ mmol L⁻¹ s⁻¹ for V_max (maximum reaction rate). The results indicate that superatmospheric oxygen concentrations could be effective in preventing enzymatic browning by PPO. Copyright © 2006 Society of Chemical Industry     

Michaelis–Menten kinetics for enzymatic depolymerization of a linear polyester synthesized from Z‐protected glutamic acid

A biodegradable polyester resin was polymerized from N‐benzyloxycarbonyl‐L ‐glutamic acid and ethylene glycol. Rhizopus delemar lipase was used as a biocatalyst for the rupture of ester bonds during the hydrolysis studies. Depolymerization was observed to follow a Michaelis–Menten mechanism, with the maximum rate of monomer formation dP/dt_max = 1.12 × 10⁻⁸ mol/s and the rate constant K_m × 2.03 × 10⁻⁴ mol. Subject to initial conditions described by the most probable distribution and Michaelis–Menten–type depolymerization rate expressions, population density distribution dynamics of the polymeric molecules that formed the resin were explicitly described using a deterministic approach. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 80: 514–520, 2001     

Flow through diffusion cell method: A novel approach to study in vitro enzymatic degradation of a starch‐based ternary semi‐interpenetrating network for gastrointestinal drug delivery

A ter‐polymeric semi‐IPN has been synthesized by aqueous polymerization of methacrylamide in the presence of polyethylene glycol (PEG) and natural polysaccharides starch, and its enzymatic degradation has been studied in the phosphate buffer medium of pH 6.8 at the physiological temperature 37°C. With the increase in content of enzyme in the external solution and starch in the hydrogel, the degradation is enhanced while the extent of degradation is lowered with the increase in the amount of PEG in the hydrogel. The initial water content also affects the degradability of the polymer matrix. The degradation follows Michaelis–Menten kinetics and K_M was found to be 3.92 × 10^?5 mol dm^?3. The hydrogel exhibits different degradation behavior when studied by “traditional degradation method” (TDM) and “flow through diffusion cell” (FTDC) method. The degradability is suppressed in FTDC method because of the absorption of amylase molecules onto filler particles. Finally the nature and size of the filler particles also affects the degradation behavior of hydrogels. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 100: 2975–2984, 2006     

Irregular Fractions of the 2 n Factorial Experiments

The development of fractional replicate plans which consist of irregular fractions of factorial experiments is presented. The method of constructing irregular fraction plans is developed for the general s ⁿ factorial experiment. However, the plans which are found to be of greatest practical value are plans for the 3/2 ^m replicate of the 2 ⁿ experiment. Although these plans introduce correlations between some of the estimates, the correlations do not affect individual tests on the parameters. Some irregular fraction plans permit the estimation of main effects and two-factor interactions with fewer trials than is required with an orthogonal plan. A straightforward procedure for obtaining estimates of the main effects and “important” interactions and estimates of their variances, covariances and correlation coefficients is presented for the 3/2 ^m replicate plans.     

按零级吸收,（一级并行）米氏过程消除药物给药方案设计的数值方法

根据药物动力学基本原理，推导出了符合零级吸收、（一级并行）米氏过程消除药物的动力学方程与稳态性质，并据此首次提出了按９种目标设计这类药物的给药方案的准确数值方法，编制了相应的计算机程序并给出了应用例子。当一种药物的基本动力学参数及血药浓度与药物效应的关系确定后，根据本文提出的方法，可设计出药物的给药方案，使药物在体内的浓度按一定的要求准确、可靠地达到目标水平。