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Food and Beverage Chemistry/Biochemistry

Stoichio-kinetic modeling of Fenton chemistry in a meat-mimetic aqueous phase medium Khaled Oueslati, Aurelie Promeyrat, Philippe Gatellier, Jean-Dominique Daudin, and Alain KONDJOYAN J. Agric. Food Chem., Just Accepted Manuscript • DOI: 10.1021/acs.jafc.7b06007 • Publication Date (Web): 21 May 2018 Downloaded from http://pubs.acs.org on May 21, 2018

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Journal of Agricultural and Food Chemistry

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Stoichio-kinetic modeling of Fenton chemistry in a meat-mimetic

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aqueous phase medium

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Khaled Oueslati, Aurélie Promeyrat, Philippe Gatellier, Jean-Dominique Daudin, and Alain

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Kondjoyan*

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INRA, UR370 Qualité des Produits Animaux, 63122 Saint-Genès-Champanelle, France

*Corresponding author: Alain Kondjoyan, tel. +33 (0)4 73 62 44 92; fax: +33 (0)4 73 62 40

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89;

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Email: [email protected]

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ABSTRACT

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Fenton reaction kinetics, which involved an Fe(II)/Fe(III) oxidative redox cycle, were studied

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in a liquid medium that mimics meat composition. Muscle antioxidants (enzymes, peptides

17

and vitamins) were added one by one in the medium to determine their respective effects on

18

the formation of superoxide and hydroxyl radicals. A stoichio-kinetic mathematical model

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was used to predict the formation of these radicals under different iron and H2O2

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concentrations and temperature conditions. The difference between experimental and

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predicted results was mainly due to iron reactivity, which had to be taken into account in the

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model, and to uncertainties on some of the rate constant values introduced in the model. This

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stoichio-kinetic model will be useful to predict oxidation during meat processes, providing it

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can be completed to take into account the presence of myoglobin in the muscle.

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KEYWORDS: model, meat, free radicals, iron oxidation, iron reactivity, antioxidants


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INTRODUCTION

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Meat is an important source of iron in the human diet. Iron in meat exists in two forms, called

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heme and non-heme iron. During meat processing and storage non-heme iron can react with

33

oxygen and its peroxide derivatives to give oxygen-centered free radicals. These reactions are

34

part of the Fenton chemistry system. Superoxide radicals (O2°-) and hydroxyl radicals (HO°)

35

are the precursors to a cascade of reactions leading to lipid and protein oxidation with

36

negative impact on meat qualities. Postmortem protein oxidation can affect negatively fresh

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meat colour and tenderness while lipid oxidation is connected with the development of

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warmed-over flavour

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presence of various antioxidants in the product. Studying Fenton reactions directly in meat is

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a complex challenge, as it is difficult to get any precise control over composition of the

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medium and physicochemical conditions. Thus a meat-mimetic medium was developed to

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modulate concentration of iron, of oxygen and hydrogen peroxide, and temperature, to mimic

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storage and cooking conditions. Firm control of food-process oxidation reactions requires

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quantification of the effect of a huge number of storage and processing scenarios on the

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formation of free radicals in the meat. As any purely experimental approach would always be

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costly, time consuming and incomplete, we developed a stoichio-kinetic model to address this

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challenge 3. Stoichio-kinetic modeling has already been used in food-mimetic media to predict

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time-course of Maillard reactions or protein oxidation processes

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extended in this paper to analyze the reactivity of a catalyst, iron, which is a key factor in the

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evolution of the Fenton system.

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Reliability of calculations with stoichio-kinetic models is based on the correctness of the

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reactional scheme and of the two parameters associated with each chemical reaction: rate

53

constant (at a reference temperature) and activation energy. An initial critical review of

1,2

. The superoxide and hydroxyl formation is modulated by the


4, 5

. This approach is


54

literature data dealing with Fenton chemistry in aqueous solutions (mainly diluted mineral

55

solutions and sea water) was done to determine the set of the elementary chemical reactions

56

involved, and to compare, and range, the constant rates identified by many authors 5. In

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parallel a preliminary sensitivity study was conducted to identify by calculations the

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parameters that have a decisive effect on the superoxide or hydroxyl radical kinetics under the

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physicochemical conditions examined here. When the parameters had little incidence, or

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when their values were well documented, the reported values were used as they were. On the

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contrary the parameters values were considered 'uncertain' when there were large differences

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between authors or when the values were identified from data obtained under

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physicochemical conditions far from ours. In this case the parameter values were re-examined

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using our experimental data.

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The first part of the paper presents the experiments used to measure the kinetics of the

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formation, or disappearance, of the O2°- and HO° radicals. The second part summarizes the

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knowledge relative to the chemical system and reviews the parameters values found in

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literature. The third part is dedicated to the stoichio-kinetic model and to the identification of

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the 'uncertain' parameters values. The last part compares calculations to measurements and

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discusses the performances and limits of the mathematical model.

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EXPERIMENTS

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Composition of the mimetic medium. Free-radical production was evaluated in a 40 mM

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sodium phosphate buffer at pH 6, corresponding to the ionic strength and pH of meat.

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Phosphate was used as model buffer due to its high concentration in meat. Four

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concentrations of iron (50, 200, 400 and 600 µM) were tested with or without addition of

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various levels of hydrogen peroxide (200, 1000 and 2000 µM). Temperatures were fixed at

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different values from 4 to 75°C. Temperatures higher than 30°C were used to study the effect


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of meat cooking on oxidation. Selected antioxidants present in meat were also tested:

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superoxide dismutase (240 U/ml), catalase (640 U/ml), carnosine (20000 µM), glutathione

81

(850 µM), Trolox C (11.6 µM), and ascorbate (100 µM). Trolox C was used instead of

82

vitamin E because vitamin E precipitates in aqueous medium. These oxidants were prepared

83

as 200-fold stock solutions in water, before addition to the reaction medium. All the reagents

84

used in this study were purchased from Sigma Aldrich, France.

85 86

Free radical determination. The literature reports a number of probes for the detection of

87

free radicals, but their use was rarely adapted to the experimental conditions of this study.

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After different tests not reported here, our choice turned to two specific probes: nitroblue

89

tetrazolium (NBT), which reacts specifically with superoxide radical to form formazan,

90

detectable by visible spectroscopy; and terephthalate (TP), which reacts with hydroxyl

91

radicals to form fluorescent hydroxyterephthalate (hTP). The advantages of these probes are

92

that they are specific and sensitive as well as soluble in aqueous solution, stable in a broad

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temperature spectrum, and simple to use (without complicated extraction), making them

94

suitable for our meat-mimetic medium. The production of oxygen-centered free radicals was

95

evaluated in separate experiments.

96

In a first set of experiments, O2°- and its protonated form (HO2°) were detected together by

97

the reduction of NBT (500 µM) into formazan. One mole of NBT reacts with two moles of

98

radical to give one mole of formazan. The production of formazan was evaluated at 530 nm

99

with an absorption coefficient of 12.8 mM-1 cm-1. Triton X100 was added (at 1/1000

100

concentration) to stabilize the insoluble formazan in its colloidal form 6. Absorbance

101

measurements were performed on a Jasco V-770 spectrometer equipped with a Peltier

102

temperature controller and magnetic stirrer.

103

In a second series of experiments, HO° formation was evaluated by the hydroxylation of TP



104

(1000 µM) into hTP. hTP level in samples was determined by fluorescence spectroscopy (λex

105

= 320 nm and λem = 420 nm), and comparison with a calibration curve was performed in

106

parallel with commercial hTP 7. The fluorescence measurements were performed on a Jasco

107

FP-8300 spectrofluorometer equipped with a Peltier temperature controller and magnetic

108

stirrer. When the antioxidants were added, their absorbance or fluorescence was subtracted by

109

measuring in parallel a control with antioxidants and the chemical traps, but without oxidants.

110 111

Physicochemical conditions of the trials. Four concentrations of iron (50, 200, 400 and 600

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µM) were tested to cover the range of iron content found in various meat tissues. The trials

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were carried out without or with addition of various levels of hydrogen peroxide (200, 1000

114

and 2000 µM). Temperatures were fixed at different values from 4 to 75°C. Temperatures

115

higher than 30°C were used to study the effect of meat cooking on oxidation. The experiments

116

lasted from 30 min to 1200 min depending on temperature. Whatever this duration more than

117

30 measures were taken, regularly distributed along the experiment. The trials with

118

antioxidants were carried out at: 4°C, 10°C, 45°C or 60°C, and with an initial concentration of

119

the antioxidant of: 240 U(mL)-1 for the SOD, 640 U(mL)-1 for the Catalase, 20000 µM for the

120

Carnosine, 850 µM for the Gluthation, 2.9 ugL-1 for the Trolox, or 100 µM for the Ascorbate.

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During these antioxidant trials O2°- was measure by adding 200 µM of FeS04 and no H2O2,

122

and HO° by adding 200 µM of H2O2 and no FeS04.

123

Finally a set of 930 measurements were collected during all these trials to be compared to the

124

calculated results

125 126

Experimental error. Experiments were repeated 4 successive times for each experimental

127

condition. Relative standard deviations calculated from these repeated data were always < 5%

128

of their mean value. However, the value of the standard deviation on non-successive


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experimental repetitions was higher, close to 10% of the final concentration value. Some iron

130

was always present during the experiments even when it was not directly added in the

131

medium, so the effect of this residual concentration brought by the phosphate buffer, which

132

was assessed at around 1 µM, was taken into account during data processing by subtracting its

133

influence on the formation of the radicals.

134 135

BIBLIOGRAPHY ON THE CHEMICAL REACTION PATHWAYS AND KINETICS

136

PARAMETERS VALUES

137

Fenton system. The pioneering work of 8 and then 9 sparked a surge in fundamental science

138

studies on Fenton chemistry over the rest of the 20th century. The Fenton reaction system has

139

huge importance in biological systems

140

treatment-process technologies for the disposal of waste, nonbiodegradable toxic effluent, etc.

141

12

142

those found in meat. The Fenton system encompasses a large number of elementary reactions.

143

The numbering used here borrows the number system from a previous study 5, with missing

144

numbers corresponding to simplifications of the initial system. For example, the perhydroxyl

145

radical (HO2°), a weak acid, and the superoxide radical (O2°-), its conjugate base (their pKa

146

being 4.8), were considered as a single compound or a couple (HO2°/O2°-) which proportion

147

varied with the pH following the approach adopted by 13, 14. When pH value is 6, percentage

148

of superoxide radical is 94%.

149

The proposed reaction scheme counts 11 elementary reactions (Table 1). Reactions 1, 2 and

150

10 are theoretically rate limiting as they have much lower rate constant values than the other

151

reactions. Reactions 1 and 10 are particularly pivotal, as they are responsible for the formation

152

of hydroxyl radicals (reaction 1, R1) and superoxide radicals (reaction 10, R10) from Fe(II) at

153

the start of the experiment. The rate constant (k) values of the other reactions, where iron is

10, 11

and is mobilized for applications in a number of

. However, these studies were conducted in very different physicochemical conditions to



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either oxidized or reduced, can be taken from the literature. Nevertheless, the rate constant

155

value for reaction 5 is harder to define as reaction 5 pools the effect of the two elementary

156

reactions that involve both perhydroxyl radical and superoxide radical in the formation of

157

H2O2 from Fe(II). The rate constants for each of these reactions are 1.2 106 s-1 for the reaction

158

involving perhydroxyl radical and 107 s-1 for the reaction involving superoxide radical 16 citing

159

31 and 21

160

two values weight-corrected by percentage superoxide radical and percentage perhydroxyl

161

radical found in solution at pH 6 (Table 1).

162

All the radical–radical reactions (from R18 to R20) are known to have high rate constants

163

from 106 to 109 M-1.s-1. In the absence of metal ions, hydrogen peroxide is very stable at low

164

temperature, so k21 is logically very low. The literature also states that rate of reactions 1, 2

165

and 10 is temperature-dependent. However more data measured at different temperatures are

166

needed to determine accurately these activation energy values

167

influences the complexation and solubility of iron, and therefore its reactivity; unfortunately

168

there is no theoretical link between these properties. Iron complexes have notoriously

169

sophisticated chemistry

170

from 3.0 to 6.0 precipitates iron, more so for Fe(III) than Fe(II)

171

important to identify and account for “iron speciation”, in order to predict the formation of

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superoxide and hydroxyl radicals by Fenton chemistry. The high phosphate content in our

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mimetic medium adds complexity to the process of identifying in-solution iron complexes, as

174

phosphate is described as a strong enough chelator to promote the auto-oxidation of Fe(II) 35.

175

At pH 6–8, H2PO4- and HPO42- are reported as the major chemical species involved in iron

176

complexation 36.

177

In the paper Fe(II) and Fe(III) reactivities are accounted for in the model via two

178

proportionality coefficients, P2 and P3 respectively. A value of 1 means that iron acts without

, respectively). The k5 value given in Table 1 is an estimate based on the mean of these

32

22, 15

. The pH of the medium

). Fe(II) and Fe(III) are both very soluble at pH 3. Increasing pH


33, 34

. It is therefore hugely

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any complexation or precipitation. Visual MINTEQ 3.0 software

180

thermodynamics of chemical equilibria in aqueous solutions was used to attempt to explain

181

the P2 and P3 values determined using the model. Visual MINTEQ 3.0 was used after

182

selecting an extended Debye-Hückel model compatible with ions concentrations up to 1M.

183

The calculations done were for mixtures of ions representative of our mimetic medium, i.e.

184

Fe2+, Fe3+, SO42-, PO43-, Na+, Cl-. To reproduce the experimental conditions, concentration of

185

PO43- ions was set at 40 mM, then pH of the solution was adjusted to 6 by adding 44700 µM

186

Na+, as per experimental practice.

187

Reactions and parameters connected with the probes systems. The systems corresponding

188

to the NBT and TP probes introduced in the mimetic medium to measure free radical

189

formation are represented by reactions 30–38 (Table 1). NBT reduces to monoformazan (MF)

190

then diformazan (DF). The model-calculated sum of MF plus DF will be collapsed under the

191

term “formazan”. The rate constant assigned to these reactions came from

192

reactions 32–38 make up the reaction path specific to the formation of hTP

193

formed is oxidized by HO°, creating another compound (reaction 38) called “compound 3” in

194

the Table 1 reaction scheme 39.

195

Reactions and parameters in the antioxidant systems. Antioxidants either promote or

196

inhibit the formation of superoxide and hydroxyl radicals. Superoxide dismutase (SOD) is an

197

enzyme that catalyzes the dismutation of the (HO2°/O2°-) couple into hydrogen peroxide

198

(Table 1, R18 with SOD). Catalase (Cat) is an enzyme with a complementary role to SOD, as

199

it catalyzes the decomposition of hydrogen peroxide into water and molecular oxygen (Table

200

1, R21 with catalase). Glutathione (GSH) can chelate ferrous ions and react with hydroxyl

201

radicals (reaction 50, Table 1; 40). The thiyl radical (GS°) produced can—if not neutralized by

202

auto-oxidation (GSSG)—drive oxidative processes through reactions with oxygen that lead to

203

the formation of a peroxide or the superoxide anion

25

, which predicts the

23, 38

. Elementary 24

. The hTP

. Carnosine presents antioxidant



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properties, binding iron or trapping oxygen-centered free radicals. The rate constant of the

205

iron binding reaction is not well known, unlike the rate constant of the reaction between

206

carnosine and HO2°/O2°- couple (Table 1). All these antioxidants are endogenous antioxidants

207

as they are produced by the muscular cell.

208

Vitamins are exogenous antioxidants provided by the diet. Trolox C (a hydrosoluble form of

209

vitamin E = α-TocH) can react directly with the hydroxyl radical (HO°). The reaction of

210

vitamin E with the superoxide anion O2°- is very slow and, consequently, very unlikely.

211

Vitamin C is a diacid that is found in four different forms: ascorbic acid (AH2), ascorbate

212

(AH-), ascorbate dianion (A2-) and dehydroascorbate (A). At the pH of meat, which is

213

between 5 and 7, ascorbate (AH-) is the predominant form. Its antioxidant activity operates by

214

trapping superoxide and hydroxyl radicals. Vitamin C can also recycle oxidized vitamin E.

215

Vitamin C reacting with reactive oxygen species (ROS) gets oxidized into an ascorbyl radical

216

(A°- or AH° depending on pH of the medium). The ascorbyl radicals are unstable forms that

217

are either convert to dehydroascorbate or get regenerated as ascorbate. Vitamin C is generally

218

thought of as an excellent antioxidant, but it is also widely used as a prooxidant

219

paradoxical behaviour that arises from its potent transition metal-reducing properties—

220

vitamin C reduces iron—and it is the redox cycling of these metals that is deeply involved in

221

the oxidation processes (R55–R60, Table 1).

41

. This

222 223

MODELING THE REACTION-SYSTEM CHEMISTRIES

224

Constructing and solving the system of ordinary differential equations. The rate of a

225

chemical reaction is proportional to the reaction rate constant and concentration of each

226

reactant raised to the nth power. For an elementary reaction, n is the stoichiometric coefficient.

227

The flux balance of formation and disappearance of each compound involved in the reactions

228

listed under Table 1 can be written as an ordinary differential equation (ODE). Taking


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perhydroxyl ion as an example, flux balance in the absence of antioxidants and without

230

considering the presence of the probe derives as:

231 232

ࢊ[ࡴࡻ°] ࢊ࢚

= ࢑૚ [ࡴ૛ ࡻ૛ ][ࡲࢋࡵࡵ] − ࢑૜ [ࡴ૛ ࡻ૛ ][ࡴࡻ°] − ࢑૝ [ࡲࢋࡵࡵ][ࡴࡻ°] − ૛࢑૚ૢ [ࡴࡻ°]૛ (I)

(II)

(III)

(1)

(IV)

233 234

The complete set of these reactions makes an ODE system that can be written in a matrix

235

form. To account for iron reactivity, we have introduced two coefficients in the equations, i.e.

236

P2 and P3. For example, the rate of reaction 4 was modified to become:

237 238

V4 = k4 P2 [FeII] [HO°]

(2)

239 240

We proceeded the same way for all the reactions containing Fe(II) and Fe(III). However, this

241

way of accounting for iron reactivity led to a proportionality in the Fenton system between P2

242

and k1, k4, k5, k10 and between P3 and k2, k6. This was a potential problem to determine the

243

respective values of these parameters from experimental results.

244

The stoichio-kinetic model was implemented using Matlab® R2012a software. The ODE

245

system was solved using time discretization to calculate the kinetics of the formation and/or

246

consumption of all the compounds derived from the reactions schemed in Table 1. As the

247

oxidation reactions had rate constants of very different magnitudes, a solver for stiff systems

248

was required 42; thus we used the Matlab® solver ODE15s.

249

A simulation calculation was initiated by defining pH, temperature and initial concentration of

250

all the compounds. The values of the rate constants were recalculated if necessary as a

251

function of temperature using the Arrhenius law. As the medium was assumed to be oxygen-

252

saturated, its concentration was calculated as a function of temperature using Henry’ law.



253

The respective proportion of HO2° and O2°- radicals were derived from pH.

254 255

Procedure for determining the influential but uncertain parameters. The first step of our

256

procedure was to pull together as much information as possible from the literature to narrow

257

down the parameters range and to determine if the values of literature are directly applicable

258

in the studied conditions (Table 1). Next, the reactions which have the greatest influence on

259

HO° and O2°- were determined by analysing the contribution of each of the reactions of the

260

system to the rate of formation, or of the consumption, of the radicals. Then the values of the

261

parameters both influent and uncertain were identified. This was performed by minimizing the

262

sum of squared difference (SSD) between the predictions and the measurements. It must be

263

outlined that about 690 measurements that cover a large domain of reaction conditions were

264

taken into account at the same time. The active-set algorithm of the mincon function of

265

Matlab® was used (tolerance = 10-6, max iterations = 400). The gradient of the objective

266

function was calculated numerically, supplied to the algorithm, and the constraints derived

267

from the preliminary analysis of the bibliography. It was checked at the end that the resulting

268

parameter set was the global minimum of the objective function in the studied range of

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parameter values. Variations of the objective function close the minimum were also used to

270

determine numerical accuracy on the resulting parameter values. The confidence interval on

271

these values was assessed based on the analysis of the Fisher information matrix.

272 273

RESULTS AND DISCUSSION

274

This modeling work focused first on the formation of superoxide and hydroxyl radicals in the

275

absence of antioxidants but in the presence of probes (Table 1, reactions 1 to 38). Studying

276

their respective contributions enabled us to know which of these reactions drive the formation


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and consumption of O2°- and HO° radicals. With these predominant reactions now known, it

278

became possible to get a first rough estimate of the values of P2 and P3, and then to get more

279

accurate picture of the P2 and P3 values and the uncertain rate constants of these predominant

280

reactions. Then the system is completed by reactions 48 to 60 to predict the effect of added

281

antioxidants on the production of O2°- and HO°. Finally, the ability of the stoichio-kinetic

282

model to reproduce the time-course pattern of oxidation in a representative meat-mimetic

283

medium is discussed.

284 285

Predominant reactions driving the formation/consumption of O2°- and HOo radicals.

286

During experiments the Fenton’s reactions starts due to the adding of Fe(II) to the mimetic

287

medium. In this case, the formation of O2°- is explained at over 99% by reaction 10, as the

288

contribution of reaction 2 is < 2%. Consumption of the superoxide radical is due to both

289

reaction 5 and the reactions related to the add-in of NBT probe (Fig. 1a). Among the reactions

290

related to use of the NBT probe, reaction 30 is the biggest consumer of O2°-, with reaction 31

291

contributing < 2%. The relative importance of reactions 5 and 30 for O2°- consumption

292

depends on both time and operating conditions. Figure (1a), calculated for a temperature of

293

60°C and an initial Fe(II) concentration of 600 µM, shows that reaction 5 is the biggest

294

consumer of O2°- radicals in the first 2 minutes of the experiment, after which it gradually

295

gives way to reaction 30 over time. This system time-course pattern stays exactly the same

296

whatever the temperature, but is different at initial Fe(II) concentrations < 600 µM. When

297

initial iron concentration is decreased, reaction 30 becomes the predominant driver of O2°-

298

consumption, right from the start of the experiment

299

During our experiments, the formation of the hydroxyl radical is explained wholly (over

300

99.5%) by reaction 1. The consumption of hydroxyl radical is essentially related to the

301

reactions using the hTP probe (Fig. 1b). Reaction 3 also has an effect on HoO radical



302

consumption, but only a minor one (i.e. < 2% and so not plotted on Fig.1b). Among the

303

reactions related to the add-in of hTP probe, reaction 32 is the biggest consumer of HOo,

304

followed to a lesser extent by reactions 36 and 38 (Fig. 1b).

305 306

A first estimation of values for P2 and P3. We ran a first comparison between experimental

307

and predicted results after introducing the rate constant values taken from the literature,

308

without detailing the rate constants of reactions related to the probes (Table 1). In a first step,

309

we assumed that 100% of the concentration of iron added into the test tube was involved in

310

the Fenton-like reactions without complexation or precipitation (i.e. P2 = P3 = 1 in the model).

311

The predicted results were wildly different from the experimental values (Table 2). Mean

312

difference in amount of hTP and formazan formed under the conditions located at the centre

313

of the experimental domain, (200 µM of FeSO4, 200 µM of H2O2 added in tube in the case of

314

hTP only) across all-dataset results at 10 minutes came to 66.6% and 50% of the experimental

315

value and 12.5% and 40% at 30 minutes. When runs moved away from these conditions, the

316

differences between predicted and measured values were even bigger. This very big gap

317

between predicted and measured values was primarily due to the fact that the model assumed

318

that 100% of iron introduced in the medium was reactive. However, there is ample evidence

319

in the literature that this is not the case. We therefore ran new calculations in which we

320

independently decreased the values of P2 and of P3. Results showed that introducing P2 and P3

321

values of 0.050 while keeping the rate constants taken from the literature more than halved

322

the gap between predicted and measured values (step 2 compared with 1 in Table 2). The fact

323

that concentration of reactive iron was well below concentration of added iron can be

324

explained by the physicochemistry of our reaction medium held at pH 6 in a phosphate

325

buffer—a special physicochemistry that can be analyzed using software like Visual MINTEQ

326

3.0. It is thus possible to show that Fe(II), which is totally soluble at pH 3, steadily


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precipitates as pH increases, and ultimately accounts for less than 5% of total Fe(II)

328

concentration at pH 6, while Fe(III) is 100% precipitated at this same pH 6. This precipitation

329

could decrease the reactivity of the iron, although it would still necessarily remain part-

330

reactive, even as concerns the Fe(III) (otherwise there would be zero Fo and zero hTP

331

produced). Note that this persistent reactivity of Fe precipitates at pH 6 fits the findings of 43.

332

Simulations run from the Debye-Hückel model bundles with the Visual MINTEQ 3.0

333

software also made it possible to know the relative concentration of iron complexes in our

334

mimetic medium. The three dominant compounds in solution were the phosphate complexes

335

FeHPO4 and FeH2PO4 and the Fe(II) ion, found in far bigger proportions than the aqueous

336

form of FeSO4 or the FeOH+ ion. However, we cannot firmly conclude on the net overall

337

reactivity of iron in our medium. Indeed, even if the concentration of Fe(OH+) is well below

338

the concentration of the other compounds, Fe(OH+) is known to have a thousand-fold higher

339

reactivity than Fe(II) 44.

340 341

Identifying the value of uncertain parameters in the Fenton model. Parameter sensitivity

342

analysis showed that the predominant reactions in Fenton chemistry for the formation or for

343

the consumption of O2°- and HO° were respectively reactions 5, 10 and 30 for the superoxide

344

radical and reactions 1, 32, 36 and 38 for the hydroxyl radical. We elected not to change the

345

rate constant value of reaction 1 given in Table 1, as it comes from a huge number of

346

experiments, all in pH and temperature conditions that overlap with those studied here 45, 15, 36.

347

However, we accepted a degree of uncertainty over the rate constant values for reactions 5,

348

10, 30, 32, 36 and 38 reported in Table 1, as they were often determined in different

349

experimental conditions to here (pH, T, etc.) and/or from a more limited number of

350

experiments than Millero’s or ours experiments. We worked to the assumption of null-value

351

activation energies of the radical reactions (i.e. Ea1 = Ea5 = Ea30 = Ea32 = Ea36 = Ea38 = 0), as



352

widely accepted in the literature. As iron reactivity also has a decisive effect on the predicted

353

kinetics, we systematically accounted for parameters P2 and P3 at every later step of the

354

determinations. Equation (2) led to a possible correlation between the solutions of P2 and of

355

k5, k10. Thus there existed a potential risk to find a set of solutions which was not the global

356

minimum of the objective function in the domain, even if the fact that the rate of reaction 1

357

was proportional to P2, tended to narrow the range of the possible (P2, k5, k10) solutions. It was

358

thus absolutely necessary to check that the final solution was actually the global minimum in

359

the domain under studied.

360 361

The identification process accounted for all experiments except those concerning zero Fe(II)

362

concentrations. It began by taking P2 = P3 = 0.050 as the starting point, taking the k5, k10 and

363

Ea10 values found in the literature, and setting probe reaction rate constants k30, k32, k36 and k38

364

to the same high fixed value 109, all to be coherent with values found in the literature for

365

radical reactions (step 2, Table 2). The rate constants determined by 23, 24 were then introduced

366

to account for details of the reaction-path schemes related to the formazan and hTP probes,

367

respectively. Introducing the k30, k32, k36 and k38 values found in these papers tended to

368

increase the gap between model-predicted and experimentally-measured formazan and hTP

369

concentrations (step 3, Table 2). An optimization process to minimize the root-mean-square

370

error between all-dataset predicted and experimental values was carried out by constraining P2

371

and P3 to values ≤ 0.1 and identifying the constants of reactions 5 and 10 (k5, k10 and Ea10) that

372

essentially concern formation and consumption of the O2°- radical (step 4, Table 2). The final

373

step was to simultaneously identify the previous constants along with the constants for

374

reactions related to use of the two probes, i.e. formazan and hTP k30, k32, k36, k38, (step 5, Table

375

2). The minimizations were run with the constraint that the reaction rate constants could not

376

diverge more than 20-fold from the initial values given in the literature. Results showed that it


Page 16 of 35

Page 17 of 35


377

was effectively necessary to vary both the values for P2 and P3 along with the values for all

378

these reaction rate constants to narrow the gap to experimental results.

379 380

The systematic study of variations in objective function that was undertaken here showed that

381

the solution found in step 5 was effectively a net-overall minimum in the domain of variation

382

on the parameters factored here. It was especially checked that no other (P2, k5, k10)

383

parameters set led to a value of the objective function that was smaller than the solution found

384

in step 5.

385

The accuracy connected to the use of numerical methods to identify the parameters listed in

386

Table 2 was around ±20% the values of P2 and P3 (P2 = 0.040 ±0.009; P3 = 0.085 ±0.015) and

387

< 1% on all the rate constants of reactions 5, 10, 30, 32, 36 and 38 and on the energy of

388

activation of reaction 10. The width of the confidence intervals on the above parameters was

389

estimated, from relations connected to use of the Fisher-information matrix, as spanning at

390

least 25–30% of the value of these parameters, which is far greater than the uncertainties

391

related to applying the above numerical minimization methods. However, determination using

392

the Fisher-information matrix to estimate confidence intervals is questionable in our case

393

here, as it presupposes that the model is complete. In our case, the gap between predicted and

394

measured values spans not only an uncertainty on the value of parameters listed in Table 2 but

395

also on the differences stemming from the incompleteness of the model.

396

Note, however, that despite these caveats, the parameter values identified here are still near

397

the values found in the literature. The value identified here for k5 (6 106 s-1) remains within

398

the brackets of values reported by 18 for O2°- radical (1.2 106 s-1) and its conjugate base HO2°-

399

(10 106 s-1). The difference could be explained by a greater affinity of Fe(II) for the O2°-

400

radical than for HO2°-. The new reaction rate constant values identified here for use of the



401

hTP probe range from 8 108 to 6 109 and are close to those initially proposed by Fang et al.

402

(1996). They also rank-order in the same way here (i.e. k36 < k32 < k38).

403

That said, our value for rate constant k30 was around 10-fold higher than the value proposed

404

by Altman (1976). However,

405

experimental media or tissues to here. The k10 value derived from our identification process

406

was also 10-fold higher than the value found in the literature, but this difference is almost

407

certainly explained by a difference in the way the effect of temperature on reaction rate was

408

integrated, since the increase in k10 value following our minimization process came with a

409

simultaneous decrease in Ea10 value.

23

k30 constant is an estimation that was obtained in different

410 411

Ability of the model to predict Fenton chemistry. Figure 2ab compares the kinetics of

412

formazan and hTP predicted by the model, with the parameters’ values identified at the end of

413

the identification process (Step 5, Table 2) against the kinetics measured for iron

414

concentrations of 50, 200 and 600 µM and at temperatures of 25°C and 60°C, respectively.

415

The model-predicted values reproduce the experimentally-measured time-course systems,

416

even though differences persist. The slopes of simulated formazan kinetics match the

417

variations measured over the first 10 minutes of the experiment, whereas predicted

418

concentrations overestimate the experimental values for a 30-minute reaction time (Fig. 2a).

419

Conversely, the model clearly overestimates hTP formation over the first ten minutes of the

420

experiment, whereas predicted values are close to measured values at 30 minutes. A more in-

421

depth detailed analysis of the residuals between predicted and measured results was carried

422

out for all experiments as a whole and for each of the O2°- and HO° radicals taken separately.

423

The analysis emerged total mean difference of 13 µM (Step 5, Table 2), with less prediction

424

error for HO° (mean difference of 10 µM) than for O2°- (mean difference of 16 µM).

425

Regardless of the O2°- or HO° radical under study, the residual is fairly evenly spread across


Page 18 of 35

Page 19 of 35


426

the entire experimental domain, even if the differences tend to be bigger after 10 minutes than

427

30 minutes of reaction. These points are favourable to our food-system application, as the

428

oxidative phenomena in meat take place over long periods and mainly involve HO° radicals

429

that drive the degradation of lipids and proteins.

430

Figure 3a plots the formazan and hTP concentrations measured after 30 minutes of

431

experiment for in-media iron concentrations varying from 50 to 600 µM and a constant H2O2

432

concentration, i.e. either 0 or 200 µM. The model predicts hTP concentrations close to

433

experimentally-measured

434

experimentally-measured formazan concentrations. Figure 3b charts the effect of varying

435

H2O2 level from 200 to 2000 µM on hTP concentration measured after 30 minutes of

436

experiment and a constant iron concentration of 200 µM. The model reliably describes the

437

time–course of experimental results, even if it tends to underestimate measured values at a

438

H2O2 level of 1000 µM. Overall, model-predicted results over a 30-minute reaction window

439

fit with the experimental results, and within a range of iron and H2O2 concentrations wider

440

than the physiological variations found in meat.

values,

whereas

it

tends

to

systematically

overestimate

441 442

Ability of the model to predict the effect of antioxidants. The model effectively predicts

443

the experimentally-observed promoter or conversely inhibitor effects of carnosine, GSH,

444

vitamin C and vitamin E on the formation or consumption of superoxide and hydroxide

445

radicals at 4°C and at 60°C (Table 3). However, the plots of model-predicted variations fit

446

less well to the experiments led with SOD or catalase. The gaps between experimental and

447

predicted values may come from a number of sources. First and foremost, the rate constant

448

values for reactions (48) to (60) taken from the literature may still carry uncertainty, as they

449

were determined from a small number of experiments, or in a medium or conditions different

450

to those used here. Furthermore, the model ignores potential interactions between iron and



451

certain antioxidants, as is the case for vitamin C, and especially carnosine. Finally, no new

452

energy activation value has been introduced in the calculations on the antioxidants, as to our

453

knowledge there are no such values in the literature, so the effect of temperature variations is

454

only related to the variations measured on reactions 1 and 10 of the Fenton chemistry.

455 456

Conclusion of the discussion. We developed a stoichio-kinetic mathematical model which is

457

reasonably able to predict Fenton chemistry in our simplified meat-mimetic medium. It can be

458

used to assess the relative impact of key factors like: pH, temperature and iron content, on the

459

formation/disappearance of O2°- and HO°. It has now to be completed by adding myoglobin,

460

which is a potent pro-oxidant that is found in high concentrations in muscle tissue, especially

461

in red meat. The next step will be to add proteins and lipids. The introduction of lipids in the

462

meat-mimetic medium will both lead to the formation of: (i) other radicals than O2°- and HO°,

463

and (ii) a second phase in the medium. This more complex medium will still remain

464

simplified compared to the real meat tissue which is structured. However, even incomplete,

465

this progressive modeling approach will improve our knowledge on the kinetics of meat

466

oxidation, and increase our ability to predict the effect of muscle composition and processing

467

conditions on this oxidation.

468 469

ACKNOWLEDGEMENTS

470

This work, including the PhD of Khaled Oueslati, were funded by INRA CEPIA department

471

(Grant IB 2013), the Carnot Institute “Qualiment” (INRA AIB 75000032_STABOXAL),

472

ADIV (INRA Agreement FC 3522), and the Tunisian ministry of research. The authors are

473

grateful to Professor Bertrand Broyart for his help during the first stage of the writing of the

474

model under Matlab®.

475


Page 20 of 35

Page 21 of 35


476 477

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478

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Kwan, W. P.; Voelker, B. M., Decomposition of hydrogen peroxide and organic

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Ramirez, J. H.; Duarte, F. M.; Martins, F. G.; Costa, C. A.; Madeira, L. M., Modelling

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Water Science 1999, 12, 713-728.

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solutions Part I: the chemistry underlying the terephthalate dosimeter. Ultrasonics

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Vitamin C: its functions and biochemistry in animals and plants, Oxford, E., Ed. May

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JM, Asard H., Smirnoff, N. Bios Scientific Publishers.: Oxford, 2004; pp 173-188.

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radicals. Journal of the Chemical Society, Faraday Transactions 1: Physical Chemistry

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Iron(III) Ion. II. Polynuclear Species1. Journal of the American Chemical Society 1955,

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Turner, D. R.; Whitfield, M.; Dickson, A. G., The equilibrium speciation of dissolved

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Cosmochimica Acta 1981, 45, 855-881.

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Welch, K. D.; Davis, T. Z.; Aust, S. D., Iron Autoxidation and Free Radical Generation:

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Humic Substances with the Stockholm Humic Model. Journal of Colloid and Interface

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Science 2001, 244, 102-112.

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Bielski, B. H. J.; Richter, H. W., Study of the superoxide radical chemistry by stopped-

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Halliwell, B.; Gutteridge, J. M., Role of free radicals and catalytic metal ions in human

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Buettner, G. R.; Jurkiewicz, B. A., Catalytic metals, ascorbate and free radicals:

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Millero, F. J.; Sotolongo, S., The oxidation of Fe(II) with H2O2 in seawater. Geochimica et Cosmochimica Acta 1989, 53, 1867-1873.

601


Page 26 of 35

Page 27 of 35


602

Legend of the figures

603 604 605

Figure 1: Contribution of the different reactions to the consumption of: (a) the superoxide

606

radical, and (b) the hydroxyl radical. Contributions of less than 2% are not presented in the

607

figure. Calculations were performed at pH = 6, T = 60°C, and adding, in (a), 600 µM of

608

Fe(II), and (b) 200 µM of Fe(II), and 200 µM of H2O2 .

609 610

Figure 2: Comparison between the kinetics of (a) formazan and (b) hTP (b) predicted by the

611

model (black lines), with parameter values identified at Step 5 in Table 2, against the kinetics

612

measured for iron concentrations of 50 (●), 200 (∆) and 600 (♦) µM. Formazan concentrations

613

were measured at 25°C without added H2O2, whereas hTP concentrations were measured at

614

60°C for an initial H2O2 concentration of 200 µM. Error bars correspond to 10% of the

615

experimentally-measured value.

616 617

Figure 3: Comparison between predicted and measured values after 30 minutes of

618

experiment, symbols being experimental values and error bars corresponding to 10% of these

619

values, lines being model’s predictions, for: (a) various initial Fe(II) concentrations, (□) =

620

hTP concentrations measured for [H2O2] =200 µM, (■) = formazan concentrations measured

621

without H2O2; (b) various initial H2O2 concentrations and initial [Fe(II)] = 200 µM, (□) =

622

results obtained at 25°C; (■) at 60°C.

623 624 625 626 627 628



629

Figure 1

630

(a)

90

Consumption (%)

80 70 R5

60

R30

50 40 30 20 10 0

0

20

30

Time (min.)

631 632

10

(b)

Consumption (%)

90 80 70 60 50

R32

40

R36

30

R38

20 10 0

0

633

10

20

30

Time (min.)

634 635 636


Page 28 of 35

Page 29 of 35


637 638

Figure 2

639

(a)

Formazan (µM)

120 100 80 60 40 20 0 0

10

20

30

Time (min.) 640 641

(b) 70

hTP (µM)

60 50 40 30 20 10 0 0

10

20

30

Time (min.) 642



643

Figure 3

644

(a)

Page 30 of 35

160 [hTP] or [Fo] (µM)

140 120 100 80 60 40 20 0 0

100

200

300

400

500

600

[Fe] µM 645 646 647 648 649

(b)

[hTP] (µM)

650 100 90 80 70 60 50 40 30 20 10 0 0

500

1000 [H2O2] µM

1500

651 652 653 654


2000

Page 31 of 35


655

Legend of the tables

656 657 658

Table 1: Roll-up of the reaction rate constants k and activation energies (Ea) selected for the

659

mathematical model.

660 661

Table 2: Root of the mean of the squared difference between the calculated and experimental

662

values (RMSE) calculated at the different steps of the identification process. The constants

663

values in bold are different from the ones introduced at the beginning of the optimization

664

process in step 1. Step 1, rate constant values of k5, k10

665

reactivity is assumed to be 1, the constants values related to the probes, k30, k32, k36, k38 are all

666

assumed to be 109. Step 2, same as in step 1 but P2 and P3 values are decreased to 0.050. Step

667

3, introducing rate constant values for the probes found in literature while keeping P2 = P3 =

668

0.050. Step 4 identification of the constants of reactions 5 and 10 (k5, k10 and Ea10) and of P2

669

and P3, while keeping the same values as in step3 for k30, k32, k36, k38. Step 5 simultaneous

670

identification of all the constants values given in Step 1.

are

taken from the literature, iron

671 672

Table 3: Measurements and numerical simulations of the promotor or inhibitor effect of the

673

antioxidants, in percentage of the reference without antioxidant, at two temperatures: 4°C and

674

60°C, and under the standard conditions (200 µM of FeSO4, and 200 µM of H2O2 in the case

675

of hTP only). The duration of the experiment is 30 minutes at 60°C and 120 hours at 4°C.

676 677 678



Page 32 of 35

Table 1 Reaction number

Reactions

kreference

Ea (kJ/mole)

Main bibliographic sources

at pH 6, 25°C 1

Fe(II) + H2O2 → Fe(III) + HO- + HO°

1.5 103 M-1.s-1

40

14

2

Fe(III) + H2O2 → Fe(II) + H+ + (HO2°-/ O2°-)

2 M-1.s-1

65

15

3

HO° + H2O2 → H2O + (HO2°-/ O2°-)

3 107 M-1.s-1

13

4

Fe(II) + HO° → Fe(III) + HO-

3.5 108 M-1.s-1

16

5

Fe(II) + (HO2°-/ O2°-)→ Fe(III) + H2O2

9.5 106 M-1.s-1

17

6

Fe(III) + (HO2°-/ O2°-)→ Fe(II) + O2 + H+

1 104 M-1.s-1

18

10

Fe(II) + O2 → Fe(III) + (HO2°-/ O2°-)

3 M-1.s-1

18

(HO2°-/ O2°-) + (HO2°-/ O2°-) → H2O2 + O2

5.4 106 M-1.s-1

19

HO° + HO° → H2O2

5 109 M-1.s-1

20

-

-

HO° + (HO2° / O2° ) → H2O + O2

10 109 M-1.s-1


65

19 20

13

Page 33 of 35


21

H2O2 → 1/2(O2) + H2O

1 10-4 s-1

30

NBT + 2 O2°-+H+ → MF +2 O2

5.9 104 M-3.s-1

31

°-

5.9 104 M-3.s-1

+

MF+ 2 O2 + H → DF+ 2 O2

32

HO°+TP → HO-TP°

2.8 109 M-1.s-1

33

HO-TP°+O2→HO-TP-O2°-

1.6 107 M-1.s-1

34

HO-TP-O2°- → HO-TP°+O2

3.4 103 s

35

HO-TP-O2°- → HTP+ (HO2°/O2°-)

175 s-1

36

HO°+TP → lost compound 1

0.5 109 M-1.s-1

37

HO-TP-O2°- → lost compound 2 +O2

215 s-1

38

HTP+ HO° → lost compound 3

6.3 109 M-1.s-1

48

(HO2°-/ O2°-) + (HO2°-/ O2°-) + SOD → H2O2 + O2

1.6 109 M-2.s-1

49

H2O2 + catalase→ 1/2(O2) + H2O

107 M-1.s-1

50

GSH + HO° GS° + H2O

1.3 1010 M-1.s-1

40

21

22

-1

23

24

25



Page 34 of 35

51

Carnosine + (HO2°-/ O2°-) lost compound 4

0.83 105 M-1.s-1

26

52

Carnosine + (HO°) lost compound 5

9 109 M-1.s-1

26

53

α-tocopherol + (HO2°-/ O2°-) lost compound 6

6 M-1.s-1

27

54

α-tocopherol + (HO°) lost compound 7

6.9 109 M-1.s-1

28

55

(AH2/AH-) + Fe(III) (AH°/A°-) + Fe(II)

10 M-1.s-1

56

(AH2/AH-) + (HO2°-/ O2°- ) + H+ H2O2 + (AH°/A°-)

0.1 10 M-1.s-1

57

(AH2/AH-) + HO° H2O + (AH°/A°-)

1100 10 M .s

7

7

7

-1 -1

58

2(AH°/A° ) + H (AH2/AH ) + A

0.02 10 M .s

59

A2- + O2 (AH°/A°-) + (HO2°-/ O2°-)

10 M-1.s-1

60

(AH2/AH-) + (AH°/A°-) 2(A)

1.24 10 M .s

-

+

-

-2 -1

2

-4

-1 -1


29

Page 35 of 35


1

Table 2 Step 1 2 3 4 5

k5 9.50E+06 9.50E+06 9.50E+06 6.00E+06 6.00E+06

k10 3.0E+00 3.0E+00 3.0E+00 3.0E+01 3.0E+01

k30 1.0E+09 1.0E+09 5.9E+04 5.9E+04 6.0E+05

k32 1.00E+09 1.00E+09 2.80E+09 2.80E+09 9.60E+08

k36 1.00E+09 1.00E+09 5.80E+08 5.80E+08 8.90E+08

k38 1.00E+09 1.00E+09 6.30E+09 6.30E+09 3.00E+09

Ea10 6.5E+01 6.5E+01 6.5E+01 2.9E+01 2.9E+01

P2 1.000 0.050 0.050 0.040 0.040

P3 1.000 0.050 0.050 0.085 0.085

2

3 4 5

Table 3

Antioxidants SOD Catalase Carnosine GSH Vit C Vit E

Model results Measured results hTP formazan hTP formazan 60°C 4°C 60°C 4°C 60°C 4°C 60°C 4°C -13.6 32.2 14.4 92.9 15 -18 -14 -59 -13.6 32.2 14.4 47 -50 -81 19 1684 -95.7 -89 90 -14 -97 -95 6 138 -74.7 -61.7 19 93 -63 -73 85 94 -26.3 74.8 26 95 -18 8 19 50 -13.6 42 16.7 83.8 175 19 1 24

6


RMSE 47 µM 18 µM 29 µM 21 µM 13 µM

TOC Graphic - American Chemical Society

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