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Density Functional Computational Studies on the Glucose and Glycine Maillard Reaction: Formation of the Amadori Rearrangement Products ABRAHAM F. JALBOUT,1 AMLAN K. ROY,2 ABUL HAIDER SHIPAR,3 M. SAMSUDDIN AHMED3 1

Instituto de Quimica, Universidad Nacional Autonoma de Mexico, Mexico City, Mexico D. F. Department of Chemistry, University of California at Los Angeles, Los Angeles, California 3 Faculty of Engineering, Chiba University, Japan 2

Received 11 April 2007; accepted 2 May 2007 Published online 26 September 2007 in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/qua.21438

ABSTRACT Theoretical energy changes of various intermediates leading to the formation of the Amadori rearrangement products (ARPs) under different mechanistic assumptions have been calculated, by using open chain glucose (O-Glu)/closed chain glucose (A-Glu and B-Glu) and glycine (Gly) as a model for the Maillard reaction. Density functional theory (DFT) computations have been applied on the proposed mechanisms under different pH conditions. Thus, the possibility of the formation of different compounds and electronic energy changes for different steps in the proposed mechanisms has been evaluated. B-Glu has been found to be more efficient than A-Glu, and A-Glu has been found more efficient than O-Glu in the reaction. The reaction under basic condition is the most favorable for the formation of ARPs. Other reaction pathways have been computed and discussed in this work. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem 108: 589 –597, 2008

Key words: density functional computational study; glucose; glycine; Maillard reaction; Amadori rearrangement products

Correspondence to: A.F. Jalbout; e-mail: [email protected] or M.D. Shipar; e-mail: [email protected] This article contains supplementary material available via the Internet at http://www.interscience.wiley.com/jpages/00207608/suppmat.

International Journal of Quantum Chemistry, Vol 108, 589 –597 (2008) © 2007 Wiley Periodicals, Inc.

JALBOUT ET AL.

Introduction

T

he complexity of nonenzymatic browning, also known as the Maillard reaction [1] is well known. The reaction occurs between carbonyl compounds, especially reducing sugars, and compounds with free amino groups, such as amines, amino acids, and proteins [1– 4]. The reaction is vital to food science as well as to general biochemistry [2– 4] and even medicine [5–7]. The reaction is a complex series of chemical reactions, which occurs in biological systems. It tends to follow different routes to produce various final products or melanoidines, which tend to be found in complex mixtures, through the formation of various complex intermediates. Because of the complexity of intermediates and melanoidines, controlling the reaction associated with food quality, nutritional value, and medicinal aspects, is still a great challenge. To control the reaction, it is necessary for the reaction mechanism to be well studied and understood. The premise that experiment is unable to provide detailed explanations and mechanisms is certainly valid. Therefore, computational chemistry is likely to be useful to determine a proper mechanism of the reaction. In the present study, glucose (Glu) and glycine (Gly) are taken as the model in the Maillard reaction for computational investigation. Many studies have been conducted to learn the pathways leading to the formation of melanoidines. However, the mechanism is still obscure and proven specific pathways for the formation of Maillard colors, flavors, antioxidants, etc., are not available. By following the most accepted Hodge-scheme [8] for Maillard reaction, mechanisms for the formation of the Amadori rearrangement products (ARPs) in the initial stage of Glu⫹Gly Maillard reaction under different pH conditions are proposed. Density functional theory (DFT) computations have been performed on the proposed mechanisms and the possibility of the formation of different compounds under different pH conditions has been tested by estimating the Gibb’s free energy changes for different steps of the reaction through following the total mass balance. By following the total mass balance, electronic energy changes during the formation of different compounds in the proposed mechanisms have also been calculated to observe the possible internal energy changes during the reaction.

Glu is the most abundant organic species in foods and human body, and therefore, is the most important reducing sugar [4, 9, 10]. Interconversion of open chain glucose (O-Glu) and closed chain glucose, i.e. ␣-glucose (A-Glu) and ␤-Glucose (BGlu), is also possible [9, 10]. All of these three forms of Glu (i.e., O-Glu, A-Glu, and B-Glu) are considered in the present study to evaluate their efficiency in the Maillard reaction involving Gly. Notably, Gly can be found in its four forms. Unionized or unprotonated glycine (UGly, H2NOCH2OCO2H) becomes the dominant species in the gaseous state, and can exist at a very low concentration in neutral (pH ⫽ 7) aqueous solution [9, 10]. In acidic solution, Gly is completely protonated and exists as the conjugated acid [9, 10]. Hence, under acidic conditions, e.g. pH ⬍ 5.5, protonated glycine (PGly, H3N⫹O CH2OCO2H) becomes the dominant species. Possible mechanisms for O-Glu/␣-Glu/BGlu⫹UGly/PGly reactions are proposed and presented in Scheme 2. Production of the basic amino groups is facilitated by the alkaline medium, and therefore, deprotonated glycine (DGly, H2NO CH2OCO⫺ 2 ) becomes the dominant species under basic conditions (pH ⬎ 8) [4]. The glycine zwitter ion (GlyZ, H3N⫹OCH2OCO2:⫺) becomes the dominant species at the isoelectric point of glycine (I ⫽ pH ⬇ 6) [2, 9, 10]. O-Glu/A-Glu/B-Glu⫹DGly/ GlyZ reactions may follow the mechanisms as proposed and presented in Scheme 3. In addition, OGlu can be formed through the “formose reaction” of ribose (Rib) with formaldehyde (Fald), [11] and reversibly, cleavage of O-Glu can produce Rib (Scheme 4). This possibility has also been tested by using DFT computations. Comprehensible information with regards to the role of the neutral, acidic, basic, and isoelectric amino groups in the Maillard reaction is still insufficient, and therefore, the mechanism is obscure. Previous studies were related mainly to the role of unprotonated amino groups, and generally overlooked the function of assumed to be a natural process in foods, especially during the storage process [2– 4, 12]. The rate of the Maillard reaction at low temperatures, e.g. at the standard state, is assumed to be very slow, and therefore, the concentration of the produced intermediates and melanoidines is typically small. Almost all previous studies were performed mainly at high temperatures for producing more intermediates and melanoidines, which permitted the detection of the intermediates and melanoidines effortlessly. The role of pressure on the Maillard

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FORMATION OF THE AMADORI REARRANGEMENT PRODUCTS reaction has not been studied sufficiently. The present study will be helpful to evaluate the role of different Gly species (UGly, PGly, DGly, and GlyZ) under various pH conditions involving Glu (O-Glu, A-Glu, and B-Glu), and especially at low temperatures and pressures, i.e. at the standard state. Because of the comparatively unstable nature for spontaneous performance in further reactions, experimental evaluation of the role of these complex species in the Maillard reaction is complicated at the standard state, and therefore, computational methods are used.

O-Glu

A-Glu +H

H-C-OH |

CHOH |

B-Glu

+ PGly H-NH-Y

N H -Y

CHOH

HC -OH

+ UGly

CHOH

|

CHOH

|

H

CH2OH

|

|

H

|

OH

H

C

C

C HO

|

|

H

|

O

X [2]

X [3]

X [4]

NH-Y

CH2

CH

|

C

|

H OH

|

OH A-Glu

H

|

|

H

|

OH

C HO

|

|

H

H

CH2OH

H

O

C

C

|

C

|

O H

H

O

C |

|

H

|

OH

C HO

|

OH O-Glu

|

|

H

H

C

|

C

OH H

|

OH B-Glu

SCHEME 1. Interconversion of ␣-glucose (A-Glu), BGlucose (B-Glu), and open-chain glucose (O-Glu).

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|

CHOH

|

NH-Y

|

H-N -Y

|

KET

C-O-H |

-H

CH |

H-COH |

CHOH

CHOH

CHOH

X [7]

X

X [5]

|

CH2OH

|

+H

|

C

|

CH CHOH

CHOH

|

C=O

All compounds in the proposed mechanisms (Schemes 1– 4) were studied in their gaseous and aqueous phases at the standard state. As all compounds in the proposed mechanisms can have many conformations in the gaseous state and aqueous solution, it is not possible to consider all of these conformations for calculating the energy changes for different steps in a reaction, especially when it is a complex one, such as the Maillard reaction. Therefore, only minimum energy structures, optimized at RB3LYP [13, 14] by using Gaussian 98 program [15], of the compounds were used to avoid complexities and to simplify the calculations. The 6-31G(d) polarized basis set [13, 14] was used for all calculations. For the PCM/RB3LYP/631G(d) optimizations (in aqueous solution), frequencies were obtained on the final solution phase geometrical parameters. Relevant ZPE values were added to the electronic energies to get the total electronic energies (E°). Finally, the free energy changes (⌬G° ⫽ G°Product(s) ⫺ G°Reactant(s)) for different compounds in the proposed mechanisms (Schemes 1– 4) were calculated by following the total mass balance of the reaction (which is displayed in the supplementary materials).

- H2O

CHOH

CHOH

|

Computational Details

|

-H

|

|

X [1]

N-Y

|

|

|

[6]

|

SCHEME 2. Proposed mechanisms for the formation of the Amadori rearrangement products in the initial stage of Glu⫹UGly and Glu⫹PGly Maillard reactions. Abbreviations: Glu, glucose; UGly, unionized or unprotonated glycine; PGly, protonated glycine; KET, ketoenolic tautomerization. Numerical abbreviations: 1, protonated form of Glu; 2, ionic addition adduct of Glu and UGly or PGly (1-protonated glycino-hex-1,2,3,4,5,6-ol); 3, addition compound of Glu and UGly or PGly (1-glycino-hex-1,2,3,4,5,6-ol); 4, Schiff base of 3; 5, ionic adduct of 4; 6, enol form of the Amadori rearrangement product (1-glycino-hex-2,3,4,5,6-ol-1-ene); 7, keto form of the Amadori rearrangement product (1-glycino-hex3,4,5,6-ol-2-one). X and Y refer the O[CH(OH)]2OCH2OH and OCH2OCO2H groups, respectively. Glurefers ␣-glucose (A-Glu), B-Glucose (B-Glu), or open-chain glucose (O-Glu).

Results and Discussion At a constant temperature and pressure, the ⌬G of a reaction indicates the spontaneity of the reaction, whereas ⌬E indicates the internal energy changes during the production of different compounds in the reaction. However, the ⌬G is a more useful parameter in obtaining information about the plausibility of different steps that may take place in a reaction. The ⌬G° for the formation of different compounds in the proposed mechanisms for Glu (O-Glu, A-Glu, and B-Glu)⫹Gly (UGly, PGly, DGly, and GlyZ) reaction under different pH conditions (Schemes 2 and 3) are presented in Table I. We have included the values of the ⌬E as well as

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JALBOUT ET AL. selected geometrical parameters of the studied complexes in the supplementary material. During the calculation of ⌬G°, O-Glu/A-Glu/B-Glu⫹ UGly/PGly/DGly/GlyZ total free energies (G°O-Glu/ ␣ -Glu/ ␤ Glu⫹G°UGly/PGly/DGly/GlyZ ) have been used as the standard in the equation ⌬G° ⫽ G°Product(s) ⫺ G°Reactant(s). Table I also represents ␮ of different compounds of the proposed mechanisms in gaseous state and aqueous solution. The total mass balance of any reaction is important as it is related to the energy changes. The total mass balance of the reaction under different pH conditions has been maintained during the calculation of ⌬G°. The main problem in balancing the

A-Glu

O-Glu + GlyZ

total mass arises for protonation and deprotonation. Therefore, the following equations have been used during balancing the total mass:

B-Glu

+ DGly N H -Y-

H-NH-Y-

H-NH-Y-

|

|

|

:O-CH

CHOH

|

|

IMR

CHOH

CHOH

CHOH

X [2b]

X [2a]

X [3a]

|

-H

NH-YCH2 |

C=O |

|

- H2O N-Y-

NH-Y|

|

KET

CH C-O-H |

IMR

CH |

H-COH |

CHOH

CHOH

CHOH

X [7a]

X

X

|

|

[6a]

water

hydroxonium ion

(protonation and deprotonation)

CHOH |

|

Proton

|

CHOH

|

H ⫹ ⫹ H 2O 7 H 3O ⫹

HC -OH

CHOH |

SCHEME 4. Formation of open-chain glucose (O-Glu) through the “formose reaction” of ribose (Rib) and formaldehyde (Fald), and cleavage of O-Glu to Rib.

|

[4a]

SCHEME 3. Proposed mechanisms for the formation of the Amadori rearrangement products in the initial stage of Glu⫹DGly and Glu⫹GlyZ Maillard reactions. Abbreviations: DGly, deprotonated glycine; GlyZ, glycine zwitter ion; IMR, intramolecular rearrangement. Numerical abbreviations: 2a, ionic addition adduct of Glu and DGly; 2b, ionic addition adduct of Glu and GlyZ; 3a, addition compound of Glu and DGly or GlyZ (1-deprotonated glycino-hex-1,2,3,4,5,6-ol); 4a, Schiff base of 3a; 6a, enol form of the Amadori rearrangement product (1-deprotonated glycino-hex-2,3,4,5,6-ol1-ene); 7a, keto form of the Amadori rearrangement product (1-deprotonated glycino-hex-3,4,5,6-ol-2-one). Y⫺ refers the OCH2OCO2H⫺ group. For other abbreviations, see the caption of Scheme 2.

A-Glu⫹UGly/PGly/DGly/GlyZ reactions. According to the ⌬G° (Table I), interconversion of A-Glu to B-Glu or O-Glu in A-Glu⫹UGly/PGly/ DGly/GlyZ reactions is not feasible in both of gaseous and aqueous solution, which is also supported by the ⌬E° values (see supplementary material). A-Glu⫹UGly reaction is feasible for the formation of protonated glucose, 1, the ionic addition adduct, 2 (1-protonated glycino-hex-1,2,3,4,5,6-ol), the ionic adduct, 5 (ionic adduct of the Schiff base of 1-glycino-hex-1,2,3,4,5,6-ol), and the keto form of the Amadori rearrangement product, 7 (1-glycino-hex3,4,5,6-ol-2-one) in both of gaseous state and aqueous solution (Table I). However, A-Glu⫹UGly reaction in aqueous solution is more favorable than the gaseous state reaction to produce different compounds in the proposed mechanism (Scheme 2). In both of gaseous state and aqueous solution, A-Glu⫹UGly reaction is found not to be favorable for producing the addition compound, 3 (1-glycinohex-1,2,3,4,5,6-ol), the Schiff base, 4 (Schiff base of 1-glycino-hex-1,2,3,4,5,6-ol), and the enol form of the Amadori rearrangement product, 6 (1-glycinohex-2,3,4,5,6-ol-1-ene). Therefore, it is assumed that in both of gaseous state and aqueous solution, AGlu may directly protonated to 1, which can consequently form 2. Furthermore, direct elimination of one molecule of H2O from 2 may lead to production of 5, and deprotonation and keto-enolic tau-

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B-Glu O-Glu 2a 2b 3a 4a 6a 7a

Compounds

— 14.0 12.0 ⫺300.5 ⫺416.4 85.7 75.9 ⫺377.9 115.7 ⫺18.1

16.0 2.5 ⫺31.1 — ⫺38.3 ⫺66.7 ⫺29.3 ⫺84.7

Gaseous

14.0 12.0 ⫺298.6 — ⫺235.0 ⫺247.4 ⫺251.0 ⫺275.0

Aqueous

〈-Glu⫹DGly

— 16.1 2.5 ⫺97.3 ⫺171.9 110.0 102.2 ⫺158.3 138.4 ⫺2.3

A-Glu B-Glu O-Glu 1 2 3 4 5 6 7

Aqueous

A-Glu⫹UGly

Gaseous

Compounds — 13.9 11.9 — ⫺177.5 324.6 314.8 ⫺139.0 354.6 220.7

16.32 2.4 — 72.3 687.3 659.0 696.3 641.0

Gaseous 13.9 11.9 — 6.4 567.7 555.2 551.7 527.7

Aqueous

〈-Glu⫹GlyZ

— 16.3 2.4 — 41.6 323.5 315.8 55.2 351.9 211.2

Aqueous

A-Glu⫹PGly Gaseous — — ⫺2.0 ⫺314.4 ⫺430.3 71.7 61.9 ⫺391.8 101.7 ⫺32.1

— ⫺13.63 ⫺47.1 — ⫺54.4 ⫺82.7 ⫺45.4 ⫺100.8

Gaseous — ⫺1.9 ⫺312.6 — ⫺249.0 ⫺261.4 ⫺265.0 ⫺289.0

Aqueous

B-Glu⫹DGly

— — ⫺13.6 ⫺113.3 ⫺188.0 94.0 86.2 ⫺174.4 122.3 ⫺18.4

Aqueous

B-Glu⫹UGly Gaseous — — ⫺1.9 — ⫺191.4 310.6 300.8 ⫺152.9 340.6 206.8

Aqueous

— ⫺13.51 — 56.2 671.3 642.9 680.3 624.9

Gaseous

— ⫺1.9 — ⫺7.6 553.7 541.3 537.7 513.7

Aqueous

B-Glu⫹GlyZ

Reactions

— — ⫺13.5 — 25.5 307.5 300.0 39.1 335.9 195.1

Gaseous

B-Glu⫹PGly

Reactions

— — — ⫺312.4 ⫺428.4 73.7 63.9 ⫺389.9 103.7 ⫺30.2

Aqueous

— — ⫺33.5 — ⫺40.8 ⫺69.1 ⫺31.8 ⫺87.2

Gaseous

— — ⫺310.6 — ⫺247.0 ⫺259.4 ⫺263.0 ⫺287.0

Aqueous

O-Glu⫹DGly

— — — ⫺99.7 ⫺174.4 107.5 99.8 ⫺160.8 135.9 ⫺4.8

Gaseous

O-Glu⫹UGly

— — — — ⫺189.4 312.6 302.8 ⫺150.9 342.6 208.8

Aqueous

— — — 69.8 684.8 656.5 693.8 638.5

Gaseous

— — — ⫺5.6 555.7 543.3 539.7 515.7

Aqueous

O-Glu⫹GlyZ

— — — — 39.1 321.1 313.3 52.7 349.4 208.7

Gaseous

O-Glu⫹PGly

— — 14.9 15.2 10.2 10.8 13.5 6.8

Gaseous

5.5 5.1 6.1 5.5 1.95 6.95 7.8 1.93 5.2 3.3

Gaseous

␮

␮

— — 17.4 18.1 12.9 13.2 16.5 8.8

Aqueous

6.9 6.2 7.5 6.4 2.6 9.15 9.9 1.97 6.4 3.96

Aqueous

TABLE I ________________________________________________________________________________________________________________________________ ⌬G° (in kJ/mol) for different compounds presented in Schemes 2 and 3.

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JALBOUT ET AL. tomerization (KET) of 5 may take place concurrently resulting in the formation of 7. In the gaseous state as well as in aqueous solution, both A-Glu⫹PGly and A-Glu⫹GlyZ reactions are found not feasible for producing all compounds in the proposed mechanisms (Schemes 1 and 2, Table I). Therefore, the rate of browning in A-Glu⫹PGly and A-Glu⫹GlyZ reactions is assumed to be hindered. Except B-Glu and O-Glu, A-Glu⫹DGly reaction is feasible for the formation of all other compounds in the proposed mechanism in gaseous state and aqueous solution (Scheme 2, Table I). A-Glu⫹DGly reaction favors the formation of both of the enol and keto forms of ARP (6a and 7a). Therefore, the rate of browning in A-Glu⫹DGly reaction is assumed higher than A-Glu⫹UGly reaction. Interconversion of B-Glu to O-Glu in B-Glu⫹ UGly/PGly/DGly/GlyZ reactions is feasible in both the gaseous state and in aqueous solution. However, the gaseous state reaction is more feasible than aqueous solution for the interconversion of B-Glu to O-Glu (Table I). This phenomenon is also supported by the ⌬E° values (in the supplementary material). Similar to A-Glu⫹UGly, B-Glu⫹UGly reaction is feasible for producing 1, 2, 5, and 7, and not for producing 3, 4, and 6 in both of gaseous state and aqueous solution (Table I). Therefore, it is assumed that elimination of one molecule of H2O from the consequently formed 2 (Scheme 1) may form 5, which may produce 7 through deprotonation and KET at the same time. Except O-Glu, B-Glu⫹UGly reaction in aqueous solution is more favorable than the gaseous state for producing all other compounds (Table I). B-Glu⫹PGly and B-Glu⫹GlyZ reactions are not feasible for producing all other compounds in the proposed mechanisms except for the interconversion of B-Glu to O-Glu in the gaseous state and in aqueous solution (Schemes 1 and 2, Table I). Therefore, similar to the A-Glu⫹PGly and A-Glu⫹GlyZ reactions, the rate of browning in B-Glu⫹PGly and B-Glu⫹GlyZ reactions is assumed to be lowered. In this mechanism, the B-Glu⫹DGly reaction favors formation of all compounds in the proposed mechanism (Scheme 2, Table I). Therefore, as in the A-Glu⫹DGly reactions, the B-Glu⫹DGly reaction is assumed to be more favorable than the B-Glu⫹UGly reaction in browning. Similar to the A-Glu⫹UGly and B-Glu⫹UGly, the O-Glu⫹UGly reactions also favors production of 1, 2, 5, and 7, and does not favors production of 3, 4, and 6 in both of gaseous state and aqueous solution (Table I). Hence, the consequently formed

2 (Scheme 1) may form 5 through the elimination of one molecule of H2O, and 7 may produce from 5 through deprotonation and KET at the same time. In producing different compounds in the proposed mechanism, the gaseous state O-Glu⫹UGly reaction is less favorable than that in aqueous solution (Table I). Except 2 and 5 in aqueous solution, O-Glu⫹PGly reaction is not favorable for forming all compounds in the proposed mechanisms (Scheme 2) in gaseous state and aqueous solution (Table I). The O-Glu⫹GlyZ reaction is not favorable for producing all compounds in the proposed mechanisms (Scheme 2, Table I). Therefore, the rate of browning in O-Glu⫹GlyZ reaction is assumed to be lower than the O-Glu⫹PGly reaction. Both gaseous and aqueous O-Glu⫹DGly reactions are favorable for producing all compounds in the proposed mechanism (Scheme 2, Table I). Therefore, similar to ␣-Glu⫹DGly and B-Glu⫹DGly reaction, the browning rate is assumed higher for O-Glu⫹DGly reaction than O-Glu⫹UGly reaction. In both the gaseous state and aqueous solution, interconversion of A-Glu to B-Glu or O-Glu in A-Glu⫹UGly/PGly/DGly/GlyZ reactions is not feasible, whereas interconversion of B-Glu to O-Glu in B-Glu⫹UGly/PGly/DGly/GlyZ reactions is feasible (Table I). The gaseous state B-Glu⫹UGly/ PGly/DGly/GlyZ reactions are more favorable for interconversion of B-Glu to O-Glu. Nucleophilic addition compounds of carbonyl and amino compounds are generally formed in the Maillard reaction [2– 4, 8]. In gaseous state and aqueous solution, A-Glu/B-Glu/O-Glu⫹UGly/ PGly/GlyZ reactions are not favorable for formation of the addition compound (3 or 3a), whereas A-Glu/B-Glu/O-Glu⫹DGly reactions favor producing the addition compound (3a) [Table I]. In producing 3a, B-Glu⫹DGly reaction is more feasible than ␣-Glu⫹DGly and O-Glu⫹DGly reactions in both of gaseous state and aqueous solution, and aqueous solution is more feasible than gaseous state (Table I). Dipole moments in gaseous state and aqueous solution (␮gas and ␮aq, respectively) of 3a is higher than 3, and for both 3 and 3a, ␮aq is higher than ␮gas (Table I). The addition compound, 3, is electronically more stable in gaseous state than aqueous solution in A-Glu/B-Glu/O-Glu⫹UGly reactions, and is less stable in gaseous state than aqueous solution in A-Glu/B-Glu/O-Glu⫹PGly reactions (see ⌬E values in supplementary materials). On the other hand, 3a is electronically more stable in gaseous state than aqueous solution in A-Glu/ B-Glu/O-Glu⫹DGly reactions, but less stable in

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FORMATION OF THE AMADORI REARRANGEMENT PRODUCTS gaseous state than aqueous solution in A-Glu/BGlu/O-Glu⫹GlyZ reactions as is evident from the data. The Schiff bases are one of the most common intermediates in the Maillard reaction, which can undergo further reactions to form intermediates that are more reactive [2– 4, 8, 16]. Production of the Schiff base (4 or 4a) in A-Glu/B-Glu/OGlu⫹UGly/PGly/GlyZ reactions is found not to be feasible, and A-Glu/B-Glu/O-Glu⫹DGly reactions facilitate production of the Schiff base (4a) [Table I]. The B-Glu⫹DGly reaction is more favorable than the A-Glu⫹DGly and O-Glu⫹DGly reactions for producing 4a in both the gaseous state and in aqueous solution (Table I). However, the B-Glu⫹DGly reaction in aqueous solution is more favorable than gaseous state for the formation of 4a (Table I). The ␮gas and ␮aq values of 4 is lower than 4a, and for both 4 and 4a, ␮aq is higher than ␮gas (Table I). ARPs are the primary precursors of melanoidines, and therefore, having great importance in the Maillard reaction [8, 17–20]. However, because of comparatively less stability of these species, their isolation and detection in the Maillard reaction is assumed to be complicated. ARPs readily undergo further reactions to produce melanoidines through the formation of relative deoxyosones. ARPs have been reported as less reactive than reductones, and about 10 –100 times more reactive than the parental reducing sugars [3, 17]. ARPs can be produced at physiological conditions if sufficient reactants are present and the reaction time is long enough [2– 4]. ARPs can be found in equilibrium with their cyclic forms. For example, ARPs, derived from the reaction between D-glucose and amino acids in aqueous solutions, have been found in equilibrium mixtures of the open and closed chain forms, furanoid and pyranoid structures, in which ␤-pyranoses predominate [2– 4]. Moreover, direct cleavage or retro-aldolization of ARPs, glucosylamines or Schiff bases may also take place in the reaction [2– 4, 8, 21]. In the gaseous state and in aqueous solution, A-Glu/B-Glu/O-Glu⫹PGly/ GlyZ reactions are not favorable for producing both of the enol and keto forms of ARP (6, 6a, 7, and 7a) [Table I]. Therefore, the browning reaction is assumed to be hindered under these conditions. It is in agreement with the previous statement that acidic or protonated forms of amino groups of amino compounds are not favorable for the Maillard reaction [2– 4]. Production of ARPs (6a and 7a) in A-Glu/B-Glu/O-Glu⫹GlyZ reactions is more unfeasible than production of ARPs (6 and 7) in

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A-Glu/B-Glu/O-Glu⫹PGly reactions (Table I). Therefore, the rate of browning in A-Glu/B-Glu/ O-Glu⫹GlyZ reactions is assumed to be lower than that of the A-Glu/B-Glu/O-Glu⫹PGly reactions. However, some other mechanisms may be involved under these conditions. A-Glu/B-Glu/O-Glu⫹ UGly reactions are only favorable for producing 7 and not for producing 6, whereas A-Glu/B-Glu/OGlu⫹DGly reactions are favorable for producing both 6a and 7a (Table I). Therefore, the rate of browning in A-Glu/BGlu/O-Glu⫹DGly reactions is assumed to be higher than that of the A-Glu/B-Glu/O-Glu⫹UGly reactions. It is in agreement with the previous reports that the basic condition facilitates the Maillard reaction spontaneously [2– 4]. The B-Glu⫹UGly reaction is more feasible for producing ARPs than the A-Glu⫹UGly and O-Glu⫹UGly reactions (Table I). Similarly, the B-Glu⫹DGly reaction is more favorable for the production of ARPs than A-Glu⫹DGly and O-Glu⫹DGly reactions (Table I). In producing ARPs, aqueous solution is more favorable than gaseous state of A-Glu/B-Glu/O-Glu⫹UGly/DGly reactions (Table I). Values of ␮gas and ␮aq for 6 and 6a are found as higher than 7 and 7a, respectively (Table I). According to the total mass balance of the reaction, water plays an important role in A-Glu/ B-Glu/O-Glu⫹UGly/PGly/DGly/GlyZ reactions. Water is necessary for the initiation of the reaction. One molecule of water in the initial step for each of A-Glu/B-Glu/O-Glu⫹UGly/DGly reactions is necessary for balancing the total mass, whereas two molecules of water for each are needed in the initial step of A-Glu/B-Glu/O-Glu⫹PGly/GlyZ reactions. It is in agreement with the earlier findings that water is essential for the Maillard reaction to take place [2– 4, 22–25]. On the basis of the total mass balance, water is also a by-product in the reaction, which can be involved in further reactions to produce more melanoidines. During the formation of ARPs, one molecule of water is produced as by-product in each of A-Glu/B-Glu/O-Glu⫹UGly/ PGly/DGly/GlyZ reactions. It is also in consistence with previous reports that water is a by-product in the Maillard reaction [2– 4]. The ⌬G°gas and ⌬G°aq values for the formation of O-Glu Glu through the “formose reaction” of Rib and Fald (Scheme 4) are found as 18.8 kJ/mol and ⫺3.4 kJ/mol calculated by using Rib⫹Fald free energies (G°Rib⫹Fald) as the standard in the ⌬G° ⫽ G°Product(s) ⫺ G°Reactant(s) expression. It reveals that formation of O-Glu from Rib and Fald is suitable in

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JALBOUT ET AL. aqueous solution, which is also supported by ⌬E° (displayed in the supplementary material). The same value for ⌬G° with opposite signs (⫺18.8 kJ/ mol) are found for the formation of Rib through the cleavage of O-Glu (Scheme 4), obtained by using O-Glu free energy (G°O-Glu) as in the ⌬G° ⫽ G°Product(s) ⫺ G°Reactant(s) equation. It reveals that formation of Rib through the cleavage of O-Glu is more feasible in gaseous state than aqueous solution, and Rib, formed through this way, is electronically more stable in gaseous state than aqueous solution.

Conclusion It is clear from the present DFT study that both open (O-Glu) and closed chain glucose (A-Glu and B-Glu) can perform in the Maillard reaction involving Gly species (UGly, PGly, DGly, and GlyZ). The reaction under acidic conditions and at the isoelectric point of glycine is not favorable for the formation of ARPs. The reaction under neutral conditions is only favorable for producing the enol form of ARP, whereas the reaction under basic conditions is favorable for producing both of the enol and keto forms of ARP. Basic conditions also favor production of the addition compound and the Schiff base. Therefore, the rate of browning under basic conditions is assumed higher than that of the others. B-Glu⫹DGly reaction under basic condition is found as the most favorable to produce ARPs, and aqueous solution is more favorable than gaseous state reaction. Interconversion of B-Glu to O-Glu is found as favorable, and therefore both B-Glu and O-Glu can perform in the reaction, resulting into more browning compounds. Interconversion of A-Glu to B-Glu or OGlu is found to be unfavorable, and therefore, the rate of browning in A-Glu⫹DGly reaction is lower than the B-Glu⫹DGly reaction. Overall, the reaction under basic conditions is most favorable for following the general Hodge-scheme [8] of the Maillard reaction. ACKNOWLEDGMENT We appreciate the financial and computational resources allocated for the current investigations from the UNAM and the Mexican government. Geometrical parameters, ⌬E values and other information can be found in the supplementary material of this article.

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