Kinetic modelling of Amadori N-(1-deoxy-D-fructos-1-yl)-glycine degradation pathways. Part II - Kinetic analysis

Article abstract of DOI:10.1016/S0008-6215(03)00174-5

A kinetic model for N-(1-deoxy-D-fructos-1-yl)-glycine (DFG) thermal decomposition was proposed. Two temperatures (100 and 120°C) and two pHs (5.5 and 6.8) were studied. The measured responses were DFG, 3-deoxyosone, 1-deoxyosone, methylglyoxal, acetic acid, formic acid, glucose, fructose, mannose and melanoidins. For each system the model parameters, the rate constants, were estimated by non-linear regression, via multiresponse modelling. The determinant criterion was used as the statistical fit criterion. Model discrimination was performed by both chemical insight and statistical tests (Posterior Probability and Akaike criterion). Kinetic analysis showed that at lower pH DFG 1,2-enolization is favoured whereas with increasing pH 2,3-enolization becomes a more relevant degradation pathway. The lower amount observed of 1-DG is related with its high reactivity. It was shown that acetic acid, a main degradation product from DFG, was mainly formed through 1-DG degradation. Also from the estimated parameters 3-DG was found to be the main precursor in carbohydrate fragments formation, responsible for colour formation. Some indication was given that as the reaction proceeded other compounds besides DFG become reactants themselves with the formation among others of methylglyoxal. The multiresponse kinetic analysis was shown to be both helpful in deriving relevant kinetic parameters as well as in obtaining insight into the reaction mechanism.

Full text of DOI:10.1016/S0008-6215(03)00174-5

Carbohydrate Research 338 (2003) 1665ꢀ1678
/
www.elsevier.com/locate/carres
Kinetic modelling of Amadori N-(1-deoxy-
D
-fructos-1-yl)-glycine
degradation pathways. Part II*Kinetic analysis
/
Sara I.F.S. Martins, Martinus A.J.S. Van Boekel*
Department of Agrotechnology and Food Sciences, Product Design and Quality Management Group, Wageningen University, P.O. Box 8129, 6700 EV,
Wageningen, The Netherlands
Received 11 December 2002; accepted 11 April 2003
Abstract
A kinetic model for N-(1-deoxy-D-fructos-1-yl)-glycine (DFG) thermal decomposition was proposed. Two temperatures (100 and
20 8C) and two pHs (5.5 and 6.8) were studied. The measured responses were DFG, 3-deoxyosone, 1-deoxyosone, methylglyoxal,
1
acetic acid, formic acid, glucose, fructose, mannose and melanoidins. For each system the model parameters, the rate constants,
were estimated by non-linear regression, via multiresponse modelling. The determinant criterion was used as the statistical fit
criterion. Model discrimination was performed by both chemical insight and statistical tests (Posterior Probability and Akaike
criterion). Kinetic analysis showed that at lower pH DFG 1,2-enolization is favoured whereas with increasing pH 2,3-enolization
becomes a more relevant degradation pathway. The lower amount observed of 1-DG is related with its high reactivity. It was shown
that acetic acid, a main degradation product from DFG, was mainly formed through 1-DG degradation. Also from the estimated
parameters 3-DG was found to be the main precursor in carbohydrate fragments formation, responsible for colour formation. Some
indication was given that as the reaction proceeded other compounds besides DFG become reactants themselves with the formation
among others of methylglyoxal. The multiresponse kinetic analysis was shown to be both helpful in deriving relevant kinetic
parameters as well as in obtaining insight into the reaction mechanism.
#
2003 Elsevier Science Ltd. All rights reserved.
Keywords: Amadori compound; N-(1-Deoxy-D-fructos-1-yl)-glycine; Maillard reaction; Multiresponse kinetic analysis
1. Introduction
the sense that it describes not only the way in which the
rate of the slowest step of a reaction changes with
reaction variables, e.g., temperature and pH, but also
that those changes can be predicted in a quantitative
way.
The control of N-(1-deoxy-
(
D
-fructos-1-yl)-glycine
DFG) degradation pathways is a subject in chemical
kinetics and can be treated in the same way as any
chemical reaction, that is by measuring the concentra-
tions of the reactants, intermediates and products with
time. General kinetic data describing Maillard reaction
pathways are lacking. Also, most studies apply simple
kinetics, which does not provide any understanding of
Concerning Amadori compound decomposition ki-
3
ꢀ6
netics only few studies have been published,
from
which only the first had ARP as starting reactant and
still simple kinetics was applied. The multiresponse
kinetics analysis considers reaction pathways in more
detail. It provides extra information about the reaction
mechanism since the reactants degradation is analyzed
simultaneously with the intermediates formation. The
advantage is that the information in various responses
can be used simultaneously so that more precise para-
meter estimates and more realistic models can be
determined. The following steps should be taken into
1
,2
the reaction mechanism. The use of kinetic simulation
techniques for predicting and controlling properties of
interest for the chemical and food industry is becoming
increasingly important. The kinetic approach is useful in
*
Corresponding author. Tel.: ꢁ
17-483669.
E-mail address: tiny.vanboekel@wur.nl (M.A.J.S. Van
Boekel).
/
31-317-484281; fax: ꢁ31-
/
3
7
account: (i) identification and quantification of the
reactants and main products formed; (ii) identification
0008-6215/03/$ - see front matter # 2003 Elsevier Science Ltd. All rights reserved.
doi:10.1016/S0008-6215(03)00174-5

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S.I.F.S. Martins, M.A.J.S. Van Boekel / Carbohydrate Research 338 (2003) 1665ꢀ1678
/
of reaction pathways based on reaction conditions; (iii)
differentiate between primary and secondary reaction
routes; (iv) propose a kinetic model based on the
established reaction network; (v) test the hypothesized
3.1. Simple kinetics
Disregarding the actual mechanism or the number of
3
steps involved, Yaylayan and Forage assumed a
pseudo-first-order reaction in determining the degrada-
tion kinetics of Amadori product of tryptophan and D-
8
mechanism; (vi) estimate the rate constants. In Part I
the chemistry behind the degradation pathways of DFG
was extensively discussed, dealing with the initial three
steps. The present paper (Part II) is a follow up for the
complete multiresponse kinetic analysis of the thermal
degradation pathways of DFG. It deals with the last
three steps: the kinetic analysis of the reaction network
model proposed. One should keep in mind that kinetic
modelling is an iterative process: propose a model,
confront it with experimental data, criticize the model,
adjust the model and confront the adapted model with
experiments again, until an acceptable model results.
What acceptable is, is of course debatable and we will
discuss it by comparing two different possible models.
This paper can be seen as a stepping stone for a
complete kinetic analysis of the whole Maillard reaction,
as will be described in subsequent papers.
Glc. Taking this result into account, when applying
simple kinetics to the thermal degradation of DFG we
observed that DFG disappearance followed indeed a
first-order reaction model; that is Cꢂ
/
C exp(ꢃ
/
kt),
0
where
(mmol l ), C is the initial reactant concentration, k
C
ꢃ1
is the concentration of the reactant
0
the reaction rate constant and t time (min). However, no
real distinction could be made between other kinetic
orders, in particular for the reaction conditions at
100 8C and pH 5.5 (Fig. 1). First- and second-order
plots are almost the same. In fact, when optimising the
fit of the curve to the data by minimizing the sum of
squares, the reaction order was estimated to be 1.6 with
a 95% confidence interval of 0.83ꢀ2.4. These results
/
show that the use of simple kinetics is very limited. It is
important to realize that the simple kinetics approach is
actually only a mathematical fit procedure disregarding
the actual mechanism or the number of steps involved.
2
. Material and methods
2
.1. Kinetic modelling
3
.2. Complex kinetics
/
multiresponse kinetic analysis
*
Based on the established reaction network a kinetic
model was proposed and translated into a mathematical
model by setting-up differential equations for each
reaction step. The software package Athena Visual
Workbench was used for numerical integration as
well as for parameter estimation. The model parameters,
the rate constants, were estimated by non-linear regres-
sion using the determinant criterion, that is to mini-
mize the determinant of the matrix of cross-products of
the various responses, so called dispersion matrix. To
discriminate between models, a multivariate test of
goodness-of-fit was used together with two model
discrimination tests. The goodness-of-fit test is installed
in the used software package. It gives a sampling
probability by which the adequacy of the model can
be judged and was based on replicate experiments. The
model discrimination tests used were the posterior
A step further in the kinetic analysis is to consider
reaction paths in more detail. The chemistry behind the
degradation pathways of DFG has been extensively
discussed in Part I and from this, a reaction network
model was established which is summarized in Scheme
8
9
1
. The main pathways (primary routes) for the DFG
degradation are presented together with alternative
pathways that at this stage are considered as secondary.
However, confronted with the results some of the
1
0
1
1
probability (PPB), which requires replicates or an
estimation of experimental uncertainty, and the Akaike
Criterion (AIC).
1
2
3
. Results and discussion
Most literature reports regarding the kinetics of Mail-
lard reaction use simple kinetics to describe reactants
degradation or products formation. Therefore, a com-
parison with multiresponse kinetic analysis was made in
the present study.
Fig. 1. Simple kinetics analysis of N-(1-deoxy-
glycine (DFG) thermal degradation at 100 8C, pH 5.5.
Comparison of a first-order (*), estimated order of 1.6 (---)
and second-order (ꢀ ) plot.
D-fructos-1-yl)-
/
/
ꢀ
/

S.I.F.S. Martins, M.A.J.S. Van Boekel / Carbohydrate Research 338 (2003) 1665ꢀ
/
1678
1667
sugars it was assumed that Glc and Man were formed
through the same intermediate (E ) whereas fructose
1
(Fru) was preferably formed by E , even though
theoretically it can also be formed through E . The
2
1
main reason for this is that Fru was not detected at the
lower pH studied and, while E is favoured at lower pH,
1
8,19
1
E is favoured at higher pH.
However, for modelling
purposes both hypotheses were compared. Moreover,
2
Man and Glc can isomerise into each other as well as
degrade into Cn (n 56) carbonyl compounds. In the
/
sugar isomerization step it was concluded that neither
Glc nor Man isomerised into Fru, since no lag phase
2
0
was observed in its formation. From a previous study
where the kinetics of monosaccharides isomerization
was studied in alkaline conditions it was reported that
ꢃ3
ꢃ1
Man isomerised into Glc at a rate of 18ꢄ
/10
min
while the reverse was approximately half (7ꢄ
/
10ꢃ3
min ), as well as the degradation of Man into C
ꢃ1
Scheme 1. Established reaction network for DFG thermal
n
2
1
(
n 56) compounds. Also MacLaurin and Green came
/
degradation. Primary routes (
and E
/
); Secondary routes (---). E
1
are unidentified key compounds involved in rate-
*
to the same conclusion. These literature results suggest
that Man degrades preferably into Glc rather than into
carbonyl compounds. Concerning Glc the rate of its
2
determining steps that can be the Schiff’s base, the cation form
of the Schiff’s base, the 1,2 enaminol or the 2,3-enaminol,
respectively. Glycine (Gly); methylglyoxal (MG); Glc; Man;
fructose (Fru); acetic acid (AA); formic acid (FA); 3-deox-
yosone (3-DG); 1-deoxyosone (1-DG); unidentified carbohy-
degradation into C (n 56) compounds was found to be
/
n
20,21
higher than its rate of isomerization into Man.
As a
result the degradation step of Glc into Man was
neglected. The degradation of glycine was assumed to
occur only by reaction with carbonyl compounds
leading to melanoidins (Mel) formation. The Strecker
degradation (STD) to produce the corresponding
amines, carboxylic acids and Strecker aldehydes was
considered to be a minor step. These assumptions lead
us to the model presented in Scheme 2.
To fit the model to the experimental data, the reaction
network presented in Scheme 2 needs to be translated
into a mathematical model. This is done by setting-up
differential equations for each reaction step, using the
law of mass action:
n
drate fragments (C ); Strecker degradation products (STD).
secondary routes might turn into primary routes and
vice-versa. As stated above, one should be aware that
kinetic modelling is an iterative process.
3.3. Propose a kinetic model based on the established
reaction network
For modelling purposes the reaction network model
presented was simplified. The degradation of DFG
through enolization requires two intermediates E (1,2-
1
enolization) and E (2,3-enolization) which was assumed
2
1
3,14
d[DFG]
to have the amino acid still incorporated.
Due to
ꢂꢃk [DFG]ꢃk [DFG]ꢃk [DFG]
(1)
(2)
(3)
(4)
(5)
(6)
(7)
1
2
3
dt
their reactivity these compounds have not been isolated
yet from the Maillard reaction. However, in terms of
modelling it is an important step to take into account.
Moreover, besides the enolization step, DFG also
degrades through retro-aldolization reaction with the
formation of methylglyoxal (MG) together with uni-
d[E1]
ꢂk [DFG]ꢃk [E ]ꢃk [E ]ꢃk [E ]
1
4
1
10
1
11
1
dt
d[E ]
2
ꢂk [DFG]ꢃk [E ]ꢃk [E ]
2
7
2
16
2
dt
dentified carbonyl compounds (C ) and release of the
n
1
5,16
d[MG]
amino acid.
intermediate in between. The intermediates E and E by
It was assumed to be a fast step with no
ꢂk [DFG]
3
dt
1
2
release of glycine lead to the formation of 3-deoxyosone
3-DG) and 1-deoxyosone (1-DG), respectively. 3-DG
and 1-DG, due to their reactive functional group, can
easily degrade to produce reactive C (n 56) carbonyl
d[3DG]
dt
ꢂk [E ]ꢃk [3DG]ꢃk [3DG]
(
4
1
5
6
d[1DG]
dt
/
n
ꢂk [E2]ꢃk [1DG]ꢃk [1DG]
1
7
7
8
9
compounds as well as organic acids. As we mentioned
8
in Part I, the acids formation occurs preferably by
d[Man]
direct cleavage of 3-DG and 1-DG with formic and
acetic acid formation, respectively. Concerning the
ꢂk [E ]ꢃk [Man]
10 1 12
dt

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S.I.F.S. Martins, M.A.J.S. Van Boekel / Carbohydrate Research 338 (2003) 1665ꢀ1678
/
was slightly overestimated, while formic acid and
melanoidins were underestimated at the beginning and
overestimated at the end of heating period. Similar
results were obtained at 100 8C, pH 5.5. When the pH
was increased to 6.8 (Fig. 2B) there was clearly a miss fit
for the organic acids formation, namely for formic acid,
as well as for Glc. Both compounds were underesti-
mated. Also a lack of fit was observed for MG
formation. It was overestimated at the beginning and
underestimated as the reaction proceeded. The results
forced us to reconsider the kinetic model. This shows the
power of the iterative modelling approach. To begin
with, an extra step was added to the model. Incorporat-
ing step 15 as a primary route would induce both formic
acid (C ) and acetic acid (C ) formation from MG (C ).
Scheme 2. First proposed kinetic model, Model 1 (M
on the established reaction network. Primary routes (
1
), based
/);
*
1
2
3
Secondary routes (---). E1 and E2 are unidentified key
compounds involved in rate-determining steps that can be
the Schiff’s base, the cation form of the Schiff’s base, the 1,2
enaminol or the 2,3-enaminol, respectively. Glycine (Gly);
methylglyoxal (MG); glucose (Glu); mannose (Man); fructose
Not only the underestimation of formic acid could be
solved as well as it would induce 3-DG, instead of Glc,
to form more C (n 56). However, it appeared that the
/
n
estimation of this parameter lead to an indeterminate
result for all the studied systems, which means that this
step is not important for the model. Also it suggests that
the organic acids formation does not result from MG
degradation.
(Fru); acetic acid (AA); formic acid (FA); 3-deoxyosone (3-
DG); 1-deoxyosone (1-DG); unidentified carbohydrate frag-
ments (C ); melanoidins (Mel). A (secondary route) and B
n
(
primary route) hypothesis for fructose formation.
From a chemical point of view it is clear that the
2
model is not completely correct. Isbell and co-workers
2
d[Glc]
dt
ꢂk [E ]ꢁk [Man]ꢃk [Glc]
(8)
(9)
11
1
12
13
have postulated the existence of cis- and trans-isomers
of the 1,2-endiol to explain the transformation of
various sugars. It was suggested that both enolization
and ring opening might be involved in the rate-
determining steps of the process. Moreover, the relative
d[Fru]
dt
ꢂk [E ]
16
2
d[FA]
dt
ꢂk [3DG]
(19)
(11)
6
rates of enolization for Glc and Man were found to be
ꢃ1
1.0 and 0.5 h , respectively. If that is the case then Glc
has a higher ability to transform into 1,2-endiol and not
d[AA]
dt
ꢂk [1DG]
9
so much to degrade into sugar fragments (C ) involved
n
in colour formation. Apparently, the transformation
step of Glc into 3-deoxyosone that initially has been
considered as a secondary route might be in fact a
primary route. Also, the observation that at the begin-
ning of the reaction MG was overestimated leads us to
the assumption that a rate-determining intermediate
might be formed previously to MG. The initial assump-
tion that MG formation from DFG was a fast step
might not be correct.
When calculating the reaction mass balance (evolu-
tion of each intermediate towards the reactant (DFG)
initial concentration) we observe that at the initial stage
of the reaction the products identified and quantified in
the present study do not count for the total DFG
degradation. However, as the degradation reaction
proceeded, within experimental error, 100% was
reached. In Fig. 3, we can observe the results for pH
6.8. Besides melanoidins, and glycine, the other main
d[Gly]
dt
ꢂk [DFG]ꢁk [E ]ꢁk [E ]ꢁk [E ]ꢁk [E ]
3
4
1
10
1
11
1
7
2
ꢁ 16
k [E ]ꢃk [Gly][C ]
(12)
2
14
n
d[Cn]
ꢂk [DFG]ꢁk [3DG]ꢁk [1DG]ꢁk [Glc]
3
5
8
13
dt
ꢃk [Gly][C ]
(13)
(14)
14
n
d[Mel]
ꢂk [Gly][C ]
14
n
dt
These coupled differential equations are difficult to
solve analytically but can be solved by numerical
integration. Nowadays different software packages are
able to this, like Nsolve or Mathematica. In the present
study, the used subroutine was DDAPLUS, which is
available in the software package Athena Visual Work-
9
bench. The results of the fit for the experimental data at
5
1
20 8C are presented in Fig. 2 (A and B).
For the reaction conditions at pH 5.5 the model fitted
end products obtained were the organic acids, in
8
particular acetic acid, as mentioned in Part I.
possible explanation for the observed gap is that, as
A
the data reasonably well (Fig. 2A). Note that the
observations were done in at least duplicate. Glycine
the reaction proceeds besides DFG other compounds

S.I.F.S. Martins, M.A.J.S. Van Boekel / Carbohydrate Research 338 (2003) 1665ꢀ
/
1678
1669
formed during its degradation become reactants them-
selves with the formation of the same end products.
As a result a modified simplified model is proposed,
as shown in Scheme 3. To fit the model to the
experimental data, the same procedure was taken by
coupling differential equations to each reaction step.
The approach of numerical integration followed by
fitting to the data is flexible because changing relevant
differential equations and fitting them to experimental
data can easily test different models. The results of the
fit for the experimental data taken at all the studied
systems are presented in Figs. 4ꢀ7.
/
A major improvement in the organic acids fit was
observed, as well as in the sugars and MG formation.
Independently of the reaction conditions the model
seems to fit the experimental data quite well. However,
an important question is still not clear: is Fru preferably
formed through E or E ? To answer this question both
1
2
hypotheses (A and B, respectively) were tested for both
proposed models, through model discrimination.
Fig. 2. Model 1 fit (lines) to experimental data (dots) of DFG thermal degradation at 120 8C: pH 5.5 (A) and 6.8 (B). Glycine (Gly);
methylglyoxal (MG); Glc; Man; fructose (Fru); acetic acid (AA); formic acid (FA); 3-deoxyosone (3-DG); 1-deoxyosone (1-DG).

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S.I.F.S. Martins, M.A.J.S. Van Boekel / Carbohydrate Research 338 (2003) 1665ꢀ
/
1678
Fig. 2 (Continued)
9
,10
3.4. Test the hypothesized mechanism (goodness-of-fit
and model discrimination)
before
and was based on replicate experiments. Apart
from each model there is an error associated with the
data, the experimental error. If this is too high any
model is in principle able to fit the data. However, if the
experimental error is small the discrimination between
the data and the model estimation gives a better
understanding how good the model fits the data. As
The question how well the proposed model describes the
experimental data must be addressed from a statistical
point of view. One could be led to choose a poor model
because it was not as bad as the other models. To avoid
such a mistake it is recommended to use a multivariate
can be seen in the Figs. 4ꢀ7, the scatter in replicates was
not very high which allowed a goodness-of-fit test. The
quality of experimental data is therefore very important.
/
1
1
test of goodness-of-fit (or its counterpart lack-of-fit).
This test is installed in the same software package as

S.I.F.S. Martins, M.A.J.S. Van Boekel / Carbohydrate Research 338 (2003) 1665ꢀ
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1678
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Scheme 3. Second proposed kinetic model, Model 2 (M2),
based on the established reaction network. E and E are
1
2
unidentified key compounds involved in rate-determining steps
that can be the Schiff’s base, the cation form of the Schiff’s
base, the 1,2 enaminol or the 2,3-enaminol, respectively.
Glycine (Gly); methylglyoxal (MG); Glc; Man; fructose
(
Fru); acetic acid (AA); formic acid (FA); 3-deoxyosone (3-
DG); 1-deoxyosone (1-DG); unidentified carbohydrate frag-
ments (C ); melanoidins (Mel). A (secondary route) and B
primary route) hypothesis for fructose formation.
n
(
absolute one, meant for comparison. It provides in-
formation about the most plausible model, not necessa-
rily the true one. In model construction additions of
parameters are favored when they yield higher posterior
probabilities; deletions are favored when they do not
make the PPB appreciably worse.
Fig. 3. Mass balance: evolution of each intermediate towards
the reactant initial concentration in heated N-(1-deoxy-
D
-
fructos-1-yl)-glycine (DFG) at 100 8C, pH 6.8 (A) and 120 8C,
pH 6.8 (B). Glycine (Gly); Deoxyosones (DG); Sugars (Sug);
organic acids (OA); methylglyoxal (MG); melanoidins (Mel).
However, it is also known that the higher the number
1
of parameters the better fit the fit will be. In order to
The fit of the mathematical model to the data was done
simultaneously with parameter estimation, which will be
addressed in Section 3.5.
have a second opinion the model discrimination was
1
2
also performed by using the Akaike criterion (AIC)
which, can be expressed in the case of least-squares
approximation as:
As mentioned before, kinetic modelling is an iterative
process: propose a model, confront it with experimental
data, criticise the model, adjust the model and confront
the adapted model with experiments again, until an
acceptable model results. What is acceptable though, is
of course debatable. Alternative models may be formed
from a candidate model by adding or deleting para-
meters. Once models show an acceptable fit, there may
still be many models left, so the next step is model
2
AICꢂn ln(s )ꢁ2(pꢁ1)
(15)
and the maximum likelihood estimator for the variance
is:
SS
2
s ꢂ n
(16)
1 to
in which p is the number of estimated parameters (ꢁ
/
2
3
discrimination. According to the Bayesian concept, on
which Athena Visual Workbench is based, the plausi-
bility of a model results from the combination of
likelihood (given by the data) with prior probability
include the variance estimate). The 2p term is the
penalty in the Akaike criterion for the use of more
parameters. When the number of data points n is
relatively small compared to p (say n/p B40) the
/
corrected AIC should be used:
ꢀ
(
given by previous results or personal belief). This
ꢁ
combination is called Posterior Probability (PPB). The
model with the highest posterior probability performs
then the best. It is required to have replicates (or an
estimate of experimental uncertainty) in order to execute
model discrimination. It is a relative concept, not an
n
2
AIC ꢂn ln(s )ꢁ2(pꢁ1)
c
n ꢃ p
Because the AIC criterion is on a relative scale it is
common practice to calculate AIC differences, taking

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/
Fig. 4. Model 2 (M2) fit (lines) to experimental data (dots) of N-(1-deoxy-
D-fructos-1-yl)-glycine (DFG) thermal degradation at
100 8C and pH 5.5. Glycine (Gly); methylglyoxal (MG); Glc; Man; acetic acid (AA); formic acid (FA); 3-deoxyosone (3-DG); 1-
deoxyosone (1-DG).
the model with the lowest value (AICmin) as the
reference:
3) using PPB and the AIC criterion. At lower pH (Table
1) according to the Akaike criterion the results are
contradictory. At 100 8C, M is less supported whereas
2
DAIC ꢂAICꢃAICmin
(17)
at 120 8C M1 can be discarded, which was also
supported by the PPB values. It should be taken into
account that under these conditions (pH 5.5), for the
studied heating period, the DFG degradation rate is
quite small as well as the amount of products formed,
which gives the models more flexibility to fit the
experimental data. When the pH was increased to 6.8
A rule of thumb is that models with DAIC
5
/
2ꢀ
/
3 are
worthwhile to consider, values of DAIC between 4 and 7
indicate that models are less supported, and values
higher than 10 indicate that models may be discarded.
In Tables 1 and 2 the results of the model discrimina-
tion tests are shown for M (Scheme 2) and M (Scheme
1
2

S.I.F.S. Martins, M.A.J.S. Van Boekel / Carbohydrate Research 338 (2003) 1665ꢀ
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1678
1673
Fig. 5. Model 2 (M2) fit (lines) to experimental data (dots) of N-(1-deoxy-
20 8C and pH 5.5. Glycine (Gly); methylglyoxal (MG); glucose (Glu); mannose (Man); acetic acid (AA); formic acid (FA); 3-
deoxyosone (3-DG); 1-deoxyosone (1-DG).
D-fructos-1-yl)-glycine (DFG) thermal degradation at
1
(Table 2), besides M and M model discrimination,
hypotheses A and B for Fru formation via E and E ,
discrimination tests, it was clear that M2 performed
better than M . Also the obtained fits at pH 6.8 come
1
2
1
2
1
respectively, were also tested. Note that this test is only
relevant for the systems at pH 6.8, since at lower pH Fru
was not detected. According to the Akaike criterion,
independently of the chosen hypothesis A or B, M2
always performed better than M . The results for M
into agreement with this conclusion. When comparing
hypotheses A and B for M the PPB values as well as the
2
AIC values of hypothesis B are higher than those of
hypothesis A.
These results suggest that fructose was mainly formed
1
1
indicated that this model could be discarded (DAIC
1
]
/
through the intermediate E
2
, supporting the assumption
made in Part I. Also that model M is more likely than
model M , giving some evidence that the transformation
8
0). These findings are confirmed by the obtained PPB
2
values that were always higher in M . As for both model
2
1

1674
S.I.F.S. Martins, M.A.J.S. Van Boekel / Carbohydrate Research 338 (2003) 1665ꢀ1678
/
Fig. 6. Model 2 (M2) fit (lines) to experimental data (dots) of N-(1-deoxy-
D-fructos-1-yl)-glycine (DFG) thermal degradation at
100 8C and pH 6.8. Glycine (Gly); methylglyoxal (MG); glucose (Glu); mannose (Man); acetic acid (AA); formic acid (FA); 3-
deoxyosone (3-DG); 1-deoxyosone (1-DG).
step of Glc into 3-deoxyosone that initially has been
considered as a secondary route might be in fact a
primary route and that the initial assumption that MG
formation from DFG was a fast step was indeed not
correct.
step is to fit the model to the experimental data to obtain
estimates for the model parameters, i.e., the rate
constants. In general, this is accomplished by solving
an optimization problem in which the objective function
(the function being minimized or maximized) relates the
response variable and the functional part of the model,
in a way that will produce parameter estimates that will
be closest to the true, unknown parameter values. In
3
.5. Estimate the rate constants
4
,5
previous studies with multi-step kinetic analysis of
glucoseꢀamino acid Maillard reaction the approach
As mentioned before, once the basic form of the
functional part of the model is established, the next
/

S.I.F.S. Martins, M.A.J.S. Van Boekel / Carbohydrate Research 338 (2003) 1665ꢀ
/
1678
1675
Fig. 7. Model 2 (M2) fit (lines) to experimental data (dots) of N-(1-deoxy-
D-fructos-1-yl)-glycine (DFG) thermal degradation at
120 8C and pH 6.8. Glycine (Gly); methylglyoxal (MG); glucose (Glu); mannose (Man); acetic acid (AA); formic acid (FA); 3-
deoxyosone (3-DG); 1-deoxyosone (1-DG).
Table 1
Model discrimination tests for the systems studied at pH 5.5
a
System
Model
Parameters
SS
5.14
n
AICc
DAICc
PPB
A (100 8C)
M
M
1
2
14
15
13
15
100
100
90
ꢃ
/
261.92
250.96
117.22
128.72
0
34.11
32.28
14.78
17.65
5.58
17.01
14.05
ꢃ
/
10.96
11.50
0
B (120 8C)
M1
M2
ꢃ
/
90
ꢃ
/
a
1 2
Model 1 (M ) presented in Scheme 2; Model 2 (M ) presented in Scheme 3.

1676
S.I.F.S. Martins, M.A.J.S. Van Boekel / Carbohydrate Research 338 (2003) 1665ꢀ1678
/
Table 2
Model discrimination tests for the systems studied at pH 6.8
System
Hypotheses
A
Model *
Parameters
SS
n
AIC
c
D
AICc
PPB
C (100 8C)
M
1
14
14
13
15
12
15
13
15
50.05
8.69
99
99
99
99
ꢃ
/
32.60
173.32
0
127.86
16.20
19.80
15.78
21.25
Indt.
29.09
14.59
21.77
M2
M1
ꢃ
/
205.92
D (120 8C)
C (100 8C)
D (120 8C)
A
B
B
49.85
12.96
754.67
9.61
ꢃ
/
35.69
M
M
2
1
ꢃ
/
163.55
0
423.88
a
99 230.67
M2
99
99
99
ꢃ
/
193.21
0
M
M
1
2
49.08
13.32
ꢃ
/
37.22
123.62
0
ꢃ
/
160.85
*
a
Model 1 (M ) presented in Scheme 2; Model 2 (M ) presented in Scheme 3.
1
2
Indeterminate (low trust region).
used was to minimize the overall residual sum of squares
RSS) from all the responses. However, the RSS
in Scheme 3 (M ) using the determinant criterion are
2
8
shown in Table 3. The assumptions made in Part I can
(
criterion is based on the assumption that the data on
each response have the same variance and there is no
correlation between the variances of the individual
measurements of the response, which is not very
realistic. In the present study several responses were
measured from which some were measured from the
same sample (e.g., formic and acetic acid) and with
different degrees of precision. For cases of multire-
sponse modelling the fit criterion to be used depends on
the experimental error structure of the data. Box and
Draper provided a solution for this problem assuming
normally distributed errors. The best-fit criterion is the
minimization of the determinant of the matrix of cross-
products of the various responses, the so-called disper-
sion matrix from the responses. If the determinant of the
dispersion matrix is minimized, the most probable
estimates of the parameter will be found. The resulting
parameter estimates for the hypothesized B mechanism
now be confronted with the estimated rate constants.
DFG was assumed to degrade preferably through E1
(1,2-enolization) at lower pH. In fact at pH 5.5 step 1
prevailed to steps 2 and 3, especially when the tempera-
ture was increased. At higher pH (6.8) on the other hand
step 2 gained importance, which is evident at lower
temperature, suggesting that 2,3-enolization becomes
more relevant by increasing the pH. Moreover, from
DFG enolization step it becomes clear that indepen-
dently of the reaction conditions, deoxyosones forma-
tion prevail to sugars formation. The rate constant for
step 4 is always higher than for step 10 and for step 11.
Also, Fru formation is only a minor step from the 2,3-
enolization pathway. The rate constant for step 7 is
always higher than for step 16. Moreover, the results
suggest that sugar formation is mainly pH dependent.
At lower pH Man formation was favored towards Glc
and no other sugar was detected, whereas at higher pH
2
3
Table 3
ꢃ2
Rate constants (10 )9
/
95% highest posterior density (HPD) as found by kinetic modelling for hypothesis B of Model 2 (M
2
)
Rate constant (minꢃ1
) A (100 8C, pH 5.5) B (120 8C, pH 5.5) C (100 8C, pH 6.8) D (120 8C, pH 6.8)
k
k
k
1
2
3
0.199
0.109
0.189
20.149
1.389
0.199
60.179
5.909
3.939
11.319
6.429
0.399
0.739
0.129
1.459
/
0.02
0.04
0.01
3.37
0.39
0.04
9.11
4.06
0.21
1.94
1.07
0.13
0.28
0.03
0.42
1.119
0.869
0.889
31.139
2.239
4.309
76.799
15.419
22.509
19.429
10.969
1.279
1.419
70.689
5.159
/
0.07
0.40
0.28
9.97
1.17
0.69
10.65
1.71
1.81
6.84
4.25
0.24
0.26
3.93
0.99
0.579
1.569
1.559
7.949
9.079
2.749
21.259
0.009
190.859
7.079
11.319
0.089
0.229
0.349
1.599
1.349
/
0.03
0.09
0.11
1.51
3.45
2.82
9.18
0.00
22.85
1.11
1.81
0.05
0.05
0.06
0.22
0.59
8.899
6.299
8.629
215.799
506.699
30.419
55.939
0.009
653.559
25.079
50.559
1.069
2.039
2.479
16.829
4.519
/
0.83
0.66
0.36
50.08
62.87
2.17
2.14
0.00
94.08
5.28
10.63
0.17
0.23
0.99
5.91
1.72
/
/
/
/
/
/
/
/
k4
/
/
/
/
k
k
5
6
/
/
/
/
/
/
/
/
k7
/
/
/
/
k
k
8
9
/
/
/
/
/
/
/
/
k10
/
/
/
/
k
k
11
12
/
/
/
/
/
/
/
/
k13
k14
/
/
/
/
/
/
/
/
k
k
15
16
/
/
/
/
/
/

S.I.F.S. Martins, M.A.J.S. Van Boekel / Carbohydrate Research 338 (2003) 1665ꢀ
/
1678
1677
not only Fru was formed but also Glc was formed in
higher amounts than Man. Besides enolization, DFG
was also assumed to degrade through retro-aldolization,
the reaction mechanism and the number of steps
involved. The multiresponse modelling approach as
used in this study is a helpful tool to unravel compli-
cated reaction routes. Acetic acid, identified as a main
end product in DFG thermal degradation, is according
to the kinetic analysis mainly formed through 1-DG
degradation. Also 3-DG was determined as a main
precursor in carbohydrate fragments responsible for
colour formation. As the reaction proceeded other
compounds besides DFG are suggested to become
reactants themselves with the formation among others,
of methylglyoxal. Kinetic modelling is an iterative
process: propose a model, confront it with experimental
data, criticise the model, adjust the model and confront
the adapted model with experiments again, until an
acceptable model results. If more models are possible
from a scientific point of view, then a statistical
treatment may help to choose. We would like to stress
that scientific insight should be the first and the
foremost discrimination tool in discussing model dis-
crimination. Model discrimination is not about finding
out whether or not the model is right or wrong, but
rather to find the best performing model, from a
scientific and statistical point of view.
where the rate determining step leads to C , the
n
fragment without the amino group. In a previous
5
multi-step kinetic analysis study 1-morpholino-1-
deoxy-D-fructose degradation was also assumed to
undergo retro-aldolization reaction but in that case the
resulting product kept the amino group. No attempt was
made however in identifying and quantifying any
reaction product that might be formed from it. The
same assumption was tested in the present study and it
showed a lack-of-fit in particular in the MG as well as in
the organic acids formation. These results support the
hypothesis that from DFG retro-aldolization the rate-
determining step leads to the fragment without the
amino group.
In Scheme 3 both deoxyosones are presented as
essential steps in organic acids formation. In fact, steps
6
and 9 are the most significant in formic and acetic acid
formation, respectively. The same result was observed in
2
a previous study with different sugars and casein. In
8
Part I, the obtained results suggested that 1-DG was
4
more reactive than 3-DG. Also, acetic acid was identi-
fied as one of the main end products of DFG decom-
position. From the kinetic analysis these results are
supported. Not only the rate constant for the degrada-
tion of 1-DG into acetic acid (step 9) prevailed to the
degradation of 1-DG into carbohydrate fragments (Cn)
Acknowledgements
The authors would like to thank the Funda c¸ a˜ o para a
Ci eˆ ncia e Tecnologia, Minist e´ rio da Ci eˆ ncia e Tecnolo-
gia (Portuguese foundation for science and technology,
Ministry of Science and Technology) for its financial
support.
(
step 8), in particular at pH 6.8, but also under these
conditions the rate constant of step 9 is the highest of
the system. However, in terms of colour formation the
influence of 1-DG seems to be very low compared with
3
-DG. As the pH increased 1-DG is no longer involved
in carbohydrate fragments responsible for colour for-
mation, but mainly in acetic acid formation. Under
these conditions 3-DG becomes the main precursor in
6
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carbohydrate fragments involved in colour formation
raises an important question about the importance of
ARP reversibility in Maillard reaction. This question
will be addressed in a following paper.
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