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Báo cáo khoa học: Quantitative assessment of the glyoxalase pathway in Leishmania infantum as a therapeutic target by modelling and computer simulation pot

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Quantitative assessment of the glyoxalase pathway in
Leishmania infantum as a therapeutic target by modelling
and computer simulation
Marta Sousa Silva
1
, Anto
´
nio E. N. Ferreira
1
, Ana Maria Toma
´
s
2,3
, Carlos Cordeiro
1
and Ana Ponces Freire
1
1 Centro de Quı
´
mica e Bioquı
´
mica, Departmento de Quı
´
mica e Bioquı
´
mica, Faculdade de Cie
ˆ
ncias da Universidade de Lisboa, Portugal
2 ICBAS – Instituto de Cie
ˆ
ncias Biome


´
dicas Abel Salazar, Universidade do Porto, Portugal
3 Instituto de Biologia Molecular e Celular, Universidade do Porto, Portugal
All trypanosomatids share two characteristics that set
them apart from other eukaryotic cells. The first is
the functional replacement of glutathione by N
1
,N
8
-
bis(glutathionyl)-spermidine (trypanothione) whereby
most glutathione-dependent enzymes are replaced by
trypanothione-dependent ones [1]. The second is the
compartimentation of glycolysis, which occurs in a
specific organelle, the glycosome [2]. These differences
may be exploited in the development of novel thera-
peutic strategies based on the disruption of trypano-
thione-dependent biochemical processes and glycolysis
inhibition, both essential for the survival of these intra-
cellular parasites.
An often overlooked aspect of glycolysis arises from
the chemical instability of dihydroxyacetone phosphate
and d-glyceraldehyde-3-phosphate [3]. In physiologic
Keywords
Leishmania; trypanothione; methylglyoxal;
glyoxalase; modelling
Correspondence
C. Cordeiro, Centro de Quı
´
mica

e Bioquı
´
mica, Departmento de Quı
´
mica
e Bioquı
´
mica, Faculdade de Cie
ˆ
ncias
da Universidade de Lisboa, Edifı
´
cio C8,
Lisboa, Portugal
Fax: +351 217500088
Tel: +351 217500929
E-mail:
⁄ enzimol
Note
The mathematical model described here has
been submitted to the Online Cellular Sys-
tems Modelling Database and can be
accessed free of charge at chem.
sun.ac.za/database/silva/index.html
(Received 12 November 2004, revised 21
January 2005, accepted 28 February 2005)
doi:10.1111/j.1742-4658.2005.04632.x
The glyoxalase pathway of Leishmania infantum was kinetically character-
ized as a trypanothione-dependent system. Using time course analysis
based on parameter fitting with a genetic algorithm, kinetic parameters

were estimated for both enzymes, with trypanothione derived substrates. A
K
m
of 0.253 mm and a V of 0.21 lmolÆmin
)1
Æmg
)1
for glyoxalase I, and a
K
m
of 0.098 mm and a V of 0.18 lmolÆmin
)1
Æmg
)1
for glyoxalase II, were
obtained. Modelling and computer simulation were used for evaluating the
relevance of the glyoxalase pathway as a potential therapeutic target by
revealing the importance of critical parameters of this pathway in Leishma-
nia infantum. A sensitivity analysis of the pathway was performed using
experimentally validated kinetic models and experimentally determined
metabolite concentrations and kinetic parameters. The measurement of
metabolites in L. infantum involved the identification and quantification of
methylglyoxal and intracellular thiols. Methylglyoxal formation in L. infan-
tum is nonenzymatic. The sensitivity analysis revealed that the most critical
parameters for controlling the intracellular concentration of methylglyoxal
are its formation rate and the concentration of trypanothione. Glyoxalase I
and II activities play only a minor role in maintaining a low intracellular
methylglyoxal concentration. The importance of the glyoxalase pathway as
a therapeutic target is very small, compared to the much greater effects
caused by decreasing trypanothione concentration or increasing methyl-

glyoxal concentration.
Abbreviations
DHAP, dihydroxyacetone phosphate; GAP,
D-glyceraldehyde-3-phosphate; Glx I, glyoxalase I; Glx II, glyoxalase II; HTA, hemithioacetal;
MG, methylglyoxal; TFA, trifluoroacetic acid; T(SH)
2
, N
1
,N
8
-bis(glutathionyl)-spermidine; SDL-TSH, S-D-lactoyltrypanothione.
2388 FEBS Journal 272 (2005) 2388–2398 ª 2005 FEBS
conditions, these trioses readily undergo an irreversible
b-elimination reaction of the phosphate group from
their common 1,2-enediolate form, forming oxopro-
panal (methylglyoxal) [4]. Methylglyoxal is also formed
as a by-product of the triose phosphate isomerase cata-
lysed reaction [5] and in bacteria may be enzymatically
synthesized from dihydroxiacetone phosphate by meth-
ylglyoxal synthase (EC 4.1.99.11), an enzyme not
found in eukaryotic cells [6–8]. Once formed, methyl-
glyoxal irreversibly modifies amino groups in lipids,
nucleic acids and proteins, forming advanced glycation
end products [9]. It is therefore toxic, mutagenic and
an inhibitor of glycolytic enzymes [10]. The glutathi-
one-dependent glyoxalase pathway is the main detoxifi-
cation system for methylglyoxal [11]. It first reacts
nonenzymatically with glutathione, forming a hemithio-
acetal that is isomerized to the thiol ester S-d-lactoyl-
glutathione by glyoxalase I (Glx I; lactoylglutathione

lyase, EC 4.4.1.5). S-d-Lactoylglutathione is then
hydrolysed to d-lactate and glutathione by glyoxalase
II (Glx II; hydroxyacyl glutathione hydrolase, EC
3.1.2.6) as shown in Fig. 1.
Enhancing methylglyoxal formation or inhibiting its
main catabolic pathway may lead to an increase of
methylglyoxal concentration with harmful effects on
trypanosomatids that might be exploited for therapeu-
tic purposes.
Little is known regarding methylglyoxal metabolism
in trypanosomatids and the first reference to the
presence of the glyoxalase pathway in Leishmania
braziliensis dates from 1988 [12]. Only 16 years later
was glyoxalase II characterized in Trypanosoma brucei
[13]. In this case, lactoyltrypanothione was found to be
a better substrate for this enzyme than S-d-lactoylgluta-
thione (SDL-TSH), the substrate for all glyoxalase II
enzymes known so far.
In this work we investigated the kinetics of the
glyoxalase pathway enzymes in L. infantum by time
course analysis based on modelling and parameter fit-
ting with a genetic algorithm. The best-fit parameters
were used to set up a mathematical model of the path-
way in L. infantum. Computer simulation of the sys-
tem’s behaviour resulting from excursions around a
reference state were performed to reveal the most sen-
sitive points of the glyoxalase pathway, towards pos-
sible pharmacological opportunities.
The mathematical model described here has been
submitted to the Online Cellular Systems Modelling

Database and can be accessed at .
ac.za/database/silva/index.html free of charge.
Results and Discussion
The potential of the glyoxalase system as a possible
therapeutic target relies on its role as the main cata-
bolic pathway for methylglyoxal in eukaryotic cells. To
cause damage to Leishmania, or to any other trypano-
somatid, conditions must be sought that lead to an
increase of methylglyoxal concentration. A quantitative
analysis of the most critical parameters of the pathway
regarding this goal requires the knowledge of the intra-
cellular concentrations of all metabolites involved and
a kinetic model that accurately describes the glyoxalase
system in Leishmania.
Methylglyoxal was identified in Leishmania infantum
by HPLC and appears to be the only 2-oxoaldehyde
detected. This metabolite is present, in early stationary
phase cells, at a concentration of 9.67 pmol per 10
8
promastigotes. This low methylglyoxal concentration
suggests that its formation in L. infantum is nonenzy-
matic as observed in other cells [14,15]. To confirm this
hypothesis, methylglyoxal synthase activity was
assayed by measuring methylglyoxal formation from
dihydroxyacetone phosphate (DHAP). When compar-
ing the rates of methylglyoxal formation in the pres-
ence and in the absence of L. infantum extract, no
significant differences were found. DHAP forms
methylglyoxal at a rate of 0.17 lmÆmin
)1

and with
L. infantum extract the rate was 0.18 lmÆmin
)1
. Data-
base mining of the L. infantum genome did not reveal
any possible sequences for a methylglyoxal synthase
gene. The low intracellular methylglyoxal concentration
Thiol esther
CH
3
O
O
H
CH
3
OH
O
S
R
H
CH
3
OH
O
OH
H
RSH
D-Lactate
Glutathione
or

trypanothione
-SH group
Hemithioacetal
Methylglyoxal
Dihydroxyacetone
phosphate
3-P-1,2-enediol
D-glyceraldehyde
-3-phosphate
O
3
POCH
2
O
H
OH
H
H
OH
O
3
POCH
2
OH
O
3
POCH
2
OH
O

H
H
(non-enzymatic)
Glyoxalase I
Glyoxalase II
(non-enzymatic)
2-2-
2-
CH
3
S
R
O
OH
H
Fig. 1. Methylglyoxal metabolism. Methylglyoxal is formed from
the glycolytic intermediates dihydroxyacetone phosphate (DHAP)
and
D-glyceraldehyde-3-phosphate (GAP), and is dismutated to
D-lactate by the glyoxalase pathway. R-SH represents thiol group(s)
of reduced glutathione (GSH) or reduced trypanothione [T(SH)
2
].
M. Sousa Silva et al. The glyoxalase pathway in Leishmania infantum
FEBS Journal 272 (2005) 2388–2398 ª 2005 FEBS 2389
and the absence of methylglyoxal synthase activity sug-
gest that this metabolite is most improbably originated
from this enzyme’s activity. Therefore, in our model,
we considered only the nonenzymatic formation of
methylglyoxal from DHAP and d-glyceraldehyde-

3-phosphate (GAP) (Fig. 2) using the steady state
concentrations of these trioses as previously reported
[16]. Concerning the intracellular low molecular mass
thiols of L. infantum, at early stationary phase of
growth, HPLC analysis of monobromobimane deriva-
tives revealed the presence of GSH and T(SH)
2
at
retention times of 13.6 and 21.2 min, respectively
(Fig. 3B). T(SH)
2
was present at a concentration of
3.04 nmol per 10
8
promastigotes, while GSH concen-
tration was 0.50 nmol per 10
8
promastigotes, a much
lower value. Unidentified thiols (U marked peaks)
were also shown to be present in this parasite, at
retention times of 14.5 and 23.3 min (Fig. 3B). GSH
is present at a molar ratio of 1 : 6 relative to trypan-
othione, making T(SH)
2
a good candidate for repla-
cing GSH in the glyoxalase pathway in L. infantum,
as occurs in other enzymatic systems in trypanosom-
atids. Substrate dependence of the glyoxalase enzymes
was then evaluated in this parasite by initial rate ana-
lysis.

Using the methylglyoxal glutathione hemithioacetal
as substrate, the kinetic parameters for L. infantum
glyoxalase I, were a K
m
of 1.85 ± 0.35 mm and a V of
0.19 ± 0.02 lmolÆmin
)1
Æmg
)1
(Table 1). The K
m
for
Glx I, using this hemithioacetal, is about five times
higher than that described for all known glyoxalase I
enzymes with the methylglyoxal glutathione hemithio-
acetal as substrate [11]. Additionally, Glx II activity
could not be detected in L. infantum using S-d-lac-
toylglutathione as substrate, either by following its
hydrolysis at 240 nm or by monitoring GSH formation
at 420 nm with 5,5¢-dithiobis(2-nitrobenzoic acid), a
more sensitive assay [17]. Given these results and the
much lower concentration of GSH compared to
T(SH)
2
, it is likely that trypanothione hemithioacetal
and lactoyltrypanothione might be the physiological
substrates for glyoxalase I and glyoxalase II in
L. infantum, respectively. Indeed, the kinetic parame-
ters for Glx I were a K
m

of 0.24 ± 0.04 mm and a
V of 0.19 ± 0.02 lmolÆmin
)1
Æmg
)1
using methyl-
glyoxal trypanothione hemithioacetal (Table 1). For
Fig. 2. The glyoxalase pathway in Leishmania infantum. Reactions
1 and 2 correspond to the nonenzymatic (n.e.) formation of MG
from dihydroxyacetone phosphate (DHAP) and
D-glyceraldehyde-3-
phosphate (GAP). Reactions 3 and 4 correspond to the reversible
reaction between MG and reduced trypanothione [T(SH)
2
]. Reac-
tions 5 and 6 are catalysed by Glx I and Glx II, respectively. Num-
bered reactions are described in Table 3.
A
B
Fig. 3. HPLC analysis of the glyoxalase pathway metabolites in
Leishmania infantum promastigotes. (A) Analysis of 2-oxoalde-
hydes, showing the presence of MG as 2-methylquinoxaline and
the internal standard (IS, 1 l
M 2,3-dimethylquinoxaline). Other
peaks are due to the reagent. (B) Thiol analysis, as monobromobi-
mane derivatives. Glutathione (GSH) and trypanothione (T(SH)
2
)
were identified. Peaks marked R are due to the derivatizing reagent
monobromobimane, while U marked peaks are unidentified thiols.

The glyoxalase pathway in Leishmania infantum M. Sousa Silva et al.
2390 FEBS Journal 272 (2005) 2388–2398 ª 2005 FEBS
Glx II, the activity could be measured and we obtained
a K
m
of 0.073 ± 0.020 mm and a V of 0.22 ±
0.0005 lmolÆmin
)1
Æmg
)1
with bis(lactoyl)trypanothione
(Table 2). The kinetic constants for both enzymes are
similar to those found for glutathione or trypanothi-
one-dependent glyoxalase I and II in other systems
(Tables 1 and 2) [13,18–20].
The determination of detailed rate laws for enzyme
systems is very difficult, unless a very large number of
experiments is performed. This is seldom possible with
trypanothione-dependent enzymes, given the scarcity
of this thiol. Initial rate analysis is also limited to the
study of isolated enzymes and does not provide a good
approach to understanding the kinetics of a metabolic
pathway. A better strategy is the use of time course
analysis, which requires fitting of a set of parameters
from a system of ordinary differential equations that
describe a given kinetic model to a set of concentration
time courses. So far, this analysis of the glyoxalase
pathway has only been performed in yeast [20].
The glyoxalase pathway enzymes catalyse irreversible
reactions and can be considered as single substrate

Michaelian enzymes [11,20]. When fitting a single-
enzyme model for glyoxalase I (single substrate
irreversible Michaelis–Menten) to time courses for
lactoyltrypanothione concentration, only a poor fit was
possible (Fig. 4A,A¢). Other rate laws were investigated
as possible alternatives and again no better fitting was
achieved (data not shown). As we could detect the
activity of both enzymes with trypanothione derived
substrates we next fitted a two-enzyme kinetic model
(single substrate irreversible Michaelis-Menten). In this
case an excellent fit was achieved (Fig. 4B,B¢) and the
kinetic parameters for both enzymes were determined
(Tables 1 and 2). This fit was obtained using only
two progress curves corresponding to 0.14 mm and
0.27 mm hemithioacetal. The analysis was also per-
formed with more than two curves and identical results
were obtained. For Glx I we determined an apparent
K
m
of 0.253 mm and an apparent V of 0.21 lmolÆ
min
)1
Æmg
)1
(Table 1) while for Glx II a K
m
of
0.098 mm and a V of 0.18 lmolÆmin
)1
Æmg

)1
were deter-
mined (Table 2). Other models were tested, namely gly-
oxalase II inhibition by methylglyoxal trypanothione
hemithioacetal, but the fitting was not improved (data
not shown). A possible effect of competitive product
inhibition on glyoxalase I was also investigated, but a
worse fitting was obtained (Fig. 4C,C¢). A K
m
of
0.801 mm and a V of 0.5 lmolÆmin
)1
Æmg
)1
were deter-
mined, markedly different from the ones estimated
from initial rate and time course analysis using the
two-enzyme model. Moreover, the obtained K
i
of
0.02 mm would imply that the enzyme should have an
abnormally high affinity for the product.
With our experimental conditions, where native
enzymes are present at their relative activities with
Table 1. Glyoxalase I kinetic parameters in Leishmania infantum and other cells.
Glx I Substrate
Initial rate analysis Time course analysis
K
m
(mM)

V
(lmolÆmin
)1
Æmg
)1
)
K
m
(mM)
V
(lmolÆmin
)1
Æmg
)1
)
Leishmania infantum GSH 1.85 ± 0.35 0.19 ± 0.02 – –
T(SH)
2
0.24 ± 0.04 0.19 ± 0.02 0.253 0.21
Plasmodium falciparum [19] GSH 0.77 ± 0.15 NC
a
––
Leishmania major [18] T(SH)
2
0.32 ± 0.03 NC
a
––
Saccharomyces cerevisiae [20] GSH 0.51 ± 0.06 NC
b
0.62 ± 0.18 NC

b
a
NC, not comparable (data from recombinant enzyme).
b
NC, not comparable (data from permeabilized cells).
Table 2. Glyoxalase II kinetic parameters in Leishmania infantum and other cells. ND, not detected.
Glx II Substrate
Initial rate analysis Time course analysis
K
m
(mM)
V
(lmolÆmin
)1
Æmg
)1
)
K
m
(mM)
V
(lmolÆmin
)1
Æmg
)1
)
L. infantum SDL-GSH ND ND – –
SDL-TSH 0.073 ± 0.020 0.22 ± 0.0005 0.098 0.18
T. brucei [13] SDL-TSH 0.086 ± 0.004 NC
a

––
S. cerevisiae [20] SDL-GSH 0.32 ± 0.13 NC
b
0.09 ± 0.05 NC
b
a
NC, not comparable (data from recombinant enzyme).
b
NC, not comparable (data from permeabilized cells).
M. Sousa Silva et al. The glyoxalase pathway in Leishmania infantum
FEBS Journal 272 (2005) 2388–2398 ª 2005 FEBS 2391
possible post-translational modifications preserved, we
achieved a characterization of the glyoxalase system
sufficient to elaborate a minimal model of its global
kinetic behaviour (Fig. 2). A reference steady state was
defined by the experimentally determined enzyme
activities using time course analysis and the measured
intracellular trypanothione concentration. The rate of
methylglyoxal formation was calculated using the pre-
viously determined triose phosphate concentrations
[16] and rate constants [21].
When simulating the effects of changing glyoxalase
I or glyoxalase II activities on methylglyoxal steady-
state concentration, surprising results were obtained
(Fig. 5A,B). To increase methylglyoxal concentration
by about 50%, glyoxalase I activity must be
decreased to 10% of its reference value (Fig. 5A).
Varying glyoxalase II activity causes no noticeable
change on the concentration of methylglyoxal within
the tested range of variation (Fig. 5B). By contrast,

methylglyoxal input and trypanothione concentration
show a linear and an inverse hyperbolic effect on the
steady-state concentration of methylglyoxal, respect-
ively (Fig. 5C,D).
In search for synergistic effects, the dependence of
methylglyoxal steady-state concentration on the joint
variations of two parameters at a time was also simu-
lated (Fig. 6). Focusing on the glyoxalase activities,
trypanothione concentration, and methylglyoxal for-
mation rate as model parameters, there are six possible
two-parameter combinations to be considered. Among
these, a significant increase in methylglyoxal is
only achieved when trypanothione concentration is
decreased (Fig. 6A,B). The greatest effect is observed
for the simultaneous increase of methylglyoxal forma-
tion rate and decrease of trypanothione concentration.
In all other combinations there is only a slight effect
on methylglyoxal concentration suggesting that a signi-
ficant increase of this metabolite would only be
AA'
BB'
CC'
Fig. 4. Time course analysis of the glyox-
alase pathway in Leishmania infantum. Two
concentrations of methylglyoxal trypanothi-
one hemitioacetal were studied (0.14 and
0.27 m
M). Lactoyltrypanothione concentra-
tion was monitored at 240 nm. Experimental
data (black line, A,B,C), fitting a single-

enzyme model (blue line, A), fitting a two-
enzyme model (red line, B) and fitting a
single-enzyme model with competitive prod-
uct inhibition (yellow line, C). The best fit for
each model was obtained by least squares
minimization using two time courses and a
genetic algorithm to search the parameter
space. Numerical solvers of ODE initial
value problems and the genetic algorithms
were implemented in the software package
AGEDO. For each model, plots of residuals
are shown in A¢,B¢ and C¢.
The glyoxalase pathway in Leishmania infantum M. Sousa Silva et al.
2392 FEBS Journal 272 (2005) 2388–2398 ª 2005 FEBS
possible for extreme modulations of enzyme activities.
In particular, in the combinations involving the
decrease of glyoxalase II activity the effect is equival-
ent to the modulation of the other parameters alone,
as shown in the combination involving glyoxalase I
and glyoxalase II (Fig. 6C).
The simulation results, based on experimentally
determined parameters and a kinetic model of the
AB
DC
Fig. 5. Sensitivity analysis of the glyoxalase
pathway in Leishmania infantum. The effects
of system parameters on the intracellular
steady-state concentration of methylglyoxal
were investigated by finite parameter chan-
ges (between 0.05- and three-fold) around

the reference steady state. All values are
fold variations relative to the reference state
(normalized values). System parameters
were: glyoxalase I activity (A), glyoxalase II
activity (B), methylglyoxal input (C), and
initial trypanothione concentration (D).
0
20
40
60
80
1.0
1.5
2.0
2.5
3.0
0.2
0.4
0.6
0.8
1.0
MG
MG input
initial SH
0
20
40
60
80
0

20
40
60
80
0.2
0.4
0.6
0.8
1.0
0.2
0.4
0.6
0.8
1.0
MG
GLX I
initial SH
0
20
40
60
80
0
20
40
60
80
0.2
0.4
0.6

0.8
1.0
MG
GLX I
GLX II
0
20
40
60
80
0
20
40
60
80
0.2
0.4
0.6
0.8
1.0
1.0
1.5
2.0
2.5
3.0
MG
GLX I
MG input
0
20

40
60
80
AB
C
D
0.2
0.4
0.6
0.8
1.0
Fig. 6. Sensitivity analysis of the glyoxalase
pathway in Leishmania infantum, studying
the effects of two simultaneous system
parameters on the intracellular steady-state
concentration of methylglyoxal, by finite
parameter changes (between 0.05- and
onefold, except for MG input that was
between one- and 3.5-fold) around the
reference steady state. All values are fold
variations relative to the reference state
(normalized values). System parameters
were: initial trypanothione concentration and
methylglyoxal input (A), initial trypanothione
concentration and glyoxalase I activity (B),
glyoxalase II activity and glyoxalase I activity
(C), methylglyoxal input and glyoxalase I
activity (D).
M. Sousa Silva et al. The glyoxalase pathway in Leishmania infantum
FEBS Journal 272 (2005) 2388–2398 ª 2005 FEBS 2393

pathway, clearly show that the glyoxalase enzymes are
poor therapeutic targets. This view is supported by
growth experiments with single gene deletion yeast
mutants for glyoxalase I and II [21]. Both strains grow
in d-glucose containing media in exactly the same way
as the reference strain. Only when methylglyoxal is
added to the growth medium at a concentration of
0.5 mm a slight reduction of growth rate is observed
for the DGLO1 strain. Growth of the DGLO2 strain is
not affected even in the presence of 1 mm of methyl-
glyoxal. Moreover, glyoxalase II is absent in some
mammals with no harmful consequences [22].
Methylglyoxal formation is nonenzymatic in eukary-
otic cells and Leishmania is no exception. Its formation
rate is dependent of triose phosphates concentrations
and may be changed by controlling triose phosphate
isomerase (TPI) activity, for a given glycolytic flux. In
a case study of human TPI deficiency, increased con-
centrations of DHAP and methylglyoxal were detected,
related to mental illness [23]. Additionally, reduction
of TPI activity in Trypanosoma brucei causes an inhibi-
tion of growth, likely due to increased methylglyoxal
formation [24]. A detailed kinetic and molecular char-
acterization of L. infantum TPI may lead to the devel-
opment of specific inhibitors granting a selective
inhibitory effect that may prove to be useful against
trypanosomatids.
The intracellular concentration of trypanothione is
another critical parameter that will lead to an increase
of the steady-state concentration of methylglyoxal.

Again, in the work with yeast referred to above, the
most sensitive strain to methylglyoxal is the one lack-
ing glutathione synthase I, DGSH1, with a lower intra-
cellular GSH concentration [21]. In Trypanosoma
brucei, trypanothione depletion results in growth arrest
and increased sensitivity to oxidative stress [25]. Inhibi-
tion of trypanothione biosynthesis most likely impairs
several pathways vital to the survival of the parasite.
Moreover, resistance to carbonylic stress caused by
methylglyoxal will be compromised. From a practical
point of view, trypanothione depletion might be
achieved by inhibiting trypanothione synthetase the
enzyme that in T. brucei, T. cruzi and L. major was
shown to catalyse the formation of that thiol from
spermidine and glutathione [26–28]. This enzyme,
essential to T. brucei [29] and very likely to the other
trypanosomatids, is considered one of the most prom-
ising targets for chemotherapy.
In summary, research efforts in search for more
effective drugs against trypanosomatids have revealed
important aspects of these parasites’ biochemistry.
Effective therapies must rely on unique aspects such as
glycolysis compartimentation and thiol metabolism.
Trypanothione is essential for cell viability and plays a
major role in the defence against oxidative stress
caused by hydrogen peroxide and organic hydroper-
oxides. It is also the physiological substrate of the gly-
oxalase pathway, the main detoxification system for
methylglyoxal and other 2-oxoaldehydes, arising from
nonenzymatic reactions.

As any prospects to fulfil this goal rely on increasing
methylglyoxal concentration, our results clearly show
that reduction of glyoxalase I or glyoxalase II activities
will have only a slight to no effect, respectively, on
steady-state concentration of methylglyoxal. On the
contrary, focusing on increasing methylglyoxal forma-
tion or reducing trypanothione concentration are more
attractive approaches. In the case of trypanothione, a
synergistic effect, whereby oxidative and carbonylic
stresses are increased, may be achieved with lethal
consequences to trypanosomatids.
Experimental procedures
Reagents and equipment
S-d-Lactoylglutathione (SDL-GSH), yeast glyoxalase I
(530–550 UÆmg
)1
protein), bovine liver glyoxalase II
(% 29 UÆmg
)1
protein), N-ethylmaleimide, dithiothreitol,
DHAP, methylglyoxal dimethylacetal, trifluoroacetic acid
(TFA), monobromobimane, 1,2-diaminobenzene, 5,5¢-
dithiobis(2-nitrobenzoic acid) and Coomassie Brilliant Blue
G were purchased from Sigma Chemical Co (St Louis,
MO, USA). 2,3-Dimethylquinoxaline was obtained from
Aldrich. Reduced and oxidized glutathione (GSH and
GSSG) were obtained from Boehringer Mannheim GmbH
(Mannheim, Germany). Trypanothione disulfide (TS2) was
purchased from Bachem. RPMI Medium was purchased
from Gibco-BRL (Paisley, UK). Other reagents were of

analytical grade and all solvents were of HPLC grade.
A Beckman DUÒ (Fullerton, CA, USA) 7400 diode array
spectrophotometer with a thermostated multicuvette holder,
with stirring, was used for the determination of protein con-
centration and to monitor enzyme activity. Centrifugations
were performed in a refrigerated Eppendorf (Hamburg,
Germany) 5804R centrifuge. Thiol determinations and
methylglyoxal (MG) quantifications were performed in a
Beckman Coulter HPLC coupled with a Jasco FP-2020 Plus
(Tokyo, Japan) fluorescence detector. In these assays, a
Merck LichroCART (Darmstadt, Germany) 250–4
(250 · 4 mm) column with stationary phase Merck LiChro-
spher
Ò
(Darmstadt, Germany) 100 RP-18 (5 lm) was used.
Preparation of metabolites
High-purity MG was prepared by acid hydrolysis of meth-
ylglyoxal dimethylacetal, in 10% (v ⁄ v) H
2
SO
4
, and purified
The glyoxalase pathway in Leishmania infantum M. Sousa Silva et al.
2394 FEBS Journal 272 (2005) 2388–2398 ª 2005 FEBS
by fractional distillation under reduced pressure in nitrogen
atmosphere [30]. The solution obtained was calibrated with
yeast Glx I and bovine liver Glx II.
Oxidized glutathione (GSSG) and oxidized trypanothione
(TS
2

) were reduced with dithiothreitol, in the proportion of
1mm GSSG or TS
2
)3.2 mm dithiothreitol. The reaction
was performed at 60 °C for 20 min, in a 1.5 mL reaction
system, in 0.1 m potassium phosphate buffer, pH 6.8.
SDL-TSH was prepared from reduced trypanothione and
MG using yeast glyoxalase I. MG was added in excess
(3.34 mm in a 2 mL reaction system), and the hemithio-
acetal concentration was calculated using the value of
3.0 mm for the dissociation constant [31]. Glyoxalase I
reaction was started by the addition of yeast Glx I. The
formation of SDL-TSH was followed at 240 nm, and its
concentration was calculated using a e
240
of 6.5 mm
)1
Æcm
)1
[13]. The enzyme was removed after completing the reaction
using an Ultrafree-MC Filter 5KDa (Millipore, Billerica,
MA, USA), and the recovered solution was used for the
glyoxalase II activity assay.
Leishmania infantum culture
Promastigotes of Leishmania infantum clone MHOM ⁄
MA67ITMAP263 were grown in RPMI medium supple-
mented with 10% fetal bovine serum, 2 mml-glutamine,
50 mm Hepes sodium salt (pH 7.4), 35 UÆmL
)1
penicillin

and 35 l g ÆL
)1
streptomycin, at 25 °C [32].
Preparation of Leishmania infantum extracts
Promastigotes of L. infantum at early stationary phase of
growth (about 150 mL, containing approximately 10
9
cells)
were washed twice in NaCl ⁄ P
i
, and suspended in 1 mL
NaCl ⁄ P
i
. To prepare the protein extracts for enzyme assays,
cells were submitted to eight freeze–thaw cycles (on ice and
50 °C) and the supernatant was recovered after centrifuga-
tion at 10 500 g for 10 min. Protein concentration was quan-
tified according to Bradford using BSA as the standard [33].
For thiol identification and MG quantification, cells were
lysed and deproteinized with 0.5 m perchloric acid. The sus-
pension was kept on ice for 10 min, vortexed for 2 min and
centrifuged at 4 °C, 10 500 g, for 5 min. The recovered
supernatant was immediately analysed or stored at )80 °C
[14].
Thiol assay
Intracellular thiols were derivatized with the fluorescent
label monobromobimane and analysed by HPLC. The deri-
vatization procedure was based on the methods described
by Tang et al. [34] and by Ondarza et al. [35], with some
modifications. A 100 lL aliquot of the L. infantum extract

(containing 10
8
cells) was neutralized with KOH and
centrifuged at room temperature for 3 min at 10 500 g. The
reduction of oxidized thiols was performed with dithiothrei-
tol at a final concentration of 0.4 mm in 0.5 m Tris ⁄ HCl
pH 8.0, for 20 min at 60 °C. Monobromobimane (in aceto-
nitrile) was added to a final concentration of 1 mm (200 lL
reaction system) and the derivatization was carried out at
60 °C for 35 min, in the dark. Perchloric acid, at a final
concentration of 0.5 m, was added to stop the reaction.
Thiol standards GSH and T(SH)
2
were submitted to the
same treatment. A 20 lL sample volume was injected. Elu-
tion of bimane-derivatized compounds was monitored by
fluorescence detection with excitation at 397 nm and emis-
sion at 490 nm, using a binary gradient of acetonitrile with
0.08% (v ⁄ v) TFA (solvent A) and water with 0.08% (v ⁄ v)
TFA (solvent B). The gradient program was: 0–5 min, 10%
(v ⁄ v) solvent B isocratic; 5–35 min, 10–30% (v ⁄ v) solvent
B; 35–40 min, 30–10% (v ⁄ v) solvent B. Separation was car-
ried out at a flow rate of 1.0 mLÆmin
)1
. GSH and T(SH)
2
were identified and quantitated by comparison with stand-
ards. Thiol concentrations were calculated from calibration
curves performed with known concentrations of monobro-
mobimane-derived thiols. For control samples, thiols were

blocked with 5 mm N-ethylmaleimide for 20 min at 60 °C
before derivatization.
Methylglyoxal assay
Intracellular methylglyoxal was measured in L. infantum
(100 lL extract) with a specific HPLC-based assay, by deri-
vatization with 1,2-diaminobenzene and using 2,3-dimethyl-
quinoxaline as internal standard [36].
Methylglyoxal synthase activity was assayed by measuring
methylglyoxal formation from DHAP. The reaction
occurred in 1 mL reaction volume, in 0.1 m potassium phos-
phate buffer, pH 6.8, at 30 °C. DHAP was added to a 50-
and a 100-lL aliquot of the L. infantum extract, to a final
concentration of 1 mm. The reaction was stopped with the
addition of perchloric acid to 0.5 m final concentration.
Controls were performed without L. infantum extract and
the rates of methylglyoxal formation compared. Methylgly-
oxal was measured in all samples, at time zero and after
2.5 h of incubation, with the HPLC assay referred to above.
Enzyme kinetic assays
Enzyme activities were determined at 30 °C in a 2 mL reac-
tion volume, in 0.1 m potassium phosphate buffer, pH 6.8.
Magnetic stirring in the spectrophotometer cuvette was
used to maintain isotropic conditions.
The Glx I activity assay was based on the method des-
cribed by Martins et al. [20] with some modifications. Glx I
activity was assayed with GSH, with dithiothreitol reduced
GSSG, and with reduced trypanothione [T(SH)
2
], using
MG in excess (3.34 mm). Initial concentrations of GSH and

GSSG were calculated to give hemithioacetal concentra-
tions from 0.16 to 3.8 mm. Initial concentrations of T(SH)
2
M. Sousa Silva et al. The glyoxalase pathway in Leishmania infantum
FEBS Journal 272 (2005) 2388–2398 ª 2005 FEBS 2395
were calculated to give substrate concentrations from 0.035
to 0.97 mm. Hemithioacetal concentration was calculated
using the value of 3.0 mm for the dissociation constant [31],
and its formation was followed for 20 min after the addi-
tion of MG. Glyoxalase I reactions were started by the
addition of the protein extract (15 lg of total parasite pro-
tein) and the formation of SDL-GSH or SDL-TSH was fol-
lowed at 240 nm. The concentration of these compounds
was determined using a e
240
of 2.86 mm
)1
Æcm
)1
[37] and
6.5 mm
)1
Æcm
)1
[13] for the SDL-GSH and SDL-TSH,
respectively. dithiothreitol does not interfere with Glx I
assays.
Glyoxalase II activity assay was performed using the
commercially available SDL-GSH and SDL-TSH prepared
from T(SH)

2
and MG using yeast glyoxalase I, as previ-
ously described. Concentrations of SDL-GSH between 0.5
and 4 mm were used and SDL-TSH concentrations between
0.05 and 0.10 mm were prepared. The reactions occurred in
the same conditions, and were started with the addition of
protein extract (15 lg of total protein). The hydrolysis of
both thiolesthers was followed at 240 nm. Glyoxalase II
activity with SDL-GSH was also assayed by following
GSH formation at 412 nm with 5,5¢-dithiobis(2-nitro-
benzoic acid) [20].
Determination of kinetic parameters
The kinetic parameters for glyoxalase I and II were deter-
mined using two different approaches, initial rate analysis
and time course analysis.
Initial rate data were fitted to irreversible single substrate
Michaelis–Menten models. Non-weighted hyperbolic regres-
sion by the method of least squares was performed with the
program HYPER (J. S. Easterby, University of Liverpool,
UK; />In time course analysis the parameters were determined
by minimization of the difference between experimental
time course data and the corresponding values predicted by
the solution of the differential equations derived from a
mathematical model of the kinetic assay. In this analysis,
different models were tested. In ‘single-enzyme model’, only
the reaction of glyoxalase I with an irreversible Michaelis–
Menten rate law was considered (Scheme 1).
HTA
SDL-TSH
[]

[]
HTA
HTA
1
1
1
+
=
m
K
V
v
In the ‘two-enzyme model’, the consecutive reactions of gly-
oxalase I and glyoxalase II, both with irreversible Michaelis–
Menten rate laws were considered (Scheme 2).
[]
[]
HTA
HTA
1
1
1
+
=
m
K
V
v
[]
[]

TSH-SDL
TSH-SDL
2
2
2
+
=
m
K
V
v
HTA
SDL-TSH
In ‘single-enzyme model with product inhibition’, only
the reaction of glyoxalase I was considered, with an irre-
versible Michaelis–Menten rate law with competitive prod-
uct inhibition (Scheme 3).
HTA
SDL-TSH
[]
[]
[]
HTA
TSH-SDL
1
HTA
1
1
1
1

+








+
=
iP
m
K
K
V
v
The best fit for each model was obtained with the program
AGEDO [38] using two time courses of SDL-TSH. Minimi-
zation over the parameter space was performed using the
genetic algorithm ‘differential evolution’ [39]. In each search,
the best fit vector of kinetic parameters h was defined by the
minimum of the objective function SS(h) given by Eqn (1):
SS hðÞ¼
X
p
k¼1
X
n
k

i¼1
X
OBS
k
t
i
ðÞÀX
SIM
k
t
i
hðÞ
ÀÁ
2
Eqn ð1Þ
In this equation, p is the number of time courses used in
the analysis, n
k
is the number of points in time course k,
X
OBS
k
t
i
ðÞis the experimental value of the SDL-TSH for time
Table 3. Rate equations and kinetic parameters of the glyoxalase
pathway model. Rate equations are shown in Fig. 2. Kinetic models
for the two enzymes were experimentally validated by time course
analysis. Intracellular concentrations of methylglyoxal and trypano-
thione were calculated using an estimate of the L. infantum cell

volume of 75 lm
3
, based on cell measurement. Other constants
and metabolite concentrations were from previously published
works. Initial concentrations of MG, hemithioacetal and SDL-TSH
were zero.
Differential equations
dMG ⁄ dt ¼ (v
1
+ v
2
)–v
3
+ v
4
dHTA ⁄ dt ¼ v
3
– v
4
– v
5
dSDLTSH ⁄ dt ¼ v
5
– v
6
dT(SH)
2
⁄ dt ¼ – v
3
+ v

4
+ v
6
Rate equations
v
1
¼ k
1
GAP
v
2
¼ k
2
DHAP
v
3
¼ k
3
MG T(SH)
2
v
4
¼ k
4
HTA
v
5
¼ V
5
HTA ⁄ (K

m5
+ HTA)
v
6
¼ V
6
SDLTSH ⁄ (K
m6
+ SDLTSH)
Parameters
k
1
¼ 6.4 · 10
)3
min
)1
k
2
¼ 6.6 · 10
)4
min
)1
k
3
¼ 0.34 mM
)1
Æmin
)1
k
4

¼ 1.01 min
)1
V
5
¼ 2 · 3.042 mMÆmin
)1
V
6
¼ 2 · 2.653 mMÆmin
)1
K
m5
¼ 2 · 0.253 mM
K
m6
¼ 2 · 0.0980 mM
GAP ¼ 0.0072 mM
DHAP ¼ 0.16 mM
T(SH)
2
(at time zero) ¼ 2 x 0.45 mM
The glyoxalase pathway in Leishmania infantum M. Sousa Silva et al.
2396 FEBS Journal 272 (2005) 2388–2398 ª 2005 FEBS
course k at time t
i
, and X
SIM
k
t
i

hðÞis the corresponding value
predicted by the numerical solution of the differential equa-
tions of each kinetic model with parameters h. Differential
equations were solved by an Adams ⁄ BDF pair as imple-
mented in the LSODA routine of odepack [40].
Modelling and computer simulation
Mathematical modelling and computer simulation were
used to evaluate the relative importance of critical parame-
ters of the glyoxalase pathway in L. infantum .
Simulations were performed with the software package
plas (A. E. N. Ferreira, University of Lisbon, Portugal;
based
on a kinetic model of the glyoxalase pathway (Fig. 2) des-
cribed in Table 3.
In this model, we assumed that the glyoxalase pathway is
only dependent on trypanothione and all the variables rep-
resent the concentration of total free thiol groups (T(SH)
2
),
total hemithioacetals and total lactoyl-thiol derivatives
(SDL-TSH). Bis and mono forms were not differentiated in
the model.
The response of steady-state concentrations to variations
of model parameters (flux of methylglyoxal formation, ini-
tial T(SH)
2
concentration and glyoxalase activities) were
simulated.
Acknowledgements
Work supported by project POCTI ⁄ ESP ⁄ 48272 ⁄ 2002

from the Fundac¸ a
˜
o para a Cieˆ ncia e a Tecnologia,
Ministe
´
rio da Cieˆ ncia e Tecnologia, Portugal.
References
1 Muller S, Liebau E, Walter RD & Krauth-Siegel RL
(2003) Thiol-based redox metabolism of protozoan
parasites. Trends Parasitol 19, 320–328.
2 Hannaert V, Saavedra E, Duffieux F, Szikora JP, Rig-
den DJ, Michels PA & Opperdoes FR (2003) Plant-like
traits associated with metabolism of Trypanosoma para-
sites. Proc Natl Acad Sci USA 100, 1067–1071.
3 Lohman K & Meyerhof O (1934) U
¨
ber die enzyma-
tische umwandlung von phosphoglyzerinsa
¨
ure in brenz-
traubensa
¨
ure und phosphorsa
¨
ure (Enzymatic
transformation of phosphoglyceric acid into pyruvic and
phosphoric acid). Biochem Z 273, 60–72.
4 Richard JP (1984) Acid-base catalysis of the elimination
and isomerization reactions of triose phosphates. JAm
Chem Soc 106, 4926–4936.

5 Richard JP (1991) Kinetic parameters for the elimin-
ation reaction catalyzed by triosephosphate isomerase
and an estimation of the reaction’s physiological signifi-
cance. Biochemistry 30, 4581–4585.
6 Ferguson GP, Totemeyer S, MacLean MJ & Booth IR
(1998) Methylglyoxal production in bacteria: suicide or
survival? Arch Microbiol 170, 209–219.
7 Saadat D & Harrison DH (1998) Identification of cata-
lytic bases in the active site of Escherichia coli methyl-
glyoxal synthase: cloning, expression, and functional
characterization of conserved aspartic acid residues.
Biochemistry 37, 10074–10086.
8 Cooper RA (1984) Metabolism of methylglyoxal in
microorganisms. Annu Rev Microbiol 38, 49–68.
9 Westwood ME & Thornalley PJ (1997) Glycation and
advanced glycation endproducts. In The Glycation
Hypothesis of Artherosclerosis (Colaco C, ed.), pp.
57–87. Springer-Verlag, Heidelberg.
10 Leoncini G, Maresca M & Bonsignore A (1980) The
effect of methylglyoxal on the glycolytic-enzymes. FEBS
Lett 117, 17–18.
11 Thornalley PJ (1990) The glyoxalase system: new devel-
opments towards functional characterization of a meta-
bolic pathway fundamental to biological life. Biochem J
269, 1–11.
12 Darling TN & Blum JJ (1988) d-Lactate production by
Leishmania braziliensis through the glyoxalase pathway.
Mol Biochem Parasit 28, 121–127.
13 Irsch T & Krauth-Siegel RL (2004) Glyoxalase II of
African trypanosomes is trypanothione-dependent.

J Biol Chem 279, 22209–22217.
14 Martins AM, Cordeiro CA & Ponces Freire AM (2001)
In situ analysis of methylglyoxal metabolism in Saccharo-
myces cerevisiae. FEBS Lett 499, 41–44.
15 Mclellan AC, Phillips SA & Thornalley PJ (1992) The
assay of methylglyoxal in biological-systems by derivati-
zation with 1,2-diamino-4,5-dimethoxybenzene. Anal
Biochem 206, 17–23.
16 Bakker BM, Michels PAM, Opperdoes FR &
Westerhoff HV (1997) Glycolysis in bloodstream form
Trypanosoma brucei can be understood in terms of the
kinetics of the glycolytic enzymes. J Biol Chem 272,
3207–3215.
17 Martins AM, Cordeiro C & Freire AP (1999) Glyoxa-
lase II in Saccharomyces cerevisiae: in situ kinetics using
the 5,5¢-dithiobis (2-nitrobenzoic acid) assay. Arch Bio-
chem Biophys 366, 15–20.
18 Vickers TJ, Greig N & Fairlamb AH (2004) A trypa-
nothione-dependent glyoxalase I with a prokaryotic
ancestry in Leishmania major. Proc Natl Acad Sci USA
101, 13186–13191.
19 Iozef R, Rahlfs S, Chang T, Schirmer H & Becker K
(2003) Glyoxalase I of the malarial parasite Plasmodium
falciparum: evidence for subunit fusion. FEBS Lett 554,
284–288.
20 Martins AM, Mendes P, Cordeiro C & Freire AP
(2001) In situ kinetic analysis of glyoxalase I and
glyoxalase II in Saccharomyces cerevisiae. Eur J Bio-
chem 268, 3930–3936.
M. Sousa Silva et al. The glyoxalase pathway in Leishmania infantum

FEBS Journal 272 (2005) 2388–2398 ª 2005 FEBS 2397
21 Freire AP, Ferreira A, Gomes R & Cordeiro C (2003)
Anti-glycation defences in yeast. Biochem Soc Trans 31,
1409–1412.
22 Agar NS, Board PG & Bell K (1984) Studies of erythro-
cyte glyoxalase-II in various domestic species – discov-
ery of glyoxalase-II deficiency in the horse. Anim Blood
Groups Bi 15, 67–70.
23 Karg E, Nemeth I, Horanyi M, Pinter S, Vecsei L &
Hollan S (2000) Diminished blood levels of reduced glu-
tathione and alpha-tocopherol in two triosephosphate
isomerase-deficient brothers. Blood Cells Mol Dis 26,
91–100.
24 Helfert S, Estevez AM, Bakker B, Michels P & Clayton
C (2001) Roles of triosephosphate isomerase and aero-
bic metabolism in Trypanosoma brucei. Biochem J 357,
117–125.
25 Comini MA, Guerrero SA, Haile S, Menge U, Lunsdorf
H & Flohe L (2004) Validation of Trypanosoma brucei
trypanothione synthetase as drug target. Free Radic Biol
Med 36, 1289–1302.
26 Oza SL, Shaw MP, Wyllie S & Fairlamb AH (2005)
Trypanothione biosynthesis in Leishmania major. Mol
Biochem Parasitol 139, 107–116.
27 Comini MA, Guerrero SA, Haile S, Menge U, Lunsdorf
H & Flohe L (2004) Validation of Trypanosoma brucei
trypanothione synthetase as drug target. Free Radic Biol
Med 36, 1289–1302.
28 Oza SL, Tetaud E, Ariyanayagam MR, Warnon SS &
Fairlamb AH (2002) A single enzyme catalyses forma-

tion of trypanothione from glutathione and spermidine
in Trypanosoma cruzi. J Biol Chem 277, 35853–35861.
29 Oza SL, Ariyanayagam MR, Aitcheson N & Fairlamb
AH (2003) Properties of trypanothione synthetase from
Trypanosoma brucei. Mol Biochem Parasitol 131, 25–33.
30 Mclellan AC & Thornalley PJ (1992) Synthesis and
chromatography of 1,2-diamino-4,5-dimethoxybenzene,
6,7-dimethoxy-2-methylquinoxaline and 6,7-dimethoxy-
2,3-dimethylquinoxaline for use in a liquid-chromato-
graphic fluorometric assay of methylglyoxal. Anal Chim
Acta 263, 137–142.
31 Vander Jagt DL, Han LP & Lehman CH (1972) Kinetic
evaluation of substrate specificity in the glyoxalase-I-
catalyzed disproportionation of ketoaldehydes. Biochem-
istry 11, 3735–3740.
32 Castro H, Sousa C, Novais M, Santos M, Budde H,
Cordeiro-da-Silva A, Flohe
´
L & Tomas A (2004) Two
linked genes of Leishmania infantum encode tryparedox-
ins localised to cytosol and mitochondrion. Mol Bio-
chem Parasit 136, 137–147.
33 Bradford MM (1976) Rapid and sensitive method for
quantitation of microgram quantities of protein utilizing
principle of protein-dye binding. Anal Biochem 72, 248–
254.
34 Tang D, Shafer MM, Vang K, Karner DA & Arm-
strong DE (2003) Determination of dissolved thiols
using solid-phase extraction and liquid chromatographic
determination of fluorescently derivatized thiolic com-

pounds. J Chromatogr A 998, 31–40.
35 Ondarza RN, Iturbe A, Hurtado G, Tamayo E,
Ondarza M & Hernandez E (1999) Entamoeba histoly-
tica: a eukaryote with trypanothione metabolism instead
of glutathione metabolism. Biotechnol Appl Biochem 30,
47–52.
36 Cordeiro C & Ponces Freire A (1996) Methylglyoxal
assay in cells as 2-methylquinoxaline using 1,2-diamino-
benzene as derivatizing reagent. Anal Biochem 234, 221–
224.
37 Thornalley PJ (1988) Modification of the glyoxalase
system in human red blood cells by glucose in vitro.
Biochem J 254, 751–755.
38 Abecasis J, Ferreira AE & Ponces Freire A (2004)
Metabolic modelling using evolutionary algorithms. Eur
J Biochem 271 (Suppl. 1), 88.
39 Price KV (1999) An introduction to differential evolu-
tion. In New Ideas in Optimization (Corne D, Dorigo M
& Glover F, eds), pp. 79–108. McGraw-Hill, London.
40 Hindmarsh AC (1983) ODEPACK, a Systematized
Collection of ODE Solvers in Scientific Computing
(Stepleman RS, ed), pp. 55–64. North-Holland,
Amsterdam.
The glyoxalase pathway in Leishmania infantum M. Sousa Silva et al.
2398 FEBS Journal 272 (2005) 2388–2398 ª 2005 FEBS

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