40
Part 3.1
Chapter
#
REGULATION OF THE PENTOSE PHOSPHATE
PATHWAY IN ESCHERICHIA COLI:
GENE NETWORK RECONSTRUCTION
AND MATHEMATICAL MODELING
OF METABOLIC REACTIONS
Ratushny A.V.*1, Smirnova O.G.1, Usuda Y.2, Matsui K.2
1
Institute of Cytology and Genetics, SB RAS, Novosibirsk, 630090, Russia; 2 Institute of Life Sciences,
Ajinomoto, Co., Inc., Kawasaki, Japan
*
Corresponding author: e-mail: [email protected]
Key words:
mathematical modeling, gene network, regulation, pentose phosphate pathway, glucose
6-phosphate-1-dehydrogenase, Escherichia coli
SUMMARY
Motivation: Development of an in silico cell, a computer resource for modeling and
analysis of physiological processes, is an urgent task of systems biology and
computational biology. Mathematical modeling of the genetic regulation of one of the
basic metabolic processes, the pentose phosphate pathway, is an important problem to be
solved as part of this line of work.
Results: By using the GeneNet technology, we reproduced the gene network of the
regulation of the pentose phosphate pathway in the E. coli cell. Mathematical models
were constructed by the method of generalized Hill functions to describe the efficiency of
enzyme systems.
Availability: Models are available on request. Gene network is available at
http://wwwmgs.bionet.nsc.ru/mgs/gnw/genenet/viewer/index.shtml.
INTRODUCTION
Apart from glycolysis, the pentose-phosphate pathway is a major route of
intermediary carbohydrate metabolism. In addition to its role as a route for the breakdown
of sugars such as glucose or pentoses, the pentose phosphate pathway is involved in the
generation of reducing power (NADPH) for biosynthesis and provides the cell with
intermediates for the anabolism of amino acids, vitamins, nucleotides, and cell wall
constituents. In E. coli, two branches of the pentose-phosphate pathway occur: (1) the
oxidative branch, in which pentose phosphate is formed from glucose-6-P, and (2) a nonoxidative branch in which fructose-6-P and glyceraldehydes-3-P, participants of the
Embden-Meyerhof-Parnas pathway, are formed. Moreover, the pentose-phosphate
pathway is the only pathway that allows E. coli to utilize sugars such as D-xylose, Dribose, or L-arabinose, which cannot be catabolized by other routes (Sprenger, 1995).
The gene network of regulation of the pentose phosphate pathway in the E. coli cell
was reconstructed. Mathematical models of the efficiency of enzyme systems were
constructed. A database storing experimental data on the behavior of components of this
gene network was developed (Khlebodarova et al., this issue). Parameters of the models
were determined by numerical simulation. The results of calculation of steady-state
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Modelling of molecular genetic systems in bacterial cell
41
properties and behavior of the components of the molecular system derived from the
models are in agreement with experimental evidence.
METHODS AND ALGORITHMS
The gene network was reconstructed using the GeneNet system (Ananko et al., 2005).
The method of generalized Hill functions (Likhoshvai, Ratushny, 2006) was used to
model the regulation of the functioning efficiency of enzymatic systems.
RESULTS AND DISCUSSION
The pentose phosphate pathway of Escherichia coli involves 10 enzymatic reactions
(Fig. 1, Table 1, 2). Most of the corresponding enzymes are repressed by the final products
of the reactions: glucose 6-phosphate (G6P), 2-keto-3-deoxy-6-phosphogluconate
(2KD6PG), fructose 6-phosphate (F6P), ribose 5-phosphate (R5P), glyceraldehyde
3-phosphate (T3P1), and ribulose 5-phosphate (RL5P). Also, fructose 1,6-diphosphate
(FDP), phosphoenolpyruvate (PEP), arabinose 5-phosphate (A5P) and inorganic phosphate
(PI) are downregulators of the pentose phosphate pathway. The activities of glucose 6phosphate-1-dehydrogenase and 6-phosphogluconate dehydrogenase depend on the energy
and redox potential of the cell. They are repressed by ATP, NADH and NADPH. The
following proteins control the expression of the genes of the pentose phosphate pathway:
SoxS, MarA, Rob (zwf), GadE (gnd), FruR (edd-eda), CreB (talA-tktB), RpiR (rpiB), and
LipB. Moreover, the pentose phosphate pathway is superoxide-sensitive. An iron–sulfur
cluster of 6-phosphogluconate dehydratase coded by the edd gene is the superoxidesensitive target site, which is readily destroyed by oxidation.
Table 1 summarizes the components of the network. Table 2 shows the enzymatic
reactions present in the pentose phosphate pathway gene network, names of enzymes
catalyzing corresponding reactions, and names of genes coding for the enzymes.
Table 1. Components of the pentose phosphate pathway gene network
Operon
RNA
Protein
Reaction
Inorganic
Repressor
substance
11
11
35
104
31
19
Transcription factor
5
Table 2. Enzymatic reactions constituting the pentose phosphate pathway gene network
Enzyme
Gene
Reaction
zwf
Glucose 6-phosphate-1G6P + NADP ↔ D6PGL + NADPH
dehydrogenase
pgl
6-Phosphogluconolactonase
D6PGL → D6PGC
gnd
6-Phosphogluconate
D6PGC + NADP → NADPH +
dehydrogenase (decarboxylating)
CO2 + RL5P
rpiA, rpiB
Ribose-5-phosphate isomerase A,
RL5P ↔ R5P
B
rpe
Ribulose phosphate 3-epimerase
RL5P ↔ X5P
tktA, tktB
Transketolase I, II
R5P + X5P ↔ T3P1 + S7P
tktA, tktB
Transketolase I, II
X5P + E4P ↔ F6P + T3P1
talA, talB
Transaldolase A, B
T3P1 + S7P ↔ E4P + F6P
edd
Phosphogluconate dehydratase
D6PGC → 2KD6PG
2-Keto-3-deoxy-6-phosphogluconate eda
2KD6PG → T3P1 + PYR
aldolase
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Reference
109
EC
1.1.1.49
3.1.1.31
1.1.1.44
5.3.1.6
5.1.3.1
2.2.1.1
2.2.1.1
2.2.1.2
4.2.1.12
4.1.2.14
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Part 3.1
Figure 1. Pentose phosphate pathway gene network reconstruction in the GeneNet.
Application of the method of generalized Hill functions to modeling the molecular
processes of the pentose phosphate pathway can be exemplified by regulation of the
activity of the enzyme glucose 6-phosphate-1-dehydrogenase (G6PD) in the E. coli cell
(Table 1). The mechanism of this process is very intricate. NADH inhibits the reaction
and intricately affects the G6PD activity. The reaction rate sigmoidally depends on NADP
content with the presence of NADH. With the absence of NADH, this dependence
assumes a hyperbolic form. No sigmoidal dependence is observed at variable G6P
concentrations under the same conditions either (Sanwal, 1970). The reaction rate is
affected by NADP, which reduces G6P affinity to the enzyme. The reaction product,
NADPH, inhibits the G6PD activity. A model for the steady-state rate of the reaction
is proposed:
V=
kcat ⋅ e0 ⋅ G6P
⎛
NADP htg
K m,G6P ⋅ ⎜ 1 + ktgn ⋅ htg
⎜
ktg + NADP htg
⎝
⋅
⎞
⎟⎟ + G6P
⎠
⎛ NADP ⎞
⎜⎜
⎟⎟
⎝ K m , NADP ⎠
⎛ NADP ⎞
1 + ⎜⎜
⎟⎟
⎝ K m , NADP ⎠
1+ kdtn ⋅
⋅
1+ kdtn ⋅
NADH hdt
kdt hdt + NADH hdt
⋅
NADH hdt
kdt
hdt
+ NADH
(1)
hdt
⎛ NADPH ⎞
+⎜
⎟
⎝ k NADPH ⎠
hNADPH
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1
⎛ NADH ⎞
1+ ⎜
⎟
⎝ k NADH ⎠
hNADH
,
Modelling of molecular genetic systems in bacterial cell
43
where e0 is the concentration of the enzyme glucose 6-phosphate-1-dehydrogenase;
G6P, NADP, D6PGL, NADPH are concentrations of the corresponding low-molecularweight substances; kcat, the catalytic constant; Km,G6P, Km,NADP, Michaelis constants for
corresponding substrates; kNADPH, constant of inhibition by NADPH; hNADPH, constant
determining the nonlinearity of the effect of NADPH on the reaction rate; kdtn, kdt, kNADH,
constants of the efficiency of the effect of NADH on the reaction rate; hhdt, hNADH,
constants determining the nonlinearity of the effect of NADH on the reaction rate; ktgn, ktg,
constants of the efficiency of the effect of NADP on the reaction rate; and htg, constant
determining the nonlinearity of the effect of NADP on the reaction rate.
Experimental data obtained by Sanwal (1970) were used for testing the model of
regulation of G6P1D activity. These data illustrate the effects of the substrates G6P and
NADP on G6P1D activity with various concentrations of NADH and NADPH (Fig. 2).
Figure 2. (a) Effect of NADH on the rate of the reaction catalyzed by G6P1D at various G6P
concentrations; (b) Effect of G6P on the rate of the reaction catalyzed by G6P1D at various NADH
concentrations; (c, d) Effect of NADP on the rate of the reaction catalyzed by G6P1D at various
concentrations of (c) NADH and (d) NADPH. The enzyme activity was measured (a) with 50 μM NADP
at pH = 7.5, G6P concentrations equaling: 1, 520 μM; 2, 210 μM; (b) with 0.3 mM NADP and 5 mM
MgCl2, pH=7.5 at NADH concentrations: 1, null; 2, 176 μM; 3, 264 μM; 4, 440 μM; (c) with 0.42 mM
G6P, 5 mM MgCl2, pH=7.5 at NADPH concentrations: 1, null; 2, 37 μM; 3, 74 μM; 4, 148 μM. Dots
indicate experimental data from (Sanwal, 1970), and curves are the results of simulation according to
model (1) with the following parameters: Km,G6P =150 μM, Km,NADP =30 μM, ktgn = 1, ktg = 400,
htg = 1, kdtn = 0.3, kdt = 100, hdt = 2, kNADPH = 15, hNADPH = 1.4, kNADH = 300, and hNADH = 4.
The model takes into account the intricate nonlinear mechanism of the reaction and
dependence of the enzyme activity on various low-molecular-weight components. For
example, the mode of the NADP effect on the reaction rate changes from hyperbolic
without NADH to sigmoid with NADH. The Hill coefficient in the model functionally
depends on NADH, equaling unity with its absence and increasing in a threshold manner
with its presence, which also allows proper description of experimental evidence
(Fig. 2c). Moreover, NADH itself extremely nonlinearly influences the reaction rate by
reducing it (Fig. 2a). In model (1), inhibition by NADH is described by the product
including the last fraction, the Hill coefficient, estimated to be hNADH = 4. The model also
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Part 3.1
describes the effect of NADP on G6P affinity to the enzyme, a nonlinear twofold
increase. Model (1) takes into account the nontrivial competition between NADPH and
NADP, which allows proper description of experimental evidence (Fig. 2d).
Thus, the modeling method used in this work allows construction of proper
mathematical models with relatively simple description of the processes modeled with the
lack of knowledge on their fine mechanisms, when, for example, the King and Altman
algorithm (King, Altman, 1956; Cornish-Bowden, 1977) cannot be applied.
Reconstruction of the gene network of regulation of the pentose phosphate pathway
and development of mathematical models describing the efficiency of operation of
enzyme systems and regulation of genes coding for these enzymes is essential for
construction of an overall kinetic model of the network. Such a model will allow
determination of key links of the gene network, prediction of the course of processes
accompanying carbohydrate conversion in the pentose phosphate pathway, and analysis
of the effects of mutations on its operation. The model of the pentose phosphate pathway
will be an inextricable part of the “in silico cell” computer resource.
ACKNOWLEDGEMENTS
The authors are grateful to Vitaly Likhoshvai for valuable discussions, to Irina
Lokhova for bibliographical support, and to Victor Gulevich for translating the
manuscript from Russian into English. This work was supported in part by the Russian
Government (Contract No. 02.467.11.1005), by Siberian Branch of the Russian Academy
of Sciences (the project “Evolution of molecular-genetical systems: computational
analysis and simulation” and integration projects Nos 24 and 115), and by the Federal
Agency of Science and Innovation (innovation project No. IT-CP.5/001).
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description of kinetic data. This issue.
Likhoshvai V.A., Ratushny A.V. (2006) In silico cell I. Hierarchical approach and generalized hill
functions in modeling enzymatic reactions and gene expression regulation. This issue.
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165, 55–59.
King E.L., Altman C. (1956) A schematic method of deriving the rate laws for enzyme-catalyzed
reactions. J. Phys. Chem., 60, 1375–1378.
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