Download Structure of Tryptophan

System Biology ISA5101
Final Project
Optimization of Tryptophan Production
in Metabolic Model in Escherichia coli
Group 14
g923922 李昀
g925929 何瓊雯
Tryptophan
Structure:
Symbol : trp w
Molecular formula : C11H12N2O2
Molecular weight : 204.23
Isoelectric point (pH) : 5.89
Usage of Tryptophan
In particular, tryptophan showed considerable promise as an antidepressant, alone
and as an“augmentor”of antidepressant drugs. Other promising indications
included relief of chronic pain and reduction of impulsive, violent, manic, addictive,
obsessive, or compulsive behaviors and disorders.
Metabolic Pathway involved in the Synthesis of Tryptophan
We surveyed the database Kyoto Encyclopedia of Genes and Genomes (KEGG)
and found the metabolic pathway involved in the synthesis of tryptophan in
Escherichia coli from KEGG PATHWAY database. The enzymes and genes that
involved in these pathways were also annotated.
The enzymes and genes (also CDs) are classified into different categories of
major pathways. Also, special notations are made for those involved in more than a
single pathway. The details were shown in the appendix.
These pathways are showed down here, and the blue lines with arrows on these
figures show the paths that considered to be the main paths that involved with the
synthesis of tryptophan.
Phosphotransferase System (PTS)
Glycolysis
Pentose Phosphate Pathway
Glycine, serine and threonine metabolism
Pyruvate metabolism
Citrate cycle (TCA cycle)
Phenylalanine, tyrosine and tryptophan biosynthesis
For simplicity of analysis, we merged the pathways involved in the synthesis of
tryptophan to the pathway below to be the model that we concerned:
PEP
Pyr
Glucose
PTS
ADP
ATP
PGI
+
--
PGDH
6PG
G6P
F6P
F6P
TKb
Ribu5P
R5PI
Ru5P
Xyl5P
Rib5P
TKa
PRPP
PFK
Sed7P
E4P
FBP
ALD
G3P
TPI
G3PDH
TA
DHAP
BPG
DAHPS
PGK
Ser
SerSynth
3PG
DAHP
PGM
ChoSynth
2PG
ENO
Chorismate
PEP
+
PK
-
malate
Fumarate
Succinate
OAA
Ser
PRPP
ATP
TrpSynth
Pyr
PDH
Glyoxylate
Citrate
G3P
Pyr
AcoA
isocitrate
Tryptophan
Propose experiments to determine the metabolic fluxes of the network associated
with the product --- trptophan
Biosynthetically directed fractional 13 C labeling of the proteinogenic amino
acids is achieved by feeding a mixture of uniformly 13 C-labeled and unlabeled
carbon source compounds into a bio-reaction network. Analysis of the resulting
labeling pattern enables both a comprehensive characterization of the network
topology and the determination of metabolic flux ratios. Attractive features with
regard to routine applications include an inherently small demand for 13C-labeled
source compound and the high sensitivity of 2D [ 13 C,
spectroscopy for analysis of 13 C-labeling patterns.
1
H ]-correlation NMR
Propose ways to maximize yield
Michaelis-Menton (MM) models are long been considered as the “gold standard”
for biochemical analysis. New approaches to capture the behavior of biochemical
systems have been divesed. Of particular relevance among these are biochemical
systems theory (BST) and metabolic control analysis (MCA).
Within the framework of BST, optimization methods were developed for
biochemical processes represented as S-systems, where S indicates the fact that these
equations are suitable representations for synergistic and saturated phenomena. In an
S-system model, each rate law for synthesis and degradation is presented by a product
of power-law functions of all variables, such as the substrate (e.g. glucode, ammonia,
etc.), metabolites, biomass (DNA, RNA, protein, lipid, and carbogydrate) and the
cofactors (ATP, ADP, NADH, NADPH) that have a direct influence upon the rate law
in question.
The general S-system description is as follow:
n m
nm
X i   i  X j ij   i  X j ij  Vi   Vi 
g
j 1
h
for i = 1, …, n
j 1
where the two terms at the right side of the equation are the rate law of synthesis and
degradation, respectively. The parameters  i and  i are rate constants, while g ij
and hij are kinetic orders. Rate constants are always non-negative, while kinetic
orders may have any real value.
S-systems and related systems have been called canonical models because of
their rigid structures. In a canonical model, each kinetic order measures the slope of a
rate V as a function of a metabolite or effector X i in logarithmic coordinates. Since V
is generally a function of several variables, a kinetic order, being a slope, can be
expressed as the partial derivative of ln( Vi  ) with repect to ln( X j ) :
g ij 
 ln( Vi  )
r X j
 i  
 ln( X j ) X j Vi
which is evaluated at the chosen operating point. The rate constant is obtained by
equating the power-law term with the traditional rate at steady state and substituting
the numerical values for kinetic orders.
The steady-state equations of S-systems are linear when represented in
logarithmic coordinates and the relevant constraints on variables and fluxes also
become linear upon logarithmic transformation. This property derives the simplicity
of the optimization problem. The great advantage of optimizations with S-systems is
therefore that the optimization problem is strictly linear, even though S-system
models themselves are nonlinear and rich enough to model virtually any set of
differentiable functions or differential equations.
To construct the S-system model for a target pathway, mass balance equations and
kinetic rate equations must be fully understood. Besides, the calculation of kinetic
orders and rate constants is required the fully preparation of the steady state
concentration of each metabolite and parameter values involved in every rate equation.
However, it seems as an impossible mission!!
In our proposed model, two existing dynamic models have been merged. The first
is the dynamic model of central carbon metabolism, which includes glucose transport
system (PTS), glycolysis pathway and pentose-phophate pathway. The second is the
model of tryptophan synthesis. Further considering the repression of trp operon and
feedback inhibition of the enzymes by tryptophan, the cell growth rate and the efflux
of tryptophan, we appended the original model to a new one that includes the
consideration of these effects.
The mass balance equations in the model are listed here.
In central carbon metabolism:
In tryptophan synthesis model:
Base on the model of the main pathway of trptophan biosynthesis and regulatory
and structural gene regions of the trp operon of E. coli, proposed by Z.-L. Xiu et al. in
1997 (figure 2), Marin-Sanguino and Torres then proposed the schematic
representation of the transformations and reactions represented in the model of the trp
operon in E. coli in 2000 (figure 3).
Figure 2. The main pathway of trptophan biosynthesis and regulatory and structural gene regions of the
trp operon of E. coli.
Figure 3. Schematic representation of the transformations and reactions represented in the model of the
trp operon in E. coli.
In this model, the equations governing the tryptophan synthesis are formulated as
follows:
where M is the mRNA concentration, E represents a single enzyme in the synthetic
pathway of tryptophan for simplicity, and P is the intracellular tryptophan
concentration.
After transformation, the equations above would be transformed to
dimensionless forms:
where x, y, z,  and u are dimensionless mRNA, enzyme, and tryptophan
concentrations, time, and growth rate, respectively.
The S-system representation derived from the equation (2) is as below:
The parameters p1 ,, p6 in (3) were used in place of 1 ,..., 6 in (2), those are the
parameters related to the rate constants, saturation constant and constants that
expressing the influence of growth rate and protein concentration, etc., to avoid the
confusion on the notations. The value for the rate constants,  x , y z , in the
S-system representation were determined in such a way that the modeled rate and the
power law approximation are equivalent at the steady state.
Finally, we can get the complete S-system representation of the trp operon
model:
Noticing the fact that this equations represent the model taking into consideration
the effects of the repression of the trp operon and the feedback inhibition of the
enzymes by tryptophan, we had a thought that to use the result differential equation of
tryptophan in the S-system model in place of the mass balance equation of tryptophan
in the original model as the compensation for the effects derived from tryptophan
level.
Now back to our proposed model, the data including steady-state concentration
of the substrates and the metabolites in the central carbon metabolism model is
sufficient for us to construct the S-system model of this part. However, related data in
tryptophan synthesis model is deficient for the construction of S-system model of this
part. Therefore, even with the S-system model of trp operon at hand, we still cannot
simulate the quantitative optimization of tryptophan production with the existing
MATLAB package, BSTLab.
BSTLab is a MATLAB toolbox for BST, which is able to implement numeric
and symbolic analysis of S-systems and the System Biology Markup Language
(SBML) <-> BSTLab conversion. If we have the data of the complete related
parameters, including the steady-state concentrations of the metabolites, the rate
constants and the kinetic orders of the rate law equations representing the pathway of
our target production, the utilization of BSTLab with these parameter data would
make us an easy way to implement the analysis of the S-system model.
Steady-state concentration in central carbon metabolism model
Optimization method
The great advantage of formulating the biochemical pathway as an S-system
model is that the steady state is characterized by linear algebraic equations. Typical
objective functions and constraints on fluxes and metabolites can be formulated as
linear equations or linear inequalities. For these reasons, the optimization of our target
production can be achieved by any existing linear optimization packages.
Additionally, the steady-state solution of the S-system must be checked with
stability and possibly with robustness. If significant discrepancy between the
S-system model and the original MM model is detected, the system is to be revisited
with more stringent constraints. For example, In (Marin-Sanguino and Torres, 2000),
p5 and k i are key parameters in modulating the production of tryptophan, which
may help designing a different strain of E. coli.
Conclusion
A great deal of experimental work is still needed to implement the systematic
optimization approach presented here. Meanwhile, the natural experimental
uncertainties should also be considered, since which in some cases may cause the
deviation up to 50% in the expression of a given gene.
References
 Schmid, J.W., Mauch, K., Reuss, M., Gilles, E.D., Kremling, A., 2004.
Metabolic design based on a coupled gene expression---metabolic network
model of tryptophan production in Escherichia coli. Metabolic Engineering 6,
364-377
 Xiu, Z.-L., Zeng, A.-P., Deckwer, W.-D., 1997. Model analysis concerning the
effects of growth rate and intracellular tryptophan level on the stability and
dynamics of tryptophan biosynthesis in bacteria. J. Biotechnol. 58, 125-140
 Voit, E.O., Torres Darias, N.V., 1998. Canonical modeling of complex
pathways in biotechnology. Biotech. & Bioeng. 1, 321-341
 Chassagnole, C., Noisommit-Rizzi, N. Schmid, J.W., Mauch, K., Reuss, M.,
2002 .Dynamic modeling of the central carbon metabolism of Escherichia coli.
Biotechnol. Bioeng. 79, 53-73
 Marin-Sanguino, A., Torres, N.V., 2000. Optimization of tryptophan
production in bacteria. Design of a strategy for genetic manipulation of the
tryptophan operon for tryptophan flux maximization. Biotechnol. Prog. 16,
133-145
 Rizzi, M., Baltes, M., Theobald, U., Reuss, M., 1996. In vivo analysis of
metabolic dynamics in Saccharomyces cerevisiae:II. Mathematical model.
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