Metabolic flux elucidation of monoterpene metabolism
Bala Krishnamoorthy,PhD, Rigoberto Rios, Roberto Londono Echeverry
Introduction
Monoterpenes are known as the principal constituents of the essential oils and resins of
the common herbs and spices to which they often impart the characteristic odors and
flavors. One of the most important of commercial essential oil-producing species is
peppermint; it produces high levels or p-menthane monoteprenes, with menthone and
menthol as the major constituents. (Lawrence, 1981)
The site of monoterpene biosynthesis has been localized to the secretory cells, which
form an eight-celled apical disc inside peltate glandular trichomes that are located upon
the aerial surface (Fahn, 1979) (Fig 2). The principal pathway of monoterpene
biosynthesis in peppermint has been established, (Fig. 1), but early enzymatic steps are
still known.
Monoterpene composition changes as a function of environmental conditions. The way
the plant regulates its metabolism to account to a reduction in menthol and menthone
concentration under adverse conditions, is still a matter of debate. Knowing early
enzymatic steps would improve understanding of regulation of metabolism, so more
stress conditions and their effects on plant metabolism can eventually be avoided.
The present study is aim at proposing hypothetical early enzymatic pathways that can
be used for building a stoichiometric model of monoterpene metabolism in the secretory
cells. It is our purpose to build a metabolic model that, based on a specified topology of
the monoterpene pathway, can help us to identify optimal flux distribution leading to a
high menthol biosynthesis.
Figure 1. The principal pathway for monoterpene biosynthesis in peppermint (Turner, G.
W., et al. Plant Physiol. 2000;124:655-664)
Problem Formulation
Secretory cells of peppermint leaves are the target for this study.
Metabolic pathways occur within cells as series of chemical reactions that allow
molecular modifications to shape the final product. The final product maybe immediately
used, stored, or transformed into another molecule to initiate a new pathway, called a
flux generating step.
The first molecule that initiates the pathway is called substrate. The metabolic pathway
occurs because the cell needs more amount of the final product and there is enough
amount of substrate to start series of biochemical reactions and obtain it. However,
each molecule counts with several alternative transformations when following the
pathway, thus changing, not only composition but also flux distribution.
Secretory cells of peppermint plant leafs produce menthol. The identification of early
enzymatic steps leading to the synthesis of menthol is the main goal of this study. By
studying the secretory cells, it has been found that some glycolytic and pentose
phosphate pathway enzymes are present in crude extracts of isolated secretory cells.
Thus, as a first approach, we will consider that the early monoterpene metabolic
pathways involve the glycolysis, pentose phosphate and deoxy-xylulose phosphate
pathway, before the principal pathway of monteperpene metabolism is reached.
Fig.2
Fig. 3
Aims
This study follows the following aims:
1. To determine the metabolic flux of the proposed pathway based on 100 units of
initial substrate concentration.
2. To specify the objective function.
3. To identify the optimal flux distribution by means of linear programming.
Methodology:
The following tasks will guide us to the main purpose:
1. To create a graphical representation of the metabolic network.
2. To create the Stoichiometric Model of the metabolic system.
3. To solve the corresponding linear programming problem for the optimal flux
distribution.
Results and Discussion
1. Graphical representation of the metabolic network:
In order to simplify the proposed network, and to build the metabolic model, the fig 3
depicts edges among external and intermediates metabolites. The flux v1, represent the
external composition of Glucose feeding into the glycolytic pathway. The successive
catabolic reactions will end up in menthol as the major product with at least 23
additional intermediates metabolites. Fluxes v13 and v14, represent the building blocks
for biomass and amonoacid biosynthesis; therefore, outflows v13 and v14 should be
known, and can be used as additional constraints for the metabolic model.
2. Stoichiometric Model of the metabolic system.
A metabolic system consisting of metabolites
complex network, can be modeled by means
knowledge of the network topology. It relies on
assumption of pseudo-steady state. (Klamt &
1999).
linked each other via reactions in a
of a stoichiometric analysis, previous
mass balances of metabolites and the
Stelling, 2003; Schilling and Palsson,
In the simultaneous solution of the mass balance equations, a homogeneous system of
linear algebraic equations is set up to define a vector of metabolite concentration M, a
stoichiometric matrix S, of order mxn ( the number of pathway metabolites and of
metabolic fluxes, respectively), and a vector v of net reaction rates. The variation of a
metabolite M in a metabolic system (dM/dt), is proportional to the rate of reaction at
which it is synthesized minus the rate of reaction at which it is consumed producing the
expression:
dM
 S .v  0
dt
This is system of homogeneous linear equations that demands equal rate of production
(positive fluxes) and consumption of metabolites (negative fluxes). It is also the main
constrain in our optimization problem.
In our metabolic system, the number of metabolic fluxes is larger than the number of
metabolites and the solution of system of equations will give infinite number of possible
solutions (combination of fluxes). In other words, we have an under-determined system,
whose possible solutions are constrained in a vector called null-space of the
stoichiometric matrix, and represent the metabolic capabilities of secretory cells.
Metabolic System:
23 Equations
30 Unknown fluxes
7 free fluxes whose values need to be fixed in order to have unique solution. However,
not all the fluxes can be measured and an optimization approach needs to be used.
As an example, the balance equations can be obtained as follows:
dMi/dt = rate of synthesis – rate of degradation
Let us consider that the metabolic system is at steady state i.e. the rate of synthesis
equals the rate of degradation: (there is no accumulation of metabolites along the
pathway).
Therefore,
d[GGP]/dt = 0 = V1-V2-V3 :. V1 = V2+V3
Fig . Balance equations of the reaction system
3. Linear programming Problem
Our Linear Programming Problem is:
Objective function : Z = V28 (Maximize the menthol biosynthesis)
Constraints:
Stoichiometric Relationships :( number of moles (substrate and
product) involved in a biochemical reaction) [S] [V] = [o]
Minimum and maximum values for fluxes.
Non-negative fluxes: Vi > 0
Known external fluxes Vi
Thus,
Max Z = V28
S.t.
S.v. = 0
Vimin ≤Vi ≤Vimax
V13 > 10
V14 > 5
Future goals
To improve the flux analysis by including reversible reactions and cycles in the
proposed metabolic network. The new approach will use isotope labeling techniques
whose mathematical solution requires non-linear optimization.
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