Structural analysis of metabolic
networks
Ms. Shivani Bhagwat
Lecturer,
School of Biotechnology
DAVV
Structural analysis of metabolic networks
Global network properties
Knowledge about the topological properties of a metabolic network(MN) is central
to the understanding of its function.
Graph theoretic approaches have been extensively employed to derive global
network features such as topological organization and robustness properties
(Ravasz, 2003 and Palsson, 2006), determine the importance of individual
enzymes or metabolites and curate the network by predicting missing components.
A number of graph theoretic measures describe the global structure of MNs
(Discrete Models and Mathematics, Graph Theoretic Approaches).
The degree distribution is the probability distribution of links per node (degree) in a
network.
A small number of metabolites act as hubs involved in a very large number of
reactions (e.g. ATP, Coenzyme A), making the network extremely robust to random
loss of nodes.
Discrete Models and Mathematics: Discrete mathematics is the study of
mathematical structures that are fundamentally discrete rather than continuous.
Graph Theoretic Approaches: For many species, multiple maps are available,
often constructed independently by different research groups using different sets
of markers and different source material. Integration of these maps provides a
higher density of markers and greater genome coverage than is possible using a
single study.
Local network analysis In addition to local versions of the measures, attempts
have been made to examine the network on a local scale. Network motifs,
defined as sub-networks that occur significantly more often in a network than
expected by chance, have been identified and shown to perform specific tasks in
MNs.
Among them are futile cycles that dissipate energy in the MN, switches directing
the metabolite flux and feed-forward motifs that provide regulatory control.
Overall, it appears that the recurrence of such local architecture enables
biological adaptation to varying environments.
The number of shared neighbors between two nodes is called a topological
overlap. By calculating it for every node and subsequent clustering (Clustering),
a topological overlap map can be generated.
Metabolites with similar biochemical properties cluster together, demonstrating
functional organization of sub networks in MNs.
From static to dynamic models
Despite their usefulness, graph-based approaches do not depict the dynamical
behavior of metabolic networks.
However, stoichiometry based approaches and kinetic models permit to investigate
the fluxes of metabolites within metabolic pathways, which is of great interest with
respect to functional analysis of metabolism and pharmacological studies.
Boolean network analysis (BNA) use Boolean logic to infer the capacity to
produce given metabolites and the activities of given reactions, by treating each
node as a switch that can either be on or off. After setting appropriate starting
states, in which certain reactions are switched off, the state of all other nodes is
determined by iteratively applying Boolean rules, until no further change occurs.
BNA has been applied successfully in model curation and network robustness
analysis.
Network expansion is a method closely related to BNA: Starting with a seed of
nutrients, the so called scope (all producible metabolites and active reactions) is
determined iteratively, based on Boolean state switches. Thus, the biosynthetic
capacities of a MN can be assessed.
Petri nets are directed bipartite graphs that are capable of modelling a discrete
flow of mass within a MN. They are supported by a well--‐developed mathematical
theory that even allows a transition to continuous simulations.
Chemical reaction network theory (CRNT) and species reaction graphs (SR
graphs) use topology and a few basic assumptions to derive the stability (Stability)
and the possibility of multistability (Bistability) of a MN. However, due to their
computational complexity, they are unsuitable at present for genome scale models.
metabolic network dynamics are dependent on a multitude of factors in addition to
network structure:
reaction thermodynamics,
kinetics and rates
environmental conditions
Flux balance analysis (FBA) calculates optimal reaction rates at steady state in
the network (flux distribution) by formulating a linear optimization problem.
Reaction rates are constrained by the network stoichiometry, metabolite
availability and thermodynamic properties of the catalysing enzymes.
FBA is especially useful for simulating network disturbances, such as enzyme loss
or nutrient shortage.
STOICHIOMETRY OF CELLULAR REACTIONS
The overall result of the totality of cellular reactions is the conversion of substrates into free
energy and metabolic products (e.g., primary metabolites),more complex products (such as
secondary metabolites), extracellular proteins and constituents of biomass, e.g., cellular
proteins, RNA, DNA, and lipids. These conversions occur via a large number of metabolites,
including precursor metabolites and building blocks in the synthesis of macromolecular
pools.
In cellular reactions there are a number of cofactor pairs, with ATP/ADP, NAD+/NADH, and
NADP+/NADPH being the most important. For the two compounds in a cofactor pair, the
stoichiometric coefficients will normally be the same in magnitude but of opposite sign, e.g.
the stoichiometric coefficients for NADPH and NADP+ are -1 and 1 respectively.
Example: Mixed Acid Fermentation by E. coli
 E. coli is a facultative anaerobe that mediates a relatively complex fermentation normally
referred to as mixed acid fermentation.
Seven metabolic products are produced, and with the exception of succinate, which is
made from phosphoenolpyruvate, all metabolites are formed from pyruvate.
Succinate is formed via oxaloacetate, which undergoes transamination with glutamate to
yield aspartate (one NADPH and one ammonium are used to regenerate glutamate from aketoglutarate, so they appear as reactants.
Aspartate is then deaminated to form fumarate, which is finally reduced to succinate by
fumarate dehydrogenase (which is different from the succinate dehydrogenase that
functions in the opposite direction).
Our goal in setting up a stoichiometric model is to account for the n e t change of
metabolites in the medium in the context of catabolic reactions operative in a typical E. coli
cell.
Mixed acid fermentation by E. coli.
The conversion of glucose to phosphoenolpyruvate (PEP) is lumped into an overall reaction
with the following stoichiometry : 8 overall reactions
1.
2.
3.
4.
5.
6.
7.
8.
1/2glucose + PEP + NADH= 0
-PEP - CO 2 - 2NADH + succinate = 0
-PEP + pyruvate + ATP = 0
-pyruvate- NADH + lactate = 0
-pyruvate + acetyl-CoA + formate = 0
-formate + CO 2 + H2 = 0
-acetyl-CoA + acetate + ATP = 0
-acetyl-CoA- 2NADH + ethanol = 0
Glucose is identified as a substrate and succinate, carbon dioxide, lactate, formate,
hydrogen, acetate, and ethanol as metabolic products, with phosphenolpyruvate (PEP),
pyruvate, acetyl-CoA, ATP, and NADH as intracellular metabolites.
ATP is produced only in two reactions, namely, the conversion of PEP to pyruvate and the
conversion of acetyl-CoA to acetate.
Because the fluxes of these two reactions are measurable (the flux to acetate can be
measured directly as the formation rate of acetate, whereas the flux from PEP to
pyruvate can be measured from the sum of the rates of formation of all the metabolic
products except succinate or from the difference between the glucose uptake rate and
the rate of succinate formation), we can obtain information on the total rate of ATP
synthesis.
As there are no other sources of ATP supply under anaerobic conditions, the latter is also
an estimate of the consumption rate of ATP for growth and maintenance.
DYNAMIC MASS BALANCES
A mass balance (also called a material balance) is an application of conservation of mass to
the analysis of physical systems.
By accounting for material entering and leaving a system, mass flows can be identified
which might have been unknown, or difficult to measure.
Input = output + accumulation
Dynamics of the bioreactor
Batch: where F - Fout = 0, i.e., the volume is constant. Batch experiments have the
advantage of being easy to perform and can produce large volumes of experimental data in
a short period of time. The disadvantage is that the experimental data are difficult to
interpret as there are dynamic variations throughout the experiment, i.e., the
environmental conditions experienced by the cells vary with time. By using wellinstrumented bioreactors at least some variables, e.g., pH and dissolved oxygen tension,
may, however, be controlled at a constant level.
Continuous: where F = F out ≠ 0 , i.e., the volume is constant. A typical operation of the
continuous bioreactor is the so-called chemostat, where the added medium is designed
such that there is a single rate-limiting substrate. This allows for controlled variation in the
specific growth rate of the biomass. The advantage of the continuous bioreactor is that a
steady state can be obtained, which allows for precise experimental determination of
specific rates under well-defined environmental conditions.
The disadvantage of the continuous bioreactor is that it is laborious to operate as large
amounts of fresh, sterile medium have to be prepared and requires long periods of time
for a steady state to be achieved.
Fed-batch (or semibatch): where F ≠ 0 and F out = 0, i.e., the volume increases. This is
probably the most common operation in industrial practice, because it allows for control of
the environmental conditions, e.g., maintaining the glucose concentration at a certain
level, and it enables formation of much higher titers
Dynamic mass balances for the substrate will be :
Substrate = - rate of substrate consumption + rate of substrate addition – rate of
accumulation
substrate removal
The specific substrate consumption rate of the ith substrate,
x is the biomass concentration (g DW L -1)
D is the so-called dilution rate (h -1)
Which is zero for a batch reactor and for a chemostat and a fed-batch reactor is
given by:
D= F/V
rate of substrate consumption = specific rate of substrate consumption X biomass
concentration.
At steady state the accumulation term is equal to zero, so that the volumetric rate of
substrate consumption becomes equal to the product of the dilution rate multiplied by
the difference in the substrate concentrations between the inlet and outlet of the reactor.
Another approach is to carry out a functional representation of the data,e.g., polynomial
splining, and to calculate the derivatives and specific rates from the fitted functions.
This approach too can give rise to large fluctuations in the specific rates, because it is
difficult to find good functional representations of experimental cultivation data.
YIELD COEFFICIENTS AND LINEAR RATE EQUATIONS
Macroscopic assessment of the overall distribution of metabolic fluxes, e.g., how much
carbon in the glucose substrate is recovered in the metabolite of interest. This overall
distribution of fluxes is normally represented by the so-called yield coefficients.
Yield coefficients are, therefore, dimensionless and take the form of unit mass of
metabolite per unit mass of the reference, e.g., moles of lysine produced per moles of
glucose consumed.
The moles of carbon dioxide produced per mole of oxygen consumed, called the
respiratory quotient (RQ), frequently is used to characterize aerobic cultivations.
Metabolic Model of Penicillium chrysogenum
we consider a simple metabolic model for the filamentous fungus P. chrysogenum as
presented by Nielsen (1997).
The stoichiometric model summarizes the overall cellular metabolism, and by employing
pseudo-steady state assumptions for ATP, NADH, and NADPH metabolites, it is possible to
derive linear rate equations where the specific uptake rates for glucose and oxygen and
the specific carbon dioxide formation rate are expressed in terms of the specific growth
rate. By evaluating the parameters in these linear rate expressions, which can be done
from a comparison with experimental data, information on key energetic parameters
may be extracted.
In the analysis, formation of metabolites (both primary metabolites like gluconate and
metabolites related to penicillin biosynthesis) was neglected, because the carbon flux to
these products was small compared with the flux to biomass and carbon dioxide.
The overall stoichiometry for synthesis of the constituents of a P. chrysogenum cell can be
summarized as (Nielsen, 1997):
Biomass + 0.139 CO 2 + 0.458 NADH- 1.139 CH20 - 0.20 NH3 - 0.004 H2SO4- 0-010 H3PO4 Y xATP ATP - 0.243NADPH = 0
Material Balances and Data Consistency
Quantitative analysis of metabolism requires experimental data for the
determination of metabolic fluxes, flux distributions, and measures of flux
Control.
In the context of metabolic analysis, flux calculations are based on the
measurement of the specific rates for substrate uptake and product formation,
which represent the fluxes in and out of the cells.
Data redundancy is introduced when multiple sensors are employed for the
measurement of the same variable or when certain constraints must be
satisfied by the measurements so obtained, such as closure of material
balances. Obviously, the greater the redundancy, the higher the degree of
confidence for the data and their derivative parameters.
Experimental data that are to be used for quantitative analysis must be:
 Complete
 Noise free
There are two approaches in assessing the consistency of experimental data.
The first is based on a very simple metabolic model, the so-called black box
model, where all cellular reactions are lumped into a single one for the
overall cell biomass growth, and the method basically consists of validating
elemental balances.
The second approach recognizes far more biochemical detail in the overall
conversion of substrates into biomass and metabolic products. As such, it is
mathematically more involved, but, of course, it provides a more realistic depiction
of the actual degrees of freedom than a black box model.
THE BLACK BOX MODEL
Cell biomass is the black box exchanging material with the environment, and
processing it through many cellular reactions lumped into one, that of biomass
growth. The fluxes in and out of the black box are given by the specific rates (in
grams or moles of the compound per gram or mole of biomass and unit time).
These are the specific substrate uptake rates and the specific product formation
rates.
Representation of the black box model. The cell is considered as a black box, and
fluxes in and out of the cell are the only variables measured. The fluxes of substrates
into the cell are elements of the vector r s, and the fluxes of metabolic products out of
the cell are elements of the vector r p. Some of the mass originally present in the
substrates accumulates within the black box as formation of new biomass with the
specific rate µ.
Use of the black box model for analyzing data consistency, one may use either:
(1) A set of yield coefficients together with the specific growth rate
(2) a set of yield coefficients with respect to another reference, e.g., one of the
substrates, along with the specific rate of formation/consumption of reference
compound
(3) a set of specific rates for all substrates and products, including biomass
4) a set of all volumetric rates that are the product of the specific rates by the
biomass concentration.
Black Box Model example:
Consider the aerobic cultivation of the yeast Saccharomyces cerevisiae on a
defined, minimal medium, i.e., glucose is the carbon and energy source and
ammonia is the nitrogen source.
During aerobic growth, the yeast oxidizes glucose completely to carbon dioxide.
However, at very high glycolytic fluxes, a bottleneck in the oxidation of pyruvate
leads to ethanol formation. Thus, at high glycolytic fluxes, both ethanol and carbon
dioxide should be considered as metabolic products.
Finally, water is formed in the cellular pathways, and this is also included as a
product in the overall reaction.
The stoichiometric (or yield) coefficients are not constant, as yield is zero at low
specific growth rates (corresponding to low glycolytic fluxes) and greater than zero
for higher specific growth rates.
ELEMENTAL BALANCES
In the black box model, we have M + N + 1 variables:
M yield coefficients for the metabolic products,
N yield coefficients for the substrates,
the forward reaction rate µ or the M + N + 1 specific rates .
Because mass is conserved in the overall conversion of substrates to metabolic
products and biomass, the (M + N + 1) rates of the black box model are not
completely independent but must satisfy several constraints.
Thus, the elements flowing into the system must balance the elements
flowing out of the system, e.g., the carbon entering the system via the
substrates has to be recovered in the metabolic products and biomass.
Each element considered in the black box obviously yields one constraint.
HEAT BALANCE
In the conversion of substrates to metabolic products and biomass, part of
the Gibbs free energy in the substrates is dissipated to the surrounding
environment as heat. Especially under aerobic conditions, the energy dissipation
may be substantial.
Energy dissipation is determined by the difference between the total Gibbs free
energy in the substrates and the total Gibbs free energy recovered in the metabolic
products and biomass.
The energy dissipation normally gives rise to changes in both the enthalpy and
entropy of the system, and it is difficult to quantify.
Attention is, therefore, generally focused on heat production determined by the
change in enthalpy, as this heat production has direct consequences for process
cooling requirements for temperature control.
Metabolic flux analysis(MFA)
The first step in the process is to identify a desired goal to achieve through the
improvement or modification of an organism's metabolism or,
Step I: system definition
Step II: mass balance
Step III: defining measurable fluxes
Step IV: optimization
The databases contain genomic and chemical information including pathways for
metabolism and other cellular processes. From this an organism is chosen that will
be used to create the desired product or result.
Considerations that are taken into account are:
 how close the organism's metabolic pathway is to the desired pathway
 the maintenance costs associated with the organism
how easy it is to modify the pathway of the organism.
Escherichia coli (E. coli) is widely used in metabolic engineering to synthesize a
wide variety of products such as amino acids because it is relatively easy to
maintain and modify. If the organism does not contain the complete pathway for the
desired product or result, then genes that produce the missing enzymes must be
incorporated into the organism
Analyzing a metabolic pathway
The completed metabolic pathway is modeled mathematically to find the theoretical
yield of the product or the reaction fluxes in the cell. A flux is the rate at which a
given reaction in the network occurs.
Simple metabolic pathway analysis can be done by hand, but most require the use
of software to perform the computations.
These programs use complex linear algebra algorithms to solve these models. To
solve a network using the equation for determined systems .
Information about the reaction (such as the reactants and stoichiometry) are
contained in the matrices Gx and Gm.
Matrices Vm and Vx contain the fluxes of the relevant reactions. When solved, the
equation yields the values of all the unknown fluxes (contained in Vx).
Determining the optimal genetic manipulations
After solving for the fluxes of reactions in the network, it is necessary to determine
which reactions may be altered in order to maximize the yield of the desired
product. To determine what specific genetic manipulations to perform, it is
necessary to use computational algorithms, such as OptGene or OptFlux.
They provide recommendations for which genes should be over expressed,
knocked out, or introduced in a cell to allow increased production of the desired
product. For example, if a given reaction has particularly low flux and is limiting the
amount of product, the software may recommend that the enzyme catalyzing this
reaction should be over expressed in the cell to increase the reaction flux.
The necessary genetic manipulations can be performed using standard molecular
biology techniques. Genes may be over expressed or knocked out from an
organism, depending on their effect on the pathway and the ultimate goal.
Experimental measurements
In order to create a solvable model, it is often necessary to have certain fluxes
already known or experimentally measured. In addition, in order to verify the effect
of genetic manipulations on the metabolic network (to ensure they align with the
model), it is necessary to experimentally measure the fluxes in the network. To
measure reaction fluxes, carbon flux measurements are made using carbon-13
isotopic labeling. The organism is fed a mixture that contains molecules where
specific carbons are engineered to be carbon-13 atoms, instead of carbon-12.
After these molecules are used in the network, downstream metabolites also
become labeled with carbon-13, as they incorporate those atoms in their
structures. The specific labeling pattern of the various metabolites is determined by
the reaction fluxes in the network.
Labeling patterns may be measured using techniques such as Gas
chromatography-mass spectrometry (GC-MS) along with computational algorithms
to determine reaction fluxes.
Step I – system definition
A model system comprising three metabolites (A, B and C)
with three reactions (internal fluxes, vi including one
reversible reaction) and three exchange fluxes (bi).
Step II – mass balance
Stoichiometric matrix S
Flux matrix v
S · v = 0 in steady state.
Mass balance equations accounting for all reactions and transport
mechanisms are written for each species. These equations are then
rewritten in matrix form. At steady state, this reduces to S · V=0.
Step III – defining measurable fluxes & constraints
The fluxes of the system are constrained on the basis of
thermodynamics and experimental insights. This creates a flux
cone corresponding to the metabolic capacity of the organism.
Step 4 – optimization
Optimization of the system with different objective functions
(Z). Case I gives a single optimal point, whereas case II
gives multiple optimal points lying along an edge.