Structural analysis of metabolic networks

1
Structural analysis of metabolic networks
Ms. Shivani Bhagwat Lecturer, School of
Biotechnology DAVV
2
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.
3
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.
4
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.
5
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.
6
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
7
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.
8
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.
9
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 a-ketoglutarate, 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.

10
(No Transcript)
11
The conversion of glucose to phosphoenolpyruvate
(PEP) is lumped into an overall reaction with the
following stoichiometry 8 overall reactions

• 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.

12
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.
13
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
well-instrumented bioreactors at least some
variables, e.g., pH and dissolved oxygen tension,
may, however, be controlled at a constant level.
14
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
15
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.
16
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.
17
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
18
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.
19

• 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.

20
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.
21
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.
22
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.
23
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.
24
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.
25
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

26
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).
27
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.
28
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.
29
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).
30
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 V0.
31
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.
32
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.