Ways to improve microbial production

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MCB-221b lecture 8 Metabolic Control
Analysis and Stoichiometry networks
I (metabolic networks)
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Different levels of metabolic network
analysisExplain, categorize, predict
evolutionarymodels
abstraction
topologymodels
stoichiometrymodels
flux models
kineticmodels
mechanistic
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Metabolic Control Analysis

• A complete dynamic description of a metabolism
  would require enzyme-kinetic and regulatory
  information which is hard to obtain

dX dt
S v b v fn(X,)
X metabolite concentrations S stoichiometric
matrix v Reaction fluxes (a vector of the n
metabolic reaction rates) b Net transport (a
vector of the net metabolic uptake)

• Turn the dynamic system into a steady state model
  ?eliminate the requirement for kinetic
  information by treating the metabolic fluxes as
  the unknown properties to be determined

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Categorising methods
Engineering approach Input and output fluxes
are measured and used to determine the internal
net fluxes through the metabolic pathways. These
methods are static they describe fluxes at given
conditions and do not allow for extrapolation to
other conditions and transients. Example
Metabolic Flux Analysis (MFA), Flux Balance
Analysis (FBA). Cybernetic approaches. Based on
the hypothesis that cells react to their
environment using an optimal response for
survival and competition. Example Optimal
Metabolic Control Theory. Treat metabolism as a
limited set of enzymes with interactions that can
be described in terms of substrate, enzyme and
product levels. Example Metabolic Control
Analysis.
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Metabolic Control Analysis
Jens Nielsen, 1998, Biotechnol Bioeng
58_125-132 Furthermore, one often finds terms
like rate-limiting steps and bottleneck
enzyme when control of flux is discussed. Early
findings suggested that it is the first enzyme in
a pathway, or the first enzyme after a branch
that is under some type of control, such as
feed-back inhibition, hence the often heard
statement, The first step in a pathway is the
rate limiting step. The concept of metabolic
control analysis (MCA) tells us that these kinds
of qualitative statements have no meaning,
because flux control is distributed over all the
steps in a pathway, but some steps have a higher
degree of flux control than others.
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Metabolic Control Analysis
Regulation and control  Certain terms are
particularly important for discussion Flux is
a term used in metabolic analysis to indicate the
rate of a multi-component system (metabolic
pathway), while rate is reserved for individual
components (enzyme).   The distinction between
regulation and control Regulation is occurring
when the system maintains some variable (e.g.
temperature or concentration) constant over time,
despite fluctuations in external conditions (a
concept linked to homeostasis) Control is used
in technology to refer to adjusting the output of
a system with time. Control as a verb implies the
ability to start/stop/direct something.
  Metabolic Control is thus defined as the
power to change the state of metabolism in
response to an external signal, and it is
measurable in terms of the strength of the
metabolic response to external factors, without
any assumption about the function/purpose/mechanis
m of the response
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Metabolic Control Analysis
Critique on pre-1973 view The rate-limiting step
is defined as the slowest step in the pathway,
but in a metabolic steady state all the steps
along a linear pathway are going at the same
rate. Otherwise, you would have steadily and
infinitely increasing concentrations of
intermediates.   If slowest step is
interpreted as the step least able to go faster,
then classical biochemical observations do not
measure this inability. Evidence from the 1930s
onward show that even the rate of a sequence of
simple chemical reactions could depend on the
rate constants of all the reactions.  If a
unique rate-limiting step exists in a pathway
(e.g. J1) then varying the activity of that step
alone will change the flux in the pathway. But
there are few experimental observation of such
phenomenon. We need an alternative to the concept
of unique rate-limiting step that takes into
consideration the evidence of pathways affected
by several steps
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Metabolic Control Analysis
Flux Control Coefficients From the qualitative
is this step rate-limiting? Yes/No,  to the
quantitative How much does the metabolic flux
vary as the enzyme activity is changed?
Definition the flux control coefficient C is
the slope of the tangent (rate of change or
sensitivity) on the flux/enzyme concentration
diagram. This implies that biotechnological
engineering on a single enzyme will rarely have
the effect of significantly increasing the flux
in a pathway.
Salter et al (1986) Biochem. J. 234, 635-647
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Control is shared along the pathway
C1
C2
C3
C4
SCi1
Condition 1
C 0.6
C 0.15
C 0.05
C 0.2
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Metabolic Control Analysis
The Summation Theorem  Definition if all the
enzymes that can affect a particular metabolism
in a cell are taken and their control
coefficients are added up, the sum comes to 1
 Interpretation in most cases several enzymes
will share control over the flux. To have a step
that could be called rate-limiting one enzyme
should have a control coefficient 1 (virtually
no examples of this) and all the other enzymes
should have coefficients 0 This also shows
that the flux control coefficient of each enzyme
is a system property Since the flux control
coefficient decreases if we increase the amount
of one enzyme, the summation theorem states that
the coefficients of some other enzymes must be
increasing at the same time to maintain the sum
1. Elasticities The measure of the metabolite
effect on an enzyme is given by the Elasticity
Coefficient   Each enzyme can have more than one
elasticity elasticities have positive values for
metabolites that stimulate the rate of reactions
of the enzyme (substrates, activators) and
negative values for metabolites that slow the
reaction (product, inhibitors) Compared to the
classic Michaelis-Menten kinetic (a rectangular
hyperbola of a single-substrate enzyme in the
absence of product) the set of elasticities of an
enzyme capture a more realistic in vivo situation
where most enzymes have more than one substrate
and work in the presence of appreciable
concentrations (and hence inhibition) of
products.
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Metabolic Control Analysis
The Connectivity Theorem  How are kinetic
properties of enzymes connected to flux control
coefficients? Suppose we take a pathway
metabolite S and we find all enzymes whose rates
respond to its concentration (enzymes i, j and
k). The connectivity theorem states that the
coefficients for the action on a flux J times the
elasticities sum up to zero.  In a more general
form we can include all n enzymes in our system
since enzymes not affected by the metabolite S
will have elasticities 0 Response
Coefficients Some control mechanisms of
pathways operate on the catalytically active
amount of enzyme, like induction/repression of
enzyme synthesis, activation/inactivation by
covalent modification. Other controls do not
affect the amount of enzyme, but change the
kinetic characteristics of the enzyme instead,
like allosteric effectors changing the enzyme
affinity for its substrate. Flux control
coefficients seem to relate only to the first
class of control mechanisms To consider also
the second category, the effect of a constant
parameter P affecting the flux is defined in the
same way as a control coefficient but it is
referred to as a Response Coefficient, R.
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Metabolic Control Analysis
Conclusion MCA vs. traditional approaches  In
MCA the qualitative categories rate-limiting
and not rate-limiting are replaced by a
quantitative scale for the influence of and
enzyme on a metabolic flux the flux control
coefficients   The flux control coefficient of
an enzyme is a system property   MCA shows that
the degree of displacement of a reaction from
equilibrium is not a reliable guide to the degree
of control an enzyme can exert on a flux, despite
having been widely used in the past
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Metabolic Control Analysis
Stepanopolous and Vallino 1991 Science 252,
1675ff metabolic control theory (MCT)
have received extensive attention however, their
value in directing metabolic engineering efforts
remains questionable. . A major drawback of
these methods is that they are valid only in the
local neighborhood of the operating point
evaluated. Yet, the objective in metabolic
engineering is to modify primary metabolism such
that the resulting flux distributions .. differ
radically from those observed during growth ...
Furthermore, enzymes with large flux control
coefficients are not always the ones to be
modified, especially if they are involved in
feedback control loops. But Top down MCA,
Stephanopolous 1997
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Different levels of metabolic network
analysisExplain, categorize, predict
evolutionarymodels
abstraction
topologymodels
stoichiometrymodels
flux models
kineticmodels
mechanistic
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Pathways are arbitrary sets of preferred routes
120-150 pathways
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Development of the network-based pathway paradigm
(a) The complete stoichiometries of many
metabolic reactions have been characterized.
(b) Most of these reactions have been grouped
into traditional pathways' (e.g. glycolysis)
that do not account for cofactors and byproducts
in a way that lends itself to a mathematical
description. However, with sequenced and
annotated genomes, models can be made that
account for many metabolic reactions in an
organism.
(c) Subsequently, network-based, mathematically
defined pathways can be analyzed that account for
a complete network (black and gray arrows
correspond to active and inactive reactions).
Papin et al. TIBS 28, 250 (2003)
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Stoichiometric matrix
Stoichiometric matrix A matrix with reaction
stochio-metries as columns and metabolite
participations as rows. The stochiometric
matrix is an important part of the in silico
model. With the matrix, the methods of extreme
pathway and elementary mode analyses can be used
to generate a unique set of pathways P1, P2, and
P3 (lecture 9).
Papin et al. TIBS 28, 250 (2003)
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Flux balancing
Any chemical reaction requires mass
conservation. Therefore one may analyze metabolic
systems by requiring mass conservation. Only
required knowledge about stoichiometry of
metabolic pathways and metabolic demands For
each metabolite Under steady-state conditions,
the mass balance constraints in a metabolic
network can be represented mathematically by the
matrix equation S v 0 where the matrix S
is the m ? n stoichiometric matrix, m the
number of metabolites and n the number of
reactions in the network. The vector v
represents all fluxes in the metabolic network,
including the internal fluxes, transport fluxes
and the growth flux.
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Flux balance analysis
Since the number of metabolites is generally
smaller than the number of reactions (m lt n) the
flux-balance equation is typically
underdetermined. Therefore there are generally
multiple feasible flux distributions that satisfy
the mass balance constraints. The set of
solutions are confined to the nullspace of matrix
S. To find the true biological flux in cells
one needs additional (experimental) information
or one may impose constraints on the magnitude
of each individual metabolic flux. The
intersection of the nullspace and the region
defined by those linear inequalities defines a
region in flux space the feasible set of fluxes.
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Feasible solution set for a metabolic network
(A) The steady-state operation of the metabolic
network is restricted to the region within a
cone, defined as the feasible set. The feasible
set contains all flux vectors that satisfy the
physicochemical constrains. Thus, the feasible
set defines the capabilities of the metabolic
network. All feasible metabolic flux
distributions lie within the feasible set, and
(B) in the limiting case, where all constraints
on the metabolic network are known, such as the
enzyme kinetics and gene regulation, the feasible
set may be reduced to a single point. This single
point must lie within the feasible set.
Edwards Palsson PNAS 97, 5528 (2000)
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E.coli in silico
Best studied cellular system E. coli. In 2000,
Edwards Palsson constructed an in silico
representation of E.coli metabolism. Involves lot
of manual work! - genome of E.coli MG1655 is
completely sequenced, - biochemical literature,
genomic information, metabolic databases EcoCyc,
KEGG. Because of long history of E.coli
research, there is biochemical or genetic
evidence for every metabolic reaction included in
the in silico representation, and in most cases,
there exists both.
Edwards Palsson PNAS 97, 5528 (2000)
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Genes included in in silico model of E.coli
Edwards Palsson PNAS 97, 5528 (2000)
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E.coli in silico
Define ?i 0 for irreversible internal fluxes,
?i -? for reversible internal fluxes (use
biochemical literature) Transport fluxes for
PO42-, NH3, CO2, SO42-, K, Na was
unrestrained. For other metabolites except for
those that are able to leave the metabolic
network (i.e. acetate, ethanol, lactate,
succinate, formate, pyruvate etc.) Find
particular metabolic flux distribution with
feasible set by linear programming. LP finds a
solution that minimizes a particular metabolic
objective (subject to the imposed constraints) Z
where
In fact, the method finds the solution that
maximizes fluxes gives maximal biomass.
Edwards Palsson, PNAS 97, 5528 (2000)
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E.coli in silico
Examine changes in the metabolic capabilities
caused by hypothetical gene deletions. To
simulate a gene deletion, the flux through the
corresponding enzymatic reaction was restricted
to zero. Compare optimal value of mutant
(Zmutant) to the wild-type objective Z to
determine the systemic effect of the gene
deletion.
Edwards Palsson PNAS 97, 5528 (2000)
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Gene deletions in E. coli MG1655 central
intermediary metabolism
Maximal biomass yields on glucose for all
possible single gene deletions in the central
metabolic pathways (gycolysis, pentose phosphate
pathway (PPP), TCA, respiration). The results
were generated in a simulated aerobic environment
with glucose as the carbon source. The transport
fluxes were constrained as follows
glucose  10 mmol/g-dry weight (DW) per h
oxygen  15 mmol/g-DW per h. The maximal yields
were calculated by using FBA with the objective
of maximizing growth. The biomass yields are
normalized with respect to the results for the
full metabolic genotype. The yellow bars
represent gene deletions that reduced the maximal
biomass yield to less than 95 of the in silico
wild type.
Edwards Palsson PNAS 97, 5528 (2000)
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Interpretation of gene deletion results
The essential gene products were involved in the
3-carbon stage of glycolysis, 3 reactions of the
TCA cycle, and several points within the
PPP. The remainder of the central metabolic
genes could be removed while E.coli in silico
maintained the potential to support cellular
growth. This suggests that a large number of the
central metabolic genes can be removed without
eliminating the capability of the metabolic
network to support growth under the conditions
considered.
Edwards Palsson PNAS 97, 5528 (2000)
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E.coli in silico
and means growth or no growth. ? means that
suppressor mutations have been observed that
allow the mutant strain to grow. glc glucose,
gl glycerol, succ succinate, ac acetate. In
68 of 79 cases, the prediction is consistent with
exp. predictions. Red and yellow circles are the
predicted mutants that eliminate or reduce growth.
Edwards Palsson PNAS 97, 5528 (2000)
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Rerouting of metabolic fluxes
(Black) Flux distribution for the wild-type.
(Red) zwf- mutant. Biomass yield is 99 of
wild-type result. (Blue) zwf- pnt- mutant.
Biomass yield is 92 of wildtype result. The
solid lines represent enzymes that are being
used, with the corresponding flux value noted.
Note how E.coli in silico circumvents removal
of one critical reaction (red arrow) by
increasing the flux through the alternative G6P ?
P6P reaction.
Edwards Palsson PNAS 97, 5528 (2000)
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Summary
FBA analysis constructs the optimal network
utilization simply using stoichiometry of
metabolic reactions and capacity
constraints. For E.coli the in silico results
are consistent with experimental data. FBA shows
that in the E.coli metabolic network there are
relatively few critical gene products in central
metabolism. However, the the ability to adjust to
different environments (growth conditions) may be
dimished by gene deletions. FBA identifies the
best the cell can do, not how the cell actually
behaves under a given set of conditions. Here,
survival was equated with growth. FBA does not
directly consider regulation or regulatory
constraints on the metabolic network.
Edwards Palsson PNAS 97, 5528 (2000)