Stephanopoulos, G

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Stephanopoulos, G. and Vallino, J.J. (1991). Network rigidity and metabolic engineering in metabolite

overproduction. Science 252:1675
-
1681.

METABOLIC ENGINEERING &


METABOLIC CONTROL ANALYSIS (MCA)


File name METABOLIC ENGINEERING & MCA 2002

Metabolic En
gineering

Brief Introduction to Metabolic Engineering




Definitions & Preamble




Pot
ential




Types of approach
: extending pathways, redirecting flux



Problems
: channelling/compartmentation, network rigidity, plasticity of


(plant)
metabolism, metabolism of desired product, distributed control



References


Metabolic Control Analysis (MCA)


Traditional approaches to metabolic regulation & the
ir problems


Outline of MCA




Flux control coefficients and the summation theorem



Concentration (metabolite) control coefficie
nts



Elasticity coefficients and the connectivity theorem



Measuring control coefficients



Postscript:


Gaps in knowledge

Reference
s

Plant Metabolic Engineering Case Histories


METABOLIC ENGINEERING

DEFINITIONS & PREAMBLE

Engineering
: Application of scientific principles to practical ends as the design,
construction and operation of efficient and economical
systems


Metabolic engineering
: Improvement of cellular activities by manipulation of
enzymatic, transport and regulatory functio
ns with the use of recombinant DNA
technology


Use of recombinant DNA distinguishes metabolic engineering from classical
biochemical genetics
-

but the two are allied (MCA is equally relevant to both).


Metabolic engineering involves modifying individual

reactions, but these are embedded
in metabolic networks or systems. The power of recombinant DNA techniques exceeds
present capacity to analyze such biochemical reaction networks.


Chemical engineering of cellular processes
-

"critically different from c
olleagues in the
sciences, the chemical engineer must be willing to attempt a solution in situations in
which many of the important details of the system are undefined or uncertain" (Bailey,
Chem Eng Sci 50: 4091
-
4108, 1995).



Phases of Metabolic Engineer
ing Research:






Note that metabolic engineering is an iterative process: cycle of genetic
modification



analysis of metabolic consequences of change (identifying
limitations)



choice of next genetic modification.




Metabolic engineering is far more advanced in microorg
anisms than in plants:

o

o
Plant metabolic biochemistry (pathways, their regulation) incompletely
known

o

o
Plant gene discovery
-

many metabolic enzymes remain to be cloned, and
even more transporter and regulatory genes (genomics is of great value here)

o

o
Mo
st plant metabolic engineering work (

90%) involves single
-
gene
changes (single steps in pathways)

o

o
Few instances yet in plants of in
-
depth analysis of consequences of
change followed by design of second cycle

o

o
Plants have even more ways than bacteria to

resist metabolic intrusions
(e.g., parallel pathways in multiple compartments)

POTENTIAL OF METABOLIC ENGINEERING


Some Major Objectives in Plants:

(Note overlap with conventional plant breeding)



Improving nutritional value of crops (e.g., essential ami
no acid supply for storage
proteins, vitamin content, modifying lignin to enhance forage digestibility)



Creating new industrial crops (e.g., modified fatty acid composition of seed
triglycerides, pharmaceuticals, polyhydroxybutyrate synthesis, bioremediat
ion)



Altering photosynthate partitioning to increase economic yield



Enhancing resistance to biotic and abiotic stresses



Reduction of undesired (toxic or unpalatable) metabolites



Use as research tool to test basic ideas about metabolic regulation


Gene
s From Any Source Can Be (and Are Being) Used:



Plant or non
-
plant (bacterial, yeast, animal, viral) enzyme
-
coding genes



With or without modified kinetic or regulatory properties (protein engineering)




Current Limitations to the Potential in Plants:


(A
part from lack of known enzymes and cloned genes)
-

Concern the scientific principles
(on which engineering depends):



Theoretical framework (MCA) only now emerging, not yet well developed, few
universal principles with predictive value, many unanticipated

responses



Much present work not related to what theory does exist, may ± ignore it, may be
guided by qualitative traditional approaches that are unhelpful



Therefore metabolic engineering remains basically a trial
-
and
-
error process (best
taught as some u
seful general principles followed by case
-
histories).



TYPES OF APPROACH

Can be classified as 3 types [see Bailey (1992) for microbial examples]:


Extending an existing pathway to obtain a new product


Amplifying a flux
-
controlling step


Diverting flu
x at branch points ("nodes") to a desired product by:



circumventing a (feedback) control mechanism



amplifying the step initiating the desired branch (or the converse)



removing reaction products



manipulating levels of signal metabolites

Example: Extend
ing an existing pathway in plants

Polyhydroxybutyrate (PHB) synthesis in Arabidopsis (Poirier et al Science 256: 520;
Nawrath et al PNAS 91: 12760).PHB is a storage product of the bacterium
Alcaligenes
eutrophus
, a high mol wt polyester plastic (biodegrada
ble).Three enzymes are involved:

3
-
ketothiolaseacetoacetylCoA reductasePHB synthase


2 CH
3
COCoA

CH
3
COCH
2
COCoA

CH
3
CH(OH)CH
2
COCoA

PHB


Of these three, Arabidopsis has only the 3
-
ketothiolase (cytosolic), which is involved in
producing acetoacetylCoA for mev
alonate synthesis (mevalonate is the precursor for
isoprenoids).

Bacterial reductase and polymerase enzymes were constitutively expressed (CaMV 35S
promoter) in individual lines, combined by crossing.F1 hybrids contained up to 0.1% dry
wt PHB, but showed
severe effects on growth (possibly due to diversion of acetylCoA or
acetoacetylCoA away from essential pathways, e.g., isoprenoid synthesis).

Subsequent expression of all three genes in plastids gave far higher PHB levels (14% dry
wt) without deleterious
effects on growth or fatty acid synthesis, suggesting that synthesis
of plastid acetylCoA is regulated by a mechanism that responds to demand.

Example: Amplifying a flux
-
controlling step in plants


Inducible overexpression of oat arginine decarboxylase (A
DC) in tobacco (
Fig. 1
) (Plant
J 11: 465).


ADC is involved in polyamine synthesis (note also linkage to ethylene
synthesis, and
-

in tobacco
-

to nicotine synthesis, as putrescine enters the nicotine
pathway after N
-
methylation).


There are two pathways
to putrescine in plants, via ornithine or agmatine.


Expression of
oat ADC using a tetracycline
-
inducible promoter (to allow stage
-
specific expression)
gave a


30
-

to 60
-
fold increase in ADC activity, caused a small accumulation of
agmatine, and increased
total putrescine and spermidine levels.

Note: the increases were ~2
-
fold only, and were due to increases in conjugated forms
(e.g. hydroxycinnamic acid amides), not free forms:


i.e.



total pool/


ADC


~0.05,
and that further metabolism (conjugation) kept free polyamine pools constant.


Nonetheless there were phenotypic effects (leaf malformation, chlorosis, necrosis)
suggesting that endogenous polyamines have roles in plant growth a
nd development.

Examples: Diverting flux at branch points


1. By circumventing an endogenous regulatory mechanism


Enhanced starch synthesis in potato tubers (
Fig. 2
) (Stark et al Science 258: 287).


Starch
synthesis takes place in the plastids, and compe
tes for assimilates (triose phosphates)
with sucrose synthesis in the cytosol.


Starch synthesis involves three committed
enzymes, ADPGlucose (ADPGlc) pyrophosphorylase, starch synthase (SS) and starch
-
branching enzymes (SBE).


Of these, pyrophosphorylase
activity is under many
conditions the major factor determining the rate of starch synthesis; this enzyme is
allosterically activated by 3
-
phosphoglycerate (3
-
PGA) and inhibited by Pi.


A mutant
E.
coli

ADPGlc pyrophosphorylase that was relatively insensiti
ve to these and other
effectors was expressed constitutively in chloroplasts of tobacco, tomato and potato.


Leaves and calli accumulated more starch, although there were detrimental effects on
regeneration, attributed to reduced availabilty of sucrose for

export.

Tuber
-
specific expression in potato [using a patatin (storage glycoprotein) promoter]
gave plants with a normal phenotype and up to


~60% more starch than controls.


Note
that the starch content



was far smaller than the



in enzyme:


2. By removing products of an equilibrium reaction


Using pyrophosphatase to shift the fructose
-
1,6
-
P2 (FBP)


fructose
-
6
-
P (F6P)
equilibrium towards fructose
-
6
-
P, and hence
sucrose formation (
Fig 3
) (Sonnewald, Plant
J 2: 571; Lerchl et al, Plant Cell 7: 259).

A major controlling step in sucrose synthesis (vs. starch synthesis and
glycolysis/respiration) is interconversion of FBP and F6P, which is catalyzed by three
enzymes:




fructose
-
1,6
-
bisphosphatase, FBPase (forward direction, FPB
----

F6P)



6
-
phosphofructokinase, PFK (back direction, F6P + ATP
----

FBP + ADP)



PPi:F6P 1
-
phosphotransferase, PFP (both directions, reaction near equilibrium).

As the PFP reaction is revers
ible,
E. coli

pyrophosphatase was expressed constitutively in
tobacco and potato cytosol, to remove cytosolic PPi and so drive the reaction towards
F6P
-

and hence sucrose not starch.


(WT cytosolic PPiase levels are low).

Expressing the cytosolic pyrophos
phatase was also expected to favor flow of assimilates
to sucrose in 2 additional ways:



by increasing triose
-
P export from the chloroplast (due to increased cytosolic [Pi])



by favoring UDP
-
Glc formation via UDP
-
Glc pyrophosphorylase, which
produces PPi.


As expected, source leaves showed a 3
-

to 4
-
fold increase in the ratio of soluble sugars to
starch.


But transgenic tobacco plants were stunted and the leaves accumulated starch as
well as soluble sugars. .[This inhibition of sucrose export was hypothesi
zed to be due to
energy starvation in phloem cells via a limitation on the breakdown of sucrose via
sucrose synthase and UDP
-
Glc pyrophosphorylase. This was confirmed to be the case by
phloem
-
specific cytosolic expression of a yeast invertase, which provid
es a by
-
pass to
sucrose breakdown via sucrose synthase/UDP
-
Glc pyrophosphorylase.


Expression of the
invertase restored the WT
-
phenotype in pyrophosphatase
-
expressing plants.]

ENGINEERING PROBLEMS

(Besides achieving good mRNA expression, protein synthesis,

correct targeting,
prosthetic group insertion, asssembly of subunits and stability)


Channeling & Compartmentation.


Distinct metabolic pools may exist due to:



Same pathway in different organelles (e.g. glycolysis in plastids and cytosol)



Pathways invo
lving cooperation of


2 compartments (e.g. photorespiration, C4)



Compartmentation (channeling) via protein
-
protein interactions of pathway
enzymes

The same pathway in different organelles, or sections of a pathway in different organelles
(or cells or org
ans) may not be in rapid equilibrium via exchange of intermediates.


A
new demand for an intermediate may therefore be more readily met in one compartment
than another.


Example: acetylCoA availability for PHB synthesis was far higher (>100
-
fold) in plasti
d than cytosol.

Channeling complicates adding a novel branch that starts from an intermediate of a
pathway, because if that intermediate is channeled it will not be freely accessible to the
introduced enzyme.


Network Rigidity.


The control architecture (
positive and negative feedback loops)
around branch points in metabolic routes can render them flexible (i.e. able to respond
fully to an increased demand for the product of one branch) or more
-
or
-
less rigid (i.e. ±
locked into a constant flux split betwee
n the branches.






Control architectures that would render a branch point (A) flexible, (B)
weakly rigid, or (C) strongly rigid to modifications in flux par
titioning.


Dashed lines indicate negative (/) or positive (
---
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牥d
⤠)ee摢dc欠晲潭o
瑨攠t潲oe獰潮摩湧整b潬o瑥
.

The more rigid the branch point, the harder it is to increase the flux through one of its
branches.


Example: Met and Thr synthesis in plants.


Plasticity of Plant Metabolism.


Plants often have alterna
tive metabolic routes to the
same product.


Manipulation is then difficult because an attempt to alter flux through one
pathway may be frustrated by a compensating change in the other.


Example: Sucrose
cleavage in growing potato tubers (Zrenner et al, Pla
nt J 7: 97)(
Fig. 4
).Antisense RNA to
sucrose synthase reduced enzyme activity to 5% of wild type levels, but there were
compensatory rises of


3 & 30
-
fold in activities of neutral and acid invertases.


Metabolism of Desired Product.


Example: Polyamine co
njugation to
hydroxycinnamic acids.


Shared control of pathway flux.


A single limiting step is an attractive target for
engineering, but such a step may not exist.


Rate control is more likely to be distributed
among several steps.


In this case, no sign
ificant rate or product yield improvements will
be realized until all steps playing major roles in rate control have been manipulated.


Moreover, traditional biochemical theory can be a poor guide as to what to engineer in
order to achieve a desired change

in the flux through a pathway.


MCA is a more
appropriate framework for attempts at rational metabolic design.

REFERENCES



Stephanopoulos GN, Aristidou AA, Nielsen, J
(1998) Metabolic Engineering:
Principles and Methodologies.


Academic Press, San Diego



Bailey JE (1991)

Towards a science of metabolic engineering. Science 252:
1668
-
1675



Stephanopoulos G, Vallino JJ (1991)
Network rigidity and metabolic
engineering in metabolite overproduction. Science 252: 1675
-
1681



Hrazdina G, Jensen RA (1992)

Spatial o
rganization of enzymes in plant
metabolic pathways. Annu Rev Plant Physiol Plant Mol Biol 43: 241
-
267



ApRees T (1995)
Prospects of manipulating plant metabolism. Trends Biotechnol
13: 375
-
378



Kinney AJ (1998)
Manipulating flux through plant metabolic pat
hways. Curr
Opin Plant Biol 1: 173
-
178



Stephanopoulos G

(1999)

Metabolic fluxes and metabolic engineering.
Metabolic Engineering 1: 1
-
11



DellaPenna D (2001)
Plant metabolic engineering. Plant Physiol 125: 160
-
163



Nielsen J (2001)
Metabolic engineering.
Appl Microbiol Biotechnol. 55: 263
-
83


METABOLIC CONTROL ANALYSIS

MCA vs. TRADITIONAL APPROACHES TO METABOLIC REGULATION


Metabolic control analysis (MCA)

was developed initially by Kacser & Burns, Heinrich
& Rapoport in the early 1970's.


Related system
s approaches were developed by others.


MCA is the most widely adopted approach and the easiest to apply.


MCA is a quantitative sensitivity analysis of fluxes and metabolite concentrations.


MCA studies the relative control exerted by each step (enzyme o
r transporter) on fluxes
and metabolite concentrations in the
system
.


This control is measured by applying a
perturbation to the step under study and measuring the effect on the flux or concentration
of interest after the system has settled to a new stead
y state.


MCA emphasizes that:



Single, rate
-
limiting steps are probably rare in metabolic sequences



Control of pathway fluxes is usually shared among several steps



Their relative contribution to overall control will vary with flux rate

MCA is a quanti
tative, theoretical approach that attempts to bridge the gap between
enzymology and metabolic physiology, i.e. to deal with the emergent properties of
metabolizing systems that cannot be described in terms of the
in vitro

properties of the
individual enzym
es.

Although the predictive power of MCA is far from perfect, it can provide a framework
for rational metabolic engineering in which the likelihood of achieving a specific
modification of metabolism by a particular genetic intervention can be assessed.

Tr
aditional metabolic biochemistry

does not provide the understanding needed to do
this because it deals with metabolic regulation in terms of a few qualitative principles.


However, these traditional approaches still have a wide following among researchers
(more in N. America than Europe) and dominate biochemistry textbooks.


These qualitative principles are based mainly on the view that control of pathways must
reside in a relatively few enzymes whose in vitro properties suggest that they could be
controll
ing flux in vivo (e.g. displacement of reaction from equilibrium, irreversibility,
response to effectors, cooperative kinetics): "rate
-
limiting steps", "pace
-
maker
reactions".


These ideas are qualitative, preconceived, and teleological.


The traditional
concepts are often hard to test experimentally, due to their qualitative
nature.


Manipulating enzymes considered "rate
-
limiting" has rarely had the expected
outcome. These concepts are not a sound basis for understanding or predicting the effects
of metab
olic engineering.


Overview.


In the light of the complex nature of metabolic systems, it is remarkable that
biochemistry has taken so long to make use of mathematical and theoretical analysis
(long established in other areas of biology e.g. population ge
netics, physiology).

OUTLINE OF MCA


Web Resources


MCA Web Site (has a good tutorial on MCA basics)


Cornish
-
Bowden's Book Chapter on

MCA (more detailed treatment)


David Rhodes' Modeling Website



Types of coefficients in MCA
MCA defines a number of coefficients.

Control coefficients


refer to the whole metabolic path
way (systemic or global
properties).


A control coefficient is a relative measure of how much a perturbation to e.g.
enzyme activity E
i

affects a
system

variable, e.g. a flux or metabolite concentration:

Most important (at heart of theory) are Flux (J) co
ntrol coefficients C
J
Ei


Others:Concentration control coefficients and Response coefficients (to external
effectors)

Elasticity coefficients (elasticities)

refer to properties of individual enzymes in the
pathway (they are
local

not systemic properties, a
nd are related to classical enzyme
kinetics).

An elasticity


vi
x

of an enzyme describes how the local rate of a step (v
i
) responds to a
change in the concentration of an effector X (e.g. the enzyme's substrate or product).

The Whole System:

Flux Coefficients


The flux control coefficient is defined as the ratio be
tween the fractional change in flux J
through a pathway and the fractional change in amount or activity of an enzyme E
i.
Flux
control coefficients are highly relevant to metabolic engineering.

Once an enzyme is embedded in a pathway, its behavior is influe
nced by the flanking
enzymes.


Consider a simple pathway:

-

with enzymes E
1
-
3


-

with substrates and intermediates S
0
-
3


-

with a steady state flux J (units: e.g. mol.h
-
1
)

E
1
E
2
E
3


S
0

S
1

S
2

S
3


The flux J is equal through all steps and the intermediate co
ncentrations ("pool sizes")
remain steady, because the intermediate concentrations are used to balance each
individual reaction to the overall flux.


e.g., If the reaction catalysed by E
1

were to
proceed faster than E
2
, there would be a net increase in [S
1
].


Provided that enzyme E
2

can respond to (i.e. is not saturated with) S
1
, this increased [S
1
] will increase the rate of
E
2

until it becomes equal to that of E
1
, at which point [S
1
] will remain constant.Consider
a
small

change in the activity of one enzym
e, e.g. E
1
, on the flux J through the whole
pathway (the activity change could be due to increased amount, changed kinetic
properties, etc).

The response of flux to change in an individual enzyme is generally nonlinear, usually
more
-
or
-
less hyperbolic, th
us (Fig. 1A):





The flux control coefficient for enzyme E
1

is the ratio between the fractional change in
flux dJ/J and the fractional change in enzyme activity dE
1
/E
1
.


This is the slope of the
tangent to the plot of J vs. E
1

multiplied by the scaling factor E
1
/J (Fig. 1A), or on a
logarithmic plot of the same curve, the slope of the tangent (Fig. 1B).


Note that flux
control coefficients are dimensionless.

C
J
E1
=
dJ
/J
=dJ/dE
1
.E
1
/J=
d(ln J)


dE
1
/E
1
(slope)(scaling
d(ln E
1
)

factor)


Each enzyme in the system has a flux control coefficient, so for enzymes E
2

and E
3
:

C
J
E2
=

dJ/J
C
J
E3
=
dJ/J_


dE
2
/E
2
dE
3
/E
3


i.e. there are
as many flux control coefficients for a pathway as there

are enzymes

in the
system.

There are similar coefficients with respect to substrate concentration =
concentration
control coefficients
, that quantify the effect of enzyme activity E
i
on any metabolite S
i
.


For example, for enzyme E
1

and the concentration

of its product S
1
:

C
S1
E1
=

dS
1
/S
1
=dS
1
/dE
1
.
E
1
/S
1
=
d(ln S
1
)


dE
1
/E
1

d(ln E
1
)

Note that the value for E
1

on S
1

will usually be positive, but that for E
2

on S
1

(C
S1
E2
) will
usually be negative (E
1

produces S
1

whereas E
2

consumes it).

Response coefficients R

quantify the effect of a metabolite X external to the system, i.e.
not a substrate or a product within the pathway, e.g. a signal metabolite (allosteric
effector) such as fructose 2,6
-
bisphosphate.


For example, the strength of the effect of X
on the pathw
ay flux J is defined in the same way as other control coefficients:

R
J
X
=
dJ/J
=dJ/dX
.
X/J=
d(ln J)


dX/Xd(ln X)

The Summation Theorem

states that, for a given flux J, the sum of the flux control
coefficients of all the enzymes in the system, E
1
, E
2
.....E
n

is

unity, i.e.:

C
J
E1
+C
J
E2
+

C
J
En
=1

or in mathematical notation:



C
J
Ei
=1

i = 1 to n

Similarly, for the concentration control coefficients, for each metabolite the sum of all the
concentration control coefficients is zero:


C
Sj
Ei
=0

i = 1 to n

Note that
:



The summation theorem shows the enzymes of a pathway can share control of
flux



In a linear pathway where the enzymes have normal kinetics, all the flux control
coefficients are zero or positive, so that the maximum possible value for any
enzyme is 1 (w
hen all the other enzymes would have flux control coefficients of
zero).


This would correspond to the traditional "rate
-
limiting" enzyme.


It is rare.
In contrast, concentration control coefficients can have large positive or negative
values.



In special
cases flux control coefficients can be >1 or negative, e.g. in a branched
pathway where more flux down one branch can entail less flux down another.



Flux control coefficient = 0.01: a small increase in enzyme activity will have an
effect on flux that is o
nly 1% of the imposed change, e.g. a 10% increase in
enzyme gives only 0.1% increase in flux.



Flux control coefficient = 0.9: flux responds almost proportionately to small
changes in enzyme activity.



In practice, where measurements have been made, flux c
ontrol coefficients are
often intermediate, e.g. 0.1 to 0.5, so that control is distributed among many steps.



Because flux control coefficients vary with flux (Fig. 1), and because the enzymes
in a pathway may be operating at different points in their flu
x
vs.

enzyme level
curves, as flux changes, the share of the control exerted by each enzyme can
change, i.e.
control is redistributed

(Fig. 2).


Fig. 2 is a particularly good example
of just how misleading the concept of a "rate
-
limiting step" can be.



Fig. 2


Flux control coefficients for 4 steps in oxidative phosphorylation as a

function of respiratory flux



If a feedback loop is introduced into the simple p
athway


The concentration of S
2

is now critical to the activity of E
1
, and the concentration of S
2

is
strongly influenced by the activity of E
3
, which consumes S
2
.


This shifts control away
from E
1

to E
3
, i.e. it lowers the flux control coefficient of E
1
.

This runs counter to the conventional view that a highly
-
regulated enzyme near the start
of a pathway would be a prime candidate for a rate
-
limiting step.


But it h
as been
vindicated by many experiments.


Summarizing
: the control of fluxes (or metabolite concentrations) is generally shared
among all enzymes although a smaller number may share the majority of the control in
some systems and circumstances.


The distri
bution of control can vary with flux.

Responses to Large Changes in Enzyme Activities and Effectors.


MCA is based on
small changes; note how the slopes of the tangents in Figs. 1 A & B vary as E varies.


Therefore any prediction of flux becomes less and
less accurate the further away the new
enzyme activity is from that at which the tangent was measured.

This is important because metabolic engineering, and many experiments designed to
estimate flux control coefficients, involve relatively large changes i
n enzyme activity.

A simple modification of MCA (Small & Kacser, Eur J Biochem 213: 613, 1993)
improves the ability to handle the effects of large changes.


For a linear pathway,
measurement of the two values of the flux, J
1

and J
2
, at two widely separate
d levels of the
enzyme, E
1

and E
2
, allows calculation (to a good approximation) of the flux control
coefficient at enzyme level E1 as:

C
J
E
=
(J
2

-

J
1
) E
2
(Small & Kacser termed this approximation the deviation index)


(E
2

-

E
1
) J
2


Note that this differs fro
m the small
-
change estimate of the flux control coefficient in that
the scaling factor is E
2
/J
2
, not E
1
/J
1

(the ratio at the original operating point).

With this equation, the flux control coefficient measured at one point allows accurate
prediction of th
e flux at a markedly different enzyme level (which is what metabolic
engineering requires):



Fig. 3


The relative change of flux for large changes in enzyme acti
vity.

The
-
fold
increase of enzyme activity is shown above the curves (from 2
-

to 50
-
fold).






Thus changing the amount of a single enzyme in a pathway has quite limited effects on
flux, unless the flux control coefficient is >0.5.


If C = 0.5, the
maxim
um

increase in flux
achievable (with a very large
-
fold increase in enzyme level) is a factor of 2.0.


Only if C
is close to 1.0 are very large changes in flux possible.


This basically accounts for many results in metabolic engineering, where large
engin
eered changes in single target enzymes have not significantly increased flux.

Individual Enzymes: Elasticity Coefficients

-
related to classical enzyme kinetics

Classical enzyme kinetics considers individual enzymes, in dilute solution, acting on
substrat
e in the absence of products and all other cellular metabolites.


Consider an
enzyme

E2

that follows normal Michaelis
-
Menten kinetics, within a pathway:




E
1
E
2
E
3


S
0

S
1

S
2

S
3


v
1
v
2
v
3


Fig. 4AFig. 4B



The elasticity coefficient (elasticity,


v2
S1

) for the effect of metabolite S
1

(substrate) on
the velocity v
2

of enzyme E
2

is the ratio between the fractional change in local rate v
2

and
the fractional change in concen
tration of S
1

(with all other variables fixed at the values
they have in the pathway):


v2
S1
=
dv
2
/v
2
=dv
2
/dS
1
.S
1
/v
2
=
d(ln v
2
)


dS
1
/S
1
(slope)(scaling
d(ln S
1
)

factor)


Thus the elasticity of enzyme E
2

to metabolite S
1

can be obtained from the slope of the
fam
iliar hyperbolic velocity vs. substrate curve, scaled to make it dimensionless (Fig.
4A).


The only difference from classical kinetics is that the measurement is made at the
concentrations of enzyme, product and other metabolites found in cell in the metab
olic
state being analyzed.

The elasticity can also be obtained directly as the slope of a log
-
log plot (Fig. 4B).



Elasticities are the same as the familiar order of reaction: first order (rate directly
proportional to concn) at very low [substrate], pass
ing through non
-
integral orders
to approach zero order at saturation, with order = 0.5 at half
-
saturation (K
m
).



Elasticities have positive values for metabolites that stimulate the rate of a
reaction (substrates, activators) and negative values for metabo
lites that slow the
reaction (products, inhibitors).



Because the elasticity depends on the concentration of S
1

in a particular steady
state, and this as well as the concentration of the product S
2

and other metabolites
that may act as effectors are functi
ons of the
system.


Elasticities are therefore
related to flux control coefficients (systemic properties).

The connectivity theorem

is a key part of MCA.


This shows how the properties of
individual enzymes (represented by elasticities) affect the values
of flux control
coefficients, i.e. connects systemic properties and local properties of individual system
components

It states that for every enzyme that responds to a metabolite, S, their flux control
coefficients and elasticities are related so that if,
for each of these enzymes, we form a
term by multiplying its flux control coefficient by its elasticity to S, then the sum of these
terms is zero:



C
J
Ei

vi
S
=0

i = 1 to n

Consider the simplest example, where two enzymes have a single linking metabolite,

S
:

E
1
E
2



S



v
1
v
2


ThenC
J
E1

v1
S
+C
J
E2

v2
S
=0

or


That is, the relative values of two successive flux control coefficients depend on the
elasticities representing

the product inhibition (S on E
1
) and the substrate activation (S on
E
2
) by the intermediate metabolite.

Measuring Flux Control Coefficients




To do this, it is necessary to change the maximum catalytic activity of a specific
enzyme, and then to observe th
e effects on flux.



The four main ways to alter a given enzyme activity are: inhibitors, induction
-
repression, mutants, genetic manipulation (overexpression, antisense/co
-
suppression, RNAi).



Regardless of the type of perturbation used, the conditions that

must be met are:

o

The system must at least approximate to a steady state

o

The enzyme should act only in one reaction

o

In mutants & transgenic plants, it is crucial that only the enzyme in
question be changed, i.e. no pleiotropic, somaclonal or insertional

effects
(hence the importance of using several independent transformed lines),
and no compensatory changes in other enzymes
-

see Plasticity of Plant
Metabolism


Inhibitors.


Titration of the enzyme activity down, using specific inibitors.


This is not
s
traightforward and has not been applied to plant tissues.


Problems include side
-
effects,
assessing the in
-
vivo concentration of the inhibitor and of all other relevant effectors.


See Fell (1992) and Ap Rees & Hill (1994).



Enzyme Induction and Repressi
on.


Increasing or decreasing enzyme level by
exploiting specific induction and repression by environmental factors or signal
molecules.


The obvious problem is the degree of specificity of the effect; suites of
related enzymes are often co
-
regulated, e.g.

maize ANPs.


Opportunities for this approach
in plants are limited, and it has rarely been used.


See Ap Rees & Hill (1994).

However, note that using
inducible expression of transgenes

to alter enzyme level at
defined times in specific tissues or organs
is potentially powerful combination (see
inducible ADC expression, Plant J 11: 465).


Classical or Reverse Genetics
-

Mutants.


When null mutants are available, a series of
plants with zero, 1 and 2 doses of the gene (0, 50 and 100% of the wild
-
type enzym
e
activity) can be constructed.


Subtler variation can be achieved with leaky mutants.

Note that technical problems in quantifying enzyme levels and fluxes mean that changes
of at least 20
-
30% are usually needed to carry out accurate measurements.


For ch
anges
of this magnitude the data should be evaluated using the appropriate equation (see
Responses to Large Changes in Enzyme Activities & Effectors).


This applies equally to
transgenic plants.

Example:

Work of Stitt's group to evaluate control of flux t
o sucrose and starch by
phosphoglucoisomerase (PGI) (Biochem J 261: 457, 1989) and phosphoglucomutase
(PGM) or ADP
-
glucose pyrophosphorylase (Planta 182: 445, 1990).


Note that PGI and
PGM catalyze readily reversible reactions in vivo:

PGIPGM


Glc
-
6
-
P

---
---

Fru
-
6
-
P Glc
-
6
-
P


------


Glc
-
1
-
P

and so are traditionally considered unimportant from a control standpoint.


Nevertheless,
the estimated flux control coefficients for starch synthesis (in saturating light and CO
2
)
were 0.35 for PGI and 0.21 fo
r PGM.


These enzymes can clearly exert control as flux to
starch increases, and are obviously not present in vast excess.


Molecular Genetics
-

Overexpression and Underexpression.


This approach may well
become the preferred method, and has already been
extensively used.


Examples:




The work of Stitt's group on the control of photosynthetic C flux by Rubisco,
using antisense RNA to the small subunit (see Stitt & Sonnewald, 1995).


This gave
values for the flux control coefficient that varied from 0.1 to 0.3 (i.e. low) under
moderate
conditions, although values increased to 0.7 to 0.8 after sudden upshift in
light or downshift in CO2 concentration, or in continuous very high light.




Over
-

and underexpression of the two glycolytic enzymes traditionally viewed as
regulatory (catalyze ir
reversible reactions, controlled by various effectors):
phosphofructokinase (PFK) and pyruvate kinase (PK).


[Goodwin & Mercer,
Introduction to Plant Biochemistry, 2nd Ed, 1983, p. 207: "Two enzymes regulate the
rate of glycolysis, PFK and PK, with the for
mer probably playing the major role".]


Although they caused large changes in the levels of glycolytic intermediates, neither a
50
-
fold overexpression of PFK nor a 5
-
fold decrease in PK expression had
any

effect
on the rate of respiration, i.e. their flux

control coefficients were


~ 0.


This is because
they normally operate at a fraction of their potential catalytic activity, which is
restricted via regulation by various effectors (fine control).


See Stitt & Sonnewald,
1995.




Over
-

and underexpression o
f sucrose phosphate synthase has been used to
evaluate its control over sucrose synthesis in several plants.


A flux control coefficient
of 0.3 to 0.45 was estimated for potato leaves.


See Stitt & Sonnewald, 1995.

Postscript: Gaps in Knowledge





Much of
the metabolism of eucaryotic cells takes place in the aqueous cytoplasm
and interiors of organelles.




Conditions in the aqueous cytoplasm almost surely do not comprise enzymes,
substrates and effectors randomly dispersed in solution, i.e. interacting in a

homogeneous, bulk aqueous phase with the only links between enzymes in the
network provided by intermediate substrate/product/effector pools ("molecular
democracy")


see Mintol (2001) and Clegg (1984).




There is much evidence that cellular metabolism is

spatially organized on a very
small scale; this includes:

o

o
Evidence for membrane
-
adsorbed enzyme clusters, multienzyme
complexes and for enzymes arrays attached to the cytoskeleton

o

o

Evidence that some metabolite pools are not in free solution




So that

the assumptions about in vivo conditions that are made in MCA and in
rational metabolic engineering design are not necessarily always valid.

REFERENCES



Fell DA (1997)

Understanding the control of metabolism. Portland Press,
London, UK



Fell DA (1992)

Met
abolic control analysis: a survey of its theoretical and
experimental development. Biochem J 286: 313
-
330



Ap Rees T, Hill SA (1994)

Metabolic control analysis of plant metabolism. Plant
Cell Environ 17: 587
-
599



Stitt M (1995)

The use of transgenic plants

to study the regulation of plant
carbohydrate metabolism. Aust J Plant Physiol 22: 635
-
646



Stitt M, Sonnewald U (1995)

Regulation of metabolism in transgenic plants.
Annu Rev Plant Physiol Plant Mol Biol 46: 341
-
368



Fell DA (1998)

Increasing the flux in

metabolic pathways: a metabolic control
analysis perspective. Biotechnol Bioeng 58: 121
-
124



Minton AP (2001)

The influence of macromolecular crowding and
macromolecular confinement on biochemical reactions in physiological media. J
Biol Chem 276:10577
-
10
580



Clegg JS (1984)

Properties and metabolism of the aqueous cytoplasm and its
boundaries. Am J Physiol 246: R133
-
151


METABOLIC ENGINEERING CASE HISTORIES

References for student presentations and class discussion are in

green.



Polyhydroxyalkanoate pr
oduction



Vitamin E and Provitamin A (Golden rice)



Lysine and threonine synthesis



Shikimate pathway



Lauric acid synthesis



Key Points for Case History Analysis


1.


Project objective

2.


Metabolic context (pathways involved, control points targete
d, etc)

3.


Molecular approach (origin of the transgene, promoter type, targeting of

transgene product etc)

4.


Phenotype observed (primary and secondary effects, foreseen or not)

5.


Interpretation
-

strengths, weaknesses, relation to MCA & other prin
ciples

References
*

= Background articles

Polyhydroxyalkanoate production




*
Poirier Y, Dennis DE, Klomparens K, Somerville C (1992)
Polyhydroxybutyrate, a biodegradable thermoplastic, produced in transgenic
plants.


Science 256: 520
-
523



*
Poirier Y, Nawra
th C, Somerville C (1995) Production of
polyhydroxyalkanoates, a family of biodegradable plastics and elastomers, in
bacteria and plants.


Biotechnology (N Y) 13:142
-
150



Nawrath C, Poirier Y, Somerville C (1994) Targeting of the polyhydroxybutyrate
biosyn
thetic pathway to the plastids of Arabidopsis thaliana results in high levels
of polymer accumulation. Proc Natl Acad Sci U S A


91:12760
-
12764



Slater S et al (1999) Metabolic engineering of
Arabidopsis

and
Brassica

for poly
(3
-
hydroxybutyrate
-
co
-
3
-
hydrox
yvalerate) copolymer production.


Nature
Biotechnology 17: 1011
-
1016



*
Mitsky TA, Padgette SR, Taylor NB, Valentin HE, Gruys KJ (1999) Metabolic
modeling as a tool for evaluating polyhydroxyalkanoate copolymer production in
plants.


Metabolic Engineering 1
: 243
-
254



Bohmert K, Balbo I, Kopka J, Mittendorf V, Nawrath C, Poirier Y, Tischendorf
G, Trethewey RN, Willmitzer L (2000) Transgenic Arabidopsis plants can
accumulate polyhydroxybutyrate to up to 4% of their fresh weight. Planta: 841
-
845

Vitamin E and
Provitamin A(Golden rice)



Ye X, Al
-
Babili S, Kloti A, Zhang J, Lucca P, Beyer P, Potrykus I (2000)
Engineering the provitamin A (beta
-
carotene) biosynthetic pathway into
(carotenoid
-
free) rice endosperm. Science 287: 303
-
305



*
Guerinot ML (2000) Perspectiv
es: plant biology. The green revolution strikes
gold. Science. 287: 241
-
243



Shintani D, DellaPenna D (1998) Elevating the vitamin E content of plants
through metabolic engineering. Science 282: 2098
-
2100

Lysine and threonine synthesis




*

Galili G (1995)
Regulation of lysine and threonine synthesis. Plant Cell 7: 899
-
906



Shaul O, Galili G (1992) Increased lysine synthesis in tobacco plants that express
high levels of bacterial dihydropicolinate synthase in their chloroplasts. Plant J 2:
203
-
209



Karchi H,

Shaul O, Galili G (1993) Seed
-
specific expression of a bacterial
desensitized aspartate kinase increases the production of seed threonine and
methionine in transgenic tobacco. Plant J 3: 721
-
727



Karchi H, Shaul O, Galili G (1994) Lysine synthesis and cat
abolism are
coordinately regulated during tobacco seed development. Proc Natl Acad Sci
USA 91: 2577
-
2581

Shikimate pathway and phenylpropanoid metabolism



*

Herrmann K (1995) The shikimate pathway: early steps in the biosynthesis of
aromatic compounds. Pla
nt Cell 7: 907
-
919



*

Dixon RA, Paiva N (1995) Stress
-
induced phenylpropanoid metabolism. Plant
Cell 7: 1085
-
1097



Gaffney T, Friedrich L, Vernooj B, Negrotto D, Nye G, Uknes S, Ward E,
Kessmann H, Ryals J (1993) Requirement of salicylic acid for the induc
tion of
systemic acquired resistance. Science 261: 754
-
756



Siebert M, Sommer S, Li S, Wang Z, Severin K, Heide L (1996) Genetic
engineering of plant secondary metabolism.


Accumulation of 4
-
hydroxybenzoate
glucosides as a result of expression of the bacte
rial ubiC gene in tobacco. Plant
Physiol 112: 811
-
819

Lauric acid synthesis



*

Ohlrogge J, Browse J (1995) Lipid biosynthesis. Plant Cell 7: 957
-
970



*

Ohlrogge J (1994) Design of new plant products: engineering of fatty acid
metabolism. Plant Physiol 104:

821
-
826



Voelker TA, Worrell A, Anderson L, Bleibaum J, Fan C, Hawkins D, Radke S,
Davies HM (1992) Fatty acid biosynthesis redirected to medium chains in
transgenic oilseed plants. Science 257: 72
-
74



Voelker TA, Hayes TR, Cranmer AM, Turner JC, Davies H
M (1996) Genetic
engineering of a quantitative trait: metabolic and genetic parameters influencing
the accumulation of laurate in rapeseed. Plant J 9: 229
-
241



Eccleston VS, Ohlrogge JB (1998) Expression of lauroyl
-
acyl carrier protein
thioesterase in
Bras
sica napus
seeds induces pathways for both fatty acid
oxidation and fatty acid biosynthesis and implies a set point for triacylglycerol
accumulation. Plant Cell 10: 613
-
621