Metabolic Control Analysis
of
Biochemical Pathways
Cellular processes are continuously modified and
refined through evolution and natural selection for
adapting to environmental conditions.
Effort to manipulate the metabolism of an organism are
done in three broad areas of research and development:
(a) drug design to treat diseases,
(b) genetic engineering of organisms of
biotechnological interest,
(c) genetic syndromes therapy.
Historically, the first area, in which modification of metabolism
was tried, was drug design: the primary goal of drug
administration is the inhibition of essential metabolic
pathways, for example, in a parasite or a tumor cell.
Thus, any metabolic pathway can be a potential
therapeutic target.
In the absence of a solid theoretical background for
building a strategy for the rational design of drugs, the
pharmaceutical industry has applied the knowledge of
inorganic and organic chemistry for the arbitrary and rather
randomized modification of metabolic intermediaries by
replacing atoms in a model molecule with any other
element or compound.
This approach has been successful in the battle
against many diseases. However, in many other
instances such an approach has been unsuccessful.
A metabolic map given by reductionist
approaches can be compared to a region map -
not useful for revealing how much traffic can flow through
the streets.
Even if the map showed all the traffic signals and the width of
all streets, the actual measure of the traffic flux would still
remain quantitatively elusive.
The traditional approach (reductionist approach - the study
of a whole system by detailed examination of the properties of
its constituent parts) is unsatisfactory :
u Leads to an understanding of what determines the
local material flows in different pathways - but not of
how the production/utilisation of metabolites are kept
in balance;
u Lack of understanding of metabolic regulation
(obtained by reductionist approaches) reveals poor results
in increasing the rates of selected metabolic pathways;
u Primarily gives qualitative description. It lacks a more
rigorous specifications that could be compared with
quantitative experimental observations
Regulation and control
• Flux: 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: occurs when the system maintains some
variable (e.g. temperature or concentration) constant
over time, despite fluctuations in external conditions (a
concept linked to homeostasis) - noun
• Control: used to refer to adjusting the output of a
system with time. Control implies the ability to start/
stop/direct something. - verb
Metabolic Control
The power to change the state of metabolism in
response to an external signal.
It is measurable in terms of the strength of the metabolic
response to external factors, without any assumption
about the function/purpose/mechanism of the response.
Time Scales
• Regulation and control exist in different time scales,
from fractions of milliseconds for substrate binding to
circadian/seasonal rhythms.
• Is it legitimate to concentrate on just one time scale?
• Yes, if we consider living organism as being in a dynamic
equilibrium (steady state) ?
Metabolic Time scales and the quasi steady states
• A metabolic pathway starts with a source of material (Glucose)
derived at constant concentration from the environment, and
ends with a sink (Ethanol and CO2), that is kept at constant
concentration...
• This leads to the development of a steady state where the
concentrations of the intermediates remains constant because
their rates of formation have come to be in exact balance with
their rate of degradation
• The consequence of not reaching a steady state would be that the
metabolites would continue to accumulate in ever increasing
amounts
• A perfect steady state is a mathematical abstraction, but if the
relative changes in metabolite concentrations are small, we can
still consider it to be a “quasi steady state”
http://dbkgroup.org/mca_home.htm
• A metabolic pathway starts with a source of material (Glucose)
derived at constant concentration from the environment, and
ends with a sink (Ethanol and CO2), that is kept at constant
concentration.
• This leads to the development of a steady state where the
concentrations of the intermediates remains constant because
their rates of formation have come to be in exact balance with
their rate of degradation
• At steady state, the rate of formation of G6P in the cell by reaction
1 is equal to its consumption in reaction 2 (assuming there are no
other significant uses of G6P). Thus the rates of reactions 1 and
2 are the same. Similarly for reaction 2 and 3 …
• The steady state in metabolite concentrations is therefore
equivalent to a CONSTANT RATE THROUGH the WHOLE
pathway
The Rate-limiting Step: the slowest step in the pathway.
But at metabolic steady state all the steps along a linear pathway are
going at the same rate.
• Classical biochemical observations do not measure this “slowest step”;
• Evidences (1930s onwards) show that the rate of a sequence of simple
chemical reactions depend on the rate constants of ALL the reactions;
• If a unique rate-limiting step exists in a pathway then varying the activity
of that step alone will change the flux in the pathway, but there are few
experimental observation of such phenomenon.
An alternative to the concept of unique rate-limiting step was needed that
takes into consideration the evidence of pathways affected by several steps.
Metabolic control analysis (MCA) is a mathema.cal framework for
describing metabolic, signaling, and gene.c pathways.
MCA quan.fies how variables, such as fluxes and species
concentra4ons, depend on network parameters.
It is able to describe how network dependent proper4es (control
coefficients), depend on local proper4es called Elas4ci4es.
MCA was originally developed to describe the control in
metabolic pathways but was subsequently extended to describe
signaling and gene4c networks.
Kacser, H.; Burns, J. A. (1973). "The control of flux". Symposia of the Society for
Experimental Biology. 27: 65–104. PMID 4148886.
MCA has some4mes also been referred to as Metabolic Control
Theory
Ingalls, B. P. (2004) A Frequency Domain Approach to Sensi.vity Analysis of
Biochemical Systems , Journal of Physical Chemistry B, 108, 1143-1152.
Biochemical systems theory is a similar formalism, though with a
rather different objec4ves.
Savageau M.A (1976) Biochemical systems analysis: a study of func.on and
design in molecular biology, Reading, MA, Addison–Wesley.
Both are evolu4ons of an earlier theore4cal analysis by Joseph
Higgins.
Higgins, J. (1963). "Analysis of sequen.al reac.ons". Annals of the New York
Academy of Sciences. 108: 305–321. doi:10.1111/j.1749-6632.1963.tb13382
Flux: a term used to indicate the rate of a multi-component
system, while “rate” is reserved for individual components.
Metabolic Flux
is the rate of turnover of molecules through a metabolic
pathway. Flux is regulated by the enzymes involved in a
pathway.
Within cells, regulation of flux is vital for all metabolic pathways
to regulate the pathway's activity under different conditions.
Flux is the movement of matter through metabolic networks
that are connected by metabolites and cofactors, and is
therefore a way of describing the activity of the metabolic
network as a whole using a single characteristic.
Flux is therefore of great interest in metabolic network
modelling.
How much does the metabolic flux vary as the enzyme
activity is changed? Variation of the
FLUX ENZYME CONCENTRATION DIAGRAM pathway flux Jydh ,
measured at a
step ydh, with the
amount of an
enzyme, xase.
The FLUX
CONTROL CO-
EFFICIENT at e,j is
the slope of the
tangent to the
curve
times the scaling
factor e/j.
On a double-logarithmic plot of the same curve, the FLUX CONTROL CO-
EFFICIENT is the slope of the tangent to the curve
A control coefficient measures the rela4ve steady
state change in a system variable, e.g. pathway
flux (J) or metabolite concentra4on (S), in
response to a rela4ve change in a parameter,
e.g. enzyme ac4vity or the steady-state rate (vi)
of step i.
FLUX CONTROL CO-EFFICIENT:
δJydh
Slope of the tangent (rate of change) on the
flux-enzyme concentration diagram
δExase
Metabolic Flux is the rate of turnover of molecules through a
metabolic pathway. Flux is regulated by the enzymes involved
in a pathway.
Within cells, regulation of flux is vital for all metabolic
How much does the metabolic flux vary as the enzyme
pathways to regulate the pathway's activity under different
activity is changed?
conditions.
Flux is the movement of matter through metabolic networks
that are connected by metabolites and cofactors, and is
therefore a way of describing the activity of the metabolic
network as a whole using a single characteristic.
Metabolic control analysis (MCA) is a mathema.cal framework for
describing metabolic, signaling, and gene.c pathways.
MCA quan.fies how variables, such as fluxes and species
concentra4ons, depend on network parameters.
It is able to describe how network dependent proper4es (control
coefficients), depend on local proper4es called Elas4ci4es.
ln(FLUX, Jydh)
FLUX, Jydh
δJydh
δExase
CONCENTRATION OF ENZYME, Exase ln(CONCENTRATION OF ENZYME, Exase)
It is better to use the fractional change to obtain a dimensionless value
The dimensionless value of the flux control coefficient C is
Jydh δJydh Exase δlnJydh
Cxase δExase Jydh δlnExase
Multiply with the fractional change –
δExase/Exase & δJydh /Jydh
The response of the flux to
the concentration of enzyme
depends on the position
along the X-axis.
To know the enzyme
concentration in the cell,
and to know where the
enzyme maps on this
diagram, in vivo
measurements need to be
made.
Flux control coefficients are commonly low
This implies that biotechnological engineering on a single
enzyme will rarely have the effect of significantly
increasing the flux in a pathway
The Summation Theorem
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-limiBng” 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
Effect of Metabolites
• The flux control coefficient of an enzyme is a system property
that cannot be related to the enzyme in isolation, but there
must be links between the enzyme kinetic properties and its
potential for flux control
• If we add an extra amount of ydh to the pathway below, what
happens? xase ydh zase
X0 ⎯ ⎯ ⎯ → Y ⎯ ⎯⎯ → Z ⎯ ⎯ ⎯ → X1
1. More Y is used up, and so its concentration is reduced, this will:
• increase the rate of xase because of reduced product inhibition
• decrease the rate of ydh because of lower substrate
concentration
2. More Z is produced, and this will:
• decrease the rate of ydh because of increased product
inhibition
• Increase the rate of zase because of higher substrate conc.
In practice, the effect of metabolites tends to counteract the
change in the amount of enzyme
• Each enzyme can have more
positive values for metabolite
the enzyme (substrates, activ
metabolites that slow the rea
• Compared to the classic Mich
ln(Rate, vxase)
Rate, vxase
hyperbola of a single-substra
the set of elasticities of an en
situation where most enzyme
work in the presence of appre
inhibition) of products
15
Metabolite Concentration, S ln(Metabolite Concentration, S)
Typical variation of the rate of enzyme xase, Vxase, with the
concentration of the metabolite S. The Elasticity coefficient,
at (s, v) is the slope of the tangent to the curve
(scaled with s/v).
ELASTICITIES
The measure of the metabolite effect on an enzyme is given by
the Elasticity Coefficient
Each enzyme can have more than one elasticity:
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)
Classic Michaelis-Menten kinetics of a single-substrate enzyme
in the absence of product, shows a rectangular hyperbola.
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 presence of appreciable
concentrations (and hence inhibition) of products.
THE CONNECTIVITY THEOREM
How are kinetic properties of enzymes connected to flux
control coefficients?
Take a pathway metabolite S and 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) X (the elasticities)
sum up to zero:
In a general form, include all n enzymes
in the metabolic pathway system
(since enzymes not affected by the metabolite S
will have elasticities=0)
CONCLUSIONS
• In MCA the qualitative categories “rate-limiting” and
“not rate- limiting” are replaced by a quantitative
scale for the influence of an 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
Effort to manipulate the metabolism of an organism are
done in three broad areas of research and development:
(a) drug design to treat diseases,
(b) genetic engineering of organisms of
biotechnological interest,
(c) genetic syndromes therapy.
FLUX BALANCE ANALYSIS
is widely used now in all the three above
