METABOLIC CONTROL ANALYSIS (MCA)
File name
MCA 2013
MCA vs. TRADITIONAL REDUCTIONIST APPROACHES
TO METABOLIC REGULATION
MCA was first developed by Kacser & Burns in the early 1970's.
MCA studies the relative control exerted by each step (enzyme or transporter) on fluxes
and metabolite concentrations in a metabolic system, i.e. a pathway or set of pathways.
MCA is a quantitative, theoretical approach that bridges the gap between enzymology
and whole pathways, i.e. it deals with the emergent properties of metabolizing systems
that cannot be described in terms of the in vitro properties of the individual enzymes.
MCA emphasizes that:
 Single, rate-limiting steps are rare in metabolic pathways
 Control of pathway flux is usually shared among several steps
 Their relative contribution to overall control will vary with flux rate
MCA provides a framework for:
 Interpreting metabolomics data
 Assessing the likelihood of achieving a desired modification of metabolism by a
particular engineering intervention
Traditional, reductionist metabolic biochemistry does not provide the understanding
needed to do this because it deals with metabolic regulation in terms of a few qualitative
principles. The traditional approach unfortunately still has a wide following and is in
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
controlling 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 preconceived and teleological.
The traditional concepts are often hard to test experimentally, due to their qualitative
nature. Engineering the levels of enzymes considered to be "rate-limiting" has rarely had
the expected outcome. These concepts are not a sound basis for understanding
metabolism or predicting the effects of metabolic engineering.
MCA INTRODUCES THE POWER AND PROBLEMS OF
SYSTEMS BIOLOGY
Systems approaches are routine in chemical, electrical, and other types of engineering.
Systems Biology seeks systems-level understanding, as distinct from understanding
individual system components such as particular genes or enzymes. The systems range
from metabolic pathways and gene-regulatory networks to whole cells, organisms, and
ecosystems. See ‘Life's Complexity Pyramid’ (Oltvai & Barabasi, 2002).
Systems Biology deals with ‘emergent’ properties that arise when individual components
interact in a system.
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It is obviously distinct from reductionism (which studies only individual
components such as genes and enzymes).
Less obviously, it is also distinct from classical holism, which studies the entire
system without asking how its properties arise from interaction of its components.
Metabolic systems are relatively simple and are a logical starting point for development
of genome-scale cellular (and eventually organismal) models.
MCA is therefore a good introduction to Systems Biology. Learning about MCA also
reveals how traditional reductionist thinking differs from systems thinking – and how
reductionist ideas can be misleading when dealing with whole systems.
OUTLINE OF MCA
 Resources
http://dbkgroup.org/mca_home.htm A good introduction to MCA
http://http-server.carleton.ca/~kbstorey/mca_page.htm MCA FAQ – a good
introduction, organized as a series of questions and answers
Fell DA (1997) Understanding the control of metabolism. Portland Press,
London, UK
 Coefficients in MCA
MCA defines several coefficients.
Control coefficients refer to the whole metabolic pathway (i.e., they are systemic or
global properties). A control coefficient is a relative measure of how much a perturbation
to e.g. enzyme activity Ei affects a system variable, e.g. a flux or metabolite
concentration:
Most important (at heart of theory) are Flux (J) control coefficients CJEi
Others: Concentration control coefficients and response coefficients (to external
effectors)
Flux control coefficients
The flux control coefficient is defined as the ratio between the fractional change in flux J
through a pathway and the fractional change in amount or activity of an enzyme Ei. Flux
control coefficients are highly relevant to metabolomics and metabolic engineering.
Once an enzyme is embedded in a pathway, its behavior is influenced by the flanking
enzymes. Consider a simple pathway:
- with enzymes E1-3 (which all show typical Michaelis-Menten behavior*)
- with substrates and intermediates S0-3
- with a steady state flux J (units: e.g. mol.h-1)
* Michaelis-Menten kinetics
As substrate concentration increases the initial rise in reaction velocity is almost linear, but as concentration
increases further there are diminishing returns with the eventual saturation of the reaction at some maximal
rate. The constant Vmax is the maximal velocity of the reaction. Km is the Michaelis constant, and is the substrate
concentration at which the reaction reaches half-maximal velocity.
S0
E1
E2
E3
→ S1 → S2 → S3
The flux J is equal through all steps and the intermediate concentrations ("pool sizes")
remain steady, because the intermediate concentrations are used to balance each
individual reaction to the overall flux. e.g. If the reaction catalyzed by E1 were to proceed
faster than E2, there would be a net increase in [S1]. Provided that enzyme E2 can
respond to (i.e. is not saturated with) S1, this increased [S1] will increase the rate of E2
until it becomes equal to that of E1, at which point [S1] will remain constant.
Consider a small change in the activity of one enzyme, e.g. E1, on the flux J through the
whole pathway (the activity change could be due to altered amount of enzyme, posttranslational modification, etc).
The response of flux to change in an individual enzyme is generally more-or-less
hyperbolic, thus (Fig. 1A):
The flux control coefficient for enzyme E1 is the ratio between the fractional change in
flux dJ/J and the fractional change in enzyme activity dE1/E1. This is the slope of the
tangent to the plot of J vs. E1 multiplied by the scaling factor E1/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.
CJE1
= dJ/J = dJ/dE1 . E1/J =
dE1/E1 (slope) (scaling
factor)
d(ln J)
d(ln E1)
Each enzyme in the system has a flux control coefficient, so for enzymes E2 and E3:
CJE2
CJE3 = dJ/J_
dE3/E3
= dJ/J
dE2/E2
i.e. there are as many flux control coefficients for a pathway as there are enzymes (or
transporters) in the system.
The Summation Theorem states that, for a given flux J, the sum of the flux control
coefficients of all the enzymes in the system, E1, E2.....En is unity, i.e.:
CJE1 + CJE2
+ CJEn = 1
or in mathematical notation:
Σ CJEi
i = 1 to n
= 1
Note that:
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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 (when all the other enzymes would have flux control coefficients of
zero). This would correspond to the traditional "rate-limiting" enzyme. It is rare.
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.
When the flux control coefficient = 0.01, a small increase in enzyme activity will
have an effect on flux that is only 1% of the imposed change, e.g. a 10%
increase in enzyme gives only 0.1% increase in flux.
When the flux control coefficient = 0.9, flux responds almost proportionately to
small changes in enzyme activity.
In practice, flux control coefficients are usually 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 flux 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 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 pathway
The concentration of S2 is now critical to the activity of E1, and the concentration of S2 is
strongly influenced by the activity of E3, which consumes S2. This shifts control away
from E1 to E3, i.e. it lowers the flux control coefficient of E1.
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 has 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 distribution of control can vary with flux.
Concentration control coefficients
Concentration control coefficients quantify the effect of enzyme activity Ei on any
metabolite Si. For instance, for enzyme E1 and the concentration of its product S1:
CS1E1
= dS1/S1 = dS1/dE1 . E1/S1 =
dE1/E1
d(ln S1)
d(ln E1)
Note that the value for E1 on S1 will usually be positive, but that for E2 on S1 (CS1E2) will
usually be negative (E1 produces S1 whereas E2 consumes it). Concentration control
coefficients can have large positive or negative values.
For concentration control coefficients, for each metabolite the sum of all the
concentration control coefficients is zero:
ΣCSjEi
i = 1 to n
= 0
Why silent knockout or knockdown mutants often have large changes in metabolite pools
There is a firm theoretical basis for this in MCA. Flux control coefficients CJEi have values between 0 and 1,
typically nearer 0 than 1. In contrast, concentration control coefficients CS1Ei can have large positive or
negative values and sum to zero. Changes in the activity of a single enzyme can therefore produce very
large changes in levels of metabolites (that often minimize the effect of a change in enzyme activity on flux).
Consider the simple linear pathway:
S0
E1
E2
E3
→ S1 → S2 → S3
Suppose that in the wild type the operating point of enzyme E2 is at 0.05 x Km, and that a mutation decreases
E2 activity to 10% of the wild type value.
Since E2 operates in the near-linear part of its velocity vs. [substrate] curve, when its activity drops to 10% of
normal, it is possible for it to catalyze the same reaction rate provided that the concentration of its substrate S1
rises by about 10-fold.
Thus S1 builds up until the point (about 10x its normal concentration) at which it drives the same reaction
velocity through E2 as before. Since flux in the pathway is thereby restored to normal, there is no effect on the
function of the whole pathway, so the organism functions normally (i.e. there is no obvious phenotype).
But analysis of the pool sizes of the intermediates (metabolite profiling) will show that this apparent restoration
to normality involves a very large increase in [S1].
This is why broad-spectrum metabolite profiling is a powerful way to detect a phenotype in an otherwise silent
mutant and, from the types of metabolites that change, to infer the area of metabolism where the lesion is
located.
Responses to Large Changes in Enzyme Activities or Effectors. MCA is based on
small changes. But note how the slopes of the tangents in Figs. 1 A & B vary as E
varies. Thus 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 mutations, metabolic engineering, and experiments to
estimate flux control coefficients often involve fairly large changes in 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 two values of the flux, J1 and J2, at two widely
separated levels of the enzyme, E1 and E2, allows calculation (to a good approximation)
of the flux control coefficient at enzyme level E1 as:
CJE
= (J2 - J1) E2
(E2 - E1) J2
(termed the deviation index)
This differs from the small-change estimate of the flux control coefficient in that the
scaling factor is E2/J2, not E1/J1 (the ratio at the original operating point).
With this equation, the flux control coefficient measured at one point allows reasonably
good prediction of the 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 activity. The -fold
increase of enzyme activity (2- to 50-fold) is shown by each curve.
 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 maximum 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
engineered changes in single target enzymes do not significantly increase flux.
MEASURING FLUX CONTROL COEFFICIENTS
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Flux control coefficients are measured by changing the maximum catalytic activity of
a specific enzyme and observing the effects on flux.
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The main ways to alter a given enzyme activity are: inhibitors, induction-repression,
mutations, and engineering (overexpression, antisense, RNAi, etc).
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Regardless of the type of perturbation used, two key 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
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In mutants and transgenics, it is crucial that only the enzyme in question be
changed, i.e. that there be no pleiotropic, somaclonal or insertional effects (hence
the importance of using independent transformants), or compensatory changes in
other enzymes.
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These conditions are hard to completely satisfy, which partly explains the scarcity of
published measurements of flux control coefficients.
GAPS IN KNOWLEDGE/FLAWS IN MCA
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Metabolite pools are not merely reactants and products in metabolic pathways, they
are also signals to the genome – i.e. they regulate gene expression. Therefore
mutagenesis or transgene expression that alters metabolite levels will very likely
also alter the expression of other genes. This can:
o
Complicate interpretation of metabolomics data from mutants and transgenics
o
Reduce the predictive value of MCA in engineering
o
Compromise measurements of flux control coefficients
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Most metabolism of eukaryotic cells takes place in the aqueous cytoplasm and
interiors of organelles, but the conditions there 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") .
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There is much evidence that cellular metabolism is spatially organized on a very
small scale; this includes:
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o
Evidence for membrane-adsorbed enzyme clusters, multienzyme complexes,
and for enzymes arrays attached to the cytoskeleton
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
metabolic engineering design may not always be valid.