Introduction to MCA

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Introduction to MCA
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Models are Difficult to Understand

• The need for theory

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Introduction to MCA
It origins Three groups, Edinburgh, Berlin and
Michigan, simultaneously and independently
developed almost an identical theory to
the analysis of perturbations in biochemical
pathways. What is it? The approach (called MCA
here, also BST and MCT), aims to achieve a
quantitative understand of the relationship
between genotype and phenotype, to understand
systems behavior in terms of the unit processes
(enzymes) that make up biochemical pathways.
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Introduction to MCA
Why bother? Because a quantitative understanding
of the control and dynamics of biochemical
pathways is sorely needed, both from an
academic as well as an applied science
perspective. Such an understanding would have a
significant impact on areas such as drug
targeting, disease management, metabolic
engineering and synthetic biology (cf. Venter and
his hydrogen bug).
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Metabolic Control Analysis
Steady state flux J
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Metabolic Control Analysis
Parameters 1. Enzyme Levels 2. Kinetics
Constants 3. Boundary Conditions

• Variables
• 1. Concentrations of Molecular Species
• 2. Fluxes

MCA investigates the relationship between the
variables and parameters in a biochemical
network..
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Metabolic Control Analysis
Steady state flux J
At steady state
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Metabolic Control Analysis
Steady state flux J
If we make a change, say to the levels if E2
(change its Vmax), we will observe a change in
the steady state flux, J Let ? mean a small
change, therefore to judge the influence of
changing E2 on the steady state flux J, we could
measure the ratio
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Metabolic Control Analysis
Steady state flux J

• Unfortunately the ratio has two undesirable
  aspects
• The ratio depends on the size of the change that
  we make to E2
• The ratio depends on the units that are used to
  measure E2 and J.

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Metabolic Control Analysis
Steady state flux J
To avoid these issues, we scale the ratio to
remove the units and we also use infinitesimal
changes rather than finite small changes, as a
result we get a new formula
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Digression
Look at these two sequences, what is the
pattern? 100, 150, 200, 250, 300, ..
100, 150, 225, 337.5, 506.25, ..
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Digression
Look at these two sequences, what is the
pattern? 100, 150, 200, 250, 300, ..
100, 150, 225, 337.5, 506.25,
.. Answer The first sequence increases by a
fixed amount (50) The second sequence increases
by 50 percent
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Digression
Look at these two sequences, what is the
pattern? 100, 150, 200, 250, 300, ..
100, 150, 225, 337.5, 506.25, .. Now lets
log10 the numbers 2, 2.176, 2.301, 2.398, 2.477,
. 2, 2.176, 2.352, 2.528, 2.704, . Now whats
the pattern?
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Digression
Look at these two sequences, what is the
pattern? Now lets log10 the numbers 2, 2.176,
2.301, 2.398, 2.477, . 2, 2.176, 2.352, 2.528,
2.704, . The second sequence increases by a
fixed amount (1.176)
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Digression
Conclusion Equal distances between points on a
logarithmic scale indicate equal proportional
changes.
ln J
J
ln E
E
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Metabolic Control Analysis
Arithmetical interpretation
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Metabolic Control Analysis
The influence that a particular enzyme, say
enzyme Ei, has over a System variable, such as
the flux, is given by the expression
This is called the flux control coefficient
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Metabolic Control Analysis
Since changing the level of an enzyme activity
can also change the metabolite levels, there is a
similar control coefficient for the metabolites
This is called the concentration control
coefficient
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Rate-Limiting Steps
The concept of a "Rate-limiting (bottleneck or
pace-maker) Step" has long been suggested as the
principle means by which the flux through
metabolic pathways is controlled.
Often, however, the analysis of complex reaction
schemes can be simplified by the recognition of a
rate-limiting step. The concept is familiar to
anyone who has encountered repair work on the
highway - the slowest step in a multistep process
may determine how long the whole process
takes." from Biochemistryby Mathews van Holde
(2nd Edition) p364
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Metabolic Control Analysis
Simulation
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Metabolic Control Analysis
Some characteristics of flux control
coefficients. In a linear metabolic network, the
value of any particular flux control coefficient
is bounded between zero and one.
This condition applies to a linear chain
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Metabolic Control Analysis

• How can you measure control coefficients?
• Changing gene expression and measuring the effect
  on the system.
• Using inhibitors to change an enzymes activity
  and measuring the effect on the system.
• Building a computer model and getting the
  computer to compute the coefficients

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Metabolic Control Analysis
What about some real values? The following
information was taken from a paper by S. Thomas
et al, Biochemical Journal, 1997, 322, 119-127
Glycolysis in tuber tissue of potato. Values
computed using a combination of calculation
and experimental work.
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Metabolic Control Analysis
The Summation Theorems
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Metabolic Control Analysis
The Summation Theorems
1. The summation theorem shows that the enzymes
of a pathway can share the control of flux. 2.
Given that n gtgt 1, the average value for a
control coefficient must be 1/n, i.e. very small
most mutations are recessive 3. Changes in one
control coefficient result in changes in other
control coefficients. This means the a control
coefficient is a system property and not an
intrinsic property of the enzyme alone.
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Metabolic Control Analysis
Elasticities
If the value of a control coefficient is a system
property, what is the relationship of the control
coefficients to the individual enzymes of the
pathway? Somehow, all the enzymes contribute to
the value of a given control coefficient, how can
we describe this? In order to answer this
question we must consider another type of
coefficient, called the elasticity coefficient.
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Metabolic Control Analysis
Elasticities
Michaelis-Menten Curve for an isolated enzyme
Let us define the elasticity as
v
S
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Metabolic Control Analysis
Elasticities
Michaelis-Menten Curve for an isolated enzyme
Note that substrate elasticities are positive and
product elasticities are negative
v
S
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Metabolic Control Analysis
Another way of looking at an Elasticity
We can use an elasticity to predict the change in
the rate of a reaction given a change in the
substrate concentration.
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Metabolic Control Analysis
Another way of looking at an Elasticity
Product inhibition term
lt 0 !
In general if there are multiple changes
happening around an enzyme we can simply sum each
contribution using the appropriate elasticity.
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Metabolic Control Analysis
E
E
E
1
2
3
X
2
v
v
v
1
2
3

• Increase E3
• v3 Increases
• S2 Decreases
• v2 Increases
• S1 Decreases
• v1 Increases

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Metabolic Control Analysis
E
E
E
1
2
3
X
2
v
v
v
1
2
3
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Metabolic Control Analysis
E
E
E
1
2
3
X
2
v
v
v
1
2
3
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Metabolic Control Analysis
E
E
E
1
2
3
X
2
v
v
v
1
2
3
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Metabolic Control Analysis
E
E
E
1
2
3
X
2
v
v
v
1
2
3
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Metabolic Control Analysis
E
E
E
1
2
3
X
2
v
v
v
1
2
3
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E
E
E
1
2
3
Extra term
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E
E
E
1
2
3
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Metabolic Control Analysis
E
E
E
1
2
3
What happens as the feedback gets stronger and
stronger? i.e as we make the value of the
feedback elasticity larger?
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Metabolic Control Analysis
E
E
E
1
2
3
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Metabolic Control Analysis
E
E
E
1
2
3

• What does this mean?
• Feedback has the following consequences
• All flux control moves down stream beyond the
  signal leaving little or no flux control
  upstream. In fact, the controlled step has very
  little flux control.
• The signal molecule is locked into homoeostasis

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Metabolic Control Analysis
E
E
E
1
2
3

• What does this mean?
• The net effect of this is that feedback control
  creates a demand
• controlled network. That is, control over the
  flux through the
• pathway is determined largely by the demand for
  S2.
• Important examples is this include
• Glycolysis
• Amino acid biosynthesis

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