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All this theory is very nice, but how do we make any real use of it?
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Perturbation Methods |
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The obvious way of determining control coefficients is to follow
their definition, ie perturb one
step, let the system settle to a new steady state and then measure the
change in the variable of interest. There are many ways of perturbing
the rate of a reaction, each of them with its own advantages and
disadvantages.
Several methods can be used to determine control coefficients by
perturbation of the rate of reaction:
- Alteration of enzyme concentration by genetic means. See
for example
Flint et al. (1981) and
Niederberger et al. (1992) or
Fell (1992) for further references.
- Titration with inhibitors. See for example
Groen et al. (1982),
Westerhoff & Kell (1988),
Small (1993) or Fell (1992) for further references.
- Titration with purified enzyme.See for example
Torres et al. (1986) or
Fell (1992) for further references.
The most important points to have in mind is that each perturbation
should affect one step only. If one wants a complete picture of
the control of the variable in question, then the same procedure will
have to be repeated for each step of the system. However easy this might
appear, there are several problems associated with these approaches:
- The perturbations should be very small - because the steady
state moves when the perturbations are finite, there is an error
associated with large perturbations (the larger they are, the bigger the
error. To minimize this error the perturbations should be small,
something like 1% would be ideal. However, the effects of small
perturbations are usually also small and so are very difficult to
detect. More often perturbations of over 10% are used, even though they
imply some error in the results.
- Inhibitors must be specific - if we want to perturb the
rate of one reaction by adding an inhibitor, this must only affect that
reaction alone, not any of the others in the system. It is often
difficult to fulfil this requirement.
- The rate of reaction must change linearly with the enzyme
concentration, if we want to use the enzyme concentration as the
parameter to perturb. If the relation between rate and enzyme
concentration is not linear, then the resulting control coefficients
will not conform to the summation theorems. (In fact the control
coefficients determined, or defined, in terms of enzyme concentrations
are really response coefficients as the
enzymes are external effectors...)
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Control Coefficients from Enzyme Elasticities |
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As described in previous section control
coefficients can be calculated from enzyme elasticities using one of
several matrix methods. It is important that the elasticities are
determined in conditions exactly the same as in the steady state of
interest.Ideally these would be determined in vivo but this is
rather difficult. See
Groen et al. (1986)
for an example.
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Top-Down Control Analysis |
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Recently, a new method for analysing the control of a biochemical
pathway was developed by
Brown et al. (1990),
which is partly based on determination of some enzyme elasticities.
This method, known as top-down control analysis relies on the
fact that control coefficients are additive, i.e. the control coefficient
of a group of steps is equal to the sum of the control coefficients of
the individual steps and that one can define overall
elasticities of a metabolite towards a group of steps. In top-down
control analysis one divides the system in blocks such that each is
connected to another only by one metabolic link (one metabolite and no
feedback or feedforward loops). One can then study the control by each
of the blocks. Once this is done, one can then increase the detail by
studying each of the blocks.
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Control Coefficients from Transient Metabolite Concentrations |
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Delgado & Liao (1992a,
b) proposed a method to calculate
control coefficients from measurements of the metabolite concentrations
in the transient state (i.e. between a pertubartion is applied and the
steady state). This method relies on the kinetics of the steps in question
being quasi-linear near the steady state.
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Enzyme Elasticities from Control Coefficients |
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More recently, it has been sugested that one can also calculate the
values of the enzyme elasticities from previously determined control
coefficients. This can in theory be achieved using the method described
by Westerhoff et al. (1994)
but so far no experiments have been reported yet.
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