Introduction
All this theory is very nice, but how do we make any real use of it?
Perturbation Methods
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…)
Control Coefficients from Enzyme Elasticities
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.
Top-Down Control Analysis
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.
Control Coefficients from Transient Metabolite Concentrations
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.
Enzyme Elasticities from Control Coefficients
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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