In biochemistry, control coefficients[1] are used to describe how much influence a given reaction step has on the flux or concentration of the species at steady state.
In theory, any observables, such as growth rate, or even combinations of observables, can be defined using a control coefficient; but flux and concentration control coefficients are by far the most commonly used.
The simplest way to look at control coefficients is as the scaled derivatives of the steady-state change in an observable with respect to a change in enzyme activity (ei for each species i).
For example, the flux control coefficients (C Jei, where J is the reaction rate) can be written as:
The approximation in terms of percentages makes control coefficients easier to measure and more intuitively understandable.
A negative value indicates that the observable in question decreases as a result of the change in enzyme activity.
It is important to note that control coefficients are not fixed values but will change depending on the state of the pathway or organism.
If an organism shifts to a new nutritional source, then the control coefficients in the pathway will change.
One criticism of the concept of the control coefficient as defined above is that it is dependent on being described relative to a change in enzyme activity.
Instead, the Berlin school[2] defined control coefficients in terms of changes to local rates brought about by any suitable parameter, which could include changes to enzyme levels or the action of drugs.
The advantage is that the control coefficient becomes independent of the applied perturbation.
For control coefficients defined in terms of changes in enzyme expression, it is often assumed that the effect on the local rate by changes to the enzyme activity is proportional so that:
The flux control coefficients do not measure this kind of rate-limitingness.
For example, in a linear chain of reactions at steady-state, all steps carry the same flux.
That is, there is no slow or fast step with respect to the rate or speed of a reaction.
A step with a high flux control coefficient means that changing the activity of the step (by changing the expression level of the enzyme) will have a large effect on the steady-state flux through the pathway and vice versa.
[4] However, this drew much criticism due to a misunderstanding of the concept of the steady-state.