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 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. Hence a more general definition is given by the following expressions:
and concentration control coefficients by
In the above expression,  could be any convenient parameter. For example, a drug, changes in enzyme expression etc. 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: