Control coefficient (biochemistry)

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. This can be accomplished experimentally by changing the expression level of a given enzyme and measuring the resulting changes in flux and metabolite levels. 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 (e_i for each species i). For example, the flux control coefficients (C^J
_ei, where J is the reaction rate) can be written as:

$${\displaystyle C_{e_{i}}^{J}={\frac {dJ}{de_{i}}}{\frac {e_{i}}{J}}={\frac {d\ln J}{d\ln e_{i}}}\approx {\frac {J\%}{e_{i}\%}}}$$

while the concentration control coefficients (Csj
ei, where sj is the concentration of species j) can be written as:

$${\displaystyle C_{e_{i}}^{s_{j}}={\frac {ds_{j}}{de_{i}}}{\frac {e_{i}}{s_{j}}}={\frac {d\ln s_{j}}{d\ln e_{i}}}\approx {\frac {s_{j}\%}{e_{i}\%}}}$$

The approximation in terms of percentages makes control coefficients easier to measure and more intuitively understandable.

Control coefficients can have both negative and positive values. 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. As such, control coefficients form a central component of metabolic control analysis.