What is a flux control coefficient?

Question

In metabolic control analysis, a number of coefficients are defined, including the flux control coefficients. How is this coefficient defined and what does it measure?

Answer 1

The flux control coefficient measures the relative change in the steady state pathway flux in response to a relative change in enzyme activity. Mathematically it is defined according to:

$C^J_{e_i} = \frac{dJ}{de_i} \frac{e_i}{J}$

Because enzyme activity is proportional to enzyme concentration, the flux control coefficient is often define with respect to the enzyme concentration, $e_i$.

This can be also expressed in log form:

$C^J_{e_i} = \frac{d\ln J}{d\ln e_i}$

It can also be expressed approximately as a ratio of percentage changes:

$C^J_{e_i} = \frac{J\%}{e_i\%} $

This definition makes it easy to measure. For example, if the activity of a given enzyme is changed by a factor of 1.5 which results in a 1.25 fold change in the steady-state flux, then the value of the flux control coefficient is approximately 1.25/1.5 = 0.83. Because flux control coefficients are measured using relative changes, the coefficients are dimensionless.

Flux control coefficients are useful to gauge how much a given enzymatic reaction influences the flux in a pathway.

For further information I recommend the following paper:

Kacser, Henrik, James A. Burns, H. Kacser, and D. A. Fell. "The control of flux." (1995): 341-366.