# What is a flux control coefficient?

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?

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 make 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.

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