Metabolic Control Analysis - Three Step Pathway

Three Step Pathway

Consider the simple three step pathway:

where and are fixed boundary species, the control equations for this pathway can be derived in a similar manner to the simple two step pathway although it is somewhat more tedious.

$C^J_{E_1} = \varepsilon^{2}_1 \varepsilon^{3}_2 / D$

$C^J_{E_2} = -\varepsilon^{1}_1 \varepsilon^{3}_2 / D$

$C^J_{E_3} = \varepsilon^{1}_1 \varepsilon^{2}_2 / D$

where D the denominator is given by:

$D = \varepsilon^{2}_1 \varepsilon^{3}_2 -\varepsilon^{1}_1 \varepsilon^{3}_2 + \varepsilon^{1}_1 \varepsilon^{2}_2$

Note that every term in the numerator appears in the denominator, this ensures that the flux control coefficient summation theorem is satisfied.

Likewise the concentration control coefficients can also be derived, for

$C^{S_1}_{E_1} = (\varepsilon^{3}_2 - \varepsilon^{2}_2) / D$

$C^{S_1}_{E_2} = - \varepsilon^{3}_2 / D$

$C^{S_1}_{E_3} = \varepsilon^{2}_2 / D$

And for

$C^{S_2}_{E_1} = \varepsilon^{2}_1 / D$

$C^{S_2}_{E_2} = -\varepsilon^{1}_1 / D$

$C^{S_2}_{E_3} = (\varepsilon^{1}_1 - \varepsilon^{2}_1) / D$

Note that the denominators remain the same as before and behave as a normalizing factor.

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