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.

Read more about this topic: Metabolic Control Analysis

Famous quotes containing the words step and/or pathway:

“The glorious dream of full father involvement in infant care will not become a widespread reality overnight. But it can happen, and it eventually will happen,... A lot of progress may take place in a short period of time if we just lighten up, step back, and give the guys a decent chance.”
—Michael K. Meyerhoff (20th century)

“And open field, through which the pathway wound,
And homeward led my steps. Magnificent
The morning rose, in memorable pomp,
Glorious as e’er I had beheld—in front,
The sea lay laughing at a distance; near,
The solid mountains shone, bright as the clouds,
Grain-tinctured, drenched in empyrean light;”
—William Wordsworth (1770–1850)