Past exam of the mathematics and the environment and mathematical physiology course of the University of Oxford / 2009 / B / 4 / b / Solution

Adding the two complex and two free-carrier equations cancels binding and conformational exchange, givingEach free or bound carrier contains one carrier protein, and the model neither synthesizes nor degrades it. Adding the two free-substrate and two bound-substrate equations likewise givesBinding stores substrate temporarily and loaded conformational exchange relocates it; neither changes total substrate. The two invariants count distinct conserved chemical moieties. The constants $c_0$ and $s_0$ should not be interchanged: protein and substrate need not be present in equal amounts.