Feedback control for a metabolic pathway
I'm having a problem setting up a certain differential equation which I need to solve a problem. Here's the problem: I'm given a feedback control for a certain metabolic pathway. I've attached a picture of the network below.
Now what I can't figure out is how to write the differential equation which governs the amount that accumulates at any particular node. It says that the reactions, except for the first one, obey a first-order rate law, and that all the rate constants are proprtional. But is the time derivative of S1 equal to f(Sn), or is it equal to f(Sn) - kS2? Also, in general, should I find the time derivative of each Sn by subtracting the incoming and outgoing rates?
I'd appreciate any help that anyone can give me. Thanks.