HardBiologyHigh School (11–12)Cell BiologyNumerical

A pathway makes a product P in a pool. The first enzyme makes P at up to 8.0 µmol/min…

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

A pathway makes a product P in a pool. The first enzyme makes P at up to 8.0 µmol/min. The cell uses P at a rate of $k \times$ (the amount of P), with $k = 0.1$ per minute. With feedback, P halves the first enzyme's rate when the pool holds 4.0 µmol.

After a long time, how big is the pool without feedback?

How big is it with feedback, and how much P does the cell then use each minute?

The cell now uses P twice as fast, so $k = 0.2$ . How big is the pool with feedback?

Need a reminder? The key ideaShow

Competitive inhibitor: $K_{m,\text{app}} = K_m(1 + i)$ , $V_{\max}$ unchanged, with $i = [I]/K_i$ . Non-competitive inhibitor: $V_{\max,\text{app}} = V_{\max}/(1 + i)$ , $K_m$ unchanged. Feedback from an end product usually acts on the first committed step, and a regulated enzyme such as phosphofructokinase-1 has activators and inhibitors that bind away from its active site.

The worked solution

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Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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