how does the “sequential” and “symmetry” models, used to describe the effects of allosteric regulation, differ in their explanation of how the phenomenon of “positive co-operativity” occurs.

Answer 1

Hey, Dan here! Both the symmetry and sequential models of allosteric regulation describe two conformations for protein subunits: R (relaxed, has a greater affinity for the substrate) and T (tert, has a lower affinity for the substrate). Where they differ is how the whole protein acts as substrates are bound to each subunit.

In the symmetry model, all protein subunits are the same (symmetrical), either all T or all R. There's a rate of conversion from the T state to the R state (Kr) and a rate from the R state to the T state (Kt). When no substrates are bound, Kt is way bigger than Kr, so the vast majority of your proteins will have all-T conformations. However, as you bind substrates, the balance starts shifting to Kr, increasing the rate that your protein shifts to an all-R conformation. Note that this means that substrates can be bound to all-T proteins: Substrate binding increases the rate of all-T to all-R conversions (Kr). This is where the positive cooperativity in the symmetry model comes in: As you add substrates, the rate that your protein is shifting from all-T to all-R increases, which means that your protein is spending more time in an all-R state where it has a greater affinity to the substrate.

In the sequential model, it's a little bit more intuitive. Rather than an "all-or-nothing" model, where substrate binding increases the rate that all of your subunits switch to the R-state, a T-state subunit bound to a substrate individually converts to an R-state. Here, positive cooperativity comes from "cross-talk" between subunits. Think of it like seeing someone eat a sandwich when you're hungry: your stomach probably starts to growl, right? In the sequential model, one subunit binding to a substrate increases the affinity of other subunits around it to bind to substrates and convert to the R-state. This is why every substrate binding event increases the chance that another substrate binding event will occur.

To sum it up: Positive cooperativity in the symmetry model comes from "More substrates = More chance that all my subunits will convert to R = Greater affinity at all subunits," whereas positive cooperativity in the sequential model comes from "More substrates = Greater affinity in subunits around R-state subunits = More likely those subunits will bind substrate themselves and convert to the R-state."

Hope this helps!