Suicide substrate and kinetics

[Zealduke]

Suicide substrate. An Enzyme, E reacts with a substrate S to form an enzyme substrate-complex, ES is usual for Michaelis-Menten kinetics. However, the substrate in the enzyme-substrate complex chemically reacts with the enzyme to form a permanent covalent complex at the enzyme active site. The enzyme then becomes ED (dead enzyme). ED is no longer active and it does not turn over.

The reaction shceme is

E+S--> (k1) and <--- (k-1) ES---> (k2) ED

In this case [ET] -[ED]=[E] +[ES], where [ET] is the initial starting concentration of enzyme, [ED] is the concentration of dead enzyme,and [E] and [ES] are the concentration of viable enzyme that are respectively free and substrate bound.

Using the steady state approximation for [ES], as you would in the usual Michaelis-Menten scheme, derive an expression for the rate of creation of [ED]. That is, find d[ED]/dt. (Hint, your expression will contain the term {[ET]-[ED]} instead of the usual [ET]. Your expression also contains k1, k-1, k2)

I doubt I'm right on this...

d[ES]/dt = k1[E] - [ES](k-1 + k2)

d[ED]/dt = k2 [ES]

= k1([ET]-[ES]) - [ES](k-1 + k2)

Am I at least on the right track? If not I have a couple ideas to alternative solutions.

 

[Ygggdrasil]

d[ES]/dt = k1[E] - [ES](k-1 + k2)

d[ED]/dt = k2 [ES]

These two expressions are correct and a good starting point.

= k1([ET]-[ES]) - [ES](k-1 + k2)

I'm not sure what you did to get here.

Anyway, the problem tells you to use the steady state approximation. What is the steady state approximation and what does it tell you about one of your equations?

Also, you want to write an expression for d[ED]/dt in terms of [ET], [ED], k1, k-1, k2, and . This means you need to find some way of expressing [ES] and [E] in these terms.

 

[Zealduke]

site screwed up my last post...

ok, so with steady state i can assume negligible change in ES

with ET-ED being the total enzyme I got:

([ET]-[ED]) = [ES] + [ES] ((k-1 + k2)/k1)

i hope this is a little closer than the last one.

 

[Ygggdrasil]

site screwed up my last post...

ok, so with steady state i can assume negligible change in ES

with ET-ED being the total enzyme I got:

([ET]-[ED]) = [ES] + [ES] ((k-1 + k2)/k1)

i hope this is a little closer than the last one.

That looks correct. Now, you just have to combine this information with your equation for d[ED]/dt.

 

[DeeNos]

Yes, you are on the right track. Your expression for d[ED]/dt is correct. However, based on the given information, it is not possible to derive an expression for d[ED]/dt using the steady state approximation for [ES]. The steady state approximation assumes that the rate of formation of [ES] is equal to the rate of its consumption, which is not the case in this scenario. This is because [ES] is being consumed not only by the reaction with the substrate, but also by the reaction with the enzyme to form [ED]. Therefore, an alternative approach would be needed to derive an expression for d[ED]/dt. This could involve using the rate law for the formation of [ED] or considering the overall reaction scheme and using the law of mass action.