In order to measure the kinetics of one enzyme in a sequence of enzyme reactions, there are 2 necessary conditions I can think of.

(1) The reaction of the enzyme of interest has to be rate limiting (i.e. the slowest step). This can be achieved by keeping the concentrations of all the other enzymes very high. The test for this condition having been successfully achieved is that further increasing the concentrations of the other enzymes does not increase the rate of the E3 reaction.

(2) You have to know the concentration of the substrate of E3. This is challenging, but the way to do it is to run the reactions of E1 and E2 first with a known concentration of the substrate of E1, such that all of the E1 substrate is converted to the E3 substrate prior to the addition of E3. (This requires that the E1 and E2 reactions are essentially irreversible, otherwise the reaction will not go to completion.) Thus, the concentration of E3 substrate is equal to the input concentration of E1 substrate. I don't think you can run all the reaction concurrently and still be able to measure the kinetic constants for E3 because the concentration of the E3 substrate would be unknown. So substance C has to be stable for the amount of time needed for its formation to be completed.

You also have to measure the initial rate of E3 substrate consumption or product formation, as you would for any kinetics study. It isn't clear to me whether it is necessary for the D to E conversion step to be present in your scheme. If so, then the concentration of E4 (you labeled it E1) must also be high enough that the E3 reaction is rate limiting. You would then have to measure the rate of substrate C consumption or the rate of product E formation.

In order to measure the kinetics of one enzyme in a sequence of enzyme reactions, there are 2 necessary conditions I can think of.

(1) The reaction of the enzyme of interest has to be rate limiting (i.e. the slowest step). This can be achieved by keeping the concentrations of all the other enzymes very high. The test for this condition having been successfully achieved is that further increasing the concentrations of the other enzymes does not increase the rate of the E3 reaction.

(2) You have to know the concentration of the substrate of E3. This is challenging, but the way to do it is to run the reactions of E1 and E2 first with a known concentration of the substrate of E1, such that all of the E1 substrate is converted to the E3 substrate prior to the addition of E3. (This requires that the E1 and E2 reactions are essentially irreversible, otherwise the reaction will not go to completion.) Thus, the concentration of E3 substrate is equal to the input concentration of E1 substrate. I don't think you can run all the reaction concurrently and still be able to measure the kinetic constants for E3 because the concentration of the E3 substrate would be unknown. So substance C has to be stable for the amount of time needed for its formation to be completed.

You also have to measure the initial rate of E3 substrate consumption or product formation, as you would for any kinetics study. It isn't clear to me whether it is necessary for the D to E conversion step to be present in your scheme. If so, then the concentration of E4 (you labeled it E1) must also be high enough that the E3 reaction is rate limiting. You would then have to measure the rate of substrate C consumption or the rate of product E formation.

Your question resembles enzyme calculations using coupled enzyme assays.

As Adam stated you need to make sure the enzymes E1 and E2 are not rate-limiting. But in your case, there is an additional complication because you need to know and manipulate the concentration of C in your reaction to be able to probe the KM. However, since the system is coupled, the steady-state concentration of C depends on the amount of E1 and E2 and the concentrations of A and B. In addition as B and C concentration raise, the rate of conversion of C into B and B into A should be included in your analysis (the missing reversible arrows).

The general system seems hard to tackle, and you may be better off looking at the specific case; i.e. introducing the known details of enzymes and chemicals in the analysis. That would give you a better chance to work out a particular experimental setup for your case of study.

Best wishes,

Rogelio

If you need Km for E3 and you have E3 the best way is to use E3. Then my first question is: Do you have E3?

And the second:

DO you have C irrespective of whether is stable or not. Can you buy C?