enzymes and substrates

overall reaction: S -> P
step 1: E + S -> ES fast
step 2: ES -> E + S fast
step 3: ES -> E + P slow

what is the order of the reaction IN E and what is the order of reaction in S?

To determine the order of the reaction with respect to E and S, we need to look at the rate equations for each step.

Step 1: E + S -> ES (fast)
Since this step is fast, we can assume that the formation of the ES complex is in equilibrium. The rate equation for this step can be written as:
Rate₁ = k₁[E][S]
Here, [E] refers to the concentration of enzymes and [S] refers to the concentration of substrate.

Step 2: ES -> E + S (fast)
Similarly, since this step is also fast, we can assume it is in equilibrium. The rate equation can be written as:
Rate₂ = k₂[ES]
Here, [ES] refers to the concentration of the ES complex.

Step 3: ES -> E + P (slow)
This step is the rate-determining step, as it is the slowest step in the overall reaction. The rate equation can be written as:
Rate₃ = k₃[ES]
Here, [ES] again refers to the concentration of the ES complex.

From the rate equations of step 2 and step 3, we can see that the concentration of [ES] is the same, indicating that the concentration of the ES complex is the reaction intermediate.

Therefore, the order of the reaction with respect to E is first-order because the rate equation contains only the concentration of [E] in step 1:
Rate₁ = k₁[E][S]

On the other hand, the order of reaction with respect to S is also first-order because the rate equation also contains only the concentration of [S] in step 1:
Rate₁ = k₁[E][S]

In summary, the reaction is first-order in both E and S.