Consider the following reactions which take substrate S to product P. A->AB AB+S

Question

Consider the following reactions which take substrate S to product P.

A->AB
AB+S -> A+P

1. Find the steady state value of [AB] in terms of [A], [S],k1, and k2

2. The total amount of A is A0 = [A]+[AB]. Find the steady state value of [AB] in
terms of A0, [S],k1,k2

Consider the following reactions which take substrate S to product P. A->AB AB+S -> A+P 1. Find the steady state value of [AB] in terms of [A], [S],k1, and k2 2. The total amount of A is A0 = [A]+[AB]. Find the steady state value of [AB] in terms of A0, [S],k1,k2

Explanation / Answer

Part 1)   

d[AB]/dt = k1[A] - k2[AB][S]

For steady state approximation d[AB]/dt = 0

k1[A] -k2[AB][S] = 0

[AB] = k1[A] / k2[S]      

Part 2)

A0 = [A] + [AB]

[A] = A0 - [AB]

Put the value of [A] in above expression of [AB]

[AB] = k1[A] / k2[S] = k1(A0 - [AB]) / k2[S] = k1A0 -k1[AB] / k2[S]

[AB] = k1A0 -k1[AB] / k2[S]

k2[S][AB] = k1A0 -k1[AB]

[AB] (k2[S]+ k1) = k1A0

[AB] = k1A0 / (k2[S] + k1)

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