BIOM6636 Cell Biomechanics-identical for an elementary reaction at equilibrium

Task:

 
1. The principle of detailed balance says that the forward and reverse rates must be identical for an elementary reaction at equilibrium: 
Where []eq is the equilibrium concentration. For the reaction shown on the below, what relation should be satisfied by the six rate coefficients in order to satisfy detailed balance?

2. A bimolecular reaction in which A and B combine to form the product can be written as:
Where k1 is a diffusion-limited, molecular rate constant for forming this complex AB, k-1 is a unimolecular rate constant for the encounter complex to fall apart before the reaction occurs, and k2 is the rate constant for the reaction step.

(a) Write down the differential equation for the rate of change of the concentration for complex AB.
(b) From your results in (a), and using the steady state approximation, the rate change of AB is equal to zero, obtain expression for the steady state concentration [AB].
(c) Use your result for [AB] from part (b) to express in term of the concentration of [A] and [B], and some combination of the rate constants

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