Falls in Receptor Occupancy

Earlier, we had assumed for simplicity that the occupancy was zero when the ligand was first applied. It is straightforward to extend the derivation to predict how the occupancy will change with time even if it is not initially zero. We alter the limits of integration to 

pAR(0) is the occupancy at time zero, and the other terms are as previously defined. 

Exactly the same steps as before then lead to the following expression to replace Eq. (1.22)  

We can use this to examine what would happen if the ligand is rapidly removed. This is equivalent to setting [A] abruptly to zero, at time zero, and / (°°) also becomes zero because eventually all the ligand receptor complexes will dissociate. Eq. (1.25) then reduces to  

The time constant, x, for the decline in occupancy is simply the reciprocal of k, . A related term is the half-time (tV2). This is the time needed for the quantity (pAR(t) in this example) to reach halfway between the initial and the final value and is given by  

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