Receptor Binding The normal blood plasma concentration of insulin (hormone) in a

Question

Receptor Binding

The normal blood plasma concentration of insulin (hormone) in an experimental subject is 1 x 10-10 M. The KD (dissociation constant) for the insulin receptor in the adipose cells of this subject is 1 x 10-8 M. The dissociation constant indicates the concentration of hormone that saturates half of the available cell receptors. The dissociation constant is an equilibrium condition parameter. Given this situation:

a)Derive the expression for the fraction of insulin bound receptors as a function of the dissociation constant.

b)Approximately what percentage of the insulin receptors in these adipose cells is bound under normal conditions?

c)What percentage would be bound if the KD was 1 x 10-7?

d)What percentage would be bound if the KD was 1 x 10-9?

e)What concentration of insulin would saturate all of the receptors for KD = 1 x 10-8 M?

Explanation / Answer

Let us represent Insulin as Ins & cell receptors by R , Then the equation for binding of cell receptors with Insulin to generate insulin receptors can be expressed as-

2Ins + R ---------------> ( Ins )2 R   , given that the concentration of hormone (insulin) that saturates half of the available cell receptors .

& the equilibrium constant for this reaction can be written as -

[ ( Ins)2 R ] / [ Ins ]2 [ R ] = KD

So , a) the expression for fraction of insulin bound receptors , [(Ins)2 R ] / R = KD [ Ins ]2

b) As per above equilibrium state the % of insulin receptors in adipose cells bound under normal conditions ---------------------------------------------------------------------------------------------------------------- ={ 0. 5 x 10-10 / 1 x10-10 } (100 )

--------------------------------------------------------------------------------------------------------------- = 50%

Since the dissociation constant is an equilibrium parameter , therefore-

-

------ d ) when KD =1 x 10-9  = ( 1x 10-9 / 1 x 10-8 ) ( 100) = 10%  

------ e ) The concentration of insulin that would that would saturate all of the receptors for KD = 1 x 10-8 M would be 2 ( 1x 10-10 ) M     

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