Question

Scatchard plot for binding of estradiol to albumin. Data in the table come from a student experiment to measure the binding constant of the radioactively labeled hormone estradiol (X)to the protein, bovine serum albumin $\mathbf{\left(}\mathbf{P}\mathbf{\right)}\mathbf{.}\mathbf{Estradiol}\mathbf{}\mathbf{(}\mathbf{7}\mathbf{.}\mathbf{5}\mathbf{}\mathbf{nM}\mathbf{)}$was equilibrated with various concentrations of albumin for $\mathbf{30}\mathbf{}\mathbf{min}\mathbf{}\mathbf{at}\mathbf{}\mathbf{37}\mathbf{°}\mathbf{C}\mathbf{.}$A small fraction of unbound estradiol was removed by solid phase microextraction ($\mathbf{Section}\mathbf{}\mathbf{24}\mathbf{-}\mathbf{4}$) and measured by liquid scintillation counting. Albumin is present in large excess, so its concentration in any given solution is essentially equal to its initial concentration in that solution. Call the initial concentration of estradiol ${\left[X\right]}_{\mathbf{0}}$and the final concentration of unbound estradiol [X]. Then bound estradiol is$\mathbf{[}\mathbf{X}{\mathbf{]}}_{\mathbf{0}}\mathbf{―}\mathbf{[}\mathbf{X}\mathbf{]}$and the equilibrium constant is

$\mathbf{X}\mathbf{+}\mathbf{P}\mathbf{\rightleftharpoons }\mathbf{PX}\mathbf{\hspace{0.33em}}\mathbf{\hspace{0.33em}}\mathbf{\hspace{0.33em}}\mathbf{K}\mathbf{=}\frac{\mathbf{\left[}\mathbf{PX}\mathbf{\right]}}{\mathbf{\left[}\mathbf{X}\mathbf{\right]}\mathbf{\left[}\mathbf{P}\mathbf{\right]}}\mathbf{=}\frac{\mathbf{[}\mathbf{X}{\mathbf{]}}_{\mathbf{0}}\mathbf{-}\mathbf{[}\mathbf{X}\mathbf{]}}{\mathbf{\left[}\mathbf{X}\mathbf{\right]}\mathbf{\left[}\mathbf{P}\mathbf{\right]}}$

which you can rearrange to
localid="1663648487221" $\frac{\mathbf{[}\mathbf{X}{\mathbf{]}}_{\mathbf{0}}}{\mathbf{\left[}\mathbf{X}\mathbf{\right]}}\mathbf{=}\mathbf{K}\mathbf{\left[}\mathbf{P}\mathbf{\right]}\mathbf{+}\mathbf{1}$

A graph of ${\left[X\right]}_{\mathbf{0}}\mathbf{/}\left[X\right]$versus [P]should be a straight line with a slope of K.The quotient $\mathbf{[}\mathbf{X}{\mathbf{]}}_{\mathbf{0}}\mathbf{/}\mathbf{[}\mathbf{X}\mathbf{]}$is equal to the counts of radioactive estradiol extracted from a solution without albumin divided by the counts of estradiol extracted from a solution with estradiol. (b) What fraction of estradiol is bound to albumin at the first and last points?

Short answer

The fraction of estradiol is bound to albumin at the first and end point are 0.21 and 0.77 respectively.

Step-by-step solution

Define radioactivity.

It is property that is exhibited by certain type of matter of emitting energy and sub atomic particles spontaneously.

Calculate fraction of estradiol bound to albumin at first and end points.

Fraction of free estradiol at first point$=\frac{1}{1.26}=0.79$

Fraction of free estradiol at end point$=\frac{1}{4.36}=0.23$

Fraction of estradiol bound to albumin at first point$=1-0.79=0.21$

Fraction of estradiol bound to albumin at end point$=1-0.23=0.77$