The concentration of ligand are:
a. 133.33 Nm.
b. 600 Nm.
c. 7,600 Nm.
Given the following data:
- Dissociation constant, Kd = 400 Nm
To find the concentration of ligand, we would use the fractional saturation formula.
Fractional saturation (Y) is expressed as a ratio of protein with bound ligand to that of the total protein concentration.
Mathematically, fractional saturation (Y) is given by the formula;
[tex]Y = \frac{A}{K_d \;+ \;A}[/tex]
Where:
- Y is fractional saturation.
- A is the binding ligand concentration.
- Kd is the dissociation constant.
a. To find A, when Y = 0.25;
[tex]0.25 = \frac{A}{400 \;+ \;A}[/tex]
Cross-multiplying, we have:
[tex]0.25(400\; + \;A) = A\\\\100 + 0.25A = A\\\\A - 0.25A = 100\\\\0.75A = 100\\\\A = \frac{100}{0.75}[/tex]
A = 133.33 Nm
b. To find A, when Y = 0.6;
[tex]0.6 = \frac{A}{400 \;+ \;A}[/tex]
Cross-multiplying, we have:
[tex]0.6(400\; + \;A) = A\\\\240 + 0.6A = A\\\\A - 0.6A = 240\\\\0.4A = 240\\\\A = \frac{240}{0.4}[/tex]
A = 600 Nm
c. To find A, when Y = 0.95;
[tex]0.95 = \frac{A}{400 \;+ \;A}[/tex]
Cross-multiplying, we have:
[tex]0.95(400\; + \;A) = A\\\\380 + 0.95A = A\\\\A - 0.95A = 380\\\\0.05A = 380\\\\A = \frac{380}{0.05}[/tex]
A = 7,600 Nm
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