L5 RADIOLIGAND CALCULATIONS

Question 1

how do you calculate specific binding?

Answer 1

specific binding = total binding - NSB

Question 2

Metric prefixes

Answer 2

deci (10^-1) to centi (10^-2) to milli (10^-3) to micro (10^-6) to nano (10^-9) to pico (10^-12) to femto (10^-15) to atto (10^-18)

deca (10^1) to hecto (10^2) to kilo (10^3) to mega (10^6) to giga (10^9) to tera (10^12)

when finging out how to go to another prefix do the bigger/smaller
when going from a bigger to a smaller prefix divide
and smaller to bigger is multiply

Question 3

radioactivity conversions

Answer 3

1 disintegration per second = 1 Becquerel (Bq) the SI unit of radioactivity
1 Tera Bq (TBq) = 1012 dps
1 Bq = 60 disintegrations per minute (dpm)
1 TBq = 60 x 1012 = 6 x 1013 dpm

You may also come across radioactivity measured in Curies (Ci)
1 Ci = 3.7 x 1010 dps = 3.7 x 1010 Bq = 0.037 TBq

easier conversion: 1 CI= 37 Gb
and divide by 1000 to get Tbq

Question 4

what are the units of kd?

Answer 4

NB the units for Kd are the same as those used for the “free” radioligand added during the experiment, in this case nM.

and bmax
basically keep the units they are on the graph

Question 5

writing linear equations?

Answer 5

𝑦

Step 1: Understanding the Scatchard Plot Formula
The Scatchard plot is used to analyze receptor-ligand binding data. The equation for a Scatchard plot is:

[
𝐵
𝑜
𝑢
𝑛
𝑑
]
[
𝐹
𝑟
𝑒
𝑒
]
=
𝐵
max
𝐾
𝑑
−
[
𝐵
𝑜
𝑢
𝑛
𝑑
]
𝐾
𝑑
[Free]
[Bound]
​
=
K
d
​

B
max
​

​
−
K
d
​

[Bound]
​

Where:

[Bound] is the concentration of bound ligand (on the y-axis of the plot).

[Free] is the concentration of free ligand (on the x-axis of the plot).

Bmax is the maximum binding capacity (the maximum amount of receptor that can be bound by the ligand).

Kd is the dissociation constant, which tells us how tightly the ligand binds to the receptor (a lower value indicates stronger binding).

Step 2: General Form of the Line
The Scatchard plot equation can be written as a linear equation:

𝑚
𝑥
+
𝑐
y=mx+c
Where:

y is the bound/free ratio (which is on the y-axis).

x is the free ligand concentration (which is on the x-axis).

m is the slope (gradient) of the line.

c is the y-intercept.

In the case of a Scatchard plot:

Slope (m) =
−
1
𝐾
𝑑
−
K
d
​

1
​

Y-intercept (c) =
𝐵
max
𝐾
𝑑
K
d
​

B
max
​

​

Step 3: Using the Values Provided
Given:

Bmax = 280 (this is the maximum binding capacity, probably in nM).

Kd = 3.8 nM (the dissociation constant).

Now, let’s calculate the slope and y-intercept:

1. Slope (m):
   The slope is calculated as:

−
1
𝐾
𝑑
Slope=−
K
d
​

1
​

Substitute the value of Kd = 3.8 nM:

−
1
3.8
=
−
0.263
Slope=−
3.8
1
​
=−0.263
2. Y-intercept (c):
The y-intercept is calculated as:

𝐵
max
𝐾
𝑑
Y-intercept=
K
d
​

B
max
​

​

Substitute the values of Bmax = 280 nM and Kd = 3.8 nM:

280
3.8
=
73.7
Y-intercept=
3.8
280
​
=73.7