Hill's equation and plot-Biochem

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In summary, the experiment studied the binding of a ligand B to a protein at a protein concentration of 10^-3 M. The resulting amounts bound, b, for each added [B] were recorded. Using the hill equation, the Y-intercept was found to be -log K_d and the slope was n when plotting the left side in respect to log [A]. However, there may be confusion due to missing information about the concentration of free A in solution.
  • #1
kittybobo1
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Homework Statement



The binding of a ligand B to a protein is studied. The protein concentration it 10^-3 M. The amounts bound,b, for each added is given as the following:

(M) (b)(M)
.001 5*10^-6
.002 3.3*10^-3
.005 3.78*10^-3
.007 4.72*10^-3
.01 4.95*10^-3
.02 5*10^-3
.05 5*10^-3

Find if it is cooperative, the number of binding sites, and K_d

Homework Equations



The hills equation can be expressed as log Y/(1-Y) =n log [A] - log K_d


The Attempt at a Solution



So the y intercept is - log K_d and the slope is n when you plot the left side in respect to log [A]. Y is the fractions filled, so I think it would be (b)/(5*10^-3). But, plotting the graph.. it seems a little screwy.. the plot goes from slope of 10.9 to .5 then to ~5.. The graph is shown here.
 
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  • #2
kittybobo1 said:
So the y intercept is - log K_d and the slope is n when you plot the left side in respect to log [A]. Y is the fractions filled, so I think it would be (b)/(5*10^-3). But, plotting the graph.. it seems a little screwy.. the plot goes from slope of 10.9 to .5 then to ~5.. The graph is shown here.

If it were I could probably help, but I can't see it.:confused:

Possible sources of confusion:
1) [A] in your equation is concentration of free A in solution, did you calculate that?;
2) That's enough possible sources of confusion till I see your graph. :tongue:

And to make it easier for us and yourself put also the free A in a table with the other parameters.
 
Last edited:
  • #3


Based on the given data and the Hill's equation, it appears that the binding of the ligand to the protein is cooperative, as the slope of the plot is not constant and shows a slight increase as the ligand concentration increases. This suggests that the binding of one ligand molecule to the protein may increase the likelihood of binding for subsequent ligand molecules.

To determine the number of binding sites, we can use the slope of the plot-Biochem. As you mentioned, the slope of the plot is equal to the Hill coefficient (n) in the Hill's equation. Therefore, in this case, the number of binding sites would be approximately 5.

To find the K_d value, we can use the y-intercept of the plot, which represents -log K_d in the Hill's equation. From the given data, it appears that the K_d value is approximately 0.001 M.

It is important to note that the Hill's equation assumes a simple binding model and may not accurately describe more complex binding mechanisms. It would be beneficial to also consider other factors, such as potential cooperativity or allosteric effects, in further analyzing the data and determining the binding parameters.
 

1. What is Hill's equation and how is it used in biochemistry?

Hill's equation is a mathematical model that describes the relationship between the concentration of a molecule and its biological activity. It is commonly used in biochemistry to study the binding of ligands to proteins and enzymes.

2. How is Hill's coefficient calculated and what does it represent?

Hill's coefficient is calculated by taking the logarithm of the ratio of the concentration of the ligand at half-maximal binding to the concentration of the ligand at no binding. It represents the cooperativity of the binding process, with a higher coefficient indicating greater cooperativity.

3. What is a Hill plot and how is it interpreted?

A Hill plot is a graphical representation of Hill's equation, with the concentration of the ligand on the x-axis and the fractional occupancy of the receptor on the y-axis. It is interpreted by the slope of the line, with a slope of 1 indicating no cooperativity, a slope greater than 1 indicating positive cooperativity, and a slope less than 1 indicating negative cooperativity.

4. Can Hill's equation be used for all types of binding interactions?

Hill's equation is most commonly used for cooperative binding interactions, where the binding of one ligand molecule increases the affinity for subsequent binding. It can also be used for non-cooperative binding, but may not accurately reflect the binding behavior in those cases.

5. What are the limitations of using Hill's equation in biochemistry research?

Hill's equation assumes that the binding process is a simple equilibrium reaction, which may not always be the case in complex biological systems. It also does not take into account other factors such as enzyme kinetics or allosteric effects, and should be used with caution when studying these types of interactions.

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