Assignment - Thermodynamics of Biomolecular Interactions
This is an individual assignment.
1. One way to identify drug candidates is to measure the binding affinity of many drugs toward the natural target protein; molecules that bind with high affinity to the target but will not bind well to other cellular proteins are possible leads for designing new drugs. Often, the structure of the lead compound must be modified in order to improve its binding affinity to the target. If the atomic structure of the drug-target complex cannot be obtained, some understanding of interactions between the drug and target protein can be obtained from a thermodynamic analysis of binding data.
The table below presents results of experiment in which binding of a drug to its receptor was studied at three different temperatures. In each case, the fraction of protein molecules bound to drug (θ = [Drug · Protein]/[Drug · Protein] + [Free Protein]) was determined as a function of the drug concentration.
The drug is an organic molecule commonly used for emergency treatment for people who have overdosed on heroin. The target protein is a membrane bound receptor protein. After nearly three decades of trial and error, the target protein was finally crystallized in 2012.
|
[Drug], nM
|
θ (25oC)
|
θ (34oC)
|
θ (40oC)
|
|
10
|
0.42
|
0.25
|
0.19
|
|
20
|
0.61
|
0.42
|
0.28
|
|
30
|
0.71
|
0.55
|
0.42
|
|
40
|
0.74
|
0.60
|
0.47
|
|
50
|
0.79
|
0.65
|
0.53
|
|
60
|
0.83
|
0.69
|
0.57
|
|
70
|
0.84
|
0.74
|
0.61
|
|
80
|
0.87
|
0.76
|
0.62
|
|
90
|
0.86
|
0.78
|
0.66
|
|
100
|
0.88
|
0.79
|
0.68
|
|
110
|
0.89
|
0.81
|
0.69
|
|
120
|
0.91
|
0.81
|
0.72
|
a) Calculate the dissociation constant of the drug-protein complex at 25oC. Show your work.
b) Calculate the association constant for the drug-protein interaction at 40oC. Show your work.
c) Calculate the free energy of binding of the drug to the protein at 34oC. Show your work.
d) Based on this data, is it likely that the drug-protein interaction displays positive homotropic cooperativity? Briefly justify.
e) Calculate the binding enthalpy of the drug-protein interaction assuming that the binding enthalpy is temperature independent. Show your work.
f) Is the binding process endothermic or exothermic? Briefly justify.
g) Briefly discuss the principle behind the equilibrium dialysis method that was historically important in the determination of dissociation constants of protein-ligand complexes.