Drug binding Flashcards
What is the Hill-Langmuir equation used to describe and what can these principles apply to?
- Used to describe binding at different concentrations of ligand
- These principles can apply to agonists, antagonists and allosteric modulators
What is the Hill-Langmuir equation?
- B = Bm. [D]/Kd + [D]
- B = drug bound
- Bm = maximum binding
- Kd = equilibrium dissociation constant
- D = concentration of drug
What are our assumptions for the mathematics of drug binding?
- Our drug is binding to a protein
- Our drug has a limited number of binding sites
- Our drug binds reversibly
- We can change the concentration of drug we apply
- Drugs have different shapes and sizes
What is the equation for the drug binding reaction?
- D + R DR
D = drug
R = receptor
DR = drug receptor complex
What are the two constants in the drug binding reaction?
Bmax = R + DR (max binding)
Kd = K-1/ K+1 (backwards rate constant divided by forwards rate constant)
What is Kd and give it’s features?
- concentration of drug giving 50% max binding (measure of how well the size and shape of the drug matches receptor)
Will always have concentration units
Concentration of drug that binds half the receptor
Low Kd value – binds tightly (as you only need a low concentration for it to bind)
High Kd value – doesn’t bind as tightly
Inversely proportional to affinity of drug
What type of graphs are often used to plot drug binding?
- Rectangular Hyperbola graphs
- Log (sigmoidal) curves if the drug binding is plotted on a semi-logarithmic graph)
How does radioligand binding work?
- Need a radioactive version of our drug, incubate this with tissue
- The number of receptors we occupy depends on concentration of radioligand
- Some of our radioligand is bound to the membrane
- To measure amount of drug bound we need to separate free drug from bound drug, usually by filtration
- Bmax tells us number of receptors in our tissue
- Kd tells us how tightly our drug is bound
- Once we have our values we can use it to make comparisons
Compare the affinity of Hydrocortisone (100nM) at the GCR and Progesterone (1000 nM) at the GCR
- The higher the Kd, the lower the affinity
Hydrocortisone has a Kd of 100 nM at the GCR
Progesterone has a Kd of 1000 nM at the GCR - So hydrocortisone has 10x higher affinity than progesterone (progesterone isn’t quite the right shape for the GCR receptor)
- Divide low affinity value by high affinity value to find how many times higher the high affinity it is
With Kd why do we often work with log Kd values or pKd?
Because Kd isn’t normally distributed whereas Log Kd is
What is non-specific binding?
when a radioligand binds to the membrane as well as the receptor of interest
Is non-specific binding high or low affinity?
Low
Why do non-specific binding sites behave as if they were non-saturable?
Because there are so many potential NSB sites in the typical binding assay
Why can Non-specific binding sites be a major problem in binding assays?
because although their affinity is low, there is a huge number of NSB sites whereas the receptor only constitutes a tiny saturable pool of high affinity binding sites
What is total binding and how do you measure it?
- total binding is the sum of the binding to receptors and the NSB
- If you separate your bound radioligand from the free radioligand using a filtration assay, when you measure the radioactivity trapped on the filter disc you are measuring total binding
To get information about how our ligand interacts with the receptor we are interested in what do we need to subtract from what?
Total binding - NSB
How do you measure the NSB?
- In our binding assay, at each concentration of radioligand we use an identical tube but with the addition of a high concentration of a non-radioactive ligand at our receptor of interest. The non-radioactive ligand is of key importance here – it needs to be present at concentrations that are high enough to saturate all of the receptor binding sites.
- When the tube to determine NSB is incubated the non radioactive ligand (present in very high concentrations) will occupy all of the receptors. The radioligand will bind solely to the NSB sites
What does pKd equal?
- log Kd
When comparing Kd and pKd values in terms of affinity what do you need to keep in mind?
- when comparing pKd values the higher the pKd the higher the affinity
- when comparing Kd values the lower the Kd the higher the affinity
What concentrations should you convert to for any calculations?
Molar concentrations
What does E in 1E
x10 to the power of
What is the general rule of thumb in which we describe Kd affinities?
- 1E-10 to 1E-9 M: very high affinity
- 1E-9 to 1E-8 M: high affinity
- 1E-9 to 1E-7 M: moderate affinity
- 1E-7 or lower: low affinity
What is the Michaelis Menten equation?
• V = Vmax. [S]/ [s] + Km
- V = initial rate of reaction
- Vm = maximum reaction rate
- S is the substrate concentration
- Km is the Michaelis constant: the substrate concentration that gives 50% of Vm
How can you compare the Michaelis Menten Equation and the Hill Langmuir equation?
They are identical apart from the names of the terms being different
