Competitive binding Flashcards
What is the Hill Langmuir equation?
B = Bm x [D]/Kd + [D]
What happens when there are multiple ligands in a system?
If we introduce a second drug into a system that can also bind to a specific receptor and only one of the drugs can occupy the receptor at a given time drug 1 will not occupy the receptor as much of the time as it did when it was only the initial ligand present
What is the Gaddum equation?
• Bound* = Bmax x [D]/ [D] + Kd (1 + [I]/KI)
- B* is the binding of D in the presence of a certain concentration of I
- D is our drug
- I is our new drug
- Kd and Ki are the equilibrium dissociation constants for D and I respectively
What is the equation to work out F and what is F?
• F = 100 x B*/ B
- B* is the binding in the presence of drug I
- B is the binding in the absence of drug I
- F is simply the percentage of control binding that we see when we add the competing ligand to the system
What is a derivative of the Gaddum Equation to work out F?
100(1 - [I]/[I] + KI ( 1 + [D]/kd))
or
F = 100(1 - [I]/[I] + IC50)
If we assume we are dealing with a fixed concentration of D how can we define IC50?
KI ( 1 + [D]/kd)
What does the Gaddum equation do and why is this important?
- It relates the occupancy of the receptor by a fixed concentration of one drug (in our example D) to the concentration and affinity of a second drug, I.
- This is really important. It means that using a single detectable ligand (e.g.a radioligand) we can get information about the affinity of another compound that binds to the same site, without having to modify the second compound to make it detectable
What does the IC50 mean?
- It represents a midpoint on the curve: the concentration of inhibitor (the competing ligand I) that reduced binding to 50% of the initial value
- It’s important to realise that IC50 depends on radioligand concentration ([D]) and affinity (Kd). It’s not a constant!
- IC50 is a potency measurement
What plot does the [I]/[I] + IC50 part of the equation give us?
gives a rectangular hyperbola relationship on a linear scale, and a sigmoid curve on a log concentration scale. Subtracting this part of equation from 1 reverses the direction of the curve
If we have a drug I, that we think binds to the same receptor as D how do we use a competition assay to work out the affinity of I?
- Measure binding of a radioligand at a fixed concentration (usually we choose a value close to the Kd, so we’ll use 1 nM) – this is our control binding
- Repeat this in the presence of increasing concentrations if I
- Express the data as F (% of control binding)
- Plot the data on a log scale and work out the concentration that gives us 50% of the control binding (the IC50)
- Now rearrange the following equation to get KI instead of IC50:
- IC50 = KI (1 + [D]/kd):
- KI = IC50/(1 + [D]/kd
What is the Cheng Prusoff equation?
KI = IC50/(1 + [D]/kd
What do binding assays tell us about and not tell us about?-
- they only tell us about receptor affinity
- don’t tell us about whether we are dealing with an agonist or antagonist
What is Atenolol?
Atenolol is a beta blocker: Beta 1 adrenoceptor antagonist. It is used to treat angina and is a third line of treatment for hypertension
What is Losartan?
angiotensin II receptor antagonist: angiotensin receptor blockers are first line antihypertensive drugs. They avoid the cough associated with ace inhibitors
What is Atropine?
muscarinic receptor antagonist: can be used to treat bradycardia. Also useful for reducing secretions during surgery.
What is Efficacy?
the tendency of a drug to activate a receptor
What are drugs with maximum possible efficacy called?
Agonists
What are drugs with no efficacy called?
Antagonists?
Is efficacy related to affinity and why/ why not?
Efficacy is not related to affinity. Affinity tells us how tightly something binds, and both agonists and antagonists have affinity
What are the consequences of antagonists having zero efficacy?
- A functional assay relies on receptor activation to produce a measurable effect
- Unless there is an agonist present, there is no measurable effect
- This means that experiments to investigate antagonists are going to require us to apply antagonist and agonist simultaneously
What is the functional Gaddum equation and what does it describe?
- Effect = Emax x [D]/[D] + EC50(1 + [I]/KI)
- It describes the effect produced by agonist D in the presence of competitive antagonist I
Go through an example of the functional Gaddum equation with a tissue in an organ bath, what do you find?
- Isolate tissue
- Put tissue in organ bath – the forced transducer will convert contraction and relaxation of tissue into electrical signal
- First precontract tissue with agonist
- Relax tissue with noradrenaline
- Plot a graph
- Then add antagonist propranolol
- You see a much smaller relaxation – propranolol is occupying the receptor binding sites, inhibiting noradrenaline from the binding sites
- We repeat the control concentration response experiment with a fixed concentration of propranolol. There is no change in max but there is a parallel shift to the right. This means the EC50 has increased. But the maximum response stays the same
- These are the characteristics you see we competitive antagonists
What is Surmountable antagonism?
we can overcome the effects of the antagonists by increasing the amount of agonist. This is why we see no change in the maximum response.
What is surmountable antagonism one of the characteristics of?
Competitive antagonists
How do you work out how far to the right the curve has moved when using a competitive antagonist?
- can be worked out by the EC50:
• Concentration ratio = EC50 (with antagonist)/EC50 (without antagonist)
• For the control curve the EC50 for the functional Hill-Langmuir equation is the CR = EC50/EC50
• EC50 that came from our curve with antagonist present = EC50 (1 + [I]/KI)
• CR = 1 + [I]/KI
Does competitive antagonism reduce the efficacy of an agonist? What does it increase?
Competitive antagonism doesn’t reduce the efficacy of an agonist (as efficacy is the maximum effect) but it does increase the agonist EC50 (as there is a parallel rightward shift of the agonist concentration response curve)
Sum of Kd vs Ki
- Kd and Ki are both a measure of drug affinity
- Kd is normally used when the data have come from a saturation assay and the affinity has been measured directly
- Ki is used when the measurement of affinity has been made indirectly, such as in a competition binding assay or via calculations from the Gaddum equation
What is pKi?
We can take the negative log Ki values to generate pKi. This is because Ki values are not normally distributed but pKi values are
Sum up what pKi and pA2 are and the differences between them
antagonist, but their meanings are subtly different.
• pKi is a measure of affinity
• pA2 is defined as the ‘negative log of the concentration of antagonist required to double the EC50 for the agonist’
• pA2 is a measure of potency
• pA2 is obtained from the concentration of antagonist that gives a CR of 2
When do we get the concentration that yields pA2?
When [I] = Ki so pA2 = pKi
How does tone affect applying an antagonism to an organism?
- Tone is the level of baseline (normally parasympathetic) activity from natural agonists
- The consequence of tone is that when you apply an antagonist to an organism, tissue or sometimes even a cell, you may see a change in that system. This is not because the antagonist is acting in the absence of an agonist, but because tone means that an agonist is already present.
