Download Receptor pharmacology

Mennerick-- Ligand Binding Handout
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Pharmacology
This institution (WUMS), like many medical schools, no longer has a Department of Pharmacology.
Nevertheless all physicians prescribe drugs, and research scientists will all inevitably use pharmacology as
a tool at some point in their research. Thus, despite the poor reputation that pharmacology has in today’s
post-genomic era (“all drugs are dirty”), pharmacology continues to be ubiquitous, and I think it’s
important that students are exposed to basic pharmacology principles.
Whether we’re talking about ligand-gated ion channels or about GPCRs, some basic principles apply.
First, the ligand’s interaction with the receptor can be modeled as a reversible, bi-molecular reaction. This
means that we can write chemical equations to represent the drug-receptor interaction (subsequent pages).
Second, many terms are applicable no matter what the receptor type. Here is a partial glossary.
Ligand: any molecule that binds to a receptor. Examples: Nicotine, curare, and mecamylamine are ligands
for the muscle nicotinic receptor.
Agonist: a ligand that activates the receptor (opens a ligand-gated channel or stimulates a G protein).
Example: Nicotine is an agonist at the nicotinic receptor.
Antagonist: a ligand that has no biological effect on the receptor when it binds but reverses an agonist’s
effect. Example: Curare and mecamylamine are antagonists at the endplate nicotinic receptor.
Competitive antagonist: An antagonist that competes with an agonist for the same (or overlapping) binding
site. The effect of a competitive antagonist at steady state can therefore be overcome with higher free
[agonist]. Example: Curare is a competitive antagonist at the endplate nicotinic receptor.
Non-competitive antagonist: An antagonist that binds to a site other than the agonist binding site.
Mecamylamine is a non-competitive antagonist at the nicotinic endplate receptor. Picrotoxin is a noncompetitive antagonist at the GABAA receptor.
Uncompetitive antagonist: Like a non-competitive antagonist, binds to a separate site from the agonist, but
requires channel opening for binding. Example: Jim Huettner showed in 1988 that MK-801 is an
interesting example of an uncompetitive antagonist of the NMDA receptor (PNAS 85:1307). Ketamine (an
anesthetic) and memantine (used in treatment of Alzheimer’s disease) are additional examples of
uncompetitive NMDA receptor antagonists. [For simplicity, I sometimes dispense with the term
“uncompetitive” and use “non-competitive”. This has gotten me into trouble with some peer reviewers]
Partial agonist. An agonist that binds to the receptor but does not activate the “full” response. For ligandgated ion channels, this would be an agonist that binds but produces a lower channel opening/closing rate
ratio than a full agonist.
Inverse agonist. A ligand that binds the receptor at the agonist site, but unlike a competitive antagonist,
promotes a conformational change in the receptor that promotes channel closure. For example: Joe Henry
Steinbach’s lab showed in 1997 that bicuculline, long thought to be a competitive antagonist at the GABAA
receptor, is actually an inverse agonist (J Neurosci 17:625).
Allosteric. A ligand that works from a site other than a reference site of action, usually the site of agonist
binding. Example: benzodiazepines positively allosterically regulate GABAA receptor function.
Potency: A dangerous term because it means different things to different people. I use potency as an
empirical term equivalent to EC50 (agonist) or IC50 (antagonist) (see lecture). Others use it with a
connotation closer to Kd.
Efficacy: How “full” is the agonist action? A partial agonist is a low-efficacy agonist (but it can still have
high potency if concentration needed to generate the response is low). An antagonist has zero efficacy.
Mennerick-- Ligand Binding Handout
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Start with the simple scheme of drug binding to a single site:
A+R
k1
AR
k2
k1 = rate constant for association (units: M-1 s-1)
k2 = rate constant for dissociation (units: s-1)
A = drug
Y = proportion of receptors occupied by drug (=[AR]/([AR]+[R])
R = receptor
AR = receptors bound by agonist
Rtotal = total receptors (=[AR] + [R])
Note that AR  A + R is a first order reaction, like radioactive decay. The rate of
dissociation will be dependent on the concentration of remaining [AR]. It is an
exponential decay process with a time constant the reciprocal of k2.
The reaction A + R  AR in the other direction is called a pseudo first-order reaction.
This is when agonist [A] is present in great excess compared to [R]. [A] will not change
over the course of the experiment, and  d[AR]  k1  [A]
dt

d[AR]
 k1  [A]  [R]
dt

d[AR]
 k2  [AR]
dt
At equilibrium

(1)
(2)
d [ AR]
d [ AR]

dt
dt
Therefore,
k1  [ A]  [ R]  k2  [ AR]
Rearranging to define the ratio of the two rate constants:
[ A][ R ] k 2

[ AR]
k1
(3)
k2/k1 is the dissociation constant (KD), a measure of the receptor's affinity for the agonist.
Units are concentration2/concentration = concentration.
Mennerick-- Ligand Binding Handout
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We will uncover some more of the significance by some algebraic rearrangements.
Equations 1 and 2 can be rewritten
d[AR]
 k1[A]1  Y [ R]total
dt
d[AR]

 k2Y [ R]total
dt

Again, at equilibrium
k1[A]1  Y [ R]total  k2Y [ R]total
k1[A]1  Y   k2Y
k1[A]  k1[ A]Y   k2Y
Solve for Y:
k1[A]  Y k2  k1[ A]
k1[ A]
Y
k2  k1[ A]
[ A]
Y
k2
 [ A]
k1
[ A]
Y
k D  [ A]
Y
so
[ AR]
[ A]

[ R ]total K D  [ A]
(4)
(5)
At this point you’ve just derived the Michaelis-Menten equation, the Langmuir isotherm,
and the equation of A.J. Clark applying the law of mass action to receptors (all formally
equivalent equations).
Mennerick-- Ligand Binding Handout
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Getting back to the significance of the dissociation constant KD, consider the condition
where half the receptors are bound:
AR  Rtotal   
R total 2
2
[ AR]
1
or
Substituting from equation 5,
[ A]
1

K D  [ A] 2
2[ A]
1
K D  [ A]
2[ A]  KD  [ A]
KD  2[ A]  [ A]
SO: K D  [A] when receptors are half occupied!
This is the significance of the kD. It is the concentration of drug causing half the
receptors to be bound. For high-affinity ligand-receptor interactions this number will be
in the nanomolar range (G-protein coupled receptors), and for low-affinity interactions
the value will be in the low to high micromolar range (ligand-gated channels).
The Hill equation is used to fit functional data empirically.
Y

I
I max
[ A]n

n
EC50  [ A]n
I max
 EC 
1   50 
 [ A] 
n
n=slope factor (Hill coefficient)
EC50 = concentration at which 50% of the maximum response is obtained.
EC50Kd.
Mennerick-- Ligand Binding Handout
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Competitive antagonism
Simple competitive antagonists bind to the same site as agonist but elicit no biological
effect of their own. The effects of simple competitive inhibition can be described
intuitively: the antagonist will shift the EC50 of the agonist, but will not change the
maximum response obtainable by the agonist. In other words, one can overcome the
block of a fixed concentration of antagonist with more agonist. With a single
concentration of antagonist, the result is a parallel shift in the agonist concentration
response.
More quantitatively, we return to equilibrium conditions and where B=antagonist and Ki
is the antagonist dissociation constant:
[ A][ R]
 Kd
[ AR]
and
[ B][ R]
 Ki
[ BR ]
Fractional occupancy of receptors by agonist (Y)=
[ R][ A]
[ AR]
Kd

[ R]  [ AR]  [ BR ] [ R]  [ R][ A]  [ R][ B]
Kd
Ki


1
Kd
K [ B]
1 d 
[ A]
[ A] K i
1
 [ B] 
1 

Ki 
1  Kd 
[ A]
So addition of the simple competitive antagonist has shifted the agonist dissociation
constant by the factor of (1+[B]/Ki). This shift can be used to provide direct information
about kd than the EC50 of the response (which is influenced by opening and closing rates
of the liganded receptor). This is because the antagonist binds but elicits no
conformational change.