DRUG RECEPTOR INTERACTIONS
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Law of Mass Action When a drug (D) combines with a receptor (R), it does so at a rate which is dependent on the concentration of the drug and the concentration of the receptor. [D] + [R]
D = drug R = receptor, DR = drug-receptor complex k1 = rate for association and k2 = rate for dissociation. KD = Dissociation Constant KA = Association Constant
k2
=
k1 ď „ [DR] k2
KD =
k1 1
[D][R] [DR]
=
KA =
KD
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k1 k2
Read the Appendix at the back
=
[DR] [D] [R]
Drug-Receptor Complex
DR
SATURATION CURVE
[Drug] nM
Log [Drug] www.indiandentalacademy.com
SATURATION CURVE [DR] max
[DR]
RT = Bmax
k2
=
KD = [D][R]
k1
[Drug] nM
RT = Total number of receptors www.indiandentalacademy.com
Bmax = Maximal number of receptors Bound
[DR]
TIME COURSE [D] + [R] = [DR]
[DR]
Equilibrium
k2
=
KD
k1
0
10
= [D][R] [DR]
20
30
40
Time (min)
KD = Equilibrium Dissociation Constant www.indiandentalacademy.com
50
60
[DR]
SATURATION CURVE
KD
[Drug] nM
At equilibrium, the dissociation constant is KD and the affinity is K A = 1/KD www.indiandentalacademy.com Thus when [D] = KD , half the total number of receptors will be occupied.
Agonists and Antagonists AGONIST • A drug is said to be an agonist when it binds to a receptor and causes a response or effect. It has intrinsic activity = 1
+++
++-
---
---
+--
+++
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Depolarization
Agonists and Antagonists ANTAGONIST • A drug is said to be an antagonist when it binds to a receptor and prevents (blocks or inhibits) a natural compound or a drug to have an effect on the receptor. An antagonist has NO activity. Its intrinsic activity is = 0
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Agonists and Antagonists PHARMACOLOGICAL ANTAGONISTS 1.
Competitive They compete for the binding site • •
2.
Reversible Irreversible
Non-competitve Bind elsewhere in the receptor (Channel Blockers).
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Agonists and Antagonists FUNCTIONAL ANTAGONISTS 1. Physiologic Antagonists 2. Chemical Antagonist
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Agonists and Antagonists Physiologic ANTAGONIST • A drug that binds to a non-related receptor, producing an effect opposite to that produced by the drug of interest. • Its intrinsic activity is = 1, but on another receptor. Glucocorticoid Hormones
Blood Sugar
Insulin
Blood Sugar
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Agonists and Antagonists Chemical ANTAGONIST • A chelator (sequester) of similar agent that interacts directly with the drug being antagonized to remove it or prevent it from binding its receptor. • A chemical antagonist does not depend on interaction with the agonist’s receptor (although such interaction may occur). Heparin, an anticoagulant, acidic If there is too much bleeding and haemorrhaging Protamine sulfate is a base. It forms a stable inactive complex www.indiandentalacademy.com with heparin and inactivates it.
Competition Binding
IC50 Log [I] nM
Binding of Drug D www.indiandentalacademy.com I = Competitor
Competition Binding Four drugs
A
B
C
D
IC50 Log [I] nM
RANK ORDERwww.indiandentalacademy.com OF POTENCY: A > B > C > D
Effect or Response
SEMILOG DOSE-RESPONSE CURVE
Drug Concentration www.indiandentalacademy.com
SEMILOG DOSE-RESPONSE CURVE
Effect or Response
Maximal Effect
50% Effect
ED50
Drug Concentration www.indiandentalacademy.com
SEMILOG DOSE-RESPONSE CURVE
EFFECT
Maximal Effect
EFFICACY POTENCY
ED50
Log [Dose] www.indiandentalacademy.com
SEMILOG DOSE-RESPONSE CURVE B
C
EFFECT
A
Log [Dose]
RANK ORDERwww.indiandentalacademy.com OF POTENCY: A > B > C > D
D
SEMILOG DOSE-RESPONSE CURVE A
RESPONSE
B
C D ED50
RANK ORDER OF POTENCY: A > B > C > D www.indiandentalacademy.com RANK ORDER OF EFFICACY: A = C > B > D
Agonists and Antagonists PARTIAL AGONIST â&#x20AC;˘ A drug is said to be a partial agonist when it binds to a receptor and causes a partial response. â&#x20AC;˘ It has intrinsic activity < 1.
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Agonists and Antagonists 1. COMPETITIVE ANTAGONIST Reversible & Surmountable The effect of a reversible antagonist can be overcome by more drug (agonist). A small dose of the antagonist (inhibitor) will compete with a fraction of the receptors thus, the higher the concentration of antagonist used, the more drug you need to get the same effect. www.indiandentalacademy.com
Agonists and Antagonists RECEPTOR RESERVE OR SPARE RECEPTORS. • Maximal effect does not require occupation of all receptors by agonist. • Low concentrations of competitive irreversible antagonists may bind to receptors and a maximal response can still be achieved. • The actual number of receptors may exceed the number of effector molecules available.
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Agonists and Antagonists 1. COMPETITIVE ANTAGONIST Irreversible & Non-surmountable The effect of irreversible antagonists cannot be overcome by more drug (agonist). The antagonist inactivates the receptors.
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LINEWEAVER-BURKE PLOT
1 KD
Effect 1 KD
Bmax 1 Bmax
11 Drug Concentration [D]
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Agonists and Antagonists Synergism The combined effect of two drugs is higher than the sum of their individual effects.
Additivity The combined effect of two drugs is equal to the sum of their individual effects. www.indiandentalacademy.com
Quantal Dose-response Curves
% population responding
Frequency of distribution % population responding to drug A
1 10 20 30 40 50 60 70 80 90 100
Dose (mg/kg) www.indiandentalacademy.com
Quantal Dose-response Curves
% population responding
Cumulative distribution of population responding to drug A
ED50 ED90
ED10 1
10
100
Dose (mg/kg) log scale www.indiandentalacademy.com
Therapeutic Index
Toxic effect
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Therapeutic index Therapeutic Index = TxD50 ED50 As long as the slopes of the curves are similar, however, if not similar, we use the Standard Margin of safety: Standard Margin of safety = TxD1â&#x20AC;&#x201C;1 x 100 ED99 Which determines the percent to which the dose effective in 99% of the population must be raised to cause toxicity in 1% of the population. www.indiandentalacademy.com
Therapeutic Index ED99
Toxic effect
ED1 ED13 www.indiandentalacademy.com
WEB Sites • • • • • •
Howard University Howard University Site.htm HU College of Medicine.htm HUCM Departments.htm pharmacology.htm Pharmacology Course Materials.htm
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APPENDIX
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Law of Mass Action When a drug (D) combines with a receptor (R), it does so at a rate which is dependent on the concentration of the drug and the concentration of the receptor.
[D] + [R]
k1 ď &#x201E; k2
[DR]
(1)
D = drug R = receptor, DR = drug-receptor complex k1 = rate for association and k2 = rate for dissociation.
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Law of Mass Action At equilibrium, the rate at which the radioligand binds to the receptor is equal to the rate at which it dissociates:
association rate k1 [D][R] k2
= = =
k1 k2 k1
dissociation rate k2 [DR] [D][R] [DR]
=
KD =
(2)
(3)
[D][R] [DR]
(4)
Where KD is the equilibrium dissociation constant. The units for the K D are concentration units (e.g. nM).www.indiandentalacademy.com
Law of Mass Action Another constant related to the KD is the affinity (KA) which is essentially equivalent to the reciprocal of the K D. The units for the KA are inverse concentration units (e.g. nM-1). 1
=
KA
=
KD
k1 k2
=
[DR] [D] [R]
(5)
The relationship between the binding of a drug to a receptor at equilibrium and the free concentration of the drug provides the basis for characterizing the affinity of the drug for the receptor. The mathematical derivation of this relationship is given below: KD
=
KD [DR] =
[D][R] [DR] [D][R] www.indiandentalacademy.com
(6) (7)
Law of Mass Action Substitutions: â&#x20AC;Ś
[RT] = [R] = [DR] [R] = [RT] - [DR]
(8)
KD[DR]
=
[D]([RT] - [DR])
(9)
KD[DR]
=
[D][RT] - [D][DR]
(10)
KD[DR] + [D][DR]
=
[D][RT]
(11)
[DR](KD + [D])
=
[D][RT]
(12)
=
[D][RT] [D] + KD
(13)
[DR]
RT: Total number of receptors
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Law of Mass Action [DR]
=
[D][RT] [D] + KD
(13)
This relationship between specific binding [DR] and the free drug concentration [D] in (13) is essentially the same as the relationship between the substrate concentration ([S]) and the velocity of an enzymatic reaction (v) as described by the Michaelis-Menten relationship: v =
[S] Vmax [S] + KM
Michaelis-Menten Relationship where Vmax denotes the maximum rate of the reaction and K M denotes the Michaelis constant, which is equivalent to the concentration of substrate required for half-maximal velocity www.indiandentalacademy.com
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