Drug receptor interactions

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 = drugR = receptor, DR = drug-receptor complex

k1 = rate for association and

k2 = rate for dissociation.

KD = Dissociation Constant

KA = Association Constant

k1

[D] + [R] [DR]

k2

k2 = KD = [D][R]

k1 [DR]

1 = KA = k1 = [DR]

KD k2 [D] [R]

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Log [Drug]

Dru

g-R

ecep

tor

Com

plex

SATURATION CURVE

[Drug] nM

DR


SATURATION CURVE

[DR

]

[Drug] nM

RT = Bmax

RT = Total number of receptors

Bmax = Maximal number of receptors Bound

k2 = KD = [D][R]

k1 [DR]

[DR] max


TIME COURSE

[DR

]

Equilibrium

KD = Equilibrium Dissociation Constant

k2 = KD = [D][R]

k1 [DR]

[D] + [R] = [DR]

0 10 20 30 40 50 60

Time (min)


SATURATION CURVE

[Drug] nM

[DR

]

KD

At equilibrium, the dissociation constant is KD and the affinity is K A = 1/KD

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

+ + + + + -

- - - + - -

- - -

+ + +



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


Agonists and AntagonistsPHARMACOLOGICAL ANTAGONISTS

1. CompetitiveThey compete for the binding site

• Reversible• Irreversible

2. Non-competitveBind elsewhere in the receptor (Channel Blockers).



FUNCTIONAL ANTAGONISTS

1. Physiologic Antagonists

2. Chemical Antagonist



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



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 with heparin and inactivates it.www.freelivedoctor.com

Competition Binding

Log [I] nM

IC50

Binding of Drug D I = Competitorwww.freelivedoctor.com

Competition Binding

RANK ORDER OF POTENCY: A > B > C > D

Log [I] nM

IC50

A B C D

Four drugs


Drug Concentration

Res

pons

e

SEMILOG DOSE-RESPONSE CURVE

Eff

ect

or


Drug Concentration

Res

pons

e


ED50

50% Effect

Maximal EffectEff

ect

or


SEMILOG DOSE-RESPONSE CURVEEFFEC

T

POTENCYEFFICACY

ED50

Maximal Effect

Log [Dose]




A B C D

EFFEC

T

Log [Dose]




RANK ORDER OF EFFICACY: A = C > B > D

A

B

C

D

RES

PO

NS

E

ED50



PARTIAL AGONIST• A drug is said to be a partial agonist when it binds

to a receptor and causes a partial response.• It has intrinsic activity < 1.


Agonists and Antagonists1. COMPETITIVE ANTAGONIST

Reversible & SurmountableThe effect of a reversible antagonist can be overcome by more drug (agonist). A small dose of the antagonist (inhibitor) will compete with afraction of the receptors thus, the higher the concentration of antagonist used, the more drug you need to get the same effect. www.freelivedoctor.com


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.


Agonists and Antagonists1. COMPETITIVE ANTAGONIST

Irreversible & Non-surmountableThe effect of irreversible antagonists cannot be overcome by more drug (agonist). The antagonist inactivates the receptors.


Drug Concentration

LINEWEAVER-BURKE PLOT

1

1

KD

1

Effect

1

Bmax

KD

Bmax

1

[D]



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.


Quantal Dose-response Curves

Frequency of distribution % population responding to drug A

1 10 20 30 40 50 60 70 80 90 100

Dose (mg/kg)

% p

opu

lati

on r

esp

ondin

g


Quantal Dose-response Curves

Cumulative distribution of population responding to drug A

1 10 100

Dose (mg/kg) log scale

% p

opu

lati

on r

esp

ondin

g

ED50ED90ED10


Therapeutic IndexToxic

eff

ect


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 = TxD1–1 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.


Therapeutic IndexToxic

eff

ect

ED99

ED13ED1


APPENDIX


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.

k1

[D] + [R] [DR] (1)

k2

D = drugR = receptor, DR = drug-receptor complex

k1 = rate for association and

k2 = rate for dissociation. www.freelivedoctor.com

Law of Mass ActionAt equilibrium, the rate at which the radioligand binds to the receptor is equal to the rate at which it dissociates:

association rate = dissociation rate

k1 [D][R] = k2 [DR] (2)

k2 = [D][R]

k1 [DR] (3)

k2 = KD = [D][R]

k1 [DR] (4)

Where KD is the equilibrium dissociation constant. The units for the KD are concentration units (e.g. nM). www.freelivedoctor.com

Law of Mass ActionAnother constant related to the KD is the affinity (KA) which is essentially equivalent to the reciprocal of the KD. The units for the KA are inverse concentration units (e.g. nM-1).

1 = KA = k1 = [DR]

KD k2 [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 = [D][R] [DR] (6)

KD [DR] = [D][R] (7)www.freelivedoctor.com

Law of Mass ActionSubstitutions:

[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)

[DR] = [D][RT] (13)

[D] + KD

RT: Total number of receptors www.freelivedoctor.com

Law of Mass Action [DR] = [D][RT] (13)

[D] + KD

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 KM denotes the Michaelis constant, which is equivalent to the concentration of substrate required for half-maximal velocity


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Drug receptor interactions