QUANTATITION OF RECEPTOR LIGAND BINDING AND ITS RESPONSE

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QUANTATITION OF RECEPTOR LIGAND BINDING AND ITS
RESPONSE

• Husong Li, M.D., Ph.D.
• Department of Anesthesiology
• University of Texas Medical Branch at Galveston,
  Texas

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• A Few Concepts
• Assessment of Receptor Occupation
• Inhibition of Receptor Ligand Binding
• Quantitation of Pharmacological Response

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A Few Concepts

• 1. RECEPTORS are the specific molecular
  components of a biologic system with which drugs
  interact to produce changes in the function of
  the system.
• 2. INERT BINDING SITES are components of
  endogenous molecules that bind a drug without
  initiating events leading to any of drugs
  effect.
• 3. EFFECTORS are molecules that translate the
  drug-receptor interaction into a change in
  cellular activity (adenylyl cyclase, tyrosine
  kinase).

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• 4. LIGANDS are Chemicals that bind to
  receptors.
• 5. AGONISTS AND PARTIAL AGONISTS An agonist
  is a drug capable of fully activating the
  effector system when it binds to the receptor. A
  partial agonist produces less than the full
  effect even it has saturated the receptors.
• ANTAGONISTS are drugs that bind to the receptor
  without activating the effector system for that
  receptor. It may block the access of agonist to
  receptor.
• INVERSE AGONIST OR NEGATIVE ANTAGONIST is a
  ligand produces an effect opposite in the
  direction of the agonist.

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ASSESSMENT OF RECEPTOR OCCUPATION
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Assessment of Receptor occupation

• Assumption drug and receptor interact in a
  reversible reaction governed by the Law of Mass
  Action.
• k1 association rate constant.
• k-1 dissociation rate constant.

k1
RL
RL
k-1
RL
response
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Assessment of Receptor occupation

• rate of associationk1LR
• rate of dissociation k-1LR
• dLR dt k1LR k-1LR
•  
• at equilibrium dLR dt 0,
• then k1LR k-1LR
•  
• Dissociation Constant

LR
-K1
Kd

LR
K1
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Assessment of Receptor occupation

• Dissociation Constant (Kd) is the free ligand
  conc at which 50 of receptor is occupied.
• Kd represents affinity of ligand binding to
  receptor (1 affinity).
• Each ligand has its own specific affinity to the
  receptor. This can be used to define a new drug
  or confirm a receptor.

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Plotting Method Log-Linear Plot
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Plotting Method Scatchard Plot

• KdLR LR
• LRmax receptor density LRBound
• R LRmax LR
• LR L LR(-1 Kd) LRmax Kd

LRmaxL
LR
KdL
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Plotting Method Double Reciprocal Plot

• Transform equation of LR LRmaxL
  KdL
• 1 LR Kd LRmaxL 1 LRmax
• slope Kd LRmax
• X-intercept -1 Kd
• Y-intercept 1 LRmax

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Hill Analysis

• ligand may have multiple binding sites with
  different affinity, and binding to one site may
  change the likelihood (affinity) the ligand binds
  to other related sites.
• Oxygen binds to Hb
• B Bmax Ln Kdn Bn
• NH, Hill Coefficient, is a measure of
  cooperativity

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Hill Plot

• When NH gt 1, positive cooperativity Binding
  of ligand to one site enhances the likelihood of
  binding the same ligand or a related ligand.
• When NH lt 1, this will indicate i. Negative
  cooperativity ii. Multiple classes of
  non-interacting binding site

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Scatchard Plot Receptor Ligand Binding
Cooperativity
Positive Cooperativity
LR
LR
Negative Cooperativity
L
L
LR
LR
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Inhibition of Receptor Ligand Binding

• Competitive Binding
• Competitive Antagonism
• Noncompetitive Antagonism

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Competitive Binding

• Potency refers to the conc of the compound that
  is effective in competing for labeled site.
• Extent of competition.
• Conc. for 10-90 range competition by a unlabeled
  ligand will be 81 fold.
• These studies ascertain the specificity of
  radioligand binding sites (receptor).

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Competitive Antagonism

• Assumption i. Both RL and RI exist, not RLI.
  ii. RI will not elicit response.
• Kd RL RL
• Ki RI RI
• Ki is dissociation constant of inhibitor 
• At equilibrium, Bmax R RL RI 
•  

I

k1
L
R
RL Response
k-1
RI
BmaxL
B
Kd(1L/Ki)L
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Competitive Antagonism

• Dissociation constant for the whole reaction Kd
• Dose ratio the doses of agonist to achieve same
  response in the presence or in the absence of
  antagonist.

Kd(apparent)
Kd(1I/Ki)
Dose ratio
L'/L
1I/Ki
Log agonist
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Noncompetitive Antagonism

• Prevents the agonist, at any concentration, from
  producing max effect on a given receptor.
• Irreversibly prevent the binding of agonist to
  that site.
• Reversible or irreversible interaction with a
  component of the system to decrease the binding
  of agonist.

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Noncompetitive Antagonist

• L Bmax
• B
• L Kd X 1 I/Ki
• Kd (apparent) Kd 
• Bmax is reduced, but agonist can act normally at
  receptor-effector units which are not influenced
  by antagonist.

Bmax
B'max
1I/Ki
Log agonist
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Scatchard Plot of Antagonism
Competitive Antagonism
Nonconpetitive Antagonism
-1
-1
-
-
B
B
Kd
Kd
L
L
Bmax
B
B
Bmax
agonist
agonist antagonist
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Double Reciprocal Plot of Antagonism
Competitive Antagonist
Noncompetitive Antagonism
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Summary of Antagonism
Bmax
Kd
Competitive Antagonist
Kd(apparent)
Kd(1I/Ki)
Bmax
B'max
Noncompetitive Antagonist
1I/Ki
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Quantitation of Pharmacological Responses of
Agonist and Antagonist

• Agonist and Partial Agonist
• Pharmacological Antagonist
• Negative Antagonist or Inverse Agonist

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Agonist and Partial Agonist
A
B
C
D
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Receptor Reserve and Spare Receptor

• Spare receptor exists if the maximum drug
  response is obtained at less than saturation of
  the receptor.
• In a system with spare receptor, EC50 lt Kd
• In a system without spare receptor, EC50 Kd
• Spare receptor increases sensitivity to the
  agonist.

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Quantitation of Receptor Reserves

• Furchgott used irreversible acting compound to
  fractionally inactivate (by alkylation) the
  receptor. Hence, by diminishing the number of
  receptor, the extent of rightward shift of Dose-
  Response curve without depression of maximum
  response will reflect the receptor reserve, and
  rank of efficacy can be achieved

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Quantitation of Receptor Reserves

• 1 L 1-q qKd 1 q L
• q is the fraction of receptor remaining following
  alkylation.
• In general, muscarinic receptor in SM, B
  adrenergic receptor in myocardium, opiate
  receptors in CNS have reserves. A adrenergic
  receptor has less reserve.

Drug B
Drug D
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Pharmacological Antagonist
Competitive Antagonist
Noncompetitive Antagonist
i.e. phenoxybenzamine
i.e. phentolamine
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Inverse Agonist or Negative Antagonist

• A ligand produces an effect opposite in the
  direction of the agonist.
• Inverse agonist has higher affinity to Ri and
  will preferentially stabilize Ri in the inactive
  state.

D
D


Ra
Ri
DRi
DRa
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Inverse Agonist or Negative Antagonist
full inverse agonist
full agonist
antagonist
partial inverse agonist
partial agonist
Ri
Ra
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Summary

• A full agonist is selective for the Ra
  conformation.
• A partial agonist has slightly greater affinity
  for Ra than Ri.
• An antagonist has equal affinity to either
  conformation.
• Negative antagonist has preferential affinity for
  Ri to Ra.

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General reference

• Pratt WB and Taylor P Principles of Drug
  Actions. 3rd Ed.
• Smith CM and Rayland AM Text Book of
  Pharmacology.
• Handout from Dr. K. Johnson, Dept of Pharmacology
  and Toxicology, UTMB