biological & mathematical interpolation of receptors in tissue

Biological and mathematical interpolation of receptor in

tissue

Dr AMIT RELHAN

A MACROMOLECULAR PROTEIN WHICH

BINDS TO SPECIFIC FUNCTIONAL GROUPS OF ENDOGENOUS SUBSTANCE OR A CHEMICAL SUBSTANCE.

DEFINITION OF RECEPTOR

Dose response curve

Maximal ceiling effect Position of curve (EC50 & pD2) Slope of curve

Claude Bernard- curare- injected frog skin –

progressive dimunition of motor reflex ( electric stimulus to muscle – contraction)

Curare acting on neither muscle nor nerve- NMJ

Paul Ehrlich –preferrential accumulation of Pb in CNS

Differential staining of tissue using dyes Arsenicals for T. pallidum- some sort of

selectivity for parasite (magic bullet)

Concept of receptor

Failure of arsenical in trypanosomes – lack of

binding Agents cannot act unless they are bound Selectivity of binding

J.N.Langley –autonomic transmission & NM

communiation Frog gastrocnemius- nicotine- contraction Blocked by curare ( even after degeneration of

nerve) Direct stimulation – contrction Both curare & nicotine act on same substance Receptive substance ∞ conc. of drug (potency) & its affinity to

receptive substance

Theories of drug receptor interactions

Studied antagonism b/w Ach & atropine in various

muscle preparation

Effect of drug is proportional to the fraction of the

receptor occupied by the drug

Maximum effects are produced when all receptors

are occupied Drug receptor complex breakdown at rate

proportional to rate of complex formed Saturability, Reversbility ,Dynamic equilibrium

Classical receptor theory by Clark(1937)

Based on law of mass action(isotherm equation -

langumuir) k1

[L] + [R] < ===[LR] k2

rate of association = K1[L][R] rate of dissociation = K2 [LR] At equilibrium, rate of association=rate of

dissociation

K1[L][R]= K2[LR] K1 /K2=[LR]/[L][R]=Ka –equilibrium association

constant 1/Ka= Kd=[L][R]/[LR] Kd –equilibrium dissociation constant

Equilibrium Dissociation constant (Kd).

However, it is not possible to measure [R], So, Rtot = [R] + [LR] and [R] = Rtot -[LR]

Scatchard equation

Scatchard plot

The Kd is the same for a given receptor and

drug combination in any tissue, in any species (as long as the receptor is the same)

The Kd can therefore be used to identify an unknown receptor

The Kd can be used to quantitatively compare the affinity of different drugs on the same receptor

Studied-Ach induced contraction of frog rectus

Ms. Ach induced inhibition of electrically

stimulated frog ventricle Slope of log concentration- response curve Linear correlation b/w occupancy &response

Slope of log conc.- response curve--- steeper

than predicted from mass action equation. Sometime even supramaximal conc.—not able

to elicit maximal contractile response. Dualism of homologus series of quaternary

ammonium salt in muscle preparation• butyl-/lower member of series-full contraction• Hexyl/heptyl-higher member-weak contraction• Applied simultaneosly with butyl - antagonism

Shortcomings of Clark theory

log

Webb (1950)-  when the cholinesterase of isolated rabbit

auricles is blocked with physostigmine, the slope of the acetylcholine log-concentration-effect curve is about 10 times steeper than on normal auricles

Studied Dual behavior of phenylethylamine –in

cat BP experiments Agonistic and antagonistic effect –single

recptor Introduced intrinsic activity(IA)- ability of a

drug to elicit effect Effect ,E=α [LR] For max response –maximal occupancy not

required

Ariens theory

Explained concept of partial agonism

Not able to explain steeper log dose response relationship than expected from equation

Alquist (1948) Concentration- response curve of tissues or

organs of different receptor systems obtained rank order of potency was "adrenaline >

noradrenaline > α-methyl noradrenaline > isoprenaline" in promoting contraction of blood vessel- α-adrenoceptors

the rank order was "isoprenaline > adrenaline > α-methyl noradrenaline > norepinephrine" in the heart-β-adrenoceptors

Clark equation– conc. Of drug & conc of drug

receptor complex formed Tabulated slopes of log conc response curve in

literature- steeper than predicted Ach & histamine on guinea pig ileum- greater

response than predicted from receptor occupancy

Response not linearly ∞ to fractional receptor occupancy- only small fraction- max effect –receptor reserve

Stephenson theory

Concept of efficacy- capacity to start response Response=f. (stimulus)=f.(e.y) e=efficacy , y = fractional receptor

occupancy Explained dual behavior of homologus series Lower /butyl-high efficacy- agonist Higher/ hexyl-low efficacy- partial agonist Affinity but no efficacy- antagonist

Nickerson 1956- 1% histamine receptor occupancy

– max response in guiena pig ileum Furchgott 1955- studied antagonism by β

haloalkylamine on effect of adenaline - shift of only half log unit.

Goldstein 1974-studies on receptor antagonism β haloalkylamine- irrevesible antagonism of

histamine & catecholamine recpeptor Low dose- only rightward shift of drc(spare

receptor) High dose- both rightward shift & ↓max effect

Spare receptor

Receptors are said to be ‘spare’ for a given pharmacologicalresponse when the maximal response can be elicited by anagonist at a concentration that not result in occupancy of thefull complement of available receptors

Spare receptorEmax

Log Concentration

Res

pone

s(%

) Agonist alone

Agonist with noncompetitive antagonist in presence of

spare receptor

Agonist with noncompetitive antagonist in absence of

spare receptor

Studied competititive antagonism of

adrenaline by ergotamine on rabbit uterus. concepts of ‘dose-ratio’ Schild regresssion analysis –pA2 value & Kb DR-1=[B]/Kb Gaddum equation Log(DR-1)=log[B]-logKb Schild equation

Schild & Gaddum

Excitation by agonist (eg.nicotine)—block function Effect of agonist –fade with time Excitation ∞ rate of drug receptor interaction than

no. of receptor occupied

Agonists dissociates rapidly ,Kd-high

Antagonists slowly, Kd-low

Explained Persistent effect of an antagonist on a tissue

Explained tachypylaxis

Paton theory(1961)

Receptors exist in discrete conformational states Hill –O2 binding to Hb- steeper curve MWC model-1965 2 conformational state of receptor- equilibrium in

absence of ligand Ligand binding –displacement of equilibrium to state

having higher affinity The extent to which the equilibrium is shifted toward

the active state is determined by the relative affinity of the drug for the two conformations

Concept of coopertivity

Allosteric theory

The binding of a ligand to a macromolecule is

often enhanced if there are already other ligands present on the same macromolecule (this is known as cooperative binding). The Hill coefficient 

Log(θ/1-θ)=nlog[L] - log Kd θ – fraction of occupied site where ligand can bind n >1 - Positively cooperative binding  n<1- Negatively cooperative binding  n=1- Non cooperative binding

Hill langmuier equation

No explanation about constitutive active

receptor Not able to explain about GPCR effect coupling

Black & Leff et al- mathematical model Diff. in relative potency order of ligands in tissues

with different recp. Reserve Receptor in diff. conformational state due to allostery [LR]=[Rtot][L]/KA+[L] Rectanguler hyperbola equation Concept of transducer ratio, τ =[Rtot]/Ke τ- efficiency by which occupancy transduced to

response

Operational model of agonism(1983)

Effect, E=Em[LR]n/Ke+[LR]n n>1 steep curve n<1 shallow curve n=1 linear relation

No insight into [LR] to E –linking event ,but provide τ- quantaive measurement of effect.

Leff & Hall et al. 2000 Difference in potency order for single receptor

interacting with different G protein Difference signal trasduction output from

same receptor To isolate pathway-pertusis toxin sensitive

Gi/Go coupled signal or G protein selective disrupting peptide

3 state model /ternary complex

Seifert 2002- inverse agonist concept Inverse agonist stabilize receptor in inactive

conformation IA-0 to -1

Agonist independent /constitutive activity

Methods of Characterization of Receptors

1. On basis of Pharmacological Responses

2. Radioligand binding studies

3. Molecular Cloning techniques

4. Analysis of biochemical pathway linked to

receptor activation

On Basis of Pharmacological Responses

a) Relative potency (Affinity) measurements of a

series of Agonists

b) Determination of Affinity or Dissociation

constant of Antagonists

c) Isomeric activity ratio of agonists

Relative potency(affinity) measurements of a series of

agonists.

Alquist (1948) Furchgott(1967)observed similar potency series adrenaline > nor-adrenaline > phenylephrine>

isoprenaline By calculating correlation coefficients of two

systems

e.g.sympathomimetics-

bronchodilatation/vasodepression-0.96 (similar)

Cardiac stimulation-bronchodilation-0.31(different)

Acetylcholine (ACh): One drug with different affinities for two different receptors

(adapted from Clark, 1933)

Muscarinic receptorsEC50 = apparent Kd ~ 3 x 10-8 M, pD2 ~7.5

Nicotinic receptorEC50 = apparent Kd ~ 3 x 10-6 M, pD2 ~5.5

Different affinities of related agonist drugs for the same receptor: Different potencies

(adapted from Ariëns et al., 1964)

Determination of affinity or dissociation constant of

antagonist-p(A2) or p(KB)

Schild plot-Different tissue with similar receptors- same value

e.g. acetylcholine –atropine in frog heart ,chick amnion ,mammalian intestine

A Schild plot -compares the reciprocal of the dose ratio versus the log of the antagonist concentration

Intercept on absicca- pA2 = log Kd, which represents the affinity of the competitive antagonist

pA2 (log molar concentration of antagonist producing a 2fold shift of the concentration response curve.

Different

pA2

values (affinities)for different receptors of some clinically

useful drugs:The basis of therapeutic selectivity

ISOMETRIC ACTIVITY RATIO

IAR=Antilog (negative molar EC50 of L-isomer minusEC5O of D-isomer)

High ratio – specific interaction eg-Isoprenaline (L) -35 times potent than (D)

Similarity of ratio to Enantiomorphs- similar receptors

Experimental Condition for characterization

RESPONSE-Should be1.Solely due to action on one type of receptors 2.Not be due to release of other active

substance3.Concentration of free drug –at steady level4.Proper control –to any change in sensitivity of

agonist5.Sufficient time-for antagonist to act in

equilibrium.

USE OF RADIOLABELLED LIGANDS

USE OF RADIOLABELLED LIGANDSa) Direct binding studies

Eg labelled bungarotoxin binds specifically and irreversibly to cholinergic receptors

Phenoxybenzamine –an irreversible alpha blocker .

Relative proportion of B1 and B2 receptor 4:1-Heart 2:1cerebral cortex 1:3 lungs

Scatchard Plots

Kd and R tot cannot be measured directly. plot the ratio of bound/unbound drug,[LR]/[L]

versus bound drug[LR]. intercept of the line with the abscissa -total

number of receptors available(Bmax)or R tot. Kd (the dissociation constant) from the

negative reciprocal of the slope of the line

b) Indirect radioligand binding/Competition binding

The affinity of un-labeled compounds –by competition binding. - - displacement from the binding site.

The concentration of un-labeled ligand which displaces half of the tagged is interpolated from the curve and refered to as the IC50 value.

The IC50 value -used to estimate the affinity

of the unlabeled ligand -Ki values. Rank order Ki values are a type of fingerprint

for a receptor subtype. Comparison between EC50 values (rank order

potency) and Ki/KD values (rank order affinity)

If Bmax remains unchanged and the slope of the lines decreases with increasing concentrations of the compound, the displacement is competitive. Unchanged slope and decreased Bmax indicate that the displacement is noncompetitive

The lower the IC50 or Kd, the higher the affinity

Ki value

Ki, the inhibitory (or affinity) constant of the displacer compound

when the displacement is noncompetitive (Ki = IC50)

for a competitive displacement -Cheng-Prusoff equation

Ki = IC50/(1 + [L]/Kd) [L]= concentration of the radioactive ligand.

Peroutka & Snyder (1979) 5HT1 – high affinity for [3H]5HT 5HT2 – low affinity for [3H]5HT, but high affinity for [3H] spiperone

Allosteric interaction

The affinity shift, -the ratio of radioligand affinity in the presence (KApp) to that obtained in the absence (KA) of each concentration of antagonist.

A plot of log (affinity shift1) versus log [antagonist] should yield a straight line

slope of 1 for a competitive interaction, curvilinear plot for an allosteric interaction.

Protean Agonism

After Proteus, the Greek god

Ligands act as partial agonists in quiescent silent systems

As inverse agonists in systems that show a high level of constitutive activity.

Agonist produces an active conformation of lower efficacy than a totally active conformation

Molecular Cloning

Heterogeneity of receptor, distinct sequences and

tissue distribution

Receptor-labelling tech. made it possible to extract

and purify receptor material

Firstly this approach used on Nicotinic ACh recp. in

1970

Transgenic & receptor knockout mice- subtypes of

receptor

Sequence homology of receptor Alpha1a,1b,1d – 70% Alpha 1 & 2 – only30%

Analysis of biochemical pathway linked to receptor

activation

Images of cAMP Transients in Cultured Aplysia Sensory Neurons.

The cell was loaded with a fluorophore that would allow for the quantification of cAMP concentrations within the cell.

A: Free cAMP in the resting cell is < 5 X 10-8 M.B: Stimulation with serotonin, activates adenylate cyclase increasing cytoplasmic cAMP to ~ 1 X 10-6 M (red), especially within fine processes with a high surface to volume ratio. Thurs, within 20 sec of stimulation, the intracellular [cAMP] increased ~ 20-fold.

Greengard et al. – nigrostriatal cAMP for

dopamine receptor identification D1 - increase cAMP D2 – decrease cAMP

Thank you