analytical pharmacology

Question 1

aim of analytical pharmacology

Answer 1

create model test system which provides descriptive pharmacological outputs for the drug that are predictive in a physiological/ therapeutic situation

Question 2

law of mass action

Answer 2

rate of reaction proportional to the product of the concentration of the reactants, equilibrium dissociation constant Kd = k-1(dissociation constant)/k+1(association constant)

Question 3

Kd

Answer 3

concentration of drug required to occupy 50% of receptors at equilibrium, Bmax is the total number of receptors, affinity is measured using saturation binding

Question 4

mass action equation

Answer 4

[AR]=[A][Rt]/(Kd+[A]), derived form Langmuir and hill, [AR] - conc of occupied receptors, [A] - conc of ligand, [Rt] - total conc of receptors,

Question 5

saturation binding curve

Answer 5

in normal space the curve is hyperbolic, in semi logarithmic space the curve is sigmoidal,

Question 6

characteristics of hyperbolic curves

Answer 6

occupancy increases from 9% to 91% over two log units, symmetrical about the midpoint, your need >100x Kd to get >99% occupancy

Question 7

clarks model

Answer 7

A+R=AR, predicts affinity not efficacy, no term for ligands intrinsic efficacy - is A an agonist, partial agonist, antagonist

Question 8

scatchard plot

Answer 8

same slope = same affinity, changing receptor numbers does not change ligand affinity, the Kd concentration still occupies 50% of the calibre receptors (even though there are fewer receptors), affinity is not system dependant

Question 9

potency

Answer 9

effect = a[A]/EC50+[A], a and EC50 are system dependant - this equation is not predictive, a = intrinsic activity of drug, lower receptor numbers = lower agonist potency, potency is system dependant, full agonists reach maximal response at low receptor number, some partial agonists become full agonists at high receptor numbers, intrinsic activity (a) is system dependant, conc-response curves are not the same as ligand binding curves as changing receptor number doesn’t change ligand affinity, potency dependant on ligand affinity, ligand intrinsic efficacy and number of receptors EC50 = Kd/([Rt]/KE)+1

Question 10

operational model

Answer 10

hyperbolic function that describes how agonist activates a receptor system intrinsic activity and potency (EC50) are system dependant - cannot be used to predict in different system, first stage of operational model is ligand binding stage as clark described - controlled by Kd, described by hyperbolic function, second stage is transducer function - imagine receptor complex acts as ligand interacting with effector system to produce an effect, imagine as a theoretical binding even

Question 11

second stage - operational model

Answer 11

• KE = value of conc of AR complex required to elicit 50% of the Em response, inversely proportional to efficacy of the AR complex so relates to intrinsic efficacy - An agonist with higher intrinsic efficacy can cause an effect at lower receptor occupancy, KE is intrinsic efficacy of agonist in activating particular cellular pathway
  -Em = maximal possible effect in the system being used, hence this is a property of the system and is stated by all agonists acting on the cell or tissue
  -effect =[ARE] =Em[AR]/KE+[AR]

Question 12

operational model equation

Answer 12

combines [AR] (assumed by clark - LoMA) and [ARE] (deduced model) equations with the transducer ratio tau=[Rt]/KE - tau operationally describes the agonist’s efficacy its both ligand and system dependant
Effect=tau[A]Em/Kd+(tau+1)[A] this was what would actually be observed in an experiment, EC50 in the observed experiment is (tauEM)/(tau+1), a in observed experiment is Kd/(tau+1)

Question 13

Kd, [Rt] and KE all affect EC50 and a

Answer 13

EC50=Kd/tau+1, tau=[Rt]/KE - tau is dependant on receptor number and intrinsic efficacy of the agonist so high tau = potent system/ agonist has high potency, when tau is reduced we first see reduced potency and then see reduced maximal activity, when tau = 0 ligand is antagonist

Question 14

operational model - kenakin

Answer 14

difference between log(tau/Kd) of test agonist and standard agonist (delta log(tau/Kd)) (delta refers to difference between agonist 1st and 2nd value) remains constant over changing receptor densities hence predicts agonism in therapeutic systems from measurements made in test systems, so long as agonists are treated in same assay system, EC50 and Emax (a) are highly system dependant but delta log(tau/Kd)

Question 15

biased GPCR signalling

Answer 15

comparison of ligands standardised transduction coefficients (delta log(tau/Ka(affinity)) from two different pathways may be used to estimate the signalling bias of the ligand with respect to the two signalling cascades, a difference between two different delta log(tau/Ka) values is delta delta log(tau/Ka), signalling bias makes reference to capacity of GPCR ligands to direct pharmaceutical stimuli to a subset of effectors among all of those controlled by the receptor

Question 16

conformational induction

Answer 16

implied by operational model - agonist induces conformational change, agonist -bound active state leads to effect, bound receptors are active, free receptors are inactive

Question 17

constitutive activity

Answer 17

constitutive activity at high [Rt] suggests agonist independent conformational switching - small population of receptors will be able to to form active state without any agonist being present, very ow basal activity, may be so low non detectable, increases population of receptors = equilibrium between active and inactive state remains the same, increased receptor numbers reveals basal constitutive activity

Question 18

conformational selection by agonists

Answer 18

see agonists as molecules that don’t bind and induce conformation but bind to preformed active states and stabilise them, agonist binds to active state receptors and keeps them in that state for longer pulling equilibrium over, agonist changes dissociation constant therefore agonist will increase activity

Question 19

conformational selection by inverse agonists

Answer 19

binds inactive state receptors, pulls equilibrium over the other way reducing basal activity

Question 20

conformational model limits

Answer 20

relies on conformational induction, can explain basal activity or inverse agonism

Question 21

ternary complex model

Answer 21

• if A=agonist then [ARG]>[RG], if [ARG>[RG] then aM<M hence a<1, if a<1 then aK<K so A has higher affinity RG than R, a is a term describing efficacy
• if a<1 then aK<K so A is an agonist, if a=1 then aK=K so A is an antagonist (binds to active (RG) and inactive (R) states with equal affinity), if a>1 then aK>K so A is an inverse agonist (ligand has higher affinity for uncoupled receptors than coupled receptors

Question 22

GPCRs form a ternary complex

Answer 22

can uncouple receptors from their G-proteins in membrane preparations by blocking hydrolysis stage in G-protein cycle. if GDP cannot be generated heterodimer cannot reform, receptor remains uncoupled, result is affinity of agonist (not antagonist) will be reduced if receptor is uncoupled

Question 23

antagonists

Answer 23

IC50 values via competition of sub-maximal agonist response,
1- get conc/response curve for agonist
2- define submaximal conc (almost gets to maximal conc)
3- redefine that response as 100% then compete with agonist
4- easier to start with sub maximal response so we have to add less antagonist before seeing drop
- affinity can be measured by competition binding assays and analysed via LoMA and Cheng-prusoff equation
- cheng-prusoff equation = Ki(inhibition constant-absolute value)=IC50(conc of competing ligand which displaces 50% of specific binding of the radioligand)/1+(L/Kd(dissociation constant of radioligand for receptor), pKi - negative log of Ki value, for antagonist should theoretically be equal to it pKb (Kb determined in an in vitro experiment where functional response measured, provided assay conditions are similar)

Question 24

antagonist affinity

Answer 24

assessed using radioligand binding experiments (saturation or competition), must do functional experiments to demonstrate antagonist has no efficacy, most complete way to investigate properties of antagonist is to calculate its affect on full agonist binding curves, disadvantage is its a ‘big experiment’

Question 25

schild analysis

Answer 25

enables calculation of antagonist affinity in functional assays, agonist response required but independent of the equation, need to know conc of antagonist used and extent of rightward shift it causes to agonist curve, 2-fold shift (r=2) would be caused whenever conc of antagonist used is at its Kd conc, need bigger than 2-fold shift to see anything on conc-response curve (otherwise curves too close), child equation that of straight line so can be extrapolated, log(2-1)=0 so this occurs at the intercept with x axis when y=0, this is logKb of antagonist

Question 26

schild plot - pA2 analysis

Answer 26

pharmacological method of receptor classification, dose-effect curve for agonist determined in presence of various concs of competitive agonist, pA2 (estimate of affinity of agonist for its receptor- i.e. equilibrium dissociation constant) can be determined from experiment, once actual experiments completed series of dose ratios (DR) calculated for given effect, this is determined for several doses of antagonist then log((B/A)-1) vs negative log [antagonist] plotted (negative log more convenient), if regression is linear with slope of -1 indicates antagonism is competitive and by definition the agonist and antagonist act at the same recognition sites, x-intercept of fitted line is estimation of pA2 which is estimate of dissociation constant for antagonist (pA2 also dose of antagonist that requires 2-fold increase in agonist conc), if slope of line is not -1 then antagonist is not competitive or some other condition in effect - multiple binding sites to pharmacokinetic interactions, if hill slop and child plot are fixed to 1.0, pA2 is equal to -logKb, the negative log of equilibrium constant (molar) of inhibitors binding to receptors

Question 27

co-operative ligands

Answer 27

reciprocity - orthosteric ligand has same effect on allosteric ligands affinity as allosteric ligand has on orthosteric ligands affinity, quantified by allosteric constant, reciprocity is thermodynamic requirement of the system at equilibrium (otherwise allosteric binding would provide a route to a perpetual motion machine