PHARMACODYNAMICS Receptor Pharmacology

Home , Agonist, Endogenous agonist, Irreversible antagonist, Partial agonist

MAJID SHEYKHZADE & DARRYL S. PICKERING

10th Edition DEPT. OF DRUG DESIGN & PHARMACOLOGY FACULTY OF HEALTH & MEDICAL SCIENCES UNIVERSITY OF COPENHAGEN 2016 Preface

These notes in pharmacodynamics and receptor pharmacology are originally based on reference 1 and have since been updated with the latest and the most important basic concepts in this field. These notes are intended as a supplementary text on pharmacodynamics and receptor pharmacology but further reading has been provided for those who want to follow up on topics. (See the literature sources below). These notes are prepared for undergraduate students in their final year of study for the Master of Science degree.

The following literature sources are the bases for these notes and for further reading:

1- ”Almen Farmakologi” (Per Juul), 1984

2- ”Pharmacology” (H.P. Rang, M.M. Dale, J.M. Ritter, R.J. Flower, and G. Henderson) 8th Edition, 2016. ISBN: 978-0-7020-5362-7

3- ”Pharmacology Condensed” (M.M. Dale and D.G. Haylett), 2nd edition, 2009.

4- ”Pharmacologic Analysis of Drug-receptor interaction” (Terry Kenakin), 3rd edition, 1997.

5- ”Textbook of Receptor Pharmacology” (Edited by John C. Foreman, Torben Johansen and Alasdair J. Gibb), 3rd edition, 2011. ISBN: 978-1-4200-5254-1

6- ”A Pharmacology Primer” (Terry P. Kenakin), Theory, Applications, and Methods, third edition, 2009. ISBN: 978-0-12-374585-9

Table of Contents

PHARMACODYNAMICS 1

DRUG-RECEPTOR INTERACTIONS 1

CONCENTRATION-RESPONSE RELATIONSHIPS 6

Classical occupation theory 6

Graphic representations of concentration-response relationships 11

Unexpected deviations from theory 13

The modified occupation theory 14

INTERACTIONS AT THE RECEPTOR LEVEL 17

Reversible-competitive antagonism 17

Non-competitive antagonism 17

Reversible-competitive antagonism: mathematical models 19

Irreversible-competitive antagonism 23

Partial agonism 25

iii

PHARMACODYNAMICS

Pharmacodynamics concerns the effects and mechanism(s) of action of drugs on the intact organism, individual organ as well as at the cellular, sub-cellular and molecular levels. Whereas the effects of a majority of drugs are known, in contrast, the mechanism of action for numerous drugs is only partially understood. While medical-pharmacological research for a number of years completely focused on kinetics (because of advanced developments in analytical chemistry techniques), in the last 20-30 years research has produced increased insights into the mechanisms of action of drugs at the molecular level. That has made feasible a more rational pharmacotherapy, a more rational development of new drugs and an increased insight into the pathophysiology and pathobiochemisty of disease.

DRUG-RECEPTOR INTERACTIONS

Receptors are sensitive macromolecules that carry out a central part of a chemical communications system which has the task of regulating and coordinating the function of all cells in an organism. Many drugs exert their effects through affecting biological receptors, i.e. the prerequisite for an effect is a binding to a receptor. This binding can, in its simplest form, be described via Langmuir’s adsorption isotherm, which builds upon the law of mass action. The binding kinetics described below presume a reversible, bimolecular process, where only a small portion of the drug molecules are bound to the receptors and where all receptor molecules are identical. This model can seemingly explain a series of drug-receptor relationships and it is reasonably simple to understand. Even though it certainly doesn’t represent the whole truth, with individual modifications it will be used as in the following notes.

Drug Drug-Receptor Complex

Ligand-binding domain k k1

Effector domain k k-1 Receptor

Effect

Figure 1 Drug-receptor interaction following the law of mass action. 1

In its simplest form the drug-receptor interaction (Figure 1) can be described by:

k+1 +A R ⇔ AR

k-1 where: A = drug, [A] = concentration of drug (units of M), R = receptor, [R] = concentration of free receptor (i.e. unbound receptor), [R]t = total receptor concentration, AR = drug-receptor complex, [AR] = concentration of drug-receptor complex, k+1 = association rate constant (units -1 -1 -1 of M s ), k-1 = dissociation rate constant (units of s ), KA = equilibrium dissociation constant -1 (also sometimes designated Kd) (units of M) and the affinity is the reciprocal of KA (M ).

The rate of production (Vassoc.) of the drug-receptor complex is:

Vassoc. = k +1 R]][[A (1)

and the rate of dissociation (Vdissoc.) is:

Vdissoc. = k −1 [AR] (2)

In the equilibrium situation, where the association rate is equal to the dissociation rate,

(i.e. Vassoc. = Vdissoc.), according to the law of mass action:

[R ] [A] [R] k−1 1 = = KA = (3) [AR] k+1 Affinity

where KA is the equilibrium dissociation constant. The reaction rate for drug-receptor complex production is: d[AR] = k [A ] [R] - k [AR] (4) dt +1 −1

We know additionally that: [R]t = [AR] + [R] ⇒ [R] = [R]t – [AR]. The expression can therefore be rearranged to:

d[AR] = k [A ] [R( ] - [AR]) - k [AR] dt +1 t −1 d[AR] = k [A ] [R ] - (k [A ] + )k [AR] (5) dt +1 t +1 −1 2

The above expression is a linear differential equation of first order. Solving for [AR] gives: [A] [R ] = [AR] = t (1 - e- (k +1 [A ] + −1 t)k ) (6) [A + KA + [A ]

Figure 2 The production of the drug-receptor complex (reference nr. 5).

From equation (6) it appears that [AR] climbs exponentially with time until a constant level is attained at equilibrium (see Figure 2): [A] [R ] = [AR] = t (7) [A + K A + [A ]

The speed at which this equilibrium level is attained is given by (k+1[A] + k-1), which is dependent upon the rate constants k+1 and k-1 for, respectively, the association and dissociation as well as the drug concentration. KA is of special interest. This equilibrium constant gives the concentration of drug which occupies half of the receptors at equilibrium. Equation (7) is identical with the Michaelis-Menten equation, which describes the rate of enzymatic reactions.

Dividing by [R]t on both sides of equation (7):

[AR] [A] = = (8) [R ]t K A + [A ] 3

-pK A KA KA [AR] / [R]

[A] log [A]

Figure 3 A: The relation between drug concentration [A] and the fraction of drug-occupied receptors [AR]/[R]t. B: Same relation, but with a logarithmic x-axis (Reference nr. 4).

With [A] as x-axis and the fraction of receptors which are occupied by drug as the y-axis, the drug-receptor binding graph will be hyperbolic on a linear axis scale (going through zero). A semi-logarithmic graph with log [A] as the x-axis (and the same linear y-axis) produces a symmetric S-form curve (Figure 3). KA, the equilibrium dissociation constant can, amongst other things, be determined by means of in vitro receptor binding studies (saturation experiments), where the tissue containing the receptors in question is incubated with increasing concentrations of a radioactively labeled drug. By relating the amount of bound drug (fmol/g tissue) as a function of the drug concentration (the free, or non-bound, concentration; nmol/L) the concentration giving half-maximal binding (KA) can be determined. Sometimes, -log(KA) (or pKA) is used as a measure of affinity (the larger pKA, the larger the affinity).

‘BLACK BOX’

Initial Drug Receptor AMPLIFICATION Effector Effect Stimulus

Figure 4 Schematic representation of possible amplification steps between drug-receptor binding and effect (Reference nr. 1).

As for the link between binding and effect, we know only very little about the intracellular processes which are activated by stimulation of a receptor. This has led to introduction of the concept of the ‘black box’ (Figure 4) which is a collective term for all the processes that one cannot immediately measure.

It is only now, after many years of intensive research in intracellular reactions, that we are starting to have some insight about what happens after production of the drug-receptor complex. We now know that a stimulation of the receptor leads to a sequence of events which result in an amplification of the signal. An example of such a possible chain reaction is indicated in Figure 5, showing adrenalin’s affect upon adenylate cyclase (a membrane bound enzyme) with production of cAMP (cyclic adenosine monophosphate, a so-called “second messenger”) followed by a series of processes which result in cellular responses (e.g. glycogenolysis and energy generation).

Figure 5 The sequence of enzymatic reactions from adrenalin’s stimulation of adenylate cyclase to the resulting effect (Reference nr. 3).

CONCENTRATION-RESPONSE RELATIONSHIPS

Classical occupation theory is built upon two main assumptions:

1. The magnitude of the measured effect is proportional to the fraction of drug-occupied receptors, i.e. there is a linear relationship between the fraction of drug-occupied receptors and effect: E = α [AR] (9)

2. The maximal effect is obtained when all receptors are occupied with drug:

max =E α [R ]t (10)

If equations (9) and (10) are combined:

E α [AR] [AR] = = (11) Emax α [R ]t [R ]t

If equation (11) is combined with equation (8), the following relation between effect and drug concentration is obtained: E [A] = (12) Emax KA + [A]

[A] E ⋅ [A] = E = max Multiply both sides by Emax: (13) KA + [A]

It is apparent that here also is found an application of the Michaelis-Menten relation by a description of the concentration-response relation as in the case of enzymatic reactions. Emax (the maximal effect which can be obtained with the drug concerned) corresponds to the enzyme kinetic’s Vmax (the maximal velocity which can be obtained by the reaction). KA (equilibrium dissociation constant) corresponds to the enzyme kinetic’s Michaelis-constant (Km). Emax can be expressed in absolute units, but most often is stated as a relative percentage or fraction (i.e. 100% or 1.0).

A long series of preconditions should be fulfilled before Michaelis-Menten kinetics can be applied: i) one drug molecule should bind to one receptor molecule (a bimolecular reaction), ii) the binding should be reversible, iii) the amount of occupied receptors should be the limiting factor for the effect (in occupation theory; see Figure 6), iv) there should be a linear relationship between the number of occupied receptors and effect, and v) only a negligible portion of the drug mass must be bound to the receptors, (i.e. there is no depletion of the drug, so that [A]total ≈

[A]free).

Concentration

Figure 6 The relation between log concentration, effect and the number of drug-bound receptors. Note: Phase 2 (between 20 % and 80 % of maximum response) is almost linear.

In practice, observed departures from Michaelis-Menten kinetics are often brought about because all the preconditions are not fulfilled. By the use of more sophisticated versions of the Michaelis- Menten equation one can redress this issue, but in the present accounting only the simple formula will be employed.

Equation (13) describes the relation between the concentration of free (non protein-bound) drug at the receptor and the response. This concentration cannot be measured in vivo (at least not easily). The plasma concentration can occasionally be used but usually the total concentration of drug (free + protein bound) is measured and while the plasma concentration relates to the central compartment, it doesn’t say anything immediately about the concentration in a peripheral compartment, where the receptors often are found.

Preconditions for production of a drug effect are such that (i) the drug binds to the receptor (has affinity) and (ii) that this binding triggers a reaction (the drug possesses intrinsic activity). The effect (E) is dependent upon the number of drug-occupied receptors (AR) and the proportionality constant α (intrinsic activity). Intrinsic activity is defined as the ratio between the maximal response (Emax) produced by a test agonist and Emax produced by a full agonist (e.g. the endogenous ligand) via the same receptor. The numerical value for intrinsic activity varies from 0 (for a complete antagonist) to 1 for a full agonist. For a partial agonist: 0 < α < 1.

E produced by test agonist )(activity Intrinsic α)(activity = max

receptor same aagonist vi full aby produced E max produced aby full vi aagonist same receptor

Efficacy is an expression of a drug’s ability to produce a physiological response (e.g. muscle contraction, relaxation, etc.). The designation efficacy is used sometimes synonymously with the maximal effect (see Figure 7) which can be obtained with the drug concerned (Emax). A full agonist is a ligand that can produce the largest maximal effect (efficacy) attainable in a given tissue. By definition, an endogenous agonist for a given receptor is a full agonist. However, it is quite plausible that synthetic agonists could be produced having even greater efficacy than the endogenous agonist, so-called “super-agonists” where α > 1 (e.g. THIP or gaboxadol, is a

GABAA receptor agonist that has greater efficacy than GABA itself on α6 β1 γ2 GABAA receptors). Agonist #1 Emax (efficacy) Agonist #2 100

EC50(potency) 50 Agonist #3

Effect % Ep < Emax

* * * -10 -9 -8 -7 -6 -5 -4 log [agonist concentration] M

Figure 7 Sketch of log concentration-response curves for three drugs with different EC50’s (potencies, shown by colored asterisks) and efficacies (maximal effect). Agonists #1 and #2 are full agonists while #3 is a partial agonist. Note that a partial agonist could possess higher potency (a lower EC50) than a full agonist, although having a lower maximal effect (e.g. Agonist #3 vs. Agonist #2). 8

In functional studies, the EC50 value is also determined (i.e. the agonist concentration which produces half maximal effect) as an expression for a drug’s potency. The potency of a given drug can only be related to that of another drug; e.g. a drug which produces an effect after administration of 5 mg is more potent than a drug which requires 50 mg in order to give the same effect. In other words, potency is a relative concept and what may be considered a potent drug today may not be considered particularly potent a decade from now. It should be emphasized however that a drug’s EC50 is dependent on the drug’s ability both to bind to a receptor (affinity) and to activate the receptor (efficacy). The concepts of maximal effect and potency are illustrated in Figure 7. A drug can be stimulatory (i.e. produce a physiological response), inhibitory, or both. A stimulatory drug is defined as an agonist, an inhibitory drug an antagonist and a drug which can be both is a partial agonist. For most pharmacological agonists there is a corresponding endogenous biological ligand, but it is not always well-identified in every case. Not all drugs which are stimulatory are agonists. They can stimulate directly (via a receptor = agonist) or indirectly (e.g. by inhibition of the breakdown of an endogenous agonist; increasing release or synthesis of an endogenous agonist; by altering the receptor’s sensitivity, etc.). As an example: the drug pilocarpine stimulates cholinergic muscarinic receptors directly, similarly to the endogenous biological agonist acetylcholine, while the drug physostigmine stimulates the cholinergic nervous system indirectly by inhibiting the breakdown of acetylcholine.

Pharmacological antagonism involves antagonism at the receptor level, e.g. mepyramine’s inhibition of histamine’s effects on H1 receptors. Physiological antagonism is a more diffuse concept because it involves two (or more) different agonists/ligands which reduce or oppose each other’s effects by influencing their own individual receptors/target proteins (e.g. activation of two different receptor systems which can interact at different levels in signaling pathway). An example of this is the use of a β-adrenergic stimulator or an anti-cholinergic drug against bronchial asthma, which can be caused by histamine release, and which all acts via different receptor systems in the bronchiole’s smooth musculature. Pharmacokinetic antagonism happens when a drug reduces the concentration of another drug by interacting with its kinetics (i.e. adsorption or elimination). For example, phenobarbital increases hepatic metabolism of warfarin and oral contraceptives. A partial agonist is a drug which binds to a receptor without being able to produce a maximal biological effect at the same magnitude as full agonist in a given tissue, at the same time being able to block the binding of a ligand with larger maximal effect (efficacy) (see Figure 8). An antagonist binds with the same affinity to both the active and inactive forms of the receptor. An inverse agonist is a drug which has a larger affinity for a receptor’s inactive form and thereby produces a diminished biological response, which is typically observed as a reduction in the receptor’s basal activity (i.e. the constitutive activity measured in the absence of any agonist). Note that a true antagonist has no effect upon this basal activity whereas an inverse agonist reduces it (see Figures 8 and 9).

Max. Efficacy 100 Full Agonist

Partial agonist

% Effect % % Effect %

0 Antagonist

Inverse Agonist -50 -10 -9 -8 -7 -6 -5 -4

Log [ligand concentration] M

Figure 8 Concentration-effect characteristics for full-, partial-, inverse agonists and antagonists.

Inactive (resting) state Active state

equilibrium

Antagonist Agonist Inverse agonist

No state Depending upon the agonist A-R* complex activity, partial agonists can: preference ! Does not the basal activity change the the agonist activity equilibrium. Effect: intrinsic activity No Effect

Figure 9 Two-state model. The model is built on the assumption that receptors can exist in two conformational states, namely active and inactive.

With reference to the previously discussed nomenclature, it can be said that an agonist has both affinity and efficacy, while an antagonist has affinity but no efficacy and therefore no intrinsic activity (see Figures 8 and 9). An inverse agonist can be said to have negative efficacy! Many drugs possess both stimulatory and inhibitory properties at the same receptor system but the therapeutic application involves one of the effects. Examples: some β-blockers possess, in addition to the therapeutically useful blocking effects at the receptors, a demonstrated intrinsic stimulatory effect (intrinsic sympathomimetic effect); nalorphine is used as a morphine antagonist, but possesses also morphinomimetic effects; buprenorphine (partial agonist) is used as a painkiller, but possesses both stimulatory and inhibitory properties at the μ-opioid receptor.

Graphic representations of concentration-response relationships

Figure 10 shows on a semi-logarithmic graph scale a log concentration-response curve, where the abscissa is log (or ln) dose (concentration). One obtains a symmetrical S-shaped curve which is approximately linear in the range of 20-80% of maximum response.

Figure 10 Log concentration-response curve versus ln concentration-response curve. Note the difference in the slope (m) of the linear region (Reference nr. 1).

The Michaelis-Menten equation can be mathematically re-expressed as:

⋅ CE E C E = max = Y (14) 50 + CEC Emax - E EC50

If the logarithm of both sides of the equation is taken:

E ( log ( ) = log C - EClog 50 (15) Emax - E

If equation (15) is depicted in a linear co-ordinate system, the so-called Hill plot is obtained (Figure 11), a straight line with slope (Hill coefficient) of one. The Hill plot can thus be used to investigate whether the drug concentration and effect follow the Michaelis-Menten relation since the straight line should have a slope of 1. However, in many instances one does not have prior knowledge of the Hill coefficient for a given concentration-response relation and it could very well be that it differs significantly from unity. In the literature, the so-called modified Hill equation (16) is employed, which is more universally applicable than the Michaelis-Menten equation since it does not assume a Hill coefficient of 1 (see Figures 11 & 12).

⋅ n = E = Emax C n n (16) + EC50 + C

As the simplest explanantion, the Hill coefficient (n) can be an expression of the number of binding places on the receptor for the ligand concerned. One speaks of positive (n > 1; e.g. hæmoglobin oxygen binding) and negative (n < 1; e.g. insulin receptor insulin binding) cooperativity when binding of a ligand/agonist molecule to one binding place increases or decreases, respectively, the affinity of a second binding place for the next ligand/agonist molecule. The Hill coefficient should however be taken with a ‘grain of salt’, since its magnitude in functional experiments involving complicated receptor systems (e.g. G-protein coupled receptors) can be affected by the intracellular signaling pathway, desensitization, etc. Therefore, one should be cautious in its interpretation.

2 E log log C nn ⋅−⋅= log EC50 Hill-Plot max − EE 1 -E)] max 0 -8 -7 -6 -5 -4 log [E/(E -1 log C

-2 Figure 11 Hill plot, which is linear and has slope of n = 1, if the drug concentration and effect follows the Michaelis-Menten relation.

Figure 12 The difference between the Michaelis-Menten (M-M) graph (n=1) and the modified M-M graphs (n>1 and n<1). It is seen that the modified M-M graphs with n>1 have a

steeper rise to Emax (Reference nr. 4).

EC50

100 1 10 Concentration

Unexpected deviations from theory For a large series of drugs, the experimentally obtained results fit very well with simple theories, e.g. anti-cholinergics, anti-histaminergics and the β-blockers. A few examples among the numerous departures from the described model should be mentioned. Kinetic problems can be observed; e.g. the place of action in a peripheral compartment, or effects of active metabolites, or mixed zero and first order elimination kinetics. Some drugs should reach a threshold concentration to produce an effect. Some drugs produce a ‘hit and run’ effect, i.e. the effect lasts long after the drug has been eliminated. Disease can entail changes in receptor sensitivity, affecting the concentration-response relationship of a drug, e.g. increased sensitivity (sensitization) or decreased sensitivity (desensitization or tolerance). Genetic differences can play a role. Possible drug interactions should also be mentioned in this connection. By sudden withdrawal of a drug, in some cases, the symptoms that the drug was used against will worsen compared to the initial symptoms. This is called rebound phenomenon. 13

The modified occupation theory

A modification of the classical occupation theory is provided by Stephenson, when the maximal effect sometimes can be obtained without having all receptors occupied by drug. Furthermore, assumptions about the linearity between drug-receptor complex and effect are too simplistic in many experimental situations (Figure 13).

ten

-Men is ael h chc Mi

Figure 13 The relation between receptor occupation and size of effect (Reference nr. 3).

Stephenson formulated three postulates:

1. The maximal effect of a drug can be obtained without complete occupation of all receptors by drug. 2. The size of the effect is not linearly related to the fraction of drug-occupied receptors. 3. Production of a drug-receptor complex produces a stimulus (S) at a tissue/organ. This stimulus is directly proportional to the fraction of drug-occupied receptors. The effect is an unknown (non-linear) function (f) of the stimulus (S).

This modification (which continues to build upon the classical occupation theory) introduces the concept of intrinsic efficacy (ε), which is specific for an agonist and is defined as the agonist’s ability to produce a stimulus from an individual receptor. However, intrinsic efficacy (ε) must not be confused with intrinsic activity (α). The number of receptors ([R]t) and intrinsic efficacy (ε) represent, respectively, the tissue-dependent and the agonist-dependent elements of agonism. KA is also an agonist-dependent element. 14

⎛ e⋅[A] ⎞ Response S == ff ⎜ ⎟ () ⎜ ⎟ (17) ⎝ K A +[A]⎠

= ]R[e t ⋅ε

efficacy intrinsic efficacy receptor density

This implies that the biological effect can be divided into two phases. In the first phase, drug- receptor binding causes a stimulus S, which is linearly related to the concentration of the drug- receptor complex. In the second phase, this stimulus produces an effect which is an unknown function of the stimulus and is independent of the drug-receptor complex. Therefore, efficacy depends (in addition to being agonist dependent) additionally on the coupling efficiency between the receptor and the stimulus-response mechanism, which is tissue specific. As mentioned previously, the relation between stimulus and effect is an unknown, nonlinear function. The only assumptions tied to this function are that for S = 0, then E (response) = 0, (i.e. f (0) = 0) and the function should also be continuous. Postulate #1 says that the maximal effect can be obtained even with a small fraction of drug-occupied receptors, which has lead to the concept of ‘spare receptors’. High efficacy agonists (strong agonists) can produce maximal effects by only occupying a small portion of the existing receptor population. The rest are ‘spare’ or reserve receptors, i.e. there is an over-abundance of receptors in the tissue concerned. A system where maximal response to an agonist can be obtained by only activating 5% of the total receptor population is said to have a 95% receptor reserve. It is a misunderstanding of the concept of ‘spare receptors’ to assume that they are non-functional receptors. Complete occupation of the receptors is perhaps not necessary for obtaining a maximal response, but all receptors can contribute to the measured response. Notably, this means that the response produced by an agonist can be strengthened in the presence of spare receptors. It is important to emphasize that the general designation ”receptor reserve” not only involves the elements of receptor density and the agonist’s intrinsic efficacy, but also the coupling efficiency between the stimulus and the response mechanisms, (e.g. concentration of effector protein(s)).

By incorporation of the stimulus in the equation (18), it can be seen that if S shall be large when

[AR]/[R]t is small, then the drug’s efficacy, and therefore its intrinsic efficacy, should be large.

Drugs with small intrinsic efficacy may produce an effect which is lower than Emax even when almost all receptors are occupied. These drugs are called partial agonists. Antagonists, which cause no effect, have an intrinsic efficacy (ε) of zero. It is worthwhile noting that postulate #1 doesn’t exclude situations where a drug produces a maximal effect by occupying all receptors. Such a drug would be defined as a partial agonist according to Stephenson.

Previously, the designation EC50 was given as the concentration which produces half of the maximal effect. In the following, EC50 will be defined as the concentration which produces half of Emax for a specific tissue/organ. As a consequence of Stephenson’s postulates, the relation between stimulus and effect, E = f (S), is a property of the tissue/organ in question and is independent from the relation between drug and receptor. Different drugs are as such characterized by their ability to produce a stimulus, while the tissue/organ is characterized by the effect which is produced there. In principle, there consequently can be measured the same effect by two drugs which produce different stimuli. As mentioned earlier, the only preconditions of the function f are that it is continuous and that f (0) = 0. The units for stimulus can thus be whatever is preferred. In an attempt to define a unit for stimulus, Stephenson proposed that a stimulus unit must be able to produce an effect corresponding to half maximal effect for the specific tissue/organ, i.e. f (1) = ½ Emax. By combining equations (8), (15) and (17):

[A] [AR] e = S = e e= (18) [A ] + KA + [A] [R ]t

For S = 1:

][EC ][EC + K e = S = e 50 = 1 ⇒ e = 50 A (19) ][EC + KA + 50 ][EC 50 ][EC

[EC50] can be measured directly from the concentration-response curve for the drug, while KA must be measured from knowledge of the drug-receptor interactions. If efficacy (e) and KA are known, by virtue of equation (19) it is possible to describe the relationship between drug concentration and stimulus. A special case of equation (19) concerns a strong agonist, where

[EC50] << KA :

K e ≈ A (20) 50 ][EC

INTERACTIONS AT THE RECEPTOR LEVEL

Traditionally, antagonists are divided into competitive and non-competitive. Additionally, inhibition can be reversible or irreversible. Reversible competitive antagonists compete with agonists for binding to the same binding site on the receptor (orthosteric), and the antagonist can be displaced (out-competed) from its binding site on the receptor by increasing the agonist concentration. In cases of reversible competitive antagonism, an equilibrium between agonist, antagonist and receptor is obtained (binding is non-covalent, can easily be broken and is of short duration on the molecular scale). In cases of irreversible competitive antagonism, the antagonism can be of a more permanent nature (e.g. covalent bonds are formed) between the receptor and the antagonist such that the antagonist cannot unbind from the receptor, despite increasing concentrations of agonist (i.e. no equilibrium is reached during experimentation). The slow (or non-existing) dissociation of antagonist from the receptor means that there are fewer receptors

available for the agonist. This results in a significant fall in the maximal response (Emax) for the agonist (see Figure 14), especially when there is a situation of low receptor reserve. According to IUPHAR nomenclature, a competitive antagonist produces a concentration dependent, parallel

rightwards shift in the log concentration-response curve for an agonist without changing Emax of

the agonist (see Figure 14). A non-competitive antagonist will reduce Emax (efficacy) without

changing the agonist EC50 value significantly. Uncompetitive antagonism occurs when the antagonist only binds to the activated receptor state (e.g. MK-801 binding at NMDA-R):

[A] + [R] ↔ [AR]* + [U] ↔ [UAR]

Agonist Competitive Orthosteric Antagonist Receptor

Receptor

R R R

R R

ec ec ec

e e e

c c

ep ep ep

ep ep ep Agonist

Allosterisk Non-competitive

to to to

to to Allosteric to

Antagonist

r r r

Antagonist

U ⇔ ⇔ U R AR* UAR 17

Agonist Uncompetitive

In cases of non-competitive antagonism, the agonist and antagonist bind simultaneously to two different binding sites on the receptor (allosteric). Non-competitive antagonists, which affect the receptor function by changing the receptor conformation (i.e. the receptor’s 3D structure), can influence the agonist’s affinity and/or efficacy. This can lead to combined changes in potency and maximal response.

Often, one finds mixed competitive/non-competitive antagonism, since inhibition at lower concentrations is competitive but at higher concentrations is non-competitive, which can be due to the amount of spare receptors in the tissue. The presence of spare receptors in a tissue can hamper the distinction between reversible competitive and non-competitive, or irreversible antagonism. The phenomenon that there is reached a maximal pharmacological response with only a partial occupation of the receptors can be explained, amongst other explanations, by the presence of a large number of receptors in comparison to the coupling proteins (G-proteins). The presence of spare receptors produces, other tings being equal, a larger effect for a given drug concentration.

Increasing incubation time with antagonist E (efficacy) 01 10 100 1000 Emax (efficacy) 100 max 100 0 Control 1 10 min

EC 50 EC50(potency) 5 30 min 50 50 (potency) % Effect % Effect % 10 60 min

100 120 min -9 -8 -7 -6 -5 -4 -10 -9 -8 -7 -6 -5 -4 log [agonist concentration] (M) log [agonist concentration] (M)

Figure 14 Log concentration-response curves for an agonist without (black curve) and in the presence of increasing concentrations of a reversible, competitive antagonist (colored curves; left panel); or a

fixed concentration of an irreversible, competitive antagonist (right panel). Here, Emax is reduced by longer incubation times with an irreversible antagonist (competitive or non-competitive), which indicates

that the system is not at equilibrium. i.e. since [R]free is decreasing with time as the antagonist binds but does not unbind.

Examples of reversible competitive inhibition: H2 blockers (e.g. ranitidine), α1 blockers (e.g. phentolamine), anti-cholinergics (e.g. tubocurarine and atropine), and β1 blockers (e.g. atenolol). Examples of non-competitive inhibition: ketamine’s effect at NMDA receptors, picrotoxin’s effect at GABAA receptors and felodipine’s effect at L-type calcium channels. Examples of irreversible competitive inhibition: phosphostigmine’s effect at acetylcholinesterase, acetylsalicylic acid’s (ASA) at cyclooxygenase, phenoxybenzamine’s effect at α1 receptors and omeprazol’s effects at the K+/H+-ATPase.

Reversible competitive antagonism

With competitive antagonism, the agonist and antagonist react reversibly with the same receptor (A = agonist and B = reversible competitive antagonist):

k1 k3 A + R W AR B + R W BR

k2 k4

[R]t (total number of receptors) = [AR] + [BR] + [R]free

The reaction rate for agonist-receptor complex formation and antagonist-receptor complex formation is, respectively:

d[AR] = k ([A ]) ([R ] - [AR] - [BR]) - k [AR] (21) dt 1 t 2

d[BR] = k ([B ]) ([R ] - [AR] - [BR]) - k [BR] (22) dt 3 t 4

At equilibrium, d[AR]/dt = d[BR]/dt = 0

[A] ([R ]t - [AR] - [BR]) = K A [DR] (23)

[B] ([R ]t - [AR] - [BR]) = K B [BR] (24)

Where KA = k2/k1 and KB = k4/k3. With separation of [BR] in equation (24):

[B ] ([R ]t - [AR]) [BR] = (25) [B ] + K B 19

By substitution of the expression for [BR] from equation (25) into (23):

[A] [R ] = [AR] = t [B] (26) + (1 K A (1 + ) + [A ] K B

According to the definition of a reversible competitive antagonist, the antagonist can be displaced from the receptor by higher concentrations of agonist which means that, all else being equal, one can eventually obtain the same fraction of drug-occupied receptors and thereby the same effect as in the absence of antagonist. Hence, this has also sometimes been referred to as surmountable antagonism in the literature. [AR] [A ] A[ ′] = = = [B [R ]t A + [AK ] ] (27) + (1 K A (1 + ) + A[ ′] K B

If [EC50´] and [EC50] are designated as the agonist concentrations, which give 50% of Emax with and without antagonist, respectively; then equation (28) can be derived from equations (12) and (27) with the assumption that there is a proportionality between the fraction of drug-occupied receptors and the effect (the classical occupation theory). ′ E [EC ] [EC ] = 50 = 50 [B] Emax K A + [EC 50 ] ′ (28) A (1K + ) + [EC 50 ] K B

Thereby follows: ′ [EC50 ] [B] - 1 = (29) [EC50 ] K B

The ratio [EC'50]/[EC50] is designated the dose ratio (dr) and is an important dimension in the characterization of the antagonism. Dose-ratio is the ratio between the concentration of agonist which produces the same effect in the presence and absence of a known concentration of antagonist, [B].

From equation (29) follows: [B] = 1 -dr -dr 1 = (30) KB

Taking the logarithm of both sides:

log -(dr 1) = log [B] - Klog B (31)

In the literature, often the designation pA2 is employed for –log KB. Substituting into equation (31):

log -(dr 1) = log [B] + pA2 (32)

Equation (32) is called the Schild equation. In a Schild graph with log [B] as the x-axis and log

(dr-1) as the y-axis, we obtain a straight line with a slope of 1. The negative of pA2 value (- pA2) is read as the line’s x-intercept (see Figure 15). The bigger pA2, the stronger the antagonist is. Schil plo

2,0

Schild Plot 1,5

-pA pA readread at at x x- intercept - intercept Remember ! 1,0 22 The slope should not be significantly Log (dr-1) Log (dr-1) 0,5 different from 1

0,0 -8,0 -7,5 -7,0 -6,5 -6,0 -5,5 -5,0 log [antagonist] M

Figure 15 Schild graph for measurement of pA2.

What does the Schild equation tell us?

1- The dose ratio is only dependent upon the antagonist’s concentration and its equilibrium constant.

2- The dose ratio is identical for all agonists which act at the same receptor as the antagonist binds to.

3- The dose ratio is independent of the agonist’s characteristics, i.e. the size of the response produced by agonist or the equilibrium constant for the agonist.

Possible causes for deviation from competitive antagonism (Schild slope ≠ 1) )Antagonist is non-competitive (different binding sites)

)Agonist/antagonist undergoes enzymatic breakdown or neuronal uptake (for agonists) ) Equilibrium between antagonist and receptor does not exist; possibly because of inadequate incubation time

) The response is mediated by activation of a heterogeneous population of receptors which exhibit different affinities for the antagonist.

One of the Schild plot’s strengths is its ability to disclose “non-equilibrium steady-state” conditions in experimental preparations, such as: inadequate equilibration time and clearance of drug from the “receptor compartment”. In cases of heterogeneous receptor populations, Schild plots are obtained with different regression lines for the same antagonist in the tissue concerned when different agonists are employed to produce the response.

Schild > 1: probably inadequate equilibration time for antagonist. Repeat analysis with longer time of equilibration for antagonist.

Schild < 1: if it is close to unity (i.e. 0.7-0.9) you can refit regression to unit slope and calculate pKB. Less than 0.7: Heterogeneous receptor population sub-serving the same response observed. Agonist-uptake processes which are saturable.

A chemical non-receptor-mediated response to agonist may augment or potentiate agonist responses (i.e. caused by organ-bath pH) and therefore cause underestimation of the dose ratio (slope < 1) or depress the tissue or otherwise block agonist responses non-specifically and produce overestimation of the dose ratio (slope > 1). Whether or not the slope of the Schild regression deviates by being greater or less than unity clearly depends on the nature of the secondary effect. 22

Irreversible competitive antagonism

With irreversible competitive antagonism there exists a situation where equilibrium between agonist, antagonist and the receptor cannot be obtained. A typical situation would be when the antagonist-receptor complex does not breakdown again after initial formation. The consequence will naturally be that the number of receptors which are available for the agonist will be less than the total number which exists in the tissue/organ. This is sometimes referred to as insurmountable antagonism. Irreversible competitive antagonists are used in research with regards to determining the equilibrium dissociation constant of an agonist.

If q represents the fraction of free receptor molecules in the presence of an irreversible competitive antagonist, the concentration of agonist-receptor complex can be described with the help of equation (7), since 0 < q < 1:

[R q [R ]t [A] [AR] = (33) KA + [A]

Accordingly, the concentration-effect relation will, by use of the classical occupation theory, be described by:

q [A] = E = Emax (34) [A ] K A + [A]

Still, the classical occupation theory’s assumption of proportionality between effect and the size of drug-receptor complex concentration will not always hold. Thus, it will in these situations not be possible to read KA directly from the concentration-response curves. For measurement of KA under these circumstances, Furchgott and Bursztyn have described an experimental method where there are no assumptions made about the how receptor occupancy (or receptor binding) by agonist is linked to the observed effect (response). This means that we don’t have an idea of the mechanism involved in producing the response after receptor occupancy by the agonist (i.e. it’s a ‘black box’ situation). The method is based on the use of an irreversible competitive antagonist which binds to the same receptor as the agonist. The only assumption is that the extent of effect depends upon the size of the drug-receptor complex concentration (the degree of receptor occupancy), which means that if one measures the same effect with and without the irreversible antagonist, the drug-receptor complex concentration must be the same in both situations. From equation (7) we obtain:

[R ] [A] q [R ] ′]A[ t = t (35) [A ] + KA + [A] KA + ′]A[

where q is the fraction of free receptors and [A'] and [A] are the concentrations of agonist which give the same effect with and without irreversible antagonist.

Rearranging equation (35): 1 1 1 1/q - 1 = = + (36) [A] q ′]A[ K A

Thus, if concentration-response curves are made both with and without the irreversible antagonist, comparable values of [A'] and [A] giving the same effect (equiactive concentrations) can be determined. With the use of equation (36), 1/[A] can be plotted against 1/[A'] in a linear coordinate system (see Figure 16). The slope of this straight line will thus be 1/q, the reciprocal of

the fraction of free receptors, while the y-intercept will be: (1/q - 1)/KA.

) 1 - Slope ( Slope - 1 ) K A = -y erceptint (37)

M 30 8

1/A x 10 1/A 10

0 0 5 10 15 1/A' x 108 M

Figure 16 An example of the double reciprocal “Furchgott-Bursztyn” graph for measurement of KA.

The method has been employed for measurement of KA for different muscarinic agonists on isolated rabbit diaphragm with the use of dibenzamine as the irreversible antagonist. As well, the method has been used for measurement of KA for catecholamines at α-adrenergic receptors. The method is however generally applicable if one has an irreversible antagonist which can inactivate a fraction of the receptors. The advantage is that, in contrast to the situation with reversible competitive antagonists, no assumption of linearity is made between the effect and the size of the agonist-receptor complex concentration. Unfortunately, a major limitation of this method is that irreversible antagonists are not readily available for all receptor types. As far as the Furchgott and Bursztyn method is concerned, it should be mentioned that the signal transduction (i.e. the receptor-effector coupling) can have an influence on the size of the KA value of the agonist.

A second frequently used method for measurement of an agonist’s KA value is with in vitro binding studies, with which are associated some caveats that should be recognized. In in vitro binding studies one typically is measuring the affinity of the agonist for the inactivated/desensitized receptor conformation, which does not contribute to the measured functional response. Moreover, agonists tend to a show higher affinity for the inactivated/desensitized receptor in comparison to the active conformation of the receptor, which explains the discrepancy between KA values determined from functional experiments vs. binding experiments. Nevertheless, this method has proven to be very useful in studies of drug structure- activity relationships and in the guidance of rational drug design.

Partial agonism

As discussed earlier, partial agonists are characterized by the fact that they do not produce as large a maximal effect as is seen with a full agonist, even with complete receptor occupation. The sub-maximal response produced by a partial agonist can be explained by the fact that only a small fraction of the occupied receptors are converted into the active form. As previously mentioned, a partial agonist can exhibit both agonistic and antagonistic properties in the presence of a full agonist, which are dependent upon the basal activation state in the tissue concerned (see Figure

9). It is therefore not possible to measure KA from concentration-response curves of partial agonists. Consequently, Barlow and Waud, independently of one another, have proposed a method for determination of the KA for a partial agonist.

The method is build upon the same principle as that with the irreversible antagonist, since the size of the drug-receptor complex concentration should be related to the effect. A concentration- response curve is recorded for both a full agonist and the partial agonist one wishes to investigate. It is important that the same tissue preparation is used for both concentration-response curves so that there is no difference in receptor density and/or stimulus coupling efficiency.

Both ligands should of course bind to the same receptor. For a given level of response, one thereafter determines the comparative concentrations (equiactive concentrations) of full and partial agonist giving the same response. The fraction of drug-occupied receptors for the full and partial agonist will be, respectively:

[AR] [A] [PR] [P] = and = (38) [R ] K At + [A] [R ] KPt + [P]

where [P] is the concentration of partial agonist, [PR] the concentration of partial agonist-receptor complex, KA the equilibrium dissociation constant of the full agonist and KP the equilibrium dissociation constant of the partial agonist. By applying Stephenson’s definitions under the modified occupation theory, the effect is a function of the stimulus, which again is proportional to the fraction of drug-occupied receptors:

[AR] [PR] (e f = E = f (e ) and E = f (e ) A A P p (39) [R]t [R]t

where EA and EP is the effect of, respectively, the full agonist and the partial agonist and eA and eP are their respective efficacies.

Since the function is assumed to be continuous, SA = SP:

[A] [P] e = e A P (40) [A ] + KA + [A] KP + [P]

If it is assumed that [A] occupies few receptors, so that [A] << KA, equation (40) can be simplified:

[A] [P] eA = e P (41) KA KP + [P]

Taking the reciprocal of equation (41):

K K + [P] A = P (42) eA [A] eP [P] or, 1 Ke 1 e = = PA + A (43) [A] eP KA [P] eP KA

Equiactive concentrations (equivalent concentrations which give the same effect) of the full and partial agonist are measured from the respective concentration-response curves (Figure 17). By plotting the reciprocal of the full agonist concentration against the reciprocal of the partial agonist concentration one obtains a straight line with slope and y-intercept as given in equation (44) (Figure 17). The equilibrium dissociation constant for the partial agonist can be calculated from equation (44).

eA K P

Slope eP K A = = = K P − erceptinty eA (44)

eP K A

Figure 17 An example of the measurement of a partial agonist’s equilibrium dissociation constant, KA . [A] and [P] represent equiactive concentrations of, respectively, the full and partial agonist. The same tissue preparation is employed for both concentration—response curves (Reference nr. 6).