PHARMACODYNAMICS Receptor Pharmacology 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 ii 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 1 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 [A][R] (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: [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] + k−1 ) t ) (6) 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) KA + [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 KA + [A] 3 t -pKA 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. 4 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). 5 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: Emax = 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] 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.