Pharmacodynamics Chapter 2

Concentration/Response Relationship Can meas drug/ receptor binding directly –Ex: Radioimmunoassay Ex: radioactive drug binding  - adrenoreceptors in cardiac cell membr’s at equilibrium (steady state) Find nonspecific binding –Can be subtracted

Low concent’s: specific binding incr linear Higher concent’s: binding diminishes Highest concent’s: no further binding –Hyperbolic relationship –What does this remind you of?

Scatchard Plot –Y axis bound/free receptors –Concent on log scale  linear plot –Easier calc’n Bmax = max binding capacity KA=affinity of drug for receptor

The Math… Receptor theory based on Law of Mass Action –Rate chem rxn proportional to prod concent’s of reactants (rate law) At equilib, rate forward rxn = rate reverse rxn For agonist: A + R  AR k+1 k-1

A = x A = drug concentration R = free receptor = N tot – N A, where –N tot = total number receptors for agonist –N A = number occupied receptors AR = N A = drug/receptor complex k+1 = rate const forward (assoc’n) rxn k-1 = rate const reverse (dissoc’n) rxn Rate forward rxn = k+1(x A )(N tot -N A ) Rate reverse rxn = k-1(N A )

Assume –x A large Binding doesn’t appreciably reduce x A –Magnitude response related to number of receptors occupied

Rxn: A + R  AR At equilib: k+1(x A )(N tot -N A ) = k-1(N A ) (N A /N tot ) = proportion receptors occupied (= p A ) p A = x A /[x A + (k-1/k+1)] K A = k-1/k+1 p A = (x A /K A )/(x A /K A +1) –Hill-Langmuir equation k+1 k-1

KAKA Equilibrium Constant Char of drug and receptor = k-1/k+1 –For drug binding to receptor: rate const reverse rxn/rate const forward rxn –How quickly drug binds receptor; how long stays bound Numerically equals concent drug req’d to occupy 50% of receptor sites

K A (cont’d) Describes affinity of drug for receptor –Higher K A  lower affinity of drug for receptor –Lower K A  higher affinity of drug for receptor Lower K A identifies lower concent  given level of occupancy –And given response

Changing x axis to log scale converts hyperbola to sigmoid curve –Better visualize K A value

In direct binding experiments (in vitro), use sim math derivations Can know – Total number binding sites – x A Can measure –Amount bound Plot amt bound vs. amt bound/x A (Scatchard plot) –Straight line –Slope = K A

Your Book… D + R  DR (  DR*  Response) D = drug concentration (= x A ) DR = number of occupied receptors (= N A ) R T = total number agonist receptors (=N tot ) DR/R T = proportion receptors occ’d (= p A ) –Also called fractional occupancy K D = affinity constant (= K A )

[DR]/[R T ] = [D]/([D] + K D ) –“Proportion of bound drug, relative to max that can be bound, equals drug concent divided by drug concent plus affinity constant” –= 0 when no drug bound –= 1 when all receptors occupied

Clinically Can’t isolate receptors –So meas biological response –Suggests drug agonists act by binding to distinct class receptors w/ char affinity for drug –Quantify amt drug nec  response Can’t meas concent drug at receptor –So use dose –Relationship between concentration/dose -- next lecture

Dose/response curves can’t meas direct affinity of agonist drugs for receptors –Physio response complex –Ex: blood pressure response due to dependent variables Cardiac output Blood vessel constriction Blood vessel dilation Baroreceptor reflex

Use E = effect observed –Replaces amt bound Use E max = max response can be prod’d –Replaces max binding Use C = drug concentration (dose) Calculate EC 50 = concent drug prod’g 50% max effect –Sim to K A –OR Book: calc K D (= K A ) Affinity constant

Curve equation: E = C____ Em C + EC50 EC 50 may equal K A (or K D ) or not Use of log scale for Dose  sigmoid curve –More linear region –Easier to visualize EC 50 (or K A or K D )

If All Or None Endpoint Quantal responses Tells individual variability to drug among population Get bell- shaped curve

Competitive Antagonists Most common antagonism Most direct mech of drug decr’g effectiveness of endogenous agonist or of another drug Antagonist binds receptor but does not activate it –Chem’ly similar to agonist

Receptor binds only one mol at time –Antagonist competes w/ agonist Incr’d [agonist] restores tissue response to agonist –Antagonism “surmountable” If [antagonist] fixed, log concent/effect curve for agonist shifts right –No change in slope –No change in max response

When both agonist, antagonist present, must include antagonist concent and affinity for receptor in fractional occupancy eq’n: [DR]/[R T ]=[D]/{[D]+K D (1+[B]/K B )} Where –[B] = antagonist concent –K B = antagonist affinity for receptor Presence of competitive antagonist alters agonist affinity by 1+[B]/K B –What happens at high [B]? –What happens if [D] increased?

When both agonist/antagonist present, that w/ higher concent rel to its affinity const will dominate Magnitude of rightward shift “dose ratio” –Calc add’n agonist w/ varied concent’s antagonist –Ratio by which agonist must be incr’d to overcome competition by antagonist –Dependent on [antagonist]/K B –Can be used to calculate K B

Agonist = isoprenaline Antagonist = propranolol Tissue = guinea-pig atria

Noncompetitive Antagonists May have extremely high K B (wins competition) Mostly irreversible competitors –Mostly alkylating agents –Highly reactive functional grps –Covalently bind receptors  irreversible, insurmountable antagonism –Decr number of available receptors  decr’d agonst max response

Partial Agonists In real life, agonist act’n of receptor graded (not all/nothing) Full agonists  max response –Largest response tissue capable of Partial agonists  submax response Diff not nec related to binding affinity –Rather, relationship between occupancy, response impt

Full agonist  steep occupancy/response curve –Full ~20% occupancy Partial agonist  shallow curve –100% occupancy  ~40% response

Full agonist  steep concent/response curve –Max response 0.2  mol/L Partial agonist  shallow curve –Max response > 10  mol/L

Describes “efficacy”= ‘strength’ of single drug-receptor complex in evoking response of tissue –Proportion receptors act’d when occupied by partic agonist Diff responses not understood. Impt: –Number of receptors –Nature of coupling agonist/receptor Affinity

For D + R  DR  DR*  Response Tendency for DR  DR* depends on second equilib const DR  DR*  /  ranges from 0  1 –Antagonist ratio = 0 (no act’n) –Weak agonist ratio low –Strong agonist ratio approaches 1  

In vivo, receptors may show “constitutive act’n” –Conform’l change to R* w/out ligand binding –Agonist encounters equilib mixture R  R* Some agonists have higher affinity for R* –Binding  almost all R now in R*  max act’n  max response –So classified as strong agonist

Some agonists have higher affinity for R –Not as much effect seen –May even shift equilib toward R (negative efficacy) Some agonists don’t prefer R or R* –Natural equilib undisturbed –Drug acts as competitive antagonist by inhibiting response to full agonists same receptor Full agonist has less chance of shifting R  R* maximally

Spare Receptors Max response elicited by [agonist] that doesn’t occupy all avail receptors Exper’l: high [agonist] prod’s max response in presence of irrev antagonist Receptors may be extra (spare) in number –Make tissue more sensitive to agonist w/ no change in char affinity of agonist for receptor –Now affinity of agonist AND total # receptors impt to response

Mostly due to biochem amplification steps beyond receptor occupancy EC50 may be < concent  ½ max occupancy (K D ) –Common to have spare receptors, so commonly EC50 < K D Shifts concent/response curve to left –Degree of shift proportional to proportion of spare receptors

Results in diff tissue sensitivities to same agonist –Diff tissues have diff #’s spare receptors for same agonist –  agonist w/ full efficacy in one tissue, partial efficacy in another “Intrinsic activity” defines agonist effect in partic tissue Impt in all-or-none responses –Smooth muscle contraction –Cardiac muscle contraction

Logarithmic concent-response curves for a single agonist acting on the same receptor subtype in tissues with different proportions of spare receptors (A, B, C, and D)  muscle contraction in vitro. Note all tissues show same max response to drug (intrinsic activity). The agonist shows highest potency (lowest EC50) at tissue with greatest proportion of spare receptors (A), and lowest potency at tissue with lowest proportion of spare receptors (D).