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 ARk+1

k-1

• A = xA = drug concentration

• R = free receptor = Ntot – NA, where

– Ntot = total number receptors for agonist

– NA = number occupied receptors

• AR = NA = drug/receptor complex

• k+1 = rate const forward (assoc’n) rxn• k-1 = rate const reverse (dissoc’n) rxn

• Rate forward rxn = k+1(xA)(Ntot-NA)

• Rate reverse rxn = k-1(NA)

• Assume – xA large

• Binding doesn’t appreciably reduce xA

– Magnitude response related to number of receptors occupied

Rxn: A + R AR• At equilib:

k+1(xA)(Ntot-NA) = k-1(NA)

• (NA/Ntot) = proportion receptors occupied (= pA)

• pA= xA/[xA + (k-1/k+1)]

• KA = k-1/k+1

• pA = (xA/KA)/(xA/KA+1)– Hill-Langmuir equation

k+1

k-1

KA

• 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

KA (cont’d)

• Describes affinity of drug for receptor– Higher KA lower affinity of drug for

receptor

– Lower KA higher affinity of drug for receptor

• Lower KA identifies lower concent given level of occupancy– And given response

• Changing x axis to log scale converts hyperbola to sigmoid curve– Better visualize KA value

• In direct binding experiments (in vitro), use sim math derivations

• Can know– Total number binding sites– xA

• Can measure – Amount bound

• Plot amt bound vs. amt bound/xA (Scatchard plot)– Straight line– Straight line– Slope = KA

Your Book…

• D + R DR ( DR* Response)

• D = drug concentration (= xA)

• DR = number of occupied receptors (= NA)

• RT= total number agonist receptors (=Ntot )

• DR/RT = proportion receptors occ’d (= pA) – Also called fractional occupancy

• KD = affinity constant (= KA)

• [DR]/[RT] = [D]/([D] + KD)– “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 Emax = max response can be prod’d– Replaces max binding

• Use C = drug concentration (dose)

• Calculate EC50 = concent drug prod’g 50% max effect– Sim to KA

– OR Book: calc KD (= KA) • Affinity constant

• Curve equation: E = C____ Em C + EC50

• EC50 may equal KA (or KD) or not

• Use of log scale for Dose sigmoid curve– More linear region

– Easier to visualize EC50 (or KA or KD)

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]/[RT]=[D]/{[D]+KD(1+[B]/KB)}

• Where– [B] = antagonist concent– KB = antagonist affinity for receptor

• Presence of competitive antagonist alters agonist affinity by 1+[B]/KB

– 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]/KB

– Can be used to calculate KB

Agonist = isoprenalineAntagonist = propranololTissue = guinea-pig atria

Noncompetitive Antagonists

• May have extremely high KB (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 response @

~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 acting @ 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 (KD)– Common to have spare receptors, so

commonly EC50 < KD

• 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).