Download Pharmacodynamics

Pharmacodynamics
Chapter 2
Concentration/Response Relationship
• Can meas drug/
receptor binding
directly
– Ex:
Radioimmunoassay
• Ex: radioactive
drug binding badrenoreceptors 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
k+1
• For agonist: A + R  AR
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
k+1
Rxn: A + R  AR
k-1
• 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
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 bellshaped 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 = isoprenaline
Antagonist = propranolol
Tissue = 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 mmol/L
• Partial agonist  shallow curve
– Max response > 10 mmol/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
b
DR  DR*
a
 b/a 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).