Download The Rational Use of Drugs - Part 4

WHAT IS THE RELATIONSHIP
BETWEEN AMOUNT OF DRUG IN
THE BODY AND THE EFFECT OF
THE DRUG?
WHY BE CONCERNED ABOUT
DOSE-EFFECT RELATIONSHIPS?
DOSE-EFFECT RELATIONSHIPS:
• Predict the effects of changing the dose.
• Reveal the necessary trade-offs between
efficacy and adverse effects.
• Facilitate comparisons of alternative medications
for the same indication.
• Enhance understanding of how best to use receptor blockers.
WHAT DETERMINES THE
DOSE-EFFECT RELATIONSHIP?
The Dose-Response Causal Chain
DOSE OF
DRUG
[DRUG] AT
TARGET SITE
[DRUG-RECEPTOR COMPLEX]
RESPONSE
WHAT IS THE RELATIONSHIP
BETWEEN DOSE OF DRUG AND
[DRUG] AT TARGET SITE ?
DOSE OF
DRUG
Linear
[DRUG] AT
TARGET SITE
As a rough approximation, the relationship
between dose of drug and [drug] is
more-or-less linear at a specified
time after drug administration.
[DRUG]
DOSE
WHAT IS THE RELATIONSHIP
BETWEEN [DRUG-RECEPTOR COMPLEX]
AND RESPONSE?
CONCENTRATION OF
DRUG-RECEPTOR
COMPLEX
Linear
RESPONSE
As a rough approximation, the relationship
between concentration of drug-receptor
complex and response to the drug is
more-or-less linear.
RESPONSE
[DRUG-RECEPTOR]
WHAT IS THE RELATIONSHIP
BETWEEN [DRUG] AT TARGE SITE
AND [DRUG-RECEPTOR COMPLEX]?
[DRUG] AT
TARGET SITE
Non-Linear
[DRUG-RECEPTOR COMPLEX]
The relationship between [Drug] at target
site and [Drug-Receptor Complex]
is not linear!
WHAT DETERMINES THE
DOSE-EFFECT RELATIONSHIP?
Linear
DOSE OF
DRUG
Non-Linear
[DRUG] AT
TARGET SITE
Linear
CONCENTRATION OF
DRUG-RECEPTOR
COMPLEX
RESPONSE
In the causal chain between dose of drug and response, the dominant
non-linear step is the formation of the drug-receptor complex.
Therefore, it is this step that mainly determines the shape of the
dose-effect and the concentration-effect
relationships!!
WHAT IS THE RELATIONSHIP BETWEEN
[DRUG] AND [DRUG-RECEPTOR]?
[R]
+
[D]
[R-D]
By Law of Mass Action:
[R]free x [D]free/[R-D] = KD (Equation #1)
(Where KD is the equilibrium dissociation constant)
By Conservation of Mass:
[R]free + [R-D] = [R]total (Equation #2)
Rearranging equation #2 gives:
[R]free = [R]total - [R-D] (Equation #3)
WHAT IS THE RELATIONSHIP BETWEEN
[DRUG] AND [DRUG-RECEPTOR]?
[R]
+
[D]
[R-D]
Substitution of equation #3 into equation #1 gives:
([R]total - [R-D]) x [D]free/[R-D] = KD (Equation #4)
Rearranging equation #4 gives:
[R-D] = ([R]total x [D]free)/([D]free + KD) (Equation #5)
WHAT IS THE RELATIONSHIP BETWEEN
[DRUG] AND [DRUG-RECEPTOR]?
[R]
+
[D]
[R-D]
Note that equation #5 gives explicit relationship between [R-D],
the dependent variable, and [D]free, the independent variable:
[R-D]
=
[R]total x [D]free
[D]free + KD
WHAT IS THE RELATIONSHIP BETWEEN
[DRUG] AND [DRUG-RECEPTOR]?
[D]free versus [R-D]
150
y-axis is [R-D]
[D-R]
[D-R]
150
Log [D]free versus [R-D]
100
50
0
y-axis is [R-D]
100
50
0
250
500
750
[DRUG]free
1000
1250
0
0.01
0.1
1
10
100
1000 10000
[DRUG]free
Graphs were computer generated using equation #5
with [R]total = 100 and KD = 10
WHAT IS THE RELATIONSHIP BETWEEN
[DRUG] AND [DRUG-RECEPTOR]?
[R]
+
[D]
[R-D]
A plot of [D]free versus [R-D] is hyperbolic
A plot of log [D]free versus [R-D] is sigmoidal
WHAT IS THE
CONCENTRATION-EFFECT (RESPONSE)
RELATIONSHIP?
If we assume that the response is proportional to [R-D], then:
Response = m x [R-D] (Equation #6)
and
Maximal Response = m x [R-D]maximal = m x [R]total (Equation #7)
(where m is the proportionality constant)
WHAT IS THE
CONCENTRATION-EFFECT (RESPONSE)
RELATIONSHIP?
Substitution of equations #6 and #7 into equation #5 gives
equation #8:
Response
=
Maximal Response x [D]free
[D]free + KD
WHAT IS THE
CONCENTRATION-EFFECT (RESPONSE)
RELATIONSHIP?
[D]free versus Response
150
y-axis is Response
Response
Response
150
Log [D]free versus Response
100
50
0
0
250
500
750
[DRUG]free
1000
1250
y-axis is Response
100
50
0
0.01
0.1
1
10
100
1000 10000
[DRUG]free
Graphs were computer generated using equation #8 with
maximal response = 100 and KD = 10
WHAT IS THE
CONCENTRATION-EFFECT (RESPONSE)
RELATIONSHIP?
[R]
+
[D]
[R-D]
Response
A plot of [D]free versus response is hyperbolic
A plot of log [D]free versus response is sigmoidal
WHAT IS THE
CONCENTRATION-EFFECT (RESPONSE)
RELATIONSHIP?
Let:
We Know That:
[D]free
Response
=
=
KD
Maximal Response x [D]free
[D]free + KD
Substituting
KD for [D]free:
Response
=
Maximal Response x KD
2KD
Simplifying:
Response
=
1/2 Maximal
Response
WHAT IS THE
CONCENTRATION-EFFECT (RESPONSE)
RELATIONSHIP?
Let:
We Know That:
Response
Response
=
1/2 Maximal
Response
Maximal Response x [D]free
=
[D]free + KD
Substituting
½ Maximal Response
For Response
Simplifying:
1/2 Maximal
Response
=
Maximal Response x [D]free
[D]free + KD
[D]free
=
KD
WHAT IS THE
CONCENTRATION-EFFECT (RESPONSE)
RELATIONSHIP?
Response = 1/2 Maximal Response
[D]free = KD
(Equivalence #9)
Response
150
y-axis is Response
100
50
0
0.01
0.1
1
10
100
[DRUG]free
Maximal Response
The [drug] which causes 1/2 maximal response
is called the EC50 and corresponds
to the KD if there is a linear
relationship between
[D-R] and response.
1000 10000
EC50
1/2 Maximal Response
WHAT IS THE
CONCENTRATION-EFFECT (RESPONSE)
RELATIONSHIP?
Since EC50 corresponds to KD, can substitute EC50 for
KD in equation #8 to give equation #10:
Response
=
Maximal Response x [D]free
[D]free + EC50
WHAT IS THE
CONCENTRATION-EFFECT (RESPONSE)
RELATIONSHIP?
Response
=
Maximal Response x [D]free
[D]free + EC50
Empirically, it has been found that equation #10 (above) describes the
concentration-effect relationship for many drugs, even
when the assumption of linearity between [R-D] and
response does not hold.
WHAT IS THE
CONCENTRATION-EFFECT (RESPONSE)
RELATIONSHIP?
Response
=
Maximal Response x [D]free
[D]free + EC50
When the assumption of linearity does not hold, the EC50 no longer
approximates the KD. For example, the EC50 will be
much smaller than the KD when
“spare receptors” are present.
A tissue is said to express “spare receptors” when only a small fraction
of the receptor population must be occupied by drug to
give a maximal response.
WHAT IS THE
CONCENTRATION-EFFECT (RESPONSE)
RELATIONSHIP?
Response
=
Maximal Response x [D]free
[D]free + EC50
The term “potency” refers to the EC50 of a drug. The lower the EC50,
the greater the potency. A low KD and a high number of
spare receptors increases the potency of a drug.
WHAT IS THE
CONCENTRATION-EFFECT (RESPONSE)
RELATIONSHIP?
Response
=
Maximal Response x [D]free
[D]free + EC50
The term “efficacy” refers to the maximal response of a drug. The greater
the maximal response, the greater the efficacy. The more effectively
a drug engages signal-transduction systems in a cell per unit
receptor occupied, the greater is the efficacy of that drug.
WHAT IS THE
CONCENTRATION-EFFECT (RESPONSE)
RELATIONSHIP?
Maximal Response
To Agonist A
=, <, or >
Maximal Response
To Agonist B
Drugs that activate a given type of receptor may or may not do so equally,
i.e., the maximal response elicited by a given drug may be
the same as, less than or more than another drug
in the same pharmacological class.
WHAT IS THE
CONCENTRATION-EFFECT (RESPONSE)
RELATIONSHIP?
The “Best in Class” is called a “full agonist”, and any drug
that generates a maximal response equal to the “Best in Class” is
also referred to as a “full agonist.”
Assume:
Assume:
Agonist A is “Best in Class”, i.e., no other
agonist induces a greater maximal effect.
Maximal Response
to Agonist A
=
Maximal Response
to Agonist B
Both Agonist A and agonist B are “full agonists.”
WHAT IS THE
CONCENTRATION-EFFECT (RESPONSE)
RELATIONSHIP?
Agonist A
Response
150
Agonist B
y-axis is Response
100
50
0
0.01
0.1
1
10
Dose
100
1000 10000
Concentration of Agonist
Agonist A and agonist B
are both full agonists.
However, agonist A is
more potent than agonist B.
WHAT IS THE
CONCENTRATION-EFFECT (RESPONSE)
RELATIONSHIP?
Any drug that generates a maximal response less than that elicited
by the “Best in Class” is referred to as a
“partial agonist.”
Assume:
Assume:
Agonist A is “Best in Class”, i.e., no other
agonist induces a greater maximal effect.
Maximal Response
to Agonist A
>
Maximal Response
to Agonist B
In this case agonist B is a “partial agonist.”
WHAT IS THE
CONCENTRATION-EFFECT (RESPONSE)
RELATIONSHIP?
Full Agonist A
Response
150
Partial Agonist B
y-axis is Response
100
50
0
0.01
0.1
1
10
Dose
100
1000 10000
Concentration of Agonist
Agonist A is a full agonist and
agonist B is a partial agonist.
However, agonist A and
agonist B have equal
potency.
WHAT IS THE
DOSE-EFFECT (RESPONSE)
RELATIONSHIP?
[Drug]free = dose/volume (Equation #11)
and
EC50 = ED50/volume (Equation #12)
(where dose is the amount of the drug in the body at
some time after drug administration)
(where volume is the apparent volume in which the drug is dispersed)
(where ED50 is the dose of drug that generates an EC50)
WHAT IS THE
DOSE-EFFECT (RESPONSE)
RELATIONSHIP?
Substitution of equations #11 and #12 into equation # 10 gives
equation #13:
Response
=
Maximal Response x Dose
Dose + ED50
WHAT IS THE
DOSE-EFFECT (RESPONSE)
RELATIONSHIP?
Dose versus Response
150
y-axis is Response
Response
Response
150
Log Dose versus Response
100
50
0
0
250
500
750
Dose
1000
1250
y-axis is Response
100
50
0
0.01
0.1
1
10
100
1000 10000
Dose
Graphs were computer generated using equation #13 with
maximal response = 100 and ED50 = 10
DOSE
[R]
+
WHAT IS THE
DOSE-EFFECT (RESPONSE)
RELATIONSHIP?
[D]
[R-D]
Response
A plot of DOSE versus response is hyperbolic
A plot of log DOSE versus response is sigmoidal
WHAT IS THE
DOSE-EFFECT (RESPONSE)
RELATIONSHIP?
Response = 1/2 Maximal Response
Response
150
y-axis is Response
100
Dose = ED50
The dose which causes 1/2 maximal response is
called the ED50. Although the ED50 is affected
by the KD and EC50 it is greatly influenced
by the apparent volume in which
the drug is distributed.
50
ED50 is never equal to EC50 or KD!
0
0.01
0.1
1
10
Dose
Maximal Response
100
1000 10000
ED50
1/2 Maximal Response
WHAT IS THE EFFECT OF DRUGS THAT BLOCK
DRUG-RECEPTOR INTERACTIONS OR THAT
INHIBIT SIGNAL TRANSDUCTION
MECHANISMS ON THE DOSERESPONSE CURVE?
[R]
+
[D]
[R-D]
BLOCKING DRUG
Response
WHAT IS THE EFFECT OF BLOCKING
DRUGS ON CONCENTRATION-RESPONSE CURVES?
- Drug Antagonist
Response
150
+ Drug Antagonist
y-axis is Response
SURMOUNTABLE
ANTAGONIST
100
50
0
0.01
0.1
1
10
Dose
100
1000 10000
Concentration of Agonist
WHAT IS THE EFFECT OF BLOCKING
DRUGS ON CONCENTRATION-RESPONSE CURVES?
CHARACTERISTICS OF SURMOUNTABLE ANTAGONIST:
• Produces parallel shift in concentration-response curve of agonist
• Full effect of agonist can be restored by increasing
concentration of agonist
WHAT IS THE EFFECT OF BLOCKING
DRUGS ON CONCENTRATION-RESPONSE CURVES?
MOST COMMON MECHANISM OF SURMOUNTABLE
ANTAGONISM:
• Competitive interaction between agonist (potency and efficacy)
and antagonist (potency but no or little efficacy)
at binding site on receptor
WHAT IS THE EFFECT OF BLOCKING
DRUGS ON CONCENTRATION-RESPONSE CURVES?
Population of Inactive Receptors
WHAT IS THE EFFECT OF BLOCKING
DRUGS ON CONCENTRATION-RESPONSE CURVES?
Add an excess of high potency agonist molecules
WHAT IS THE EFFECT OF BLOCKING
DRUGS ON CONCENTRATION-RESPONSE CURVES?
Allow system to reach equilibrium
WHAT IS THE EFFECT OF BLOCKING
DRUGS ON CONCENTRATION-RESPONSE CURVES?
Add some antagonist molecules
WHAT IS THE EFFECT OF BLOCKING
DRUGS ON CONCENTRATION-RESPONSE CURVES?
Allow system to reach new equilibrium
WHAT IS THE EFFECT OF BLOCKING
DRUGS ON CONCENTRATION-RESPONSE CURVES?
It can be shown mathematically that the net effect of a competitive
antagonist is to increase the apparent KD, or said differently
to decrease the apparent potency of the agonist.
Response
=
Maximal Response x [D]free
[D]free + apparent KDagonist
Where apparent KDagonist = (1 + [Antagonist]/KDantagonist) x actual KDagonist
WHAT IS THE EFFECT OF BLOCKING
DRUGS ON CONCENTRATION-RESPONSE CURVES?
Agonist Alone
Response
150
Agonist + Competitive Antagonist
y-axis is Response
100
Note apparent shift in
EC50 for the agonist.
50
0
0.01
0.1
1
10
Dose
100
1000 10000
Concentration of Agonist
WHAT IS THE EFFECT OF BLOCKING
DRUGS ON CONCENTRATION-RESPONSE CURVES?
- Drug Antagonist
Response
150
+ Drug Antagonist
y-axis is Response
INSURMOUNTABLE
ANTAGONIST
100
50
0
0.01
0.1
1
10
Dose
100
1000 10000
Concentration of Agonist
WHAT IS THE EFFECT OF BLOCKING
DRUGS ON CONCENTRATION-RESPONSE CURVES?
CHARACTERISTICS OF INSURMOUNTABLE ANTAGONIST:
• Produces non-parallel shift in concentration-response curve of agonist
• Full effect of agonist cannot be restored by increasing
concentration of agonist
WHAT IS THE EFFECT OF BLOCKING
DRUGS ON CONCENTRATION-RESPONSE CURVES?
MOST COMMON MECHANISMS OF INSURMOUNTABLE
ANTAGONISM:
• Competitive but irreversible binding of antagonist to
binding site on receptor
• Allosteric modulation of receptor by antagonist so as to
attenuate coupling of receptor to signal transduction
• Blockade of signal transduction “downstream” of receptor
WHAT IS THE EFFECT OF BLOCKING
DRUGS ON CONCENTRATION-RESPONSE CURVES?
PHENOMENON
SURMOUNTABLE
ANTAGONISM
100
50
0
0.01
0.1
1
10
100
INSURMOUNTABLE
ANTAGONISM
150
Response
Response
150
100
1000 10000
50
0
0.01
Dose
0.1
1
10
100
1000 10000
Dose
Concentration of Agonist
Concentration of Agonist
MECHANISM
Reversible Competitive Interaction
If spare receptors & right dose & time
If spare receptors & right dose
If just the right type
Irreversible Competitive Interaction
Blockade of Signal Transduction
Allosteric Modulation
WE HAVE BEEN DISCUSSING CONCENTRATIONAND DOSE-RESPONSE CURVES WITHIN AN INDIVIDUAL.
HOW ARE THESE RELATIONSHIPS EXPRESSED
IN A PATIENT POPULATION?
We represent the effect of a drug in an INDIVIDUAL as a
concentration- or dose-response curve in which the
GRADED effects of the drug are related to
concentrations or doses of the drug.
We represent the effect of a drug in a POPULATION as a
concentration- or dose-response curve in which the
QUANTAL effect of the drug is related to
concentrations or doses of the drug.
WHAT IS A QUANTAL CONCENTRATION- OR
DOSE-RESPONSE CURVE?
A QUANTAL effect is an effect that is either present or absent
(e.g., alive vs. dead, asleep vs. awake, response = or > x vs. response < x).
A QUANTAL concentration- or dose-response curve is a plot
of concentration or dose versus % of patients in the
population who exhibit the quantal response at
the given concentration or dose.
WHAT IS A QUANTAL CONCENTRATION- OR
DOSE-RESPONSE CURVE?
150
Response
% of Individuals
Responding At
or Below Indicated
Dose or Concentration
100
50
ED50 or EC50
0
0.01
0.1
1
10
100
1000 10000
Dose
Log Dose or Concentration of Agonist
Note: If quantal response happens to be death, ED50 is called LD50.
WHAT IS A QUANTAL CONCENTRATION- OR
DOSE-RESPONSE CURVE?
Although both GRADED and QUANTAL relationships
have ED50s and EC50s, these parameter are NOT
the same for GRADED and QUANTAL
relationships!
GRADED Relationships:
ED50s and EC50s indicate doses and concentrations that
cause 1/2 maximal response in a given INDIVIDUAL.
QUANTAL Relationships:
ED50s and EC50s indicate doses and concentrations that
cause 1/2 of the POPULATION to respond.
WHAT ARE THE IMPORTANT CLINICAL
IMPLICATIONS OF WHAT
WE HAVE LEARNED?
Since the log dose-response curve is sigmoidal, increasing
the dose of a drug when the response is submaximal
will enhance the therapeutic effect.
Since the log dose-response curve is sigmoidal, increasing
the dose of a drug when the response is maximal
will not improve the therapeutic effect
but may subject the patient to toxicity.
WHAT ARE THE IMPORTANT CLINICAL
IMPLICATIONS OF WHAT
WE HAVE LEARNED?
The log dose-response curve is sigmoidal, regardless of whether the
“response” is therapeutic or toxic.
The safety of a drug can be assessed by examining the log
dose-response curves for therapeutic versus toxic effects.
The more separation between the therapeutic log
dose-response curves and the toxic log dose-response
curves, the safer the drug.
WHAT ARE THE IMPORTANT CLINICAL
IMPLICATIONS OF WHAT
WE HAVE LEARNED?
A drug with low potency and high efficacy may be better than
a drug with low efficacy and high potency.
Potency is a determinant of how much of the drug must be given to
obtain a “ceiling” effect.
Efficacy refers to magnitude of the “ceiling” effect.
WHAT ARE THE IMPORTANT CLINICAL
IMPLICATIONS OF WHAT
WE HAVE LEARNED?
If an antagonist is being employed to block the effect of an agonist, it
is important to know whether the antagonist is of the
surmountable or insurmountable type.
Dose of insurmountable antagonist usually does not need upward
adjustment as amount of agonist in body increases.
Dose of surmountable antagonist must be increased
if amount of agonist (endogenous or exogenous) in
the patient increases.
WHAT ARE THE IMPORTANT CLINICAL
IMPLICATIONS OF WHAT
WE HAVE LEARNED?
GRADED DOSE/CONCENTRATION RELATIONSHIPS
help to understand how changing dose of drug will effect
the degree of response of an individual patient.
QUANTAL DOSE/CONCENTRATION RELATIONSHIPS
help to understand how changing dose of drug will effect
the % of your patients who will experience
a defined response.
WHAT IS THE RELATIONSHIP
BETWEEN AMOUNT OF DRUG IN
THE BODY AND THE EFFECT OF
THE DRUG?
Now you know!!