rational use of drugs

WHAT IS THE RELATIONSHIP BETWEEN AMOUNT OF DRUG IN THE BODY AND THE EFFECT OF

THE DRUG?

WHY BE CONCERNED ABOUT DOSE-EFFECT RELATIONSHIPS?

• Predict the effects of changing the dose.

• Reveal the necessary trade-offs between efficacy and adverse effects.

• Facilitate comparisons of alternative medicationsfor the same indication.

• Enhance understanding of how best to use receptor blockers.

DOSE-EFFECT RELATIONSHIPS:

WHAT DETERMINES THE DOSE-EFFECT RELATIONSHIP?

DOSE OFDRUG

[DRUG] ATTARGET SITE

[DRUG-RECEPTOR COMPLEX]

RESPONSE

The Dose-Response Causal Chain

WHAT IS THE RELATIONSHIPBETWEEN DOSE OF DRUG AND

[DRUG] AT TARGET SITE ?

DOSE OFDRUG


DOSE

[DRUG]As a rough approximation, the relationship

between dose of drug and [drug] ismore-or-less linear at a specified time after drug administration.

Linear

WHAT IS THE RELATIONSHIPBETWEEN [DRUG-RECEPTOR COMPLEX]

AND RESPONSE?

CONCENTRATION OFDRUG-RECEPTOR

COMPLEX

RESPONSE

[DRUG-RECEPTOR]

RESPONSEAs a rough approximation, the relationship

between concentration of drug-receptorcomplex and response to the drug is

more-or-less linear.

Linear

WHAT IS THE RELATIONSHIPBETWEEN [DRUG] AT TARGE SITE

AND [DRUG-RECEPTOR COMPLEX]?

The relationship between [Drug] at target site and [Drug-Receptor Complex]

is not linear!

Non-Linear[DRUG] AT

TARGET SITE[DRUG-RECEPTOR COMPLEX]

DOSE OFDRUG


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!!

CONCENTRATION OFDRUG-RECEPTOR

COMPLEX

RESPONSE

Linear LinearNon-Linear

WHAT DETERMINES THE DOSE-EFFECT RELATIONSHIP?

WHAT IS THE RELATIONSHIP BETWEEN[DRUG] AND [DRUG-RECEPTOR]?

[R] [R-D][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)


[R] [R-D][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)


[R] [R-D][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


Log [D]free versus [R-D] [D]free versus [R-D]

Graphs were computer generated using equation #5 with [R]total = 100 and KD = 10

0 250 500 750 1000 12500

50

100

150

[DRUG]free

[D-R]

0.01 0.1 1 10 100 1000 100000

50

100

150

[DRUG]free

[D-R]

y-axis is [R-D] y-axis is [R-D]


[R] [R-D][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)

Maximal Response = m x [R-D]maximal = m x [R]total (Equation #7)

and

(where m is the proportionality constant)


RELATIONSHIP?

Substitution of equations #6 and #7 into equation #5 givesequation #8:

Response =Maximal Response x [D]free

[D]free + KD

Log [D]free versus Response[D]free versus Response

Graphs were computer generated using equation #8 with maximal response = 100 and KD = 10

0.01 0.1 1 10 100 1000 100000

50

100

150

[DRUG]free

Response

0 250 500 750 1000 12500

50

100

150

[DRUG]free

Response


RELATIONSHIP?

y-axis is Response y-axis is Response

[R] [R-D][D]+

A plot of [D]free versus response is hyperbolic

A plot of log [D]free versus response is sigmoidal


RELATIONSHIP?

Response

[D]freeLet:


RELATIONSHIP?


[D]free + KD

Response = Maximal Response x KD

2KD

=1/2 Maximal

Response

We Know That:

Substituting KD for [D]free:

Response

KD=

Simplifying:

[D]free

Let:


RELATIONSHIP?


[D]free + KD

=1/2 Maximal

Response

We Know That:

Substituting ½ Maximal Response

For Response

Response

KD=Simplifying:

1/2 Maximal Response

= Maximal Response x [D]free

[D]free + KD


RELATIONSHIP?

0.01 0.1 1 10 100 1000 100000

50

100

150

[DRUG]free

Response

[D]free = KDResponse = 1/2 Maximal Response

The [drug] which causes 1/2 maximal responseis called the EC50 and corresponds

to the KD if there is a linear relationship between [D-R] and response.

EC50

Maximal Response 1/2 Maximal Response

y-axis is Response

(Equivalence #9)


RELATIONSHIP?


[D]free + EC50

Since EC50 corresponds to KD, can substitute EC50 for KD in equation #8 to give equation #10:


RELATIONSHIP?


[D]free + EC50

Empirically, it has been found that equation #10 (above) describes theconcentration-effect relationship for many drugs, evenwhen the assumption of linearity between [R-D] and

response does not hold.


RELATIONSHIP?


[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.


RELATIONSHIP?


[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.


RELATIONSHIP?


[D]free + EC50

The term “efficacy” refers to the maximal response of a drug. The greaterthe 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.


RELATIONSHIP?

Maximal Response To Agonist A

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 drugin the same pharmacological class.

Maximal ResponseTo Agonist B

=, <, or >


RELATIONSHIP?

Agonist A is “Best in Class”, i.e., no other agonist induces a greater maximal effect.

The “Best in Class” is called a “full agonist”, and any drugthat generates a maximal response equal to the “Best in Class” is

also referred to as a “full agonist.”

Maximal Response to Agonist A = Maximal Response

to Agonist B

Assume:

Assume:

Both Agonist A and agonist B are “full agonists.”

0.01 0.1 1 10 100 1000 100000

50

100

150

Dose

Response

Concentration of Agonist

Agonist A Agonist B

Agonist A and agonist Bare both full agonists.However, agonist A is

more potent than agonist B.

y-axis is Response


RELATIONSHIP?


RELATIONSHIP?

Agonist A is “Best in Class”, i.e., no other agonist induces a greater maximal effect.

In this case agonist B is a “partial agonist.”

Maximal Response to Agonist A > Maximal Response

to Agonist B

Assume:

Assume:

Any drug that generates a maximal response less than that elicited by the “Best in Class” is referred to as a

“partial agonist.”

0.01 0.1 1 10 100 1000 100000

50

100

150

Dose

Response


Full Agonist A Partial Agonist B

y-axis is Response


RELATIONSHIP?

Agonist A is a full agonist andagonist 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)

EC50 = ED50/volume (Equation #12)

and

(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)


RELATIONSHIP?

Substitution of equations #11 and #12 into equation # 10 givesequation #13:

Response =Maximal Response x Dose

Dose + ED50

Log Dose versus ResponseDose versus Response

Graphs were computer generated using equation #13 with maximal response = 100 and ED50 = 10


RELATIONSHIP?

0 250 500 750 1000 12500

50

100

150

Dose

Response

0.01 0.1 1 10 100 1000 100000

50

100

150

Dose

Response

y-axis is Response y-axis is Response

[R] [R-D][D]+

A plot of DOSE versus response is hyperbolic

A plot of log DOSE versus response is sigmoidal


RELATIONSHIP?

Response

DOSE

0.01 0.1 1 10 100 1000 100000

50

100

150

Dose

Response


RELATIONSHIP?

Dose = ED50Response = 1/2 Maximal Response

The dose which causes 1/2 maximal response iscalled the ED50. Although the ED50 is affected

by the KD and EC50 it is greatly influencedby the apparent volume in which

the drug is distributed.

ED50

Maximal Response 1/2 Maximal Response

ED50 is never equal to EC50 or KD!

y-axis is Response

WHAT IS THE EFFECT OF DRUGS THAT BLOCK DRUG-RECEPTOR INTERACTIONS OR THAT

INHIBIT SIGNAL TRANSDUCTIONMECHANISMS ON THE DOSE-

RESPONSE CURVE?

[R] [R-D][D]+ Response

BLOCKING DRUG

WHAT IS THE EFFECT OF BLOCKINGDRUGS ON CONCENTRATION-RESPONSE CURVES?

0.01 0.1 1 10 100 1000 100000

50

100

150

Dose

Response


- Drug Antagonist + Drug Antagonist

SURMOUNTABLE ANTAGONIST

y-axis is Response


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


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


Population of Inactive Receptors


Add an excess of high potency agonist molecules


Allow system to reach equilibrium


Add some antagonist molecules


Allow system to reach new equilibrium


[D]free + apparent KDagonist

Where apparent KDagonist = (1 + [Antagonist]/KDantagonist) x actual KDagonist


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.


0.01 0.1 1 10 100 1000 100000

50

100

150

Dose

Response


Agonist Alone Agonist + Competitive Antagonist

Note apparent shift inEC50 for the agonist.

y-axis is Response


0.01 0.1 1 10 100 1000 100000

50

100

150

Dose

Response


- Drug Antagonist + Drug Antagonist

INSURMOUNTABLE ANTAGONIST

y-axis is Response


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


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


0.01 0.1 1 10 100 1000 100000

50

100

150

Dose

Response

Concentration of Agonist0.01 0.1 1 10 100 1000 100000

50

100

150

Dose

Response


SURMOUNTABLE ANTAGONISM

INSURMOUNTABLE ANTAGONISM

PHENOMENON

MECHANISMReversible Competitive Interaction

Irreversible Competitive InteractionIf spare receptors & right dose & time

Blockade of Signal TransductionIf spare receptors & right dose

Allosteric ModulationIf just the right type

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 HAVE BEEN DISCUSSING CONCENTRATION-AND DOSE-RESPONSE CURVES WITHIN AN INDIVIDUAL.

HOW ARE THESE RELATIONSHIPS EXPRESSEDIN A PATIENT POPULATION?

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.

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).

WHAT IS A QUANTAL CONCENTRATION- OR DOSE-RESPONSE CURVE?

A QUANTAL concentration- or dose-response curve is a plotof concentration or dose versus % of patients in the

population who exhibit the quantal response at the given concentration or dose.


0.01 0.1 1 10 100 1000 100000

50

100

150

Dose

Response

Log Dose or Concentration of Agonist

% of Individuals Responding At

or Below IndicatedDose or Concentration ED50 or EC50

Note: If quantal response happens to be death, ED50 is called LD50.


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 thatcause 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 CLINICALIMPLICATIONS 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 effectbut may subject the patient to toxicity.


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.


WE HAVE LEARNED?

A drug with low potency and high efficacy may be better thana drug with low efficacy and high potency.

Potency is a determinant of how much of the drug must be given toobtain a “ceiling” effect.

Efficacy refers to magnitude of the “ceiling” effect.


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 surmountable antagonist must be increasedif amount of agonist (endogenous or exogenous) in

the patient increases.

Dose of insurmountable antagonist usually does not need upwardadjustment as amount of agonist in body increases.


WE HAVE LEARNED?

GRADED DOSE/CONCENTRATION RELATIONSHIPShelp to understand how changing dose of drug will effect

the degree of response of an individual patient.

QUANTAL DOSE/CONCENTRATION RELATIONSHIPShelp to understand how changing dose of drug will effect

the % of your patients who will experiencea defined response.

Now you know!!

WHAT IS THE RELATIONSHIP BETWEEN AMOUNT OF DRUG IN THE BODY AND THE EFFECT OF

THE DRUG?

rational use of drugs

Education

d response

r rd d

response response

d x d free rd

r freex d free rd

r totalx d free d free

plot of d freeversus

rd yaxis