Pharmacodynamics: Dose-Response Curves

Sections

Graded Response Curves
Quantal Response Curves
Therapeutic Index & Therapeutic Window
References

Here, we'll focus on key dose-response curves in pharmacodynamics.

Overview

• Start a table.
• Denote that pharmacodynamics deals with the actions of drugs on the body (vs. pharmacokinetics, which deals with the actions of the body on drugs).
• Denote each of the following key terms:

Efficacy

• Efficacy, which is a drug's effectiveness, refers to the greatest effect a drug can produce (at the highest tolerated level).

Potency

• Potency, which is a drug's power; it's determined by the amount of drug required to produce the desired effect.

Binding Affinity

• Binding affinity, which is how well a drug binds to a receptor, is determined by the percentage of receptors bound by a drug.

Graded Response Curves

Let's create some graphs that help us quantify these concepts.

Graded Dose-Response Curve

• Title our first graph: Graded Dose-Response Curve.
  • This is a graded curve, which means that the response is graded along a continuum. Later, we'll draw out a quantal dose-response curve, which is a binary response: the responses are "either-or" or "all-or-none" (they are not measured in degrees or grades).
• Draw the X and Y axes.
• Label the Y axis as % of Maximal Effect and indicate 50% and 100%.
• Label the X axis as Drug Concentration.
• Make a note that we are using a linear scale, which generates a hyperbolic curve.
  • Later, we'll use a logarithmic scale, which generates a sigmoidal curve with a linear midpoint; this is helpful, because, as we'll see, our midpoint value is a key measurement.
• Draw a hyperbolic curve and label the following key points:

Emax

• At 100%, indicate Emax (which is the maximal effect).
  • Write out that Emax refers to the maximum biological effect (or physiological response) that a drug can generate.
  • In our table, denote that Emax is the key value for efficacy.
  • Denote that the GREATER the Emax, the GREATER the efficacy (think: amount of effect = efficacy).

EC50

• At 50% of maximal effect, draw a line that meets our hyperbolic curve.
• Indicate that this point along the X-axis is the EC50.
  • Write out that EC50 is the concentration of a drug that generates 50% of the maximal effect.
  • Return to our table and denote that EC50 is the key value for potency. As we'll see later, so can be the ED50.
  • Denote that the LOWER the EC50 (or ED50), the GREATER the potency; meaning, the less drug required to generate a specific effect, the more powerful the drug.

Example

• Putting efficacy and potency together, we can imagine that if a smaller concentration of DRUG X produces the same effect as a larger concentration of DRUG Y but both have the same ultimate, maximal effect, then DRUG X is more potent than DRUG Y but they are equally efficacious.

Graded Dose-Binding Curve

Now, let's move on to binding affinity.

• Title this graph: Graded Dose-Binding Curve
• Draw the X and Y axes.
• Label the Y axis as % of Receptor-Bound Drug and demarcate 50% and 100%.
• Label the X axis as Drug Concentration, again, in a linear scale.
• Re-draw a similar hyperbolic curve.

Bmax

• At 100%, indicate Bmax.
• Bmax is the maximal binding capacity.

Kd

• At 50%, draw a line that meets our hyperbolic curve.
• Indicate that this point along the X-axis is the Kd.
  • Write out that Kd is the equilibrium dissociation constant; it's the binding affinity.
  • Return to our table and denote that Kd is the key value for binding affinity.
  • Similar to how EC50 is inversely related to potency, also denote that the LOWER the Kd, the GREATER the binding affinity.

Spare Receptors

• Now, putting EC50 and Kd together, we can understand what's meant by spare receptors, which by definition, are present if the EC50 is less than Kd.

Let's see why:

• Draw X and Y axes.
• Label the Y axis as % of Maximum.
• Label the X axis as Drug Concentration but now in a logarithmic scale (the logarithm of the drug concentration).
• Accordingly, draw a sigmoidal curve for EC50 and then another to the right of it for Kd.
  • What we see is that if the maximal biological effect of a drug can be achieved without the binding of all available receptors (or during the time period in which a biological effect persists after a drug is released from its receptor), then spare receptors are present.

Quantal Response Curves

Now, let's shift from graded responses to quantal ones.

• Draw the X and Y axes.
• Label the Y axis as % of Individuals Responding (these are binary ("either-or" or "all-or-none") responses). Specify 50% and 100%, which we'll see are important measurements.
• Label the X axis as Dose (mg) and indicate doses from 1 mg to 7 mg.
  • Let's imagine we want to know the minimum dose required to achieve a systolic blood pressure of less than 120 mg Hg. The response we are examining is binary: is the individual's blood pressure less than 120 or not. What we really want to determine is: for the average individual what dose of drug will be required to drop blood pressure below 120. Imagine we're testing in a large population of people.
• Using a bar graph format, indicate that:
• A small percentage of people require just 1 mg of drug to achieve a systolic BP of less than 120 mmHg.
• Then, show that an increasing percentage of people require higher and higher doses to achieve this until we reach a midpoint at which time a decreasing number of people require a further increasing doses of drug.
• Show that this data fits underneath a bell-shaped curve; it fits a normal distribution.
• Next, draw a sigmoidal curve for the cumulative percentage of people that exhibit the desired therapeutic effect at increasing dose of medication.
• Accordingly, we see that this curve reaches 100% at the right-side of the corresponding bell-shaped curve.

ED50

• At the peak of the bell-shaped curve, indicate that the corresponding dose is the ED50: the median effective dose.
  • Write out that the ED50 refers to the dose at which 50% of people will achieve the specified effect: it's the effective dose for 50% of the population.
  • And it answers our original question, in the average person, what dose of drug do we expect is required to achieve a systolic BP less than 120 mmHg.

TD50 & LD50

We can also ask the question, however, what dose is too high? Meaning, what dose is toxic or lethal to the average individual?

• To the right of this curve, draw a similar quantal response, again, with a bell-shaped curve, for increasing dose of drug and with a sigmoidal curve for the cumulative percentage of responders.
• Here, label the 50% point as TD50.
• The TD50 refers to the dose at which 50% of people will achieve a toxic effect.
• LD50 refers to lethality; the LD50 is the dose at which 50% of people will die from medication.
  • So write out that TD50 or LD50 refers to the dose at which 50% of people experience Toxicity or Lethality.

Therapeutic Index & Therapeutic Window

Therapeutic Index

What we want to clinically is how much room do we have to "play" with the drug dosing – what's a safe but also effective range to work with?

• Draw a line between the ED50 and TD50 because this is the range we are interested in when calculating our therapeutic index (TI).
• Write out that the therapeutic index ratio is TD50 divided by ED50.
  • The therapeutic index is an important ratio to determine how close a toxic dose is to an effective one. Note that the term therapeutic index is often used more loosely, not just in these formulatic terms, and is often conflated with the therapeutic window, which we'll define soon.
• In our current example, indicate the therapeutic index is 6/2: it is 3.

Therapeutic Window

Now, let's address the therapeutic window.

• Draw the X and Y axes.
• Label the Y axis as Concentration (we use mg/L for example) and establish some random increasing blood concentration levels of drug.
• Label the X axis as Time (for instance, hours).
• Draw a hyperbolic curve to show that as time goes on, the concentration of drug increases within the blood.
  • Whereas with our therapeutic index, we were thinking in terms of drug dose (ED50 and TD50 were based on drug dose); here, we are thinking about the blood concentration of the drug: the drug level.
• Demarcate the minimum effective concentration (MEC), which represents the minimum blood level necessary to achieve a specified biological effect.
• Then, demarcate the minimum toxic concentration (MTC), which represents the minimum blood level at which a toxic effect occurs (we see that this level's not actually reached in this example).
• Shade in and draw a line between these two measurements and indicate that it represents the therapeutic window.
  • Write that the therapeutic window is the range of blood level wherein the drug is producing the desired effect without the feared toxicity.
  • For reference, the United States Food & Drug Administration (FDA) uses the term "narrow therapeutic index" for drugs that have a less than twofold difference in LD50 and ED50 or MTC and MEC.

Example

• Consider a seizure drug, for example, that requires a concentration of 15 mcg/mL to control seizures but causes aplastic anemia at a concentration of 25 mcg/mL.
• This drug would be considered to have a narrow therapeutic index. It may be effective in treating seizures but it is all too easily toxic to the bone marrow.

References

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