Pharmacology Concentration-Response Curve Lecture Notes

Principles of Pharmacology

Introduction

• Presented by Dr. Dibesh Thapa from Life Sciences & Medicine, School of Bioscience Education.

Learning Outcomes

• After the lecture, students should be able to:

  • Draw typical "concentration vs response" and "log concentration vs response" curves with appropriately labeled axes.

  • List some common responses to drugs and explain how they are measured.

  • Distinguish between in vitro, in vivo, and ex vivo measurements.

  • Explain the term "EC50" and how it is measured.

  • Distinguish between the terms "potency", "potency ratio", and "relative potency".

  • Explain the term "Therapeutic Index" and how it is measured.

Fundamental Quote

• "All substances are poisons: There is none which is not a poison. The right dose differentiates a poison and a remedy." - Paracelcus (1493-1541)

Concentration-Response Relationship

Overview

• The effects of drugs are "quantified" by studying the relationship between drug concentration (or dose) and the resultant response. This is visualized via concentration-response curves.

Types of Concentration-Response Curves

• Rectangular Hyperbola:

  • Represents drug concentration vs. response.

  • Y-axis represents response, x-axis is drug concentration

  • 100% response at maximum concentration.

  • 0% response with no drug.

• Symmetrical Sigmoid Response:

  • Represents log drug concentration vs. response.

  • Provides a clearer understanding of dosage effects.

  • effect plateaus off - saturated

    

Logarithmic Scales in Pharmacology

• Using logarithmic scales in pharmacology serves multiple important purposes:

• 

  • Compression of Low Concentrations:

  • Linear scales compress low drug concentrations, making it difficult to distinguish effects at nanomolar level.

  • hard to visualise what the drug is doing at a low concentration

  • Improved Visualization:

  • Logarithmic scales evenly space wide-ranging concentrations, improving visualization of pharmacodynamic profiles.

  • you have to know what exactly each concentration of the dose is doing

  • Sigmoid Response Curves:

  • Log scale reveals sigmoid response curves, useful for identifying and comparing EC₅₀ (Effective Concentration) and EC₉₀.

Types of Pharmacological Experiments

Overview

• The response measured is determined by the experiment type. There are three main types of pharmacological experiments:

  • In Vitro Experiments

  • In Vivo Experiments

  • Ex Vivo Experiments

In Vitro Experiments

• Conducted on a piece of tissue dissected from an animal (or human), kept alive outside the body.

• Commonly includes experiments on cells in tissue cultures.

• Typical responses measured:

  • Changes in muscle tension,

  • Changes in enzyme activity,

  • Changes in secretion levels of hormones or neurotransmitters.

  • rate f contraction when the drug is added to the organ bath

  • Example: Effects of nicotine on noradrenaline release from human cerebral cortex slices (British Journal of Pharmacology, 2002).

In Vivo Experiments

• Conducted within a living organism (animal or human).

• Includes tightly regulated clinical trials.

• Responses measured may include:

  • Increases in blood pressure,

  • Reductions in pain thresholds,

  • Decreases in allergen-induced bronchoconstriction.

Ex Vivo Experiments

• Involves removing a tissue or organ from an animal treated with a drug, then testing the effects in vitro.

• Similarly tightly regulated by the Home Office in the UK.

• Examples include:

  • Assessing potential liver damage from long-term drug treatment.

  • Alteration of brain biochemistry.

Measurement Units in In Vitro Experiments

Concentration Units

• For in vitro experiments, concentrations are expressed in moles per liter (Molar, M).

• 1 mole of a substance contains $6.02 imes 10^{23}$ molecules and weighs its molecular mass in grams.

• A 1 Molar solution contains 1 mole of a drug in 1 liter of solvent.

• Important:

  • 1 Molar solution of drug “X” has the same number of drug molecules as that of drug “Y” at 1 Molar concentration.

Potency of Clinically Useful Drugs

• Most clinically useful drugs act at very low concentrations, typically in the range of $1\cdot10^{-6}M$ to $1\cdot10^{-12}M$ .

• A $10^{-9}M$ solution contains approximately $6.02\cdot10^{14}$ drug molecules per liter.

• Prefixes used:

  • milli (m) for $10^{-3}$,

  • micro (µ) for $10^{-6}$,

  • nano (n) for $10^{-9}$.

• Example: A 1 micromolar (µM) solution is equivalent to a $1\cdot10^{-6}M$ solution.

Concentration-Response Curve Construction

Apparatus Overview

• Involves a simplified organ bath apparatus to study muscle reactions.

Response Measurement

• Log [X] force over time measuring various concentrations:

  • Example: Addition of various concentrations will yield different responses in force (e.g., 0.1 W, 0.3 W,… up to 30 W).

  • concentration-response curve

    • yaxis = force

    • xaxis = time

    • sigmoidal shape

    • at maximum response it will plateau off

    • exponential phase, will go up significantly

      

  cumulative concentration-response curve

  • no washing in between concentrations

  • just keep adding higher concentrations

  • e.g. it takes a long time for the drug to detatch from the receptor due to binding, no matter how much you wash the drug wont come off, high affinity

  • 

In Vivo Dosing Strategies

• In in vivo experiments, molar concentrations are impractical due to unknown solvent volumes.

• Doses are expressed as weight of drug per weight of animal (e.g., 1 mg/kg).

  • This allows extrapolating approximate

  • doses from smaller animals to larger ones, e.g., from a 20g mouse to a 70kg human.

• not possible to use molar concentrations/molarity, cant approximate how much blood volume there is between animals

Concentration-Response Curve Details

Maximum Effect (Emax)

• Represents the maximum response produced by the drug – the upper limit of the concentration-response curve.

• Increasing drug concentration beyond this point yields no further effect.

EC50 Definition

• EC50 is defined as the molar concentration that achieves 50% of the maximum response for that drug.

• Other values like EC90 or EC20 may also be referenced, indicating different response percentages.

• EC50=[0.5Emax]

  

Potency and Potency Ratio

Potency Definition

• Term for a drug's effectiveness at low doses: a potent drug works in very small amounts.

• potent drug is effective at a small amount

• Quantified by EC50: lower EC50 indicates higher potency.

• comparing EC50 values for two drugs wiht the same action allows us to calculate their relative potencies described by the potency ratio

• Potency Ratio (M) is defined as:

  • $M = \frac{EC50(test)}{EC50(standard)}$ or $log M = logEC50(test) - logEC50(standard)$.

• Allows comparison of new drugs against existing ones to see if its more effective.

Potency Example

Comparing drugs A and B:

• If drug A is more potent, M = 300/15 = 20; 20 times more B is needed to achieve the same effect.

• If B were the standard, then M would be less than 1, indicating test drug potency.

• e.g. dose A is 1um, dose B is 51mm; dose A is more potent, less drug is needed produce the same 50% response

Therapeutic Index (TI)

TI Definition

• Describes the ratio between the toxic dose (LD50) and the effective/theraputic dose (ED50).

• Higher therapeutic index indicates lower chance of toxic side-effects in therapeutic use.

• we want the TI to be as high as possible to maximize the safety and efficacy of the medication while minimizing the risk of adverse reactions.

TI Calculation

• Conventional formula: $TI = \frac{LD50}{ED50}$ where:

  • LD50 = lethal dose for 50% of the population

  • ED50 = effective dose for 50% of the population

Issues with TI

• This definition has limitations:

  • It is ethically challenging since LD50 represents extreme effects (lethal dose).

  • In human studies, can be computed as $TI = \frac{TD50}{ED50}$ (where TD50 is the toxic dose), but this is not straightforward.

  • Patient-specific variations in drug response complicate achieving a commonly applicable TI.

  • Some drugs have varying ED50 values depending on the condition treated (e.g., ibuprofen for headaches vs. arthritis).

Summary Revision Points

• True/False Section:

  • In-vivo experiment involves tissue/organ kept alive outside. (False)

  • 1nM equals $1 imes 10^{-9}M$. (True)

  • 1 mol of H₂O has the same number of molecules as 1 mol of NaCl. (True)

  • 1 mol of H₂O has the same mass as 1 mol of NaCl. (False)

Practice Session

• Express the following in scientific notation:

  • 0.1 nM; 0.5 mM; 10 mM; 30 nM.

Conclusion

• Students should be able to construct concentration-response curves, understand drug responses, and explain critical pharmacological terms such as EC50, Potency, and Therapeutic Index by the end of the session.