• Agonist, antagonist
  • Law of mass action
    • Drug concentration, binding affinity, receptor number, antagonist
  • Hill-Langmuir equation
  • Direct binding experiments
  • Potency – ED50 & pD2
  • Cooperativity
  • Intrinsic activity
  • Partial Agonists


Agonists are both endogenous and exogenous – these are small molecules which form an agonist receptor complex resulting in the activation of the receptor. Agonists are a type of ligand.

Agonists usually bond to a receptor through reversible chemical bonding. This requires bonding between the agonist and the ligand. Usually a long range force in the form of electrostatic bonding will ‘draw’ the agonist and receptor together. Following this hydrogen bonding and Van der walls bonding will allow for a close bonding. Sometimes hydrophobic bonding will also occur, however, this is not always the case.

Recall the concept of equilibrium where the rate of forward reaction is equal to the rate of reverse reaction. For reversible binding of ligands to receptors, this also holds true.

[(A) Drug] + [(R) vacant receptor]  [(AR) drug-receptor complex]

  • [(A) Drug] = XA
  • [(R) vacant receptor] = NTot – NA
  • [(AR) drug-receptor complex] = NA

The forward reaction is k+1 and the reverse reaction is k-1

A hydrogen isotope attached to the ligand is typically used in experiments to measure this, this will release radiation, allowing us to pinpoint where it is.

Therefore, the kd = k-1/k+1 this has units of moles/L. This is where half the receptors are occupied by the agonist.

The affinity is thus k+1/k-1 which is the reciprocal of the kd, therefore, an increase in the affinity results in more drug-receptor complex formation.

The kd can be used to determine what concentration of drug is effective for desired response in vivo (in living system). This is often the concentration at 3 times the kd.

An overview of pharmacodynamic modelling, ligand-binding approach and its  application in clinical practice - ScienceDirect

If with graph the concentration of drug against the pharmaceutical effect we get a rectangular hyperbole. If we log the concentration of drug we then get a sigmoidal curve.

This can be represented by the equation:

PA= XA / (XA + KD) = 1 / (1 + KD/XA)

The specific binding is found to be the total bound drug – non specific binding. This is how we find the direct binding.

Direct binding can then be sketched using a scatchard plot – this can be used to find the KD of the drug.

This is the [bound drug]/[[free drug] on the y axis against [bound] which gives a linear straight line. The x intercept is the B max where the larger the number, the more receptors. The gradient is the negative inverse of the KD.

Prism 3 -- Saturation Binding Curves and Scatchard Plots - FAQ 1748 -  GraphPad

The concentration response curves, as seen above, can also be represented with the equation:

response/ maximum response = XA / (XA + EC50)

Emax or Bmax is the total physiological response.

This is derived from the functionality assay.

Hill equation (biochemistry) - Wikipedia

When the hill coefficient (α) is:

  • greater then 1= positive cooperativity in the receptor e.g hemoglobin (2.8-3)
  • less then 1= negative cooperativity in the receptor (partial agonist) e.g insulin (.7-.8)
  • 0 = antagonist binding

pD2= – log EC50

We can now start to compare different agonists.

We can use the maximum response which is the drugs intrinsic activity divided by its effectivness.

  • Maximal physiological response is a measure of drug efficacy
  • EC50 (likewise pD2) is used for potency, where it is half the concentration of a maximum response)
  • ED50 is half the dosage for a maximum response
  • Intrinsic activity is interchangeable most of the time is efficacy which provides the maximum response.

Bolus concentration response

The drug is administered, and response is measured then the drug is washed out and and tissue recovers. This is then repeated and the concentration of drug administered is increased.

Cumulative concentration response

Add drug and measure response, add another dose before it recovers, increasing at fixed intervals. Once the response plateaus out – the Bmax is found.


Question 1.

Explain why a drug being prescribed close to it’s EC50 will have a significant increase in its response for a biological system if it’s dosage is doubled, however, this increase in response is less significant when a drug being prescribed significantly greater then it’s EC50 is prescribed.

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