Pharmacokinetics

• To allow comparison of drugs and their effects:

  • Assume the law of mass action
  • Assume a negligible amount of total drug is bound
  • Assume at equilibrium the rate of forward reaction is equal to the rate of the reverse reaction
• Rt: total number of receptors

  D: total drug concentration

  DR: concentration of bound drug

  r: fractional occupancy of receptors

  KD: equilibrium dissociation constant of the drug and receptor (measure of affinity)

  
• This equation is valid for a simple bimolecular interaction between a drug and its receptor.

  
• A plot of r against [D] will be a rectangular hyperbola. Special cases exist when r = 1/2 as [D] = KD.

  • When the hyperbola goes flat, all receptors are occupied (saturation)
  • A semi-log plot can be plotted for between 20-80% fractional occupancy
• Occupation theory:

  • Response [E] is directly proportional to the number of receptors occupied
  • Graphs of fractional response against drug concentration will have the same shape as graphs of fractional occupancy against drug concentration
  • If all assumptions correct, then at half maximal response KD = [D]

  
• pD2: a measure of affinity of an agonist for its receptor. Drugs with high values will act at low concentrations.
• The assumptions of occupation theory are not always correct and for many receptor systems pD2 overestimates the KD, giving the impression that the drug is more tightly bound than it really is.
• Competitive antagonists: binds to the same site as the agonist. The block can be overcome by increasing agonist concentration.
• Non-competitive antagonists: binds to a different site than the agonist. The block cannot be overcome by increasing agonist concentration.
• Competitive antagonism e.g., atropine against ACh in ileum, is an antagonist of muscarinic receptors.

  • With increasing [atropine] the response curve moves to the right
  • Apparent pD2 decreases in the presence of the competitive antagonist
  • There is no change in Emax

  
• Non-competitive antagonism e.g., benzilycholine mustard against ACh.

  • There is a decrease in the maximal response (Emax)
  • No change in pD2
  • Dose-response curves are not parallel

  
• The ability of the antagonist (competitive) to block the response will depend on:

  • The relative affinity of the agonist (KD) and antagonist (KA) for the receptor
  • The relative concentrations of the agonist [D] and antagonist [A]
• Dose ratio: the ratio of agonist concentrations that elicits the same response in either the absence [D0] or presence [DA] of the antagonist.

  • If the response in the presence and absence of antagonist is the same, then it is reasonable to assume that the occupancy by the agonist is the same

  
• To derive the dose ratio:

  • Choose any response (usually 50%)
  • Determine the agonist concentrations that give this response in the absence and presence of antagonist concentrations
  • Calculate the dose ratio at each antagonist concentration

  
• The Gaddum-Schild equation: used to study the effects of agonists and antagonists on the response caused by the receptor or on ligand-receptor binding.

  
• Assumptions of the Gaddum-Schild equation:

  • The analysis is based on the law of mass action and assumed simple competitive antagonism
  • No assumptions are made about the relationship between response and number of receptors occupied
  • It is independent of the agonist used so long as it competes with the antagonist for the same receptor
• When the dose ratio is equal to 2, where the concentration of agonist must be doubled in presence of agonist, this is equal to [A]/Ka, and Ka = A2
• pA2 is similar to pD2, being the negative log of the antagonist concentration that gives a dose ratio of 2. It is a measure of the affinity of an antagonist drug for its receptor.

  
• Assumptions of the occupation theory:

  • There are specific receptors for specific agonists
  • All agonists for a given receptor can produce the same maximum response
  • The drug-receptor interaction is rapidly reversible
  • All receptors are equally accessible to the drug
  • The receptors do not interact with each other
  • The maximum response occurs when all receptors are occupied
• An agonist with high efficacy may only need to bind in a small fraction of receptors to produce a maximum response.

  
• Modification of the occupation theory:

  • The effect will depend on the affinity of the drug to the receptor
  • The effect will depend on the ability of the drug to induce a conformational change in the receptor
• An agonist with high efficacy will preferentially bind to the active conformation of the receptor, giving a stabilising effect. An agonist may be able to bind to both the active and inactive conformation, whereas an antagonist may only be able to bind to the inactive conformation.

  
• Inverse agonists decrease basal activity. This concept arose from studies on anxiolytics and anxiogenics (benzodiazepines) that work through the GABA-A receptor. Some receptors may have activity in their resting state - constitutive activity. This is reversed by inverse agonists.
• r = [D]/[D]+KD
• Dose ratio: [DA]/[D0]-1 = [A]/KA
• Pharmacokinetics is the effect of the body on drug delivery to the site of action (ADME).

  A - absorption

  D - distribution

  M - metabolism

  E - excretion
• The pharmacokinetics can be affected by age, dietary factors, disease, genetics and chemicals. This is important for these processes:

  • Time of onset of action
  • Intensity and duration
  • Accumulation
  • Inter/intra-individual differences (e.g., genetic)
  • Drug interactions
  • Inter-species differences (animal testing)
• The liver is mostly involved in metabolism (enzymes acting on drugs) as well as secretion into the gall bladder and then faeces (excretion).
• Kidneys eliminate drugs through urine.
• Lungs excrete drugs through breath if they are volatile.
• Administration:

  • IV bypasses the liver initially
  • Oral dose goes to the liver first (metabolised before general circulation)
  • Intramuscular and inhaled doses avoid first-pass metabolism
• Chemical structures are present in food:

  • Tyramine in cheese (2 mg/g)
  • 5-HT in bananas (3 mg/100 g)
  • Benzopyrenes inhaled from combustion products
  • Coffee contains chlorogenic acid and caffeine
• Low molecular weight compounds - can move through pores in the cell membrane (an aqueous environment).
• Lipid soluble molecules - can diffuse directly through the membrane.
• Carrier mediated molecules - the drug must resemble natural ligands or substrate.
• Factors affecting absorption:

  • Lipid solubility (rapid from gut, slow from intramuscular)
  • Ionisation(poor for ionic drugs - pH partitioning)
  • Formulation (may limit rate or absorption)
  • GI function (may limit delivery to site and time of absorption)
  • First-pass metabolism (limits extent of absorption)
• Extent of ionisation is determined by the pKa and the pH. The Henderson-Hasselbach equation is used to determine these parameters. There is 50% ionisation when pKa = pH.

  
• Bioavailability: the fraction of dose passing from the site of administration into the general circulation as the parent compound.
• Common reasons for low bioavailability:

  • Decomposition in the gut lumen
  • First-pass metabolism in gut wall or liver
  • Not absorbed from the gut lumen
  • Tablet does not completely dissolve

  
• The bioavailability can be measured by comparing the plasma concentration when the same dose is given by IV or orally.

  • The area under the curve is representative of the total amount of drug that gets into the system