Dose response curves

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Relation between drug concentration & Response It may be: Complex as observed clinically in patients. Simple in carefully controlled in vitro systems. It can be described mathematically & represented graphically.

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Dose Response Curves/ Concentration Effect Curve Definition : A graph between doses of a drug & responses produced , using an in vitro /in vivo biological system. Doses are plotted along X-axis/ abscissa. Responses are plotted along Y-axis/ordinate. Types: i. Graded DRC ii. Quantal DRC

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Graded dose response curve: Definition : It is a quantitative curve between increasing doses/concentration of drug and varying responses . Thresh hold dose: The minimum dose which produces an observable response Maximum/ ceiling dose: The dose which produces maximum response & even with further increase in dose , there is no increase in response.

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The relation b/w conc. & effect can be described mathematically. E = E max x C C + EC50 E = Effect observed C = Concentration of the drug. E max = The maximum response produced by the drug EC50 = The conc. of drug that produces 50% of max effect. It can be represented graphically ----- Hyperbola curve.

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If the %age of receptors that bind drug is plotted against drug conc. a similar curve is obtained (because the response is due to binding to receptors) B = B max x C C + K d K d = Conc. That binds 50% of the receptor in the system. B Max =Max. no of bound receptor.

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Semi Log dose response curve: If dose is taken in logarithm & response in arithmetic / linear scale, the curve is sigmoid shape. Important characters: Potency Slope : Steep / Flat Maximum effect (E max ) Variability

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Advantages of Semi Log dose response curve: 1. It sigmoid in shape with a linear mid portion, so: It occupies less space & many observations can be recorded on same graph paper. This shapes expands the scale of dose axis at low conc. where the effect is changing rapidly & compresses is at high conc. where the effect is changing slowly. Comparison of two curves becomes easier. 2. Useful for: Determination of the potency. Determination of efficacy (EC 50 / E max ). Determination of selectivity of effect. Receptor study , Drug Antagonism. Determination of biological variation.

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Quantal dose response curve ( dose Percent curve ) Definition : Quantal DRC is a curve/graph plotted between the %age or fraction of a population that shows a specified all or none response & doses of a drug. QDRC is a cumulative graph of the frequency distribution of responders versus the log dose . On Y-axis is recorded % of responders & on X-axis log. doses are plotted. Parameter: Pre- determined criterion i.e production of convulsions , foot withdrawal Quantal response: An all or none response. Either drug can produce convulsions / no convulsions. Either drug can produce foot withdrawal / no foot withdrawal. Either at specific dose a drug can produce death / no animal dies

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Median effective dose (ED50): It is the dose that is required to produce the specified response in 50 % of population under study. Median Toxic dose (TD50): It is the dose that is required to produce the specified toxic effect in 50 % of population under study. Median lethal dose (LD50): It is the dose of the drug required to kill 50% of animals under study.

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Uses of QDRC: Indicates the potential variability of responsiveness among the population. Calculation of therapeutic index Comparing the potencies of drugs in experimental & clinical settings. It can provide a valuable index of the selectivity of drug’s action by comparing its ED 50 for two different quantal responses in a population.

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Therapeutic index: It is the ratio of median toxic dose or median lethal dose to median effective dose. Therapeutic Index (T.I) = TD50 ED50 TI indicates that safely the dose can be increased without fear of toxicity. Drugs with LOW TI--- less safe ,require monitoring of plasma concentration. Digoxin , Lithium. They have narrow Therapeutic window . Drugs with HIGH TI: Safer , They have wide Therapeutic window

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Margin of safety: LD0.1 ED 99.9 LD0.1 is the minimum lethal dose for 0.1% of the population ED99.9 is the minimum effective dose for 99.9% of population

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Therapeutic window:

Structure Activity Relationship: 

Structure Activity Relationship I- Synthesis Of New Compounds With More Specific Actions And Fewer Adverse Effects Examples:- Chlorpromazine & Trifluoperazine Procaine & Procainamide Benzyl Penicillin & ampicillin Chlorothiazide & Bendoflumethiazide Atropine & homatropine

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II. Synthesis of structurally related competitive antagonist PABA & Sulfonamides Morphine & Naloxone

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III- Understanding the Mechanism of Drug Action Example: Epinephrine & Isoprenaline