Topic 2: Reading: Dose reponse relationship

Regardless of how a drug effect occurs through binding or chemical interaction, the concentration of the drug at the site of action controls the effect. However, the relationship between response and concentration may be complex and is often nonlinear. Generally, when discussing the drug action at the tissue level, we refer to drug ‘concentration’, while when referring to drug action in the whole animal/person, we refer to the drug ‘dose’. When a drug is administered to an animal or human, the relationship between the drug dose, regardless of a route used, and the drug concentration at the cellular level is even more complex.

The concept of the dose-response curve or concentration-response curve is one of the most important parts of pharmacology. A dose-response curve describes the relationship between an effect of a drug and the amount of drug given. Dose-response curves are essential to understand the drug's safe and hazardous levels so that the therapeutic index can be determined and dosing guidelines can be created.

Dose-response curves are charted on an X-Y axis, with the drug dosage measured (usually in milligrams, micrograms, or grams per kilogram of body-weight for oral exposures or milligrams per cubic meter of ambient air for inhalation exposures) typically on the X axis and the response to the medication typically on the Y-axis. When considering responses at the tissue level, the quantity of drug is expressed as its concentration, usually expressed as a molar concentration, although where the molecular weight is unknown we would express the concentration as microgram/nanogram/ ml as appropriate.  As the relationship between response and increasing dose or concentration is best described by a logarithmic plot, dose-response curves (or concentration-response curves) are graphed with the dose or concentration on a logarithmic scale  (X-axis) as opposed to a linear scale;  in such cases the curve is typically sigmoidal, with the steepest portion in the middle (This is discussed in more detail in the final section of this module see material under ‘The relationship between drug concentration and pharmacological effects in the whole animal/human’)

When evaluating a dose-response curve (or concentration-response curve), one of the main characteristics is a graded relationship between the response and the dose or concentration; this means that as the amount of drug given is increased so is the response to the drug. There are three phases of a dose-response curve (or concentration-response curve). First, the curve is flat as the quantity of drug given is not sufficiently great to initiate a response. The first point along the graph where a response above zero (or above the control response) is reached is usually referred to as a threshold-dose. In the second phase, the curve steadily rises, with each increase in the drug dose there is also an increased in response. At higher doses, undesired side effects appear and grow stronger as the dose increases. The more potent a particular substance, the lower the concentration or dose required to produce an effect. Finally, the curve plateaus at the top, indicating that any further increases in drug dose will not produce any further increase response to the drug (Figure 1). This grading of the dose-response curve enables your healthcare provider to tailor their prescription to the individual taking the drug.

Figure 1. Relationship of drug concentration to percentage effect on a linear scale and log scale. EC50 value (the concentration which produces 50% of the maximum response) by placing it on a linear portion of the curve

2.1. Types of dose and response relationship

To make rational therapeutic decisions, it is necessary to understand the fundamental concepts linking drug doses to concentrations to clinical responses. The concentration-response relationships for drugs may be graded or quantal.

A graded concentration-response curve can be constructed for responses such as heart rate that are measured on a continuous scale. Graded concentration-response curves relate the intensity of response to the size of the dose and, hence, are used to characterize the actions of drugs. As the concentration of drug increases, the magnitude of its pharmacologic effect also increases. The relationship between dose and response can be mathematically described by application of the law of mass action, assuming the simplest model of drug binding:

[Drug] + [Receptor]⟺[Drug-Receptor complex]...............................(1)

Quantal Dose-response curve: On the other hand, when a drug is administered to the whole animal, certain types of responses may be all or none. For example, before immunoassays were developed, the potency of insulin was determined by administration to mice, where it caused convulsions due to a large reduction in the blood glucose; in this case, convulsions either occurred or did not occur – this is termed a quantal response and the relationship is defined as the percentage of animals showing the response and the dose of the drug. The doses required to produce a specified quantal effect in a population are log-normally distributed so that the frequency distribution of responses plotted against log dose is a Gaussian normal distribution curve. The percentage of the population requiring a particular dose to exhibit the effect can be determined from this curve. If the percentage of the group responding to increasing doses is plotted, a sigmoidal dose-response curve is generated. The response is represented as a cumulative percentage of subjects exhibiting a defined effect. The median toxic (TD50), and median lethal doses (LD50) are extracted from experiments carried out in this manner.

Fig-3: Quantal Dose-response Curve