Question 12
The binding of a drug (D) to a receptor (R) is illustrated by the following
expression:
where [D] and [R] are the concentrations of the drug and receptor, respectively, and k is the rate constant for the particular reaction. Using the equation given, explain the following terms: -
a) the ratio of koff/ kon
b) the implications of a low value for the ratio above
c) the term affinity
d) the clinical implications of a high value for affinity
e) two physiological factors that affect the rate constant k
College Answer
The main points expected for a pass were
• The ratio of k off/k on is the dissociation constant
• A low value indicates that less drug is required to bind to the receptors
• Affinity is the reverse of the dissociation constant
• Clinical application of high affinity include large effect at lower concentrations
• Physiological factors could include temperature
The main problem with this question was lack of knowledge.
Discussion
a) - The ratio of koff / kon is the Dissociation constant (Kd ), the rate constant of dissociation at equilibrium. koff is the rate constant of dissociation of the drug from the receptor, and kon is the rate constant of association of the drug to the receptor. To be precise, kon and koff are actually not the official terms - the International Union of Pharmacology Committee on Receptor Nomenclature and Drug Classification would prefer you to use k+1 for the association reaction and k-1 for the dissociation of drug from receptor. For that matter, IUPCRNDC wants you to call it [L] for "ligand", not [D] for "drug".
b) - a low Kd value means the same thing as a high Ka value. Kd also represents the concentration of a drug required to achieve 50% receptor occupancy at equilibrium. A low Kd value therefore means that a low concentration is required to occupy 50% of the available receptors.
c) "Affinity" is a term which only has a lay definition in pharmacology, but its mathematical representation is Ka, or the association constant. The IUPCRNDC nomenclature for Ka also permits "affinity constant" as an alternative name for this variable. It is the inverse of the dissociation constant. In chemistry on a broader scale, the definition of affinity (A) is "...is the negative partial derivative of Gibbs free energy G with respect to extent of reaction ξ at constant pressure and temperature." It is defined as the quantifiable representation of the tendency of dissimilar chemical species to form chemical compounds
d) If we use Ka as the working representation of affinity, the implication of a high value would be the same as the implication of a low Kd value, i.e. a low concentration is required to occupy 50% of the available receptors. The college answer simplifies this as " large effect at lower concentrations", which is succinct and accurate.
e)
The major factors which affect affinity and dissociation constant are temperature and the presence of a catalyst. In general, the rate of any reaction is determined by the Arrhenius equation:
So, the factors are:
- The gas constant
- A, an experimentally derived pre-exponential factor which is different for every chemical reaction and which is basically a reflection of the number of molecular collisions which occur per second, specifically ones which put the reagents in an orientation which is just right for the reaction to take place.
- Temperature, which is usually fairly constant and close to 37°C.
- Ea, which is the activation energy for the drug-receptor interaction reaction, and which can be reduced in the presence of a catalyst.
References
Neubig, Richard R., et al. "International Union of Pharmacology Committee on Receptor Nomenclature and Drug Classification. XXXVIII. Update on terms and symbols in quantitative pharmacology." Pharmacological Reviews 55.4 (2003): 597-606.
Kenakin, T. Pharmacologic analysis of drug±receptor interaction 3rd ed. New York: Raven Press, 1997.
Eddy, M. D. "Elements, principles and the narrative of affinity." Foundations of Chemistry 6.2 (2004): 161-175.
http://www.iupac.org/