Viva C(v)

This viva is relevant to the objectives of Section C(v)  of the 2017 CICM Primary Syllabus, which encourages the exam candidate to "to explain the Law of Mass Action.  

What is the Law of Mass Action?

The equation, if the candidate wishes to write one, is:

A + B ⇌ a + b

Consider two "masses", A and B.

  • These masses react and produce population of product molecules, a and b.
  • Given an infinite timeline, the concentrations of parent molecules and daughter molecules will achieve an equilibrium.  
  • At equilibrium, the product of A and B on one side of the equation divided by the product of a and b on the other side of the equation is a constant.
  • This constant (k) is independent of the absolute amount of substances at the start of the reaction.
How does the law of mass action describe drug/receptor interactions?

It can be used to describe the interaction between the drug [D] and the receptor it binds [R]:

kon[D][R] = koff [DR]

Here, the rate of association can be described as the product kon[D][R]. The rate of dissociation of the drug from the receptor can be described as koff [DR], where koff  is the rate constant for dissociation.

The mass action equation for drug/receptor interaction is therefore:

[DR] = [D][RT] / [D] + Kd

where RT is the total number of receptors, [DR] is the concentration of the complex of drug and receptor

Can you represent this relationship graphically?

Another wayy of wording this question is, "can you draw a graph which demonstrates the relationship between drug concentration and receptor occupancy?" They should drraw something like this:

Law of Mass Action

What are the limitations of applying the Law of Mass Action to pharmacodynamics?

This relationship makes several assumptions:

  • All ligands and all receptors are equally available to each other
  • The binding of drug and receptor is reversible (it frequently is not, as in the case of phenoxybenzamine)
  • The binding of drug and receptor does not alter either the drug or the receptor (that's not the case when the drug is a substrate for a receptor which is a metabolic enzyme, for one example)
  • The receptor and drug are either bound to each other, or are not bound to each other (i.e. there are no ambiguous partial states).

Moreover, there are problems when the drug and receptor exist in a complex system of interrelated and mixed mass action reactions. 

References

Kenakin, Terry. "The mass action equation in pharmacology." British journal of clinical pharmacology 81.1 (2016): 41-51.

Érdi, Péter, and János Tóth. Mathematical models of chemical reactions: theory and applications of deterministic and stochastic modelsManchester University Press, 1989.

Waage, Peter, and Cato Maximilian Gulberg. "Studies concerning affinity." J. Chem. Educ 63.12 (1986): 1044.