Letter

Karl K. Rozman, Ph.D.

Professor of Toxicology and Pharmacology, University of Kansas Medical Center, Phone: 913-588-7717, E-mail: krozman{at}kumc.edu

To the Editor:

The responses to Waddell’s paper titled "Thresholds in Carcinogenicity in ED01 Study" require clarification by a toxicologist for those who are not familiar with fundamental principles of toxicology. I hope that these authors do not mean to suggest that it is something other than Gibb’s free energy which drives all chemical reactions including all chemical reactions in our body regardless of whether covalent binding, receptor binding, or any other type of reaction is involved.

I commend Dr. Waddell in his attempt to put toxicology on firmer theoretical grounds of science by using a principle derived from thermodynamics. It is clear that chemical potential is the ultimate driving force of any effect and I show here a rigorous derivation of the mass action law as a reminder that it has a logarithmic solution and is not arbitrarily put on this scale.

The differential of Gibbs free energy for ideal gases is


for p = 1 atm, we denote G as G0, and by integration


applying it to ni moles of an ideal gas, piv = niRT, substituting and rearranging yields


After differentiation for ni with


and


we obtain


For a chemical reaction


at equilibrium,


and thus


which rearranged yields the mass action law revealing its existence on a logarithmic/exponential scale


A generalization of the mass action law for all solutes results in the definition of the chemical potential:


xi......mole fraction


ci......concentration


ai......fugacity

with corresponding mass action equations


I hope the authors of these letters recognize from this exercise (routine for chemistry students 40 years ago) that the chemical potential is the driving force for any and every process that occurs in our body. The dose is only a surrogate for the free fraction of the concentration of a chemical at the site of action, the natural logarithm of which is proportional to its chemical potential. Therefore plotting the surrogate (dose) of the natural logarithm of chemical potential will yield a straight line and not an arithmetic plot as suggested by the critique of the authors commenting on the Waddell paper. In fact, an arithmetic plot leads to the very distortion, and that on an astronomic scale, which these authors accused Waddell of having committed in his paper by using the appropriate logarithmic scale. The scale of distortion has been illustrated by Rozman et al. (1996)Go.

REFERENCES

Rozman, K. K., Kerecsen, L., Viluksela, M. K., Österle, D., Deml, E., Viluksela, M., Stahl, B. U., Greim, H., and Doull, J. (1996). A toxicologist’s view of cancer risk assessment. Drug. Metab. Rev. 28, 29–52.[ISI][Medline]

Waddell, W. J. (2003). Thresholds of carcinogenicity in the ED01 study. Toxicol. Sci. 72, 158–163.[Abstract/Free Full Text]