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 Waddells 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 Gibbs 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
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for p = 1 atm, we denote G as G0, and by integration
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applying it to ni moles of an ideal gas, piv = niRT, substituting and rearranging yields
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After differentiation for ni with
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and
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we obtain
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For a chemical reaction
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at equilibrium,
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and thus
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which rearranged yields the mass action law revealing its existence on a logarithmic/exponential scale
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A generalization of the mass action law for all solutes results in the definition of the chemical potential:
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xi......mole fraction
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ci......concentration
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ai......fugacity
with corresponding mass action equations
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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).
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 toxicologists view of cancer risk assessment. Drug. Metab. Rev. 28, 2952.[ISI][Medline]
Waddell, W. J. (2003). Thresholds of carcinogenicity in the ED01 study. Toxicol. Sci. 72, 158163.