THE PARABENS 83 k = k0(1 - asi), (I) where k0 is the growth rate constant when no antimicrobials are present and si is the saturation fraction of the ith paraben. The Ferguson principle is implied by the absence of the subscript on the dimensionless constant a (which has a value of about 2.0) all three parabens have the same inhibitory effect when their levels are expressed as fraction of saturation. By independent radiochemical measurements, Lang and Rye also showed that the intracellular paraben concentration, c5, is approximately the same for all three homologs when their equilibrium levels in the extracellular or bulk phase are expressed as saturation fractions, si: c• = f• ci = f* ci/tri = f* si, (IX) where ci is the bulk concentration and tr i is the solubility. The constant f* like the constant a in Equation I, has the same value for all three homologs (about 7.0 g/l). In the Lang and Rye study, the applicability of the Ferguson principle is both demonstrated and "explained," where "explanation" follows from the plausible assumption that the parabens are equitoxic at equal intracellular concentrations. The assumption is plausible, in turn, on the further conjecture that the parabens are toxic to microbes because they partition reversibly into the lipid bilayer of the cell membrane and disorder its barrier function and the functions of embedded transport enzymes. A molecule of one homolog ought then to be about as disruptive as that of another. In retrospect, it is not too surprising that such a structure of assumptions and conjectures failed to support extrapolation. All that remains of the Ferguson principle in the range of paraben concentrations beyond half saturation (the limit of the Lang and Rye study) is an indication that at low levels of inoculation the initial kill rate is given by Equation I. Thereafter, survival and growth are determined by the rate of adaptation which increases markedly with the molecular weight of the paraben. Solubility in the medium does not serve as the sole index of efficiency as it would if the Ferguson principle were applicable, but it remains a crucial property. Methyl paraben is a potent antimicrobial in water at saturation at 0.2%, but it fails at 0.4% in the emulsions and at 0.8% in the shampoo it is a good preservative only for products in which it is not too soluble. Propyl paraben is inadequate in water at 0.03% and remains so at 0.8% in the emulsions and even at about 2.5% in the shampoo. For practical purposes, our earlier solubility-efficacy proposal (1,2) is supplanted by a strong endorsement of methyl paraben as the best member of the series, to be used at the highest practical concentration, with a secondary recommendation of ethyl paraben as a supporting preservative when the amount of methyl paraben that can be used is limited by regulation (0.4% maximum in Brazil, for example) or by solubility at low storage temperatures. Only rarely might it be useful to include propyl paraben as a third preservative. REFERENCES (1) J.j. O'Neill, P. L. Peelor, A. F. Peterson and C. H. Strube, Application of the Ferguson principle to the selection of sparingly soluble preservatives, DeveL Indust. MicrobioL, 19, 335-345 (1978). (2) J. j. O'Neill, P. L. Peelor, A. F. Peterson and C. H. Strube, Selection of parabens as preservatives for cosmetics and toiletries,J. Soc. Cosmet. Chem., 30, 25-38 (1979).

84 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS (3) W. P. Evans, Applicability of the Ferguson principle to systems of mixed preservatives, J. Pharm. Pharmacol., 17, 217-221 (1965). (4) J. Ferguson, The use of chemical potentials as indices of toxicity, Proc. Roy. Soc. Lond., Sect B, 127, 387-404 (1939). (5) N. A. Allawala and S. Riegelman, Phenol coefficients and the Ferguson principle, J. Am. Pharm. Assoc., Sci. Ed., 43, 93-97 (1954). (6) R. T. Gottlesman and D. Chin, Salicyclic acid and related compounds in Kirk-Othmer Encyclopedia of Chemical Technology, 2nd Ed., (Interscience, New York, 1968) Vol. 17, p. 738. (7) A. F. Peterson, J.J. O'Neill and C. A. Mead, Preservation: from art to science, Devel. Indust. Microbiol., 21, 161-165 (1980). (8) R. M. Rye and D. Wiseman, Effect of Chlorhexidine upon •2p release and cell viabilky in Escherichia coli, J. Pharm. Pharmacol., 18 Suppl., 1145-1185 (1966). (9) M. Lang and R. M. Rye, The uptake by Escherichia coli and growth inhibitory properties of methyl, ethyl and propyl p-hydroxybenzoates, J. Pharm. Pharmac., 24, 160P-161P (1972).