Evaluation of the Fermi equation as a model of dose-response curves

 When plotted in linear coordinates, the dose-response curves of microorganisms exposed to a lethal agent, such as radiation or a toxic substance, often have a characteristic sigmoid shape. Irrespective of whether they are very narrow or broad they can be described by the Fermi function, which is a mirror image of the logistic function, i.e. S(X)=1/{1+ exp (X−X _c)/a]} where S(X) is the fraction of the surviving organisms, X the dose of the lethal agent, X _c a characteristic dose marking the inflection point of S(X), which corresponds to 50% mortality, and a a measure of the steepness of the survival curve around X _c. It is demonstrated that, if the susceptibilities of the individual organisms, expressed in terms of a characteristic lethal dose, have a symmetric unimodal distribution, the dose-response curve of the population has a Fermian sigmoid shape. It is also shown that the mode and variance of the distribution can be estimated from the shape parameters of the Fermian survival curve, X _c and a. Received: 7 November 1995 / Received last revision: 11 April 1996 / Accepted: 29 April 1996