HYPOTHESES ON LONGEVITY HORMESIS 17generated in this fashion. Curve C shows a linear Gompertz function.
Superimposing irreversible toxicity upon Curve C, one obtains Curve A.
Note that the intercept remains the same but that the slope becomes steeper.
The impact of longevity hormesis is illustrated by Curve E. With zero-order
input and first-order elimination, longevity hormesis quickly reaches a
steady state. When this occurs, curves C and E become parallel to one
another. The condition of having both irreversible toxicity and longevity
hormesis superimposed upon the linear Gompertz function is illustrated
with Curves B and D. Toxicity (expressed through 7 ) is greater in B than D.
A good example of a system in which pure longevity hormesis is superim
posed on a linear Gompertz function is illustrated in Figure 1.3 for procaine
administration to male rats. Interestingly, this response is not observed in
female rats. This indicates, as do some other data sets, that longevity hor-
Figure 1.3. Gompertz plots for untreated male rats (control) and those receiving procaine:
a classic longevity hormesis response in the absence of concomitant toxicity
(analogous to curve E, Figure 1.2). Animals used were white rats of the
French Wistar strain. Treated animals received procaine “ parenterally” at a
dose of 4 mg/kg three times weekly for 4 weeks, whereupon treatment was
discontinued for 1 month. Beginning at either 2 or 6 months of age, the
injections were continued for the remainder of each animal’s life span. The
control population received saline injections. As the age of initiation of
uninterrupted therapy (2 or 6 months) did not apparently affect mortality, data
from these two groups were pooled. Time on the abscissa is equivalent to
age. The linear Gompertz function (Equation 3) was used to characterize
mortality experience for the control group. Equation 11, which superimposes
a longevity hormesis term onto the linear Gompertz function, was used to
characterize the procaine-treated population. Both equations were fit (least
squares analysis) simultaneously to the data using appropriate weighting
factors (see Neafsey et al.24 for methodology). Parameter estimates were G0
= -5.810, a = 0.2323 h r 1, X = 0.4953 h r 1, and K = 0.5095 hr"1. These
data, published by Aslan et al.,26 were previously analyzed by Sacher5 and
Boxenbaum et al.;14 in both analyses, independent linear regressions
indicated that the line from the procaine-treated group was displaced
downward in a parallel fashion from that of controls. No longevity hormetic
effect was evident from data in female rats.