8 BIOLOGICAL EFFECTS OF LOW LEVEL EXPOSURES
where X is a hybridized parameter proportional to the zero-order rate con
stant specifying toxicity injury.
Hypothesis VI: Longevity hormesis is a response to a biologically nonessen
tial, exogenous agent or stimulus that reversibly reduces Gompertzians rela
tive to a control population without affecting senescence (i.e., G0 or (j>).
This hypothesis, while positing the concept of longevity hormesis, does
little more than empirically describe it. As mentioned previously, a defini
tion must await characterization of mechanism. Three points are worth
reiterating. First, longevity hormesis is reversible. Second, longevity horme
sis is presumed to be mediated through a mechanism that does not impact
on senescence, but rather superimposes its effects onto it. And third, lon
gevity hormesis is only produced by nonessential stimuli. Application of
life-enhancing essential agents (nutrients, vitamins, etc.) promote longevity
through what has been termed a “proper” action.5 Unfortunately, the dis
tinction between “proper” and “longevity hormetic” enhancement of lon
gevity is empiric, based solely on our knowledge of process and system.47
While it is possible that biologically essential agents might also prompt a
longevity hormetic response, there is no currently available data demon
strating this.
In terms of superimposition onto the Gompertz function, longevity hor
mesis is expressed by a term that reversibly reduces Gompertzians. By way
of example, assume a linear Gompertz function characterizing senescent
aging in concert with a longevity hormetic stimulus that reduces injury at a
zero-order rate; the injury reducing effect, however, is reversible and dissi
pates at a first-order rate. The function is identical with Equation 10, except
the far right term has a negative sign designating injury reduction:
( 11 )
Although this example denotes one kinetic scheme for input and dissipation
of longevity hormesis, it is emphasized that any appropriate empiric func
tion may be used. For example, Thompson et al.47 developed a model of
longevity hormesis in wild chipmunks following a single dose of ionizing
radiation; they found that aging apparently promoted the loss of longevity
hormesis. This is in contrast to Equation 11, in which dissipation of longev
ity hormesis is age-independent.
For a phenomenon to be considered longevity hormetic, reduction in
Gompertzians must be characterized by a Gompertz term different from
that observed with caloric restriction —the implication being that the mech
anisms are also different. When a linear Gompertz function describes con
trol animals, caloric restriction usually acts to reduce mortality simply by
reducing c*;28 that is, it slows the rate of endogenous injury generation.